Lifecycle Investing - Leveraging when young

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MoneyMarathon
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Re: Lifecycle Investing - Leveraging when young

Post by MoneyMarathon »

305pelusa wrote: Thu Feb 20, 2020 2:26 pm
MoneyMarathon wrote: Thu Feb 20, 2020 2:12 pm
305pelusa wrote: Thu Feb 20, 2020 11:50 am Portfolio B = Has 50k in a x2 LETF of stocks and 50k in cash. This effectively is 100% in stocks as well. Market drops 10%. You now have 40k in the x2 LETF and 50k in cash. This is an exposure of 80k in stocks and 10k in cash. That’s 88% in stocks. This isn’t satisfying what Merton is saying as your % allocation to stocks has decreased.
If you then buy 5k in the LETF, you're 45k LETF x2 and 45k cash and 100% allocated to stock. This has been discussed pretty thoroughly in the adventure thread & there's at least one mathematical paper on it for those interested in such things.
Lol ok yes, if you then go and buy more of the LETF to make up for the fact that the LETF itself lost exposure, then of course that works too. So you could create positions that resemble variable leverage (like options and futures) with LETFs provided you traded daily to undo what the LETF does.
305pelusa wrote: Thu Feb 20, 2020 11:50 amThank you for catching the math error but it makes no difference to my underlying point.
What is your underlying point?

Based on the reaction above, it seems that you did not really understand what people were saying in the LETF thread, instead relying on your own ideas of what the implications of buying LETFs would be. Those ideas bear little relationship to what people who actually were buying LETFs were actually doing with them & the actual implications of their strategy, which has the goal of maintaining a constant % allocation to stocks, on average over time if not strictly on a daily basis. The choice of LETF or options is an implementation detail, primarily decided on practical concerns, and does not represent a perspective on optimal allocation. The % allocation fluctuations in the short term, between rebalancing periods, averages out over a long enough period with frequent enough rebalancing (as discussed and shown in that thread). Someone could be allergic to relying on the law of large numbers to average things out over time, but that's just one of many personal preferences that go into the decision of how to implement a leveraged strategy and is not a universal condition that applies to every investor interested in leverage.
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Steve Reading
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Re: Lifecycle Investing - Leveraging when young

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MoneyMarathon wrote: Thu Feb 20, 2020 3:07 pm What is your underlying point?
Well, Uncorrelated said:
Uncorrelated wrote: Thu Feb 20, 2020 11:06 am It follows from Merton that if you have no human capital left, a constant amount of stocks (continuously rebalanced) is the optimal solution, a leveraged ETF comes close to this situation.
My underlying point is that uncorrelated got it backwards. LETFs do not maintain a constant % allocation to stocks (which is what Merton implies is optimal). It is in fact variable leverage like options that does. I made a small mathematical error but this point remains true.
MoneyMarathon wrote: Thu Feb 20, 2020 3:07 pm Based on the reaction above, it seems that you did not really understand what people were saying in the LETF thread, instead relying on your own ideas of what the implications of buying LETFs would be.
Dude, not only do I not know what people you’re talking about, I don’t even know what thread you’re referring to.

I’m talking specifically about Lifecycle Investing and that Merton’s model says the optimal is to maintain a constant % allocation to stocks. With options, futures and margin, this is done automatically. No need to trade. It’s fundamentally an easier vehicle to apply the Merton principle.

Can you also apply the Merton principle with LETFs and trading often to undo its constant leverage? Sure. Go nuts and you do you. In my humble opinion, it’s the wrong tool for the job but you can nail a nail with a screwdriver as long as you know what you’re doing.

Either way, this exchange was specifically to show Uncorrelated where I believe he’s incorrect.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
MoneyMarathon
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Re: Lifecycle Investing - Leveraging when young

Post by MoneyMarathon »

305pelusa wrote: Thu Feb 20, 2020 3:20 pm
MoneyMarathon wrote: Thu Feb 20, 2020 3:07 pm Based on the reaction above, it seems that you did not really understand what people were saying in the LETF thread, instead relying on your own ideas of what the implications of buying LETFs would be.
Dude, not only do I not know what people you’re talking about, I don’t even know what thread you’re referring to.
You participated in the thread and, the same as recently here, you ignored the effects of rebalancing.

viewtopic.php?f=10&t=288192&start=450#p4713969
Honest question to people invested. How does it feel to know that your funds will be selling stocks today? And will load up by buying more treasuries (which have lower yields)? I'm asking from a purely psychological perspective. Doesn't it bother you? Why/why not?

All I'd want to do is the exact opposite. Sell some bonds (which now have lower yields) and purchase some equities. I certainly wouldn't want to buy more bonds at then higher yield and sell my stocks.
It was an ugly exchange, partly because of how badly you ignored or misunderstood what the long term effects of rebalancing are in the implementation of their strategy.
305pelusa wrote: Thu Feb 20, 2020 3:20 pm No need to trade. It’s fundamentally an easier vehicle to apply the Merton principle.

Can you also apply the Merton principle with LETFs and trading often to undo its constant leverage? Sure. Go nuts and you do you.
This is part of why I don't use LETFs. I use balanced leveraged funds (NTSX, PSLDX). No need to trade often. Easy peasy.
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Steve Reading
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Re: Lifecycle Investing - Leveraging when young

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MoneyMarathon wrote: Thu Feb 20, 2020 3:41 pm
305pelusa wrote: Thu Feb 20, 2020 3:20 pm
MoneyMarathon wrote: Thu Feb 20, 2020 3:07 pm Based on the reaction above, it seems that you did not really understand what people were saying in the LETF thread, instead relying on your own ideas of what the implications of buying LETFs would be.
Dude, not only do I not know what people you’re talking about, I don’t even know what thread you’re referring to.
You participated in the thread and, the same as recently here, you ignored the effects of rebalancing.

viewtopic.php?f=10&t=288192&start=450#p4713969
Honest question to people invested. How does it feel to know that your funds will be selling stocks today? And will load up by buying more treasuries (which have lower yields)? I'm asking from a purely psychological perspective. Doesn't it bother you? Why/why not?

All I'd want to do is the exact opposite. Sell some bonds (which now have lower yields) and purchase some equities. I certainly wouldn't want to buy more bonds at then higher yield and sell my stocks.
It was an ugly exchange because of how badly you ignored or misunderstood what the long term effects of rebalancing are in the implementation of their strategy.
Whoah talk about bringing up something that has literally nothing to do with what I was talking about with Uncorrelated. LETFs vs Variable leverage in the context of the Excellent Adventure is a good discussion but one that belongs in that thread. And that comment was more from a psychological standpoint any ways, not actual risk or returns.

I’m talking about LETFs vs Variable leverage in the context of Lifecycle Investing here (since it’s what the thread is about after all...). If you want to argue that LETFs are superior to variable leverage for temporal diversification, go ahead. I’ve already explained why I don’t believe so (path dependence and non-constant % allocation to stocks being the big ones).

The Excellent Adventure has far bigger problems (starting with the inefficiency of the mental accounting, which Uncorrelated is probably tired of repeating) than which leverage vehicle you use. I’ll just leave it at that in this thread.
MoneyMarathon wrote: Thu Feb 20, 2020 3:41 pm
305pelusa wrote: Thu Feb 20, 2020 3:20 pm No need to trade. It’s fundamentally an easier vehicle to apply the Merton principle.

Can you also apply the Merton principle with LETFs and trading often to undo its constant leverage? Sure. Go nuts and you do you.
This is part of why I don't use LETFs. I use balanced leveraged funds (NTSX, PSLDX). No need to trade often. Easy peasy.
Ok so we’re talking about Lifecycle Investing.

NTSX and PSLDX make no sense in my mind for temporal diversification since they’re not even netting you additional stock exposure. They’re as good as just buying VTSAX in regards to temporal diversification.

Additionally, NTSX and PSLDX also rebalance their leverage. Not daily (which is better than a LETF for purposes of Lifecycle Investing) but maybe monthly. So they’re also not as good as, say, LEAPs with 2-3 years, or margin which goes on indefinitely.

For purpose of Lifecycle Investing, UPRO is probably far better than either of those for people like myself who are trying to get more stock exposure to null the large amount of bond-like exposure of their income.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
MoneyMarathon
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Re: Lifecycle Investing - Leveraging when young

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Whoah talk about bringing up something that has literally nothing to do with what I was talking about with Uncorrelated.
Alright, we can talk about what you were talking about with Uncorrelated.
305pelusa wrote: Thu Feb 20, 2020 11:50 am Portfolio A = Has 100k in stocks. It is 100% in stocks. Market drops 10%. You now have 90k in stocks and are still 100% in stocks. Merton is satisfied.
305pelusa wrote: Thu Feb 20, 2020 11:50 am Portfolio C = Has 50k in options with x2 leverage (strike price about half of the index) and 50k in cash.
Portfolio A is a single ticker that satisfies Merton. If you wanted to get 150% allocation to stocks, you could just buy a 150% leveraged ETF if it were on the market. Likewise if you wanted a 200% allocation to stocks or a 250% allocation or a 300% allocation. In an asset universe of stocks and cash, an appropriately geared up LETF is all you need to satisfy Merton, as long as it's 100% of assets.
305pelusa wrote: Thu Feb 20, 2020 11:50 am path dependence and non-constant % allocation to stocks being the big ones
Path dependence is a consequence of a constant % allocation to stocks that is leveraged.

UPRO and other LETFs are a constant % allocation if it is 100% of assets.
String
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Re: Lifecycle Investing - Leveraging when young

Post by String »

MoneyMarathon wrote: Thu Feb 20, 2020 4:02 pm Portfolio A is a single ticker that satisfies Merton. If you wanted to get 150% allocation to stocks, you could just buy a 150% leveraged ETF if it were on the market. Likewise if you wanted a 200% allocation to stocks or a 250% allocation or a 300% allocation. In an asset universe of stocks and cash, an appropriately geared up LETF is all you need to satisfy Merton, as long as it's 100% of assets.
Exactly, and similarly if you only want 50% stocks, holding separate 50/50 stock/cash allocation has the same problem of drifting % exposure. Does this make the only suitable holding in this case an all in one 50/50 balanced fund? (Effectively a 50% LETF)
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Steve Reading
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Re: Lifecycle Investing - Leveraging when young

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MoneyMarathon wrote: Thu Feb 20, 2020 4:02 pm
Whoah talk about bringing up something that has literally nothing to do with what I was talking about with Uncorrelated.
Alright, we can talk about what you were talking about with Uncorrelated.
305pelusa wrote: Thu Feb 20, 2020 11:50 am Portfolio A = Has 100k in stocks. It is 100% in stocks. Market drops 10%. You now have 90k in stocks and are still 100% in stocks. Merton is satisfied.
305pelusa wrote: Thu Feb 20, 2020 11:50 am Portfolio C = Has 50k in options with x2 leverage (strike price about half of the index) and 50k in cash.
Portfolio A is a single ticker that satisfies Merton. If you wanted to get 150% allocation to stocks, you could just buy a 150% leveraged ETF if it were on the market. Likewise if you wanted a 200% allocation to stocks or a 250% allocation or a 300% allocation. In an asset universe of stocks and cash, an appropriately geared up LETF is all you need to satisfy Merton, as long as it's 100% of assets.
305pelusa wrote: Thu Feb 20, 2020 11:50 am path dependence and non-constant % allocation to stocks being the big ones
Path dependence is a consequence of a constant % allocation to stocks that is leveraged.

UPRO and other LETFs are a constant % allocation if it is 100% of assets.
My example simply illustrates that where a non-levered strategy needs not rebalance, a leveraged strategy with options won’t have to rebalance either. But a LETF strategy does.

I contemplated making an example where portfolio A was 50/50, which would then require a purchase after the 10% drop to maintain constant % exposure. The option strategy would have to make just as much of a purchase. But the LETF would need to make an even bigger purchase to make up for it. But I thought it too complicated.

Leveraging with options is akin to buy and hold with no rebalancing. To the extent B&H produces non-constant % allocations, leverage with options will as well. Not more, not less. But LETF strategies will require purchase/selling just to maintain the same allocation % to the B&H and even more so to maintain constant %.

Hope that’s clear to you.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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Steve Reading
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Re: Lifecycle Investing - Leveraging when young

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String wrote: Thu Feb 20, 2020 4:22 pm
MoneyMarathon wrote: Thu Feb 20, 2020 4:02 pm Portfolio A is a single ticker that satisfies Merton. If you wanted to get 150% allocation to stocks, you could just buy a 150% leveraged ETF if it were on the market. Likewise if you wanted a 200% allocation to stocks or a 250% allocation or a 300% allocation. In an asset universe of stocks and cash, an appropriately geared up LETF is all you need to satisfy Merton, as long as it's 100% of assets.
Exactly, and similarly if you only want 50% stocks, holding separate 50/50 stock/cash allocation has the same problem of drifting % exposure. Does this make the only suitable holding in this case an all in one 50/50 balanced fund? (Effectively a 50% LETF)
No it doesn’t but to the extent you want a constant % allocation, then clearly a rebalanced balanced fund will be superior to carrying separate cash/stock allocations.

Either way, my point is that the drift that a buy and hold has is certainly true, but perhaps minor in my opinion. Rebalance every couple of years and it’s fine. This applies equally to variable leverage with options.

A portfolio that achieves the same exposure with LETFs, however, suffer far more drift.

And to be clear, this is talking about a retiree with human capital. Since we all DO have human capital, then we’re stuck with multiple assets and don’t actually get to just buy one ticket that encompasses all of our wealth. Leveraged options/futures/margin, with rebalancing once you hit your bands, will simply require less work and transactions that trying to get the same exposure with LETFs. Again, you can do it with LETFs provided you trade enough to overcome its underlying % allocation drift.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
UberGrub
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Re: Lifecycle Investing - Leveraging when young

Post by UberGrub »

It feels like this LETF debate has been beaten to death. I mean 305 has said everything he has to say and is kinda repeating himself :shock:
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Steve Reading
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Re: Lifecycle Investing - Leveraging when young

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UberGrub wrote: Thu Feb 20, 2020 5:03 pm It feels like this LETF debate has been beaten to death. I mean 305 has said everything he has to say and is kinda repeating himself :shock:
Agreed. In the grand scheme of things, it’s a minor implementation detail. I don’t have anything to say in the matter so I’m just gonna move on. I will gladly respond to other questions on Lifecycle Investing (such as discounting future savings, choosing a Samuelson share, etc)
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated »

305pelusa wrote: Thu Feb 20, 2020 11:50 am
Uncorrelated wrote: Thu Feb 20, 2020 11:06 am It follows from Merton that if you have no human capital left, a constant amount of stocks (continuously rebalanced) is the optimal solution, a leveraged ETF comes close to this situation.
No it doesn’t, and it’s surprising to see you make such a claim. Consider:
Portfolio A = Has 100k in stocks. It is 100% in stocks. Market drops 10%. You now have 90k in stocks and are still 100% in stocks. Merton is satisfied.
Portfolio B = Has 50k in a x2 LETF of stocks and 50k in cash. This effectively is 100% in stocks as well. Market drops 10%. You now have 40k in the x2 LETF and 50k in cash. This is an exposure of 80k in stocks and 10k in cash. That’s 88% in stocks. This isn’t satisfying what Merton is saying as your % allocation to stocks has decreased.
The theory is "rebalance daily is optimal". Not "if you allocate 7% of your portfolio to a 13x daily leveraged ETF, you don't have to rebalance". Although in 2 or 3 cases I mentioned, allocating 100% of your funds to a daily leveraged ETF (with the exact amount of leverage you need) would eliminate any manual rebalancing required.
UberGrub wrote: Thu Feb 20, 2020 11:58 am Ok so clearly:
- During retirement (no human capital), you’d use variable leverage (not constant) to satisfy Merton.
No, you'd use a constant proportion asset allocation. If your equity exposure is above 100% (say, 150%), then the optimal approach is to have 1.5x leverage today, 1.5x leverage tomorrow, and 1.5x leverage all days after that.

(usual assumptions apply, no transaction costs, normally distributed returns).
305pelusa wrote: Thu Feb 20, 2020 3:20 pm
MoneyMarathon wrote: Thu Feb 20, 2020 3:07 pm What is your underlying point?
Well, Uncorrelated said:
Uncorrelated wrote: Thu Feb 20, 2020 11:06 am It follows from Merton that if you have no human capital left, a constant amount of stocks (continuously rebalanced) is the optimal solution, a leveraged ETF comes close to this situation.
My underlying point is that uncorrelated got it backwards. LETFs do not maintain a constant % allocation to stocks (which is what Merton implies is optimal). It is in fact variable leverage like options that does. I made a small mathematical error but this point remains true.
To the extent that your entire portfolio is allocated to LETF's, they maintain a constant % allocation to stocks.

Anyway, the point was Merton says you should rebalance to the target allocation continuously (I translated that to daily), but you seem to think rebalancing daily is bad because of volatility decay. I was wondering if you had any evidence of that, but it appears not. I will deliver the evidence later this week.
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Re: Lifecycle Investing - Leveraging when young

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305pelusa wrote: Thu Feb 20, 2020 4:53 pm
MoneyMarathon wrote: Thu Feb 20, 2020 4:02 pm
305pelusa wrote: Thu Feb 20, 2020 11:50 am path dependence and non-constant % allocation to stocks being the big ones
Path dependence is a consequence of a constant % allocation to stocks that is leveraged.
This is important, but you don't seem to agree with it. Is that right? If so, why?
305pelusa wrote: Thu Feb 20, 2020 4:53 pm Leveraging with options is akin to buy and hold with no rebalancing
In your specific example, it worked out like that, if attempting to get 100% exposure to stocks as a percentage of net assets.

Suppose you wanted 200% exposure to stocks as a percentage of net assets. Per your example, you could buy the option with 100% of assets (100k) and have 200k exposure. You said that, if it dropped 10% then you'd be left with 80% of the value and a leverage of 2.25x. You've gone from 2x leverage to having 2.25x leverage, 225% exposure. That's not constant.

This wouldn't happen with buying a 2x LETF with all the assets. Both options don't require rebalancing in a specific set of circumstances (for the LETF that circumstance is just being 100% invested), but that doesn't mean you're going to be able to avoid rebalancing to achieve a constant % exposure to stocks in every circumstance.

You say, "I don’t have anything to say in the matter so I’m just gonna move on," which is pretty unfortunate if your current understanding isn't already complete and perfect. If it is perfect, it certainly could be explained better.
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Steve Reading
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Re: Lifecycle Investing - Leveraging when young

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Uncorrelated wrote: Thu Feb 20, 2020 5:24 pm Anyway, the point was Merton says you should rebalance to the target allocation continuously (I translated that to daily), but you seem to think rebalancing daily is bad because of volatility decay.
No, it's not quite that. I don't like the daily leverage reset to the extent it strays the portfolio away from a constant % allocation to equities. But that is also related to volatility decay because the decay comes precisely from not maintaining a constant % allocation. So I claim that if you did use LETFs in a way that produces a constant % allocation (say you buy UPRO after drops and vice-versa), you would have no volatility decay.

Not sure what you're going to show graphically but perhaps I'll be able to explain to you what I mean with your graphs :happy
MoneyMarathon wrote: Thu Feb 20, 2020 5:33 pm You say, "I don’t have anything to say in the matter so I’m just gonna move on," which is pretty unfortunate if your current understanding isn't already complete and perfect. If it is perfect, it certainly could be explained better.
A problem indeed since I do believe I understand it correctly but have no idea how to explain it any better. That's why I think there's not much left to discuss.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
MoneyMarathon
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Re: Lifecycle Investing - Leveraging when young

Post by MoneyMarathon »

305pelusa wrote: Thu Feb 20, 2020 6:06 pm
MoneyMarathon wrote: Thu Feb 20, 2020 5:33 pm You say, "I don’t have anything to say in the matter so I’m just gonna move on," which is pretty unfortunate if your current understanding isn't already complete and perfect. If it is perfect, it certainly could be explained better.
A problem indeed since I do believe I understand it correctly but have no idea how to explain it any better. That's why I think there's not much left to discuss.
You could reply to this:
MoneyMarathon wrote: Thu Feb 20, 2020 5:33 pm
305pelusa wrote: Thu Feb 20, 2020 4:53 pm
MoneyMarathon wrote: Thu Feb 20, 2020 4:02 pm
305pelusa wrote: Thu Feb 20, 2020 11:50 am path dependence and non-constant % allocation to stocks being the big ones
Path dependence is a consequence of a constant % allocation to stocks that is leveraged.
This is important, but you don't seem to agree with it. Is that right? If so, why?
And you could reply to this:
MoneyMarathon wrote: Thu Feb 20, 2020 5:33 pm
305pelusa wrote: Thu Feb 20, 2020 4:53 pm Leveraging with options is akin to buy and hold with no rebalancing
In your specific example, it worked out like that, if attempting to get 100% exposure to stocks as a percentage of net assets.

Suppose you wanted 200% exposure to stocks as a percentage of net assets. Per your example, you could buy the option with 100% of assets (100k) and have 200k exposure. You said that, if it dropped 10% then you'd be left with 80% of the value and a leverage of 2.25x. You've gone from 2x leverage to having 2.25x leverage, 225% exposure. That's not constant.

This wouldn't happen with buying a 2x LETF with all the assets. Both options don't require rebalancing in a specific set of circumstances (for the LETF that circumstance is just being 100% invested), but that doesn't mean you're going to be able to avoid rebalancing to achieve a constant % exposure to stocks in every circumstance.
Running away from specific questions and specific counter-examples, above, isn't a good look for someone claiming to have a correct understanding and no ability to clarify.

I would just say that you're wrong but I'm willing to hear your point of view, if you bother to try.
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Re: Lifecycle Investing - Leveraging when young

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MoneyMarathon wrote: Thu Feb 20, 2020 6:13 pm
305pelusa wrote: Thu Feb 20, 2020 6:06 pm
MoneyMarathon wrote: Thu Feb 20, 2020 5:33 pm You say, "I don’t have anything to say in the matter so I’m just gonna move on," which is pretty unfortunate if your current understanding isn't already complete and perfect. If it is perfect, it certainly could be explained better.
A problem indeed since I do believe I understand it correctly but have no idea how to explain it any better. That's why I think there's not much left to discuss.
You could reply to this:
MoneyMarathon wrote: Thu Feb 20, 2020 5:33 pm
305pelusa wrote: Thu Feb 20, 2020 4:53 pm
MoneyMarathon wrote: Thu Feb 20, 2020 4:02 pm
305pelusa wrote: Thu Feb 20, 2020 11:50 am path dependence and non-constant % allocation to stocks being the big ones
Path dependence is a consequence of a constant % allocation to stocks that is leveraged.
This is important, but you don't seem to agree with it. Is that right? If so, why?
It is technically true that maintaining a constant % allocation would lead to a small amount of path dependence. It's usually small though so I don't bother to differentiate. If you read the earlier part of this thread, Ben Matthews and I actually discussed which implementation might be better.

But using constant leverage products would lead to both path dependence AND non-constant % allocation.

^These are facts by the way. It's not what I agree or disagree. It is so.
MoneyMarathon wrote: Thu Feb 20, 2020 6:13 pm
MoneyMarathon wrote: Thu Feb 20, 2020 5:33 pm
305pelusa wrote: Thu Feb 20, 2020 4:53 pm Leveraging with options is akin to buy and hold with no rebalancing
In your specific example, it worked out like that, if attempting to get 100% exposure to stocks as a percentage of net assets.

Suppose you wanted 200% exposure to stocks as a percentage of net assets. Per your example, you could buy the option with 100% of assets (100k) and have 200k exposure. You said that, if it dropped 10% then you'd be left with 80% of the value and a leverage of 2.25x. You've gone from 2x leverage to having 2.25x leverage, 225% exposure. That's not constant.
I'm going to translate what you just said so you can see why what you said is trivially true:
"If your desired allocation is x2 leverage, then buying anything that does not at all times have x2 leverage would produce something other than x2 leverage". It's not an enlightening example.

How about we meaningful examples to Lifecycle Investing?
You have 750k in human capital and 250k in financial capital. Your desired allocation is 50/50. Lifecycle Investing would say you need to leverage your savings x2 to reach (that's 500k in stocks, -250k in debt, 750k in safe human capital, for a total of 50/50).

If you use a LETF
You buy 250k worth of SPUU. Say market drops 10%. You now have 200k in SPUU. So you have 400k in stocks, -200k in debt and 750k in human capital. So your allocation is now 42/58.

If you use calls
Buy 250k of call options with x2 leverage. Market drops 10%. You now have 200k in options with 2.25 leverage. That's 450k in stocks, -250k in debt and 750k in human capital. Your allocation is 47/53.

As pure illustration
Say there's also a retiree with 1M. He also wants 50/50. He is like you, except he actually has your human capital in financial capital. He invests 500k in stocks, 500k in bonds. Market drops 10%. Now he has 450k in stocks, 500k in bonds, or a 47/53 allocation.

Appreciate that symmetry. The option user with human capital is still long 450k in stocks like a retiree with no human capital and only financial assets so his allocation is the same. But the LETF user, dropped further. What's happening is that the LETF is not only dropping % allocation due to a market drop, but it's dropping further because it's selling exposure to try to maintain a constant leverage.

By the way, if the option user or retiree does not rebalance (and just continues to buy and hold), this would be path independent. But it's not constant % allocation. The LETF user is neither. It's not constant % allocation AND it's also path dependent. I leave that proof exercise to the reader.. HINT: To realize this, imagine that there's now a 10% market increase (no one rebalanced back to 50/50). Note down the allocation numbers and assets of all 3 cases. And now, simply reverse the sequence. Do the 10% gain first (again, no one rebalances), then the 10% drop. The retiree and option user will end up with identical assets to each other, regardless of the sequence. The LETF user will have different amounts of assets in one sequence than the other.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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Re: Lifecycle Investing - Leveraging when young

Post by MoneyMarathon »

305pelusa wrote: Thu Feb 20, 2020 7:00 pmIt is technically true that maintaining a constant % allocation would lead to a small amount of path dependence.
OK, makes sense. I'm glad we have the same understanding here, then.
305pelusa wrote: Thu Feb 20, 2020 7:00 pmBut using constant leverage products would lead to both path dependence AND non-constant % allocation.
I see. You'd like to vary the leverage applied to the financial capital because you have a (hidden) pile of human capital. You're not aiming for constant % leverage applied to current financial capital but to the combination of all capital (including future savings, or the present value of future savings). And (for the sake of the example) you're not yet at the limits of safe leverage, so you're able to vary the leverage.
305pelusa wrote: Thu Feb 20, 2020 7:00 pm How about we meaningful examples to Lifecycle Investing?
You have 750k in human capital and 250k in financial capital.
The example helps, especially in pointing out that a "constant % allocation" means something different if including future income. Thanks.
305pelusa wrote: Thu Feb 20, 2020 7:00 pm By the way, if the option user or retiree does not rebalance (and just continues to buy and hold), this would be path independent. But it's not constant % allocation.
Okay, that clears up a lot. In both scenarios, you'd have to rebalance to have a constant % allocation to stocks. You're trying to maintain path independence without a lot of rebalancing, so you're drawn to products that inherently vary their leverage.
305pelusa wrote: Thu Feb 20, 2020 7:00 pma 47/53 allocation
Makes more sense. I didn't believe that it could always (in every circumstance) be a constant percentage allocation without rebalancing... that's because it isn't, it's closer to being constant but rebalancing is needed for it to be truly constant.
305pelusa wrote: Thu Feb 20, 2020 7:00 pmThese are facts by the way. It's not what I agree or disagree. It is so.
I think the issue was mostly that we were using the same terms with different meanings (particularly what the denominator is in a "constant %" of stocks, where for you that included future income and therefore you could never put 100% of your capital in an investment until you stop saving). The terminology I was using would express that as a declining percentage of stocks, hence the misunderstanding between us.

PS - Uncorrelated seems right, though. He qualified his statement as "It follows from Merton that if you have no human capital left" so we're left with the situation where you can fully invest. Buying one name with all funds with the leverage you want (100%, 200%, whatever), where the leverage stays constant, trivially does the job in that scenario.
Last edited by MoneyMarathon on Thu Feb 20, 2020 7:35 pm, edited 1 time in total.
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Re: Lifecycle Investing - Leveraging when young

Post by ChrisBenn »

305pelusa wrote: Wed Feb 19, 2020 7:45 pm If your desired retirement portfolio is all bonds (so you’re effectively infinitely risk-averse since you’re not willing to hav anything in stocks), AND your income has no exposure to the market (it is a very safe source of income) then you’re set. No need to leverage. Your income is already your large bond. Its present value varies with interest rates like a bond. If rates drop, your income (which is the same before and after) is a more valuable source.

Now I understand you believe income is better modeled as cash (and for the reason above and others, I just disagree). So to the extent you have such a view, then yes, you’dshort cash (leverage) and invest in bonds.
Okay, I think I finally get what you and UberGrub where talking about previously re: modeling salaries as zero coupon bonds - specifically ones where the issue date was "today". (granted you did literally say that, I just glossed over it :) ).

So in the case of the hypothetical individual above who wants to end up at 100% bonds, they would already be temporally diversified if we assume their future income stream was exposed to the same risks/returns as the bond market (i.e. cola adjustments/promotions/job changes would be ~ to the rate of return expected on bonds; interest rate risk would be compensated for in more liquidity for the company (in times it fell), feeding into those RoR factors). Obviously pretty fuzzy, but then these future projections are inherently fuzzy - and since this problem has a binary set of asset classes as framed the exact details matter less.

Thanks for walking me through that - a few times.
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Re: Lifecycle Investing - Leveraging when young

Post by Steve Reading »

MoneyMarathon wrote: Thu Feb 20, 2020 7:28 pm
PS - Uncorrelated seems right, though. He qualified his statement as "It follows from Merton that if you have no human capital left" so we're left with the situation where you can fully invest. Buying one name with all funds with the leverage you want (100%, 200%, whatever), where the leverage stays constant, trivially does the job in that scenario.
Yes, it trivially does. I just didn't realize that's what he meant. All he said is a retiree with no human capital will be able to maintain a more constant % allocation to equities if he uses LETFs than options. I didn't realize he meant "provided he actually wanted, say 137% in equities and just such a LETF existed". But if that's it, then yes, obviously he's right 0_o
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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Re: Lifecycle Investing - Leveraging when young

Post by Steve Reading »

ChrisBenn wrote: Thu Feb 20, 2020 7:33 pm
305pelusa wrote: Wed Feb 19, 2020 7:45 pm If your desired retirement portfolio is all bonds (so you’re effectively infinitely risk-averse since you’re not willing to hav anything in stocks), AND your income has no exposure to the market (it is a very safe source of income) then you’re set. No need to leverage. Your income is already your large bond. Its present value varies with interest rates like a bond. If rates drop, your income (which is the same before and after) is a more valuable source.

Now I understand you believe income is better modeled as cash (and for the reason above and others, I just disagree). So to the extent you have such a view, then yes, you’dshort cash (leverage) and invest in bonds.
Okay, I think I finally get what you and UberGrub where talking about previously re: modeling salaries as zero coupon bonds - specifically ones where the issue date was "today". (granted you did literally say that, I just glossed over it :) ).

So in the case of the hypothetical individual above who wants to end up at 100% bonds, they would already be temporally diversified if we assume their future income stream was exposed to the same risks/returns as the bond market (i.e. cola adjustments/promotions/job changes would be ~ to the rate of return expected on bonds; interest rate risk would be compensated for in more liquidity for the company (in times it fell), feeding into those RoR factors). Obviously pretty fuzzy, but then these future projections are inherently fuzzy - and since this problem has a binary set of asset classes as framed the exact details matter less.

Thanks for walking me through that - a few times.
Glad I helped in some way :)
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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Re: Lifecycle Investing - Leveraging when young

Post by MoneyMarathon »

305pelusa wrote: Thu Feb 20, 2020 8:29 pm
MoneyMarathon wrote: Thu Feb 20, 2020 7:28 pm
PS - Uncorrelated seems right, though. He qualified his statement as "It follows from Merton that if you have no human capital left" so we're left with the situation where you can fully invest. Buying one name with all funds with the leverage you want (100%, 200%, whatever), where the leverage stays constant, trivially does the job in that scenario.
Yes, it trivially does. I just didn't realize that's what he meant. All he said is a retiree with no human capital will be able to maintain a more constant % allocation to equities if he uses LETFs than options. I didn't realize he meant "provided he actually wanted, say 137% in equities and just such a LETF existed". But if that's it, then yes, obviously he's right 0_o
Fair enough.

Somewhat related - Eureka! I have found it!

For some reason I thought Direxion shuttered their 1.25x product - and they kind of did. But they brought it back as a 1.35x product. The ticker is PPLC and it has a 0.36% net expense ratio. It could appeal to those who found 2x/3x and rebalancing frequently too much work, or too much leverage to ever get involved with on a volatile instrument like the S&P 500.

https://www.direxion.com/products/portf ... sp-500-etf

LETF fans who don't mind paying the expense ratio to be more hands off than other options (pun intended) may find it to be appealing, especially those who hate rebalancing. With 1.35x leverage, this might be the kind of LETF that even the laziest investor could love.
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Re: Lifecycle Investing - Leveraging when young

Post by MoneyMarathon »

Just reread the Ayres-Nalebuff paper. Some comments on it.

#1 They arbitrarily choose a long initial phase (as much as a decade or two, depending on how early returns pan out) of constant x2 leverage, relative to current financial assets, because it is the number used by a regulation.

This isn't rigorous. If the regulation said 4:1, apparently they'd use 4:1. If it said 1.5:1, they'd use 1.5:1. It's more reasonable to suppose that there is some non-regulatory reason for a bound or strategy on leverage to apply in the earliest phase. After all these regulations came about after the 1929 crash (first in the Securities Act of 1933). A reasonable investor (perhaps with math not yet developed...) would have had a way of determining the best margin to use other than calling their broker or lawmaker and asking their opinion on a good maximum.

"We propose a maximum leverage of 2:1."
"For most of the analysis, we assume that the maximum leverage on stocks is 2:1, pursuant to the Federal Reserve Regulation T."

Because this choice of how to leverage in the first phase is arbitrary and because the results of the first phase affect final savings, they haven't shown rigorously that their model of savings is optimal. Perhaps it should be lower, perhaps it should be higher and they should have used a technique for obtaining higher leverage. There's still a lot of value in the paper, but it does suggest more work could be done.

#2 They assume that it's only profitable to leverage stocks (implicitly or explicitly, since they don't investigate anything else), not profitable to leverage government bonds or another asset. Indeed their final asset allocation in retirement is divided between stocks and a risk-free rate of return, like T-bills. Since their model includes only stocks, margin rates, and risk-free rates, there's room for tinkering with other assets.

"the cost of borrowing on margin exceeds the bond rate"

This is true of brokerage margin rates, but with the borrowing costs implicit to the leverage implicit in treasury features, it's not true for longer duration government bonds, due to the low spread above LIBOR for borrowing and going out on the long end of the yield curve for investment. Also, government bonds have a non-interest component of their returns (price returns), which can play a part in constructing a balanced portfolio of stocks and bonds, which (under Modern Portfolio Theory) can increase risk-adjusted returns (Sharpe) and thus can increase returns over leveraging just stocks (whereas the author's framework is just leveraging up stocks).

Perhaps this chart may be illustrative of other possibilities for applying leverage to increase early returns (both positive and negative - thus also achieving temporal diversification by increasing the early volatility and returns if leverage is dialed down later), other than just leveraging stock:

https://www.portfoliovisualizer.com/bac ... ion3_3=-20

#3 They don't actually implement Samuelson-Merton's constant allocation.

They attempt to implement it by going as close as they can before bumping up into the 2:1 limit on current net assets. As Uncorrelated correctly points out, apart from the costs of the implementation (which leads the paper's authors to consider alternatives), the initial portfolio recommended by the paper is exactly the same as putting all of one's current financial wealth into a 2x stock LETF, such as SSO (Ultra S&P500) or the older mutual fund ULPIX (ProFunds UltraBull). This is constant leverage, not varying leverage, until the first phase is over.

This thread's approach is different and appears to attempt to vary leverage somewhat during the first phase, primarily in response to market movements and implicitly by holding options because this eliminates the path dependence (over a short term period). This difference isn't relevant to the point because it's still not implementing Samuelson-Merton's constant fraction of (lifetime) wealth in stocks.

The problem is that Samuelson-Merton's allocation is impossible to achieve for a very young saver with most wealth in the form of future savings, so an alternative must be considered, and the paper somewhat facilely slides into its arbitrary phase 1 recommendation as the alternative, when there are others as well. So not only is the idea of using the maximum leverage to buy stocks arbitrary, it doesn't satisfy the theory that is claimed to justify it, because it doesn't do what the theory asks for (only getting 'closer').

#4 The Samuelson-Merton recommendation assumes that all your wealth is available to invest (in stocks/t-bills) or consume.

When that assumption is contradicted, it's already unclear that Samuelson-Merton is the right framework. Instead of jerry-rigging its conclusions into a new theoretical framework where the assumptions are invalid, it would make more sense to develop the author's own justification regarding the optimal investment in stocks that is actually consistent with their assumptions. That is, to introduce the addition of income over time, as well as the various liquidity and leverage constraints, and derive the optimal investment based on utility with that model.

It's not easy, but it would seem that the right approach is to do it from scratch under the actual assumptions.

I've tried to work it out a bit on scratch paper. In the limit, when the additional income is a positive constant and it is the infinite case, the solution for the fraction to invest approaches the Merton solution (which is the Kelly limit modified by a utility function with a constant relative risk aversion) where wealth is just the same thing as current wealth. This suggests that the interesting work is to solve it for finite cases, especially in the early stages when the additional contributions are a considerable fraction of the initial investment, or in the late stages when taking money out. I'm not sure if this is an unsolved problem, or if someone has worked it out. It will take me some time to continue working on it or look up what's been done.

#5 They effectively defend the "leveraged glide path" as an approach during accumulation, empirically.

This much, taking more risk in early years, does seem justified by the empirical studies. They are persuasive in arguing that the basic problem with the old "glide path" is that it has too low of an average allocation to risky assets like stocks, as well as too small of a difference between starting risk and ending risk, to be effective. They are also persuasive in showing that a "glide path" incorporating leverage can overcome those two problems, provide enough risk up front and enough risk differential to matter and to reduce overall retirement risk through "temporal diversification."

However, the effect size isn't necessarily very large, when comparing to alternatives that are similarly exposed to stocks. Also, they've limited the solution space to those solutions that dial down to being unleveraged in retirement. This does represent a blind spot. If a portfolio is leveraged in retirement, there may be less room to create a large difference with the initial risk taken through leverage. They may have mostly just recreated an effect they criticize -- being able to achieve temporal diversification by artificially limiting later returns (as they point out, retirement accounts that are all or vastly bonds have no trouble being temporally diversified to stocks without leverage) -- in the new solution space where leverage is allowed.
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Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated »

MoneyMarathon wrote: Fri Feb 21, 2020 4:38 am Because this choice of how to leverage in the first phase is arbitrary and because the results of the first phase affect final savings, they haven't shown rigorously that their model of savings is optimal. Perhaps it should be lower, perhaps it should be higher and they should have used a technique for obtaining higher leverage. There's still a lot of value in the paper, but it does suggest more work could be done.
A literal application of Merton's model would use infinite leverage, since continuous rebalancing makes it impossible to get wiped out. In the real world this is obviously a bad idea.
#2 They assume that it's only profitable to leverage stocks (implicitly or explicitly, since they don't investigate anything else), not profitable to leverage government bonds or another asset. Indeed their final asset allocation in retirement is divided between stocks and a risk-free rate of return, like T-bills. Since their model includes only stocks, margin rates, and risk-free rates, there's room for tinkering with other assets.
This is consequence of using Merton's model with only one asset. It is possible to calculate the optimal asset for multiple assets (bonds, factors) by first calculating the efficient frontier, and then solving for max utility. If you have any particular assets in mind, I've already written the tools necessarily to perform this analysis. Due to the large number of output parameters (n time periods * m possible wealth * x possible portfolio's * y possible risk tolerances), the outcome is somewhat difficult to interpret.


You might be interested in the work of Gordon Irlam, which has written a solver (same technique that I use) that allows to solve for the optimal time-varying asset allocation in the presence of arbitrary utility functions. For example in the paper "Floor and Upside Investing in Retirement without Annuities" he investigates the optimal asset allocation and consumption for a retiree with a required spending (high risk aversion) and discretionary spending (low risk aversion): https://www.aacalc.com/about. The same method can be applied to solve for the optimal allocation in presence of liquidity constraints.

For an analytic solution, you might be interested in chapter 6 and 7 of "Strategic Asset Allocation: Portfolio choice for long term investors" by Campbell and Viceira https://faculty.fuqua.duke.edu/~charvey ... iceira.pdf
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Re: Lifecycle Investing - Leveraging when young

Post by White Oak »

Uncorrelated wrote: Fri Feb 21, 2020 7:37 am
MoneyMarathon wrote: Fri Feb 21, 2020 4:38 am#2 They assume that it's only profitable to leverage stocks (implicitly or explicitly, since they don't investigate anything else), not profitable to leverage government bonds or another asset. Indeed their final asset allocation in retirement is divided between stocks and a risk-free rate of return, like T-bills. Since their model includes only stocks, margin rates, and risk-free rates, there's room for tinkering with other assets.
This is consequence of using Merton's model with only one asset. It is possible to calculate the optimal asset for multiple assets (bonds, factors) by first calculating the efficient frontier, and then solving for max utility. If you have any particular assets in mind, I've already written the tools necessarily to perform this analysis. Due to the large number of output parameters (n time periods * m possible wealth * x possible portfolio's * y possible risk tolerances), the outcome is somewhat difficult to interpret.
Uncorrelated, I'd be interested in seeing a comparison of Ayres and Nalebuff's Lifecycle Strategy versus a similar strategy but using a stocks/bonds balanced allocation. I'm not sure how your optimizer is set up, but to start, you could test a fixed stock/bonds allocation close to the MPT tangency portfolio, say 50% S&P 500 and 50% long US treasuries. This is what EfficientInvestor described earlier in the thread (he was using STT, which would mean higher leverage):

EfficientInvestor wrote: Fri Nov 08, 2019 7:44 pm However, I also believe that asset diversification can provide a huge benefit on top of temporal diversification. I am trying to say that if you combine them together and do BOTH, it should be much better than just doing one or the other. Looking back to my 1910 backtest...P3 is how someone might invest if you are just doing asset diversification. P5 is how you are currently investing while in the earlier stages of your temporal spectrum. P4 is BOTH. Why would you not invest in something like P4 (or a more leveraged version) now and then ramp it down to 30/70? Like I said earlier, why not start at the green dot (or maybe even at the intersection of the orange line and 35% SD) and ramp down the orange line instead of starting at the blue dot and ramping down the black dashed line?

Image

It seems that you could and should use higher leverage with the stock & bond portfolio than for 100% equities.

I recently moved most of my retirement savings into a balanced, leveraged portfolio. For now I'm using 3x LETFs for the convenience, but I may move some of that to futures if I can understand the mechanics well enough. I was more nervous about leveraging 100% equites due to the historical max drawdowns, which are especially worrying as you approach the end of the fully-leveraged stage and the beginning of the deleveraging stage. I'm still nervous about the 3x balanced leverage, but the time diversification argument is strong enough that I'm taking the plunge.
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Re: Lifecycle Investing - Leveraging when young

Post by lock.that.stock »

White Oak wrote: Fri Feb 21, 2020 12:45 pm
Uncorrelated wrote: Fri Feb 21, 2020 7:37 am
MoneyMarathon wrote: Fri Feb 21, 2020 4:38 am#2 They assume that it's only profitable to leverage stocks (implicitly or explicitly, since they don't investigate anything else), not profitable to leverage government bonds or another asset. Indeed their final asset allocation in retirement is divided between stocks and a risk-free rate of return, like T-bills. Since their model includes only stocks, margin rates, and risk-free rates, there's room for tinkering with other assets.
This is consequence of using Merton's model with only one asset. It is possible to calculate the optimal asset for multiple assets (bonds, factors) by first calculating the efficient frontier, and then solving for max utility. If you have any particular assets in mind, I've already written the tools necessarily to perform this analysis. Due to the large number of output parameters (n time periods * m possible wealth * x possible portfolio's * y possible risk tolerances), the outcome is somewhat difficult to interpret.
Uncorrelated, I'd be interested in seeing a comparison of Ayres and Nalebuff's Lifecycle Strategy versus a similar strategy but using a stocks/bonds balanced allocation. I'm not sure how your optimizer is set up, but to start, you could test a fixed stock/bonds allocation close to the MPT tangency portfolio, say 50% S&P 500 and 50% long US treasuries. This is what EfficientInvestor described earlier in the thread (he was using STT, which would mean higher leverage):

EfficientInvestor wrote: Fri Nov 08, 2019 7:44 pm However, I also believe that asset diversification can provide a huge benefit on top of temporal diversification. I am trying to say that if you combine them together and do BOTH, it should be much better than just doing one or the other. Looking back to my 1910 backtest...P3 is how someone might invest if you are just doing asset diversification. P5 is how you are currently investing while in the earlier stages of your temporal spectrum. P4 is BOTH. Why would you not invest in something like P4 (or a more leveraged version) now and then ramp it down to 30/70? Like I said earlier, why not start at the green dot (or maybe even at the intersection of the orange line and 35% SD) and ramp down the orange line instead of starting at the blue dot and ramping down the black dashed line?

Image

I’m not sure I’m interpreting this chart correctly, but to me this chart suggests a few things (again someone correct me if I’m off on my interpretations):

* As your standard deviation / volatility increases, expected returns increase linearly (i.e. leverage is favored over non-leveraged, TQQQ is favored over UPRO)

* Risk parity approach if truly followed may have significant benefits over standard buy and hold 2 or 3 fund portfolio

Among other conclusions, this chart seems to suggest that a risk parity approach with high leverage has the highest expected returns.

Am I interpreting this correctly?

What is the basis for the data used to build this chart?
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Re: Lifecycle Investing - Leveraging when young

Post by MoneyMarathon »

lock.that.stock wrote: Fri Feb 21, 2020 1:07 pm Among other conclusions, this chart seems to suggest that a risk parity approach with high leverage has the highest expected returns.

Am I interpreting this correctly?
I think you are, but the chart is mislabeled. There's no magic about leveraging risk parity. The magic (the optimum) is leveraging maximum Sharpe. The maximum Sharpe portfolio has the highest slope on the tangency line of the efficient frontier, and as the graph shows this allows a leveraged portfolio with maximum Sharpe to have the same returns with lower volatility than leveraged 100% stock. But maximum Sharpe (highest return / volatility) is not the same thing as risk parity. They might both have a high ratio of bonds to stocks, but risk parity is a different way of constructing a portfolio that doesn't aim to produce the maximum Sharpe (it aims to take equal risk - sizing positions to equalize the contribution to portfolio volatility - in each asset class).

There are arguments for risk parity, of course, and they mostly involve the idea that calculating the maximum Sharpe portfolio is difficult to impossible & its composition changes over time anyway, because return characteristics are less stable and predictable than volatility characteristics. This is pretty controversial; not everyone is a risk parity advocate.
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Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated »

White Oak wrote: Fri Feb 21, 2020 12:45 pm Uncorrelated, I'd be interested in seeing a comparison of Ayres and Nalebuff's Lifecycle Strategy versus a similar strategy but using a stocks/bonds balanced allocation. I'm not sure how your optimizer is set up, but to start, you could test a fixed stock/bonds allocation close to the MPT tangency portfolio, say 50% S&P 500 and 50% long US treasuries. This is what EfficientInvestor described earlier in the thread (he was using STT, which would mean higher leverage):
A portfolio of 50 equity/50 long term treasuries is far off the efficient frontier, and will result in a poor solution. I feel unsure about running optimizations with leveraged STT, because the results are extremely sensitive to parameters estimation issues.

For an indication on what my optimizer can do, here is the optimal asset allocation for a Ayres and Nalebuff's "leveraged stocks or risk-free" allocation, assuming risk free rate of 0%, equity risk premium of 5% and borrowing cost of 1%. The borrowing cost is only applied at funds above 100%, this contradicts Ayres and Nalebuff which calculate the borrowing costs on the entire leveraged position.

Image
The diagonal line shows a certainty equivalent contour.

The next scenario will be generated using the efficient frontier in the image below. The fund selection includes a total market fund, a leveraged total market fund with a borrow rate of 2% (simulating 1% borrow rate per unit of leverage), and a leveraged bond fund similar to TMF. Note that the efficient frontier curves. (the orange line represents the efficient frontier. The other lines represents the frontier for investors with the given risk tolerance)
Image

The color axis in this image represents the amount allocated to stocks.
Image

Compared to the earlier scenario, the band where max leverage is chosen is significantly smaller. And the bands where a balanced allocation is chosen (~150% leverage) is substantially larger. The certainty equivalent contour is steeper, indicating that the certainty equivalent return (or expected utility) is higher.


Here is the fraction of wealth invested, in the first scenario. The 4 phases are clearly identifiable. For reference, the optimal Samuelson-Merton fraction with these assumptions is 65%.
Image

Here is the fraction of wealth invested for the second scenario (with TMF). The first phase almost disappeared. The second phase is completely unrecognizable. The third phase moved towards the left (indicating 80% stocks + 20% TMF). The fourth phase is the same. The Y axis represents the amount invested in stocks, with the optimal allocation to TMF being chosen.
Image


The results surprise me. I didn't expect phase 2 to be completely butchered. These results would indicate that lifecycle investing can be substantially improved by using multiple assets. Adding factor funds to the mix would also be interesting.


Finally, here is the fraction of wealth invested for Ayres and Nalebuff's assumptions, with the borrowing rate calculated on the entire position.
Image

If anyone has a better idea to visualize these results, I'm all ears...
lock.that.stock wrote: Fri Feb 21, 2020 1:07 pm
* Risk parity approach if truly followed may have significant benefits over standard buy and hold 2 or 3 fund portfolio

Among other conclusions, this chart seems to suggest that a risk parity approach with high leverage has the highest expected returns.
Aargh risk parity.

In order to use risk parity, you are required to make the following assumptions:
All asset classes have the same sharpe ratio.
All asset classes are uncorrelated.
The assets classes that you have arbitrary chosen are the only true risk factors.
Leverage is free.

I'd suggest staying far away from risk parity, it has never made any sense. The correct approach is to gather the assumptions that you think are true, and then run a mean-variance optimization or similar. If you choose the above assumptions, the results will be identical to risk parity. See also portfolio optimization humor
MoneyMarathon wrote: Fri Feb 21, 2020 3:25 pm
lock.that.stock wrote: Fri Feb 21, 2020 1:07 pm Among other conclusions, this chart seems to suggest that a risk parity approach with high leverage has the highest expected returns.

Am I interpreting this correctly?
I think you are, but the chart is mislabeled. There's no magic about leveraging risk parity. The magic (the optimum) is leveraging maximum Sharpe. The maximum Sharpe portfolio has the highest slope on the tangency line of the efficient frontier, and as the graph shows this allows a leveraged portfolio with maximum Sharpe to have the same returns with lower volatility than leveraged 100% stock. But maximum Sharpe (highest return / volatility) is not the same thing as risk parity. They might both have a high ratio of bonds to stocks, but risk parity is a different way of constructing a portfolio that doesn't aim to produce the maximum Sharpe (it aims to take equal risk - sizing positions to equalize the contribution to portfolio volatility - in each asset class).

There are arguments for risk parity, of course, and they mostly involve the idea that calculating the maximum Sharpe portfolio is difficult to impossible & its composition changes over time anyway, because return characteristics are less stable and predictable than volatility characteristics. This is pretty controversial; not everyone is a risk parity advocate.
Finding the max sharpe ratio or the tangency portfolio is an exercise in futility. It's only useful in a theoretical world where leverage is free. See the efficient frontier chart above evidence that leveraging the tangency portfolio results in a curved frontier after friction costs.
Last edited by Uncorrelated on Sat Feb 22, 2020 9:09 am, edited 1 time in total.
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Re: Lifecycle Investing - Leveraging when young

Post by MoneyMarathon »

Uncorrelated wrote: Sat Feb 22, 2020 6:27 am Finding the max sharpe ratio or the tangency portfolio is an exercise in futility. It's only useful in a theoretical world where leverage is free. See the efficient frontier chart above evidence that leveraging the tangency portfolio results in a curved frontier after friction costs.
Thanks. It is, as you point out, a theoretical simplification. (It was also the theoretical simplification reflected in the graph someone else posted, which I was commenting on.)
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Re: Lifecycle Investing - Leveraging when young

Post by Steve Reading »

Uncorrelated wrote: Sat Feb 22, 2020 6:27 am
The borrowing cost is only applied at funds above 100%, this contradicts Ayres and Nalebuff which calculate the borrowing costs on the entire leveraged position.
Could you repeat what you meant here please? If true, I would think they’re just wrong in doing that 0_o

Also, you have a neat little optimizer. Is that Matlab, or some graphical Python addon, or what?

I’d like to go ahead and code one of these. Is it actually a lot of work?
If you’d be so kind as to point me in the direction of how to do one of them (all the links to relevant equations, maybe even links to people who explain how to do it, basically the tools I’d need) then that actually would be awesome. I guess a related question is if you’d be willing to share your code; I’d like to give it a shot independently any ways but I don’t know how secretive you feel about it I mean 0_o
Thank for the help man.
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Re: Lifecycle Investing - Leveraging when young

Post by White Oak »

Thank you Uncorrelated for running these simulations and posting the results. I have a few follow-up questions:

1. Is your optimizer using historical returns data? If so, over what date range is the data from?
Uncorrelated wrote: Sat Feb 22, 2020 6:27 am
The next scenario will be generated using the efficient frontier in the image below. The fund selection includes a total market fund, a leveraged total market fund with a borrow rate of 2% (simulating 1% borrow rate per unit of leverage), and a leveraged bond fund similar to TMF. Note that the efficient frontier curves. (the orange line represents the efficient frontier. The other lines represents the frontier for investors with the given risk tolerance)
Image
2. Is your TMF-similar bond fund leveraged 3x? If I look at where cash=0, MKT is about 75% and TMF is about 25%, or 75% assuming 3x leverage. Is that about correct?


Uncorrelated wrote: Sat Feb 22, 2020 6:27 am
Here is the fraction of wealth invested, in the first scenario. The 4 phases are clearly identifiable. For reference, the optimal Samuelson-Merton fraction with these assumptions is 65%.
Image

Here is the fraction of wealth invested for the second scenario (with TMF). The first phase almost disappeared. The second phase is completely unrecognizable. The third phase moved towards the left (indicating 80% stocks + 20% TMF). The fourth phase is the same. The Y axis represents the amount invested in stocks, with the optimal allocation to TMF being chosen.
Image


The results surprise me. I didn't expect phase 2 to be completely butchered. These results would indicate that lifecycle investing can be substantially improved by using multiple assets. Adding factor funds to the mix would also be interesting.

...

If anyone has a better idea to visualize these results, I'm all ears...
Comparing the last two plots above, my intuition leads me to like the smoother transitions in the balanced portfolio rather than the corners of the Ayres & Nalebuff strategy. It seems unlikely that the optimal strategy has sharp corners. But this is just my intuitive reasoning.

3. Could you quantify for us the change in performance for the two strategies? (Maybe I could glean this from one of your charts, but it's not clear to me how I would do this.) You could do this either at an equivalent level of risk, what is the difference in expected return; or, for the same mean returns, what is the spread in returns? Ayres and Nalebuff made these comparisons in their book between their leveraged strategy and a more conventional target-date glide path. Ultimately this is the main thing I care about -- for the same risk, I can end up with X% more savings following strategy Y. Or, I can reach the same savings goal with a Z% reduction in the standard deviation of the final returns.

Thanks again for sharing your work!
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Re: Lifecycle Investing - Leveraging when young

Post by White Oak »

305pelusa wrote: Sat Feb 22, 2020 9:38 am Also, you have a neat little optimizer. Is that Matlab, or some graphical Python addon, or what?
The plots look like matplotlib to me, which is a Python module. If you have the choice between Matlab and Python, I would recommend going with Python. It is a more general-purpose language, but the community has added numerical tools that match or surpass Matlab.
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Re: Lifecycle Investing - Leveraging when young

Post by Steve Reading »

White Oak wrote: Sat Feb 22, 2020 10:10 am
305pelusa wrote: Sat Feb 22, 2020 9:38 am Also, you have a neat little optimizer. Is that Matlab, or some graphical Python addon, or what?
The plots look like matplotlib to me, which is a Python module. If you have the choice between Matlab and Python, I would recommend going with Python. It is a more general-purpose language, but the community has added numerical tools that match or surpass Matlab.
Yeah it looked like Python to me but wasn’t entirely certain. I’d prefer Python since it’s free; I don’t have Matlab at all.
Thanks
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated »

305pelusa wrote: Sat Feb 22, 2020 9:38 am
Uncorrelated wrote: Sat Feb 22, 2020 6:27 am
The borrowing cost is only applied at funds above 100%, this contradicts Ayres and Nalebuff which calculate the borrowing costs on the entire leveraged position.
Could you repeat what you meant here please? If true, I would think they’re just wrong in doing that 0_o
I think that Ayres and Nalebuff use two different optimal portfolio's:
portfolio 1, as the optimal Samuelson-Merton fraction, used in phase 4. In the paper, this is 90.6%. I suspect this is calculated as 1/γ * r/var.
portfolio 2, as the optimal Samuelson-Merton fraction with borrowing costs, used in phase 2. In the paper, this is 88.0%. I suspect this is calculated as 1/γ * (r - borrow_cost)/var.

I can't fully reproduce the numbers in the paper (I get very close), but any other interpretation would not result in a constant allocation for portfolio 2. Perhaps this was a deliberate simplification? Ayres and Nalebuff's focus was on creating something that was implementable by novices, not on creating something that was mathematically rigorous.

I used a large borrowing cost (1% above risk free), but the paper estimated borrowing costs at 0.2% above "bonds" (whatever that means. Long term bonds?). Perhaps there are some other minor differences between my implementation and their paper. I try to avoid making direct comparisons with their results.
Also, you have a neat little optimizer. Is that Matlab, or some graphical Python addon, or what?

I’d like to go ahead and code one of these. Is it actually a lot of work?
If you’d be so kind as to point me in the direction of how to do one of them (all the links to relevant equations, maybe even links to people who explain how to do it, basically the tools I’d need) then that actually would be awesome. I guess a related question is if you’d be willing to share your code; I’d like to give it a shot independently any ways but I don’t know how secretive you feel about it I mean 0_o
Thank for the help man.
I use python for both optimizers.

For the mean-variance optimizer, I use Fama&French' 5-factor + momentum model to translate the fund selection to expected return. I use this model because I believe that factors are the closest to the true underlying risk factors. For bonds, I invented my own factor model (probably a bad model, but better than nothing). The parameters were either taken from Fama & French or calculated from Simba's backtesting spreadsheet back to 1934. Once I have the factor loading, modern portfolio theory is used to calculate the expected return and standard deviation of the portfolio. The SLSQP method in scipy.optimize.minimize is used to find the efficient frontier in this model, given some constraints about fund selection and leverage. It took me a few hours to write.

The dynamic programming optimizer was invented from scratch, in about 3 days time. I formulate a terminal utility function and a probability distribution of expected returns, and then I iteratively compute the optimal asset allocation for each preceding year based on the next year. Sorry if this is a bit vague, it's pretty obvious how it works and I'm not sure how to explain it. If you're interested in implementing this method yourself, I recommend looking at Gordon Irlam's work at https://www.aacalc.com/about, the paper "Retirement Income Research: What Can We Learn from Economics?" contains a non-mathematical explanation of the method, some of his other papers contain some equations. The basic goal of the method is to solve Merton's portfolio problem with an arbitrary number of funds and arbitrary utility function (Gordon's main focus is optimizing asset allocation in retirement. His research blows the trinity study and VPW completely out of the water).

This is just a hobby project for me. The code isn't secret, but not really in a state in which it can be shared.
White Oak wrote: Sat Feb 22, 2020 10:03 am Thank you Uncorrelated for running these simulations and posting the results. I have a few follow-up questions:

1. Is your optimizer using historical returns data? If so, over what date range is the data from?
For the first scenario, the following return assumptions were used. All numbers are in excess of t-bills.
Stocks: 5% return, 16% stddev.
Bonds / risk free: 0% / 0%
Leverage cost: 1%

This choice of parameters was completely arbitrary, but are conveniently close to the numbers used by Ayres and Nalebuff.

For the second scenario, I used the same assumptions as above but also added TMF. The return parameters for TMF are an expense ratio of 1.1%, annual return of ~6% (before expenses) and standard deviation of ~30%. These parameters were estimated based on bond return data since 1934. The assumed correlation between stocks and bonds is zero.

My solver only support independently distributed returns. The point of this exercise wasn't to prove that these assumptions are the best, but to investigate how different the optional asset allocation is when allowing combinations between 2, 3 or more funds.
2. Is your TMF-similar bond fund leveraged 3x? If I look at where cash=0, MKT is about 75% and TMF is about 25%, or 75% assuming 3x leverage. Is that about correct?
Yes. Be very careful in extrapolating these results to other fund combinations. The allocation is quite sensitive to the fund universe, there are a lot of things that impact the optimal allocation.
3. Could you quantify for us the change in performance for the two strategies? (Maybe I could glean this from one of your charts, but it's not clear to me how I would do this.) You could do this either at an equivalent level of risk, what is the difference in expected return; or, for the same mean returns, what is the spread in returns? Ayres and Nalebuff made these comparisons in their book between their leveraged strategy and a more conventional target-date glide path. Ultimately this is the main thing I care about -- for the same risk, I can end up with X% more savings following strategy Y. Or, I can reach the same savings goal with a Z% reduction in the standard deviation of the final returns.
That is a good question. Here is a chart detailing the CER gain (certainty equivalent return) compared to only investing in leveraged stocks and the risk-free rate. The chart assumes an investor starts with $0, the planned years of labor participation is on the X axis.
Image
I took the liberty of adding another result based on an efficient frontier with an value and small cap value fund in addition to TMF and 3x MKT. Half the historical factor premia was used, factor clones of IJS (iShares US small cap value) and IUSV (ishares US value) were allowed to be selected in the portfolio.

In the chart we see that for an investor that has a planned labor participation of 40 years, the certainty equivalent retirement balance is around 25% higher. Adding factor funds makes another ~30% gain. I used a coefficient of relative risk aversion of 3.
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Re: Lifecycle Investing - Leveraging when young

Post by White Oak »

Uncorrelated wrote: Sat Feb 22, 2020 12:10 pm That is a good question. Here is a chart detailing the CER gain (certainty equivalent return) compared to only investing in leveraged stocks and the risk-free rate. The chart assumes an investor starts with $0, the planned years of labor participation is on the X axis.
Image
I took the liberty of adding another result based on an efficient frontier with an value and small cap value fund in addition to TMF and 3x MKT. Half the historical factor premia was used, factor clones of IJS (iShares US small cap value) and IUSV (ishares US value) were allowed to be selected in the portfolio.

In the chart we see that for an investor that has a planned labor participation of 40 years, the certainty equivalent retirement balance is around 25% higher. Adding factor funds makes another ~30% gain. I used a coefficient of relative risk aversion of 3.
Thank you for your explanations, and for generating these extra results. So it looks to me like adding TMF produces a noticeable (10-25%) increase in returns for a typical 20-40 year accumulation stage. This is a decent increase, but not life changing.

I'm a little surprised at the size of the gain with factors. Does that align with your expectations? I would have thought that we'd see diminishing returns: a decent increase with the second asset, but then decreasing gain with each additional asset. Can you give us an idea of what the asset allocation looks like for the strategy with factors?

What correlation are you using between your factor funds and MKT? You mentioned above that your optimizer only supports independently distributed returns, which is more-or-less true for MKT and LTT. However, I think the correlation is much higher for the factor funds.
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Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated »

White Oak wrote: Sat Feb 22, 2020 9:08 pm
Uncorrelated wrote: Sat Feb 22, 2020 12:10 pm
Thank you for your explanations, and for generating these extra results. So it looks to me like adding TMF produces a noticeable (10-25%) increase in returns for a typical 20-40 year accumulation stage. This is a decent increase, but not life changing.

I'm a little surprised at the size of the gain with factors. Does that align with your expectations? I would have thought that we'd see diminishing returns: a decent increase with the second asset, but then decreasing gain with each additional asset. Can you give us an idea of what the asset allocation looks like for the strategy with factors?

What correlation are you using between your factor funds and MKT? You mentioned above that your optimizer only supports independently distributed returns, which is more-or-less true for MKT and LTT. However, I think the correlation is much higher for the factor funds.
The gain with factors aligns with my expectations. The following efficient frontier was used:

Image
I don't necessarily recommend this specific asset allocation due a lack of international diversification and some other issues, but I need something to analyze. This frontier was generated with an assumed market return of 5% per year to be consistent with my previous few posts, but Fama/French estimate the market return closer to 6%.

My mean variance optimizer (shown above) supports correlations. The correlation data from Fama & French 2014/2015 paper on 5-factor asset model was used, with correlations stocks and bonds assumed to be zero. My method first calculates the factor exposure of the total portfolio, and then uses that factor data to estimate the return of the entire portfolio. I don't specify the correlations of the funds themselves, only the correlations between factors and the factor exposure of the funds.

My dynamic programming analyzer (which creates those colormaps) has the limitation that each year must be independently distributed, but the distribution can be anything. This means I can't simulate any kind of mean-reversion that may be present in the stock market. I used a normal distribution reflecting different points on the efficient frontier (image above) as input for the optimizer.
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Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated »

I promised a comparison between LETF and options, so I created a model. Model parameters:

S = 10000 (liquid savings)
W = 60000+ (Remaining human capital. Chosen high to make sure the investor leverage constrained)
gamma = 3 (risk tolerance)
total borrow cost = 1% annually for options, 2% for LETF. Both subtracted daily.
XL data series of simulated LETF, assuming a holding period of 125 trading days (6 months)
XO data series of simulated options, assuming a holding period of 125 trading days (6 months), no rebalancing, no margin calls.
The simulation was based on the daily excess return series provided by Ken French. XL and XO were generated by sampling trading days sequentially from the data.

The CER was calculated as U-1(average(U(S * X + W))) - W
With U being the utility function.

2x leverage (ending balance after 125 days):
Image

Image
The CER advantage for options is 0.15% annualized.


3x leverage
Image
Note that some option sequences result in a negative net worth. My analysis assumes you will not get margin called.

Image
The CER advantage for LETF is 1.6% annualized.


I also tested different time periods (not shown) and found that LETF generally outperforms at high leverage, and options generally outperform at low leverage. With a rebalance interval of 20 trading days, the break-even point is 2.6x leverage. With a rebalance interval of 50 trading days, the break-even point is around 2.2x leverage. With a rebalance interval of 125 trading days (6 months), the break-even point is 2.1x leverage.

Conclusion: there is no reason to fear volatility decay. If you are lazy or your desired leverage is 3x, go for LETF's. if your target leverage is 2x and you are willing to rebalance regularly (monthly), pick options.
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Re: Lifecycle Investing - Leveraging when young

Post by ChrisBenn »

So - determining one's relative risk aversion. Do people have a methodology for this?

I know I'm not risk-neutral (crra=0)
I feel fairly certain I'm more risk averse than log utility (crra=1)

Past that it seems unfortunately imprecise - and since this factor goes into calculating your Samuelson share it seems important.

Is the best method just to use the provided lifecycle investing books' formula of 1.58 / crra and proxy that to a stock/risk free asset portfolio - i.e. a crra of 1.58 is equivalent to being comfortable with 100% stocks, and if 60/40 was more my thing I would get a CRRA of ~2.6?

(related, I would be curious @Uncorrelated if your mean variance optimizer in a risk free/total market world agrees with the lifecycle formula - i.e. one hits 100% equities at a gamma of 1.58)

I found this in literature: https://files.stlouisfed.org/files/htdo ... 14-005.pdf
Even given the error bars this seemed biased a bit to the low side (as an absolute value) - but def could just be due to the methodology - since they tried to come at it from a survey angle.

Image

I didn't really see any other survey type papers in literature though.
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Re: Lifecycle Investing - Leveraging when young

Post by MoneyMarathon »

ChrisBenn wrote: Tue Mar 03, 2020 8:21 pm could just be due to the methodology - since they tried to come at it from a survey angle.
Since they directly poll reported happiness and income levels, many of the countries on the left may be showing some combination of lower materialism (less happiness derived from / explained by income) and lower income inequality (less variance in income). Hard to figure out which part of happiness is due to income. "Money isn't everything."
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Re: Lifecycle Investing - Leveraging when young

Post by Steve Reading »

ChrisBenn wrote: Tue Mar 03, 2020 8:21 pm So - determining one's relative risk aversion. Do people have a methodology for this?

I know I'm not risk-neutral (crra=0)
I feel fairly certain I'm more risk averse than log utility (crra=1)

Past that it seems unfortunately imprecise - and since this factor goes into calculating your Samuelson share it seems important.

Is the best method just to use the provided lifecycle investing books' formula of 1.58 / crra and proxy that to a stock/risk free asset portfolio - i.e. a crra of 1.58 is equivalent to being comfortable with 100% stocks, and if 60/40 was more my thing I would get a CRRA of ~2.6?

(related, I would be curious @Uncorrelated if your mean variance optimizer in a risk free/total market world agrees with the lifecycle formula - i.e. one hits 100% equities at a gamma of 1.58)

I found this in literature: https://files.stlouisfed.org/files/htdo ... 14-005.pdf
Even given the error bars this seemed biased a bit to the low side (as an absolute value) - but def could just be due to the methodology - since they tried to come at it from a survey angle.

Image

I didn't really see any other survey type papers in literature though.
That book's formula incorporates RRA, st. dev. and ERP. What you want is to simply assess RRA, which you do with the New Job question. They have a neat calculator for this:
http://www.lifecycleinvesting.net/resources.html

I determined my own RRA in two ways:
1) I answered the New Job question. I would be willing to bet about 30% of my income for the chance to double it. That's an RRA of 2.4. I wouldn't bet more, but I think I'd be willing to bet more than 20% so I know my RRA is between 2.4 and 5.1. This gave me a ball park figure. It would imply that, historically, I would be ~70% in stocks in retirement. This felt a little high to me in general considering that many others who are more experienced than myself (Bogle, Ferri, etc) recommend a little less. So then I :
2) Figured out what RRA would produce a 50% allocation to stocks in retirement (this is what many recommend and seems reasonable to me). That's an RRA of 4.1.

You might be wondering "why would you figure out your RRA from your desired retirement allocation if the RRA is to determine that allocation itself?". Two reasons:
1) If I'm borrowing at higher than the RFR, my effective ERP is lower than the historical or current one. With the RRA of 4.1, I can ask how much to put in stocks when leveraged. In other words, I can quantify how much to put in stocks when leveraged (paying more than the RFR) given that I'd like to be at 50% if I was unleveraged. So right now, I have an allocation of 41%. This idea that you'd have an allocation if leveraging at higher than the RFR and a different allocation when unleveraged (where your only investment option is the RFR) is covered in their paper but not in the book (presumably because it's a little more complicated).
2) It allows me to do some of the market-timing that they mention. If the ERP looks especially high in current conditions (better than historical), then I would be more than 50% in stocks and vice-versa. In other words, given that I'd be 50% in stocks historically, how much more/less would I be given the current conditions?

Right now, the ERP looks to me, if anything, to be a little larger than historical numbers (mostly due to the very low RFR). So if I were retired today, I would be ~53% in stocks.

I hope that's not too complicated. Hopefully it gives some perspective as to what I did.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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Re: Lifecycle Investing - Leveraging when young

Post by Maker »

Thank you 305pelusa, Uncorrelated and everyone else who participated for this awesome thread.

I only recently found out about the Kelly criterion, but I already want to learn as much as possible. I would be interested in doing some backtests, though one of the main limits of these strategies is that they are applied at a national level (on this forum the focus is always on US equities). The japanese experience leads me to believe that any strategy involving leverage should be used on a globally diversified portfolio. I know, I know, the US is not at the valuation levels that characterized Japan in the 80s, but I'm convinced global diversification would only improve this kind of strategy. The issue is the data. I am unable to find daily data for global indices, I tried both MSCI end of day index search, though they only have daily data for he last 5-6 years. Further back than that it is only monthly. I'm a second year CS undergraduate, and my university has access to Reuters' Datastream. I am currently unable to use it (it is only available locally and the university is closed because of the coronavirus contagion); do you believe it may have the kind of data I'm looking for? If not, any tips about how to obtain such data?

Another note about the implementation of this kind of strategy: I'm from Europe, and here ETFs are limited to 2x leverage. There are 3x ETNs (WisdomTree's) but those expose investors to counterparty risk, so I'm not so sure about them. Given these limits on daily resetting funds, the only alternative here in Europe may be futures and options. At this point I wonder: is daily data necessary at all?

Last question: have you considered the use of Box Spreads as a way of obtaining leverage? I found this document from CME Group (https://www.cmegroup.com/trading/equity ... g-tool.pdf) that describes the use of those spreads for financing at appealing interest rates. Is it feasible? And if so, does anyone know if it is feasible in Europe? The only thread on a local forum about Box Spreads is extremely confused, with some claiming brokers will not allow the "loan" to be accredited. I seriously wonder whether globally leveraged strategies are feasible in Europe, especially for a "nobody" like me (with a total net worth of around 2.000€). If so, it's unfortunate that european retail investors are left out.

Thanks!
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Re: Lifecycle Investing - Leveraging when young

Post by Steve Reading »

Maker wrote: Sun Mar 08, 2020 8:52 am Thank you 305pelusa, Uncorrelated and everyone else who participated for this awesome thread.

I only recently found out about the Kelly criterion, but I already want to learn as much as possible. I would be interested in doing some backtests, though one of the main limits of these strategies is that they are applied at a national level (on this forum the focus is always on US equities). The japanese experience leads me to believe that any strategy involving leverage should be used on a globally diversified portfolio. I know, I know, the US is not at the valuation levels that characterized Japan in the 80s, but I'm convinced global diversification would only improve this kind of strategy. The issue is the data. I am unable to find daily data for global indices, I tried both MSCI end of day index search, though they only have daily data for he last 5-6 years. Further back than that it is only monthly. I'm a second year CS undergraduate, and my university has access to Reuters' Datastream. I am currently unable to use it (it is only available locally and the university is closed because of the coronavirus contagion); do you believe it may have the kind of data I'm looking for? If not, any tips about how to obtain such data?

Another note about the implementation of this kind of strategy: I'm from Europe, and here ETFs are limited to 2x leverage. There are 3x ETNs (WisdomTree's) but those expose investors to counterparty risk, so I'm not so sure about them. Given these limits on daily resetting funds, the only alternative here in Europe may be futures and options. At this point I wonder: is daily data necessary at all?

Last question: have you considered the use of Box Spreads as a way of obtaining leverage? I found this document from CME Group (https://www.cmegroup.com/trading/equity ... g-tool.pdf) that describes the use of those spreads for financing at appealing interest rates. Is it feasible? And if so, does anyone know if it is feasible in Europe? The only thread on a local forum about Box Spreads is extremely confused, with some claiming brokers will not allow the "loan" to be accredited. I seriously wonder whether globally leveraged strategies are feasible in Europe, especially for a "nobody" like me (with a total net worth of around 2.000€). If so, it's unfortunate that european retail investors are left out.

Thanks!
The synthetic long I set up is essentially identical to financing at that box spread to get stock exposure. My portfolio is globally diversified; I get all my leverage on the US side while most of my stock ETFs are international equity.

I don’t know about doing this from Europe. Uncorrolated is there so he might know.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated »

I wouldn't worry about the data. I believe that markets are generally efficient and most information is priced in. If you look at the data you will probably see that international investing has been relatively pointless the last 30 years, but on a forward-looking basis I believe that a globally diversified portfolio is your best bet. You don't need daily data to draw conclusions about long term trends.

In my country (the Netherlands), it is very difficult to purchase US domiciled funds. it definitely isn't possible with a net wealth of €2.000. S&P500 mini options trade at $30k notional value and EU/emerging markets trade at approximately $200k/$100k. Options for actual ETF's (such as VT) start lower, but have early execution risk because they are American style options.

In the Netherlands it's very attractive to use student loan debt (0% interest, extremely favorable terms), so if you have the option I would recommend trying that first. The second best option is probably to purchase an all-world ETF with a margin loan at a broker until you have enough money to purchase options. To avoid margin calls you should probably not go above 3x leverage.

And don't forget about potential tax impact.
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Re: Lifecycle Investing - Leveraging when young

Post by Maker »

Thank you both for your answers.

With regards to leverage, student loans aren't really an option, as university here doesn't cost much (I'm from Italy). As a consequence, low competition has led to extremely high interest (with some reaching over 10% a year) loans. Box spreads with european style options are a great alternative but I need to find out whether they are feasible. Interactive Brokers' margin is also acceptable (1.5% IIRC). In general, I need to learn more about both options and futures as they're relevant to this strategy and I barely know anything about them (and what I know is mostly from a US point of view, which may or may not apply to me in Italy).

I would still love to find relevant data about global indices (MSCI ACWI or FTSE All-World, even MSCI World if emerging markets data isn't available) as to backtest strategies similar to the last outlined in this post: https://rhsfinancial.com/2017/06/20/lin ... -leverage/. Any thoughts about it? The main difficulty I see is that of applying crazy amounts of leverage (the look-ahead biased Kelly investor uses a whopping 10.38 leverage) that requires daily updates.

In general, is there any value in being a Kelly investor with real time data? Is there anything major I'm missing (apart from the garbage in garbage out risk and the inherent difficulty in implementing it)?

Sorry if some of my writing is most probably confusing: I only recently learned about these topics so I'm looking up to you as a way to learn as much as possible, since you both seem to have done extensive research in this area.
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Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated »

You might be interested in my topic of last week, which discusses some mathematical methods for investing: viewtopic.php?f=10&t=305919. It is very difficult to make decisions based on backtests, because backtests give only one outcome and your investment decisions should be based on the probability distribution of outcomes.

Regardless of whether or not the kelly criterion is applicable, daily data is generally not useful because trading costs and friction costs will quickly erase out your gains. I know nothing about Italian tax law, but apparently Italy has a flat transaction tax of 0.1% per transaction, I would also estimate at least 0.1% per trade for friction costs. Perhaps you can use the US daily data you collected to estimate the tax and trading cost impact of rebalancing strategies.

Ken French has daily data available for various regions. https://mba.tuck.dartmouth.edu/pages/fa ... l#Research (i.e. Fama/French Developed 3 Factors). The column Mkt-RF indicates the daily performance of a total stock market index in excess of the risk free rate. The data for international ex-us is since 1991, but you're probably better off using the US-only data because that goes back to 1927.
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Re: Lifecycle Investing - Leveraging when young

Post by NixoN94 »

Extremely interested in this concept and the way of dealing with it.

I am currently 25 years old and have been investing for 7 years.
2013: 1K invested
2019: 5K invested
2020: 25K invested

As you can see my returns were very positive percentagewise but I now have a negative end result if you would look at 2013-2020 moneywise as I had one of the most negative market timings to invest the 20K I got after buying a house.

That's why I opened a topic on this forum to see how people dealt with it. Leveraging seems like an extreme option to me personally but it also seems like there is no alternative to it (I haven't read too much on it though).

What are some alternatives to leveraging? One way I could think of was a less extreme version where one would invest 100% when younger and only about 50% at age 50 instead of leveraging to e.g. 200% at age 25.

I don't see alternatives to reducing the risk of putting more money in the market at later stages in life but would like to hear them if anyone knows them.
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Re: Lifecycle Investing - Leveraging when young

Post by Steve Reading »

NixoN94 wrote: Mon Mar 09, 2020 8:37 am Extremely interested in this concept and the way of dealing with it.

I am currently 25 years old and have been investing for 7 years.
2013: 1K invested
2019: 5K invested
2020: 25K invested

As you can see my returns were very positive percentagewise but I now have a negative end result if you would look at 2013-2020 moneywise as I had one of the most negative market timings to invest the 20K I got after buying a house.

That's why I opened a topic on this forum to see how people dealt with it. Leveraging seems like an extreme option to me personally but it also seems like there is no alternative to it (I haven't read too much on it though).

What are some alternatives to leveraging? One way I could think of was a less extreme version where one would invest 100% when younger and only about 50% at age 50 instead of leveraging to e.g. 200% at age 25.

I don't see alternatives to reducing the risk of putting more money in the market at later stages in life but would like to hear them if anyone knows them.
What occurred to you describes the problem perfectly. Had you gotten more exposure back in the good years (more even exposure through time), you would be well in positive territory. But it is having little money in good years and lots in bad that lead to the worst outcomes.

The only way to gain more exposure to stocks when you don’t have the money is through leverage, plain and simple. It’s not extreme with the right mindset. To me it’s extreme NOT to use it; you’re really putting most of your eggs on your near-retirement year baskets.

In any case, if you’re unwilling to use leverage, then get as close as you can. That means 100% in stocks, see if you can use 0% APR credit cards, don’t pay off mortgage or auto loans if the rates are reasonable, etc.

William Bernstein argues a way to mimic leverage is to factor tilt strongly to small and value. This is another avenue. I don’t feel as confident about the value premium (and certainly not the size premium) as the equity premium but it’s a reasonable idea nonetheless. I personally use it and tilt strongly to value, quality and investment to try to increase the risk of the portfolio as a form of pseudo-leverage.

Every bit counts and if the most you’re comfortable with is 100% stocks, then that’s ok too :)
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
UberGrub
Posts: 160
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Re: Lifecycle Investing - Leveraging when young

Post by UberGrub »

How are you doing in all of this 305?
NixoN94
Posts: 8
Joined: Fri Mar 06, 2020 10:00 am

Re: Lifecycle Investing - Leveraging when young

Post by NixoN94 »

305pelusa wrote: Mon Mar 09, 2020 10:16 am
NixoN94 wrote: Mon Mar 09, 2020 8:37 am Extremely interested in this concept and the way of dealing with it.

I am currently 25 years old and have been investing for 7 years.
2013: 1K invested
2019: 5K invested
2020: 25K invested

As you can see my returns were very positive percentagewise but I now have a negative end result if you would look at 2013-2020 moneywise as I had one of the most negative market timings to invest the 20K I got after buying a house.

That's why I opened a topic on this forum to see how people dealt with it. Leveraging seems like an extreme option to me personally but it also seems like there is no alternative to it (I haven't read too much on it though).

What are some alternatives to leveraging? One way I could think of was a less extreme version where one would invest 100% when younger and only about 50% at age 50 instead of leveraging to e.g. 200% at age 25.

I don't see alternatives to reducing the risk of putting more money in the market at later stages in life but would like to hear them if anyone knows them.
What occurred to you describes the problem perfectly. Had you gotten more exposure back in the good years (more even exposure through time), you would be well in positive territory. But it is having little money in good years and lots in bad that lead to the worst outcomes.

The only way to gain more exposure to stocks when you don’t have the money is through leverage, plain and simple. It’s not extreme with the right mindset. To me it’s extreme NOT to use it; you’re really putting most of your eggs on your near-retirement year baskets.

In any case, if you’re unwilling to use leverage, then get as close as you can. That means 100% in stocks, see if you can use 0% APR credit cards, don’t pay off mortgage or auto loans if the rates are reasonable, etc.

William Bernstein argues a way to mimic leverage is to factor tilt strongly to small and value. This is another avenue. I don’t feel as confident about the value premium (and certainly not the size premium) as the equity premium but it’s a reasonable idea nonetheless. I personally use it and tilt strongly to value, quality and investment to try to increase the risk of the portfolio as a form of pseudo-leverage.

Every bit counts and if the most you’re comfortable with is 100% stocks, then that’s ok too :)
The thing I'm not sure about yet, is how to decide how much to invest. I can kind of measure what I'm going to make with my job in the next 40 years but the costs are a bit harder. I will probably have kids and am not sure what the costs of living will be in the future.

Also, what about inflation ? Should I count it in already when investing now that money will be worth less in 40 years ?
User avatar
Topic Author
Steve Reading
Posts: 2959
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by Steve Reading »

NixoN94 wrote: Mon Mar 09, 2020 2:28 pm
305pelusa wrote: Mon Mar 09, 2020 10:16 am
NixoN94 wrote: Mon Mar 09, 2020 8:37 am Extremely interested in this concept and the way of dealing with it.

I am currently 25 years old and have been investing for 7 years.
2013: 1K invested
2019: 5K invested
2020: 25K invested

As you can see my returns were very positive percentagewise but I now have a negative end result if you would look at 2013-2020 moneywise as I had one of the most negative market timings to invest the 20K I got after buying a house.

That's why I opened a topic on this forum to see how people dealt with it. Leveraging seems like an extreme option to me personally but it also seems like there is no alternative to it (I haven't read too much on it though).

What are some alternatives to leveraging? One way I could think of was a less extreme version where one would invest 100% when younger and only about 50% at age 50 instead of leveraging to e.g. 200% at age 25.

I don't see alternatives to reducing the risk of putting more money in the market at later stages in life but would like to hear them if anyone knows them.
What occurred to you describes the problem perfectly. Had you gotten more exposure back in the good years (more even exposure through time), you would be well in positive territory. But it is having little money in good years and lots in bad that lead to the worst outcomes.

The only way to gain more exposure to stocks when you don’t have the money is through leverage, plain and simple. It’s not extreme with the right mindset. To me it’s extreme NOT to use it; you’re really putting most of your eggs on your near-retirement year baskets.

In any case, if you’re unwilling to use leverage, then get as close as you can. That means 100% in stocks, see if you can use 0% APR credit cards, don’t pay off mortgage or auto loans if the rates are reasonable, etc.

William Bernstein argues a way to mimic leverage is to factor tilt strongly to small and value. This is another avenue. I don’t feel as confident about the value premium (and certainly not the size premium) as the equity premium but it’s a reasonable idea nonetheless. I personally use it and tilt strongly to value, quality and investment to try to increase the risk of the portfolio as a form of pseudo-leverage.

Every bit counts and if the most you’re comfortable with is 100% stocks, then that’s ok too :)
The thing I'm not sure about yet, is how to decide how much to invest. I can kind of measure what I'm going to make with my job in the next 40 years but the costs are a bit harder. I will probably have kids and am not sure what the costs of living will be in the future.

Also, what about inflation ? Should I count it in already when investing now that money will be worth less in 40 years ?
Do you have the book? It does a reasonable job at answering some of these questions.

Long story short, with 40 years to retirement, you probably don’t have to calculate any of this. Chances are you should leverage 2:1 (the max they recommend) because even then you won’t even be close to the ideal amount of exposure.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
NixoN94
Posts: 8
Joined: Fri Mar 06, 2020 10:00 am

Re: Lifecycle Investing - Leveraging when young

Post by NixoN94 »

305pelusa wrote: Mon Mar 09, 2020 2:47 pm
NixoN94 wrote: Mon Mar 09, 2020 2:28 pm
305pelusa wrote: Mon Mar 09, 2020 10:16 am
NixoN94 wrote: Mon Mar 09, 2020 8:37 am Extremely interested in this concept and the way of dealing with it.

I am currently 25 years old and have been investing for 7 years.
2013: 1K invested
2019: 5K invested
2020: 25K invested

As you can see my returns were very positive percentagewise but I now have a negative end result if you would look at 2013-2020 moneywise as I had one of the most negative market timings to invest the 20K I got after buying a house.

That's why I opened a topic on this forum to see how people dealt with it. Leveraging seems like an extreme option to me personally but it also seems like there is no alternative to it (I haven't read too much on it though).

What are some alternatives to leveraging? One way I could think of was a less extreme version where one would invest 100% when younger and only about 50% at age 50 instead of leveraging to e.g. 200% at age 25.

I don't see alternatives to reducing the risk of putting more money in the market at later stages in life but would like to hear them if anyone knows them.
What occurred to you describes the problem perfectly. Had you gotten more exposure back in the good years (more even exposure through time), you would be well in positive territory. But it is having little money in good years and lots in bad that lead to the worst outcomes.

The only way to gain more exposure to stocks when you don’t have the money is through leverage, plain and simple. It’s not extreme with the right mindset. To me it’s extreme NOT to use it; you’re really putting most of your eggs on your near-retirement year baskets.

In any case, if you’re unwilling to use leverage, then get as close as you can. That means 100% in stocks, see if you can use 0% APR credit cards, don’t pay off mortgage or auto loans if the rates are reasonable, etc.

William Bernstein argues a way to mimic leverage is to factor tilt strongly to small and value. This is another avenue. I don’t feel as confident about the value premium (and certainly not the size premium) as the equity premium but it’s a reasonable idea nonetheless. I personally use it and tilt strongly to value, quality and investment to try to increase the risk of the portfolio as a form of pseudo-leverage.

Every bit counts and if the most you’re comfortable with is 100% stocks, then that’s ok too :)
The thing I'm not sure about yet, is how to decide how much to invest. I can kind of measure what I'm going to make with my job in the next 40 years but the costs are a bit harder. I will probably have kids and am not sure what the costs of living will be in the future.

Also, what about inflation ? Should I count it in already when investing now that money will be worth less in 40 years ?
Do you have the book? It does a reasonable job at answering some of these questions.

Long story short, with 40 years to retirement, you probably don’t have to calculate any of this. Chances are you should leverage 2:1 (the max they recommend) because even then you won’t even be close to the ideal amount of exposure.
I'll be reading the book first indeed.
One last question I have to you for now, what is a reasonable rate for a margin ? Cheapest I could find by now is 3,5% which still seems like a lot to me.
User avatar
Topic Author
Steve Reading
Posts: 2959
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by Steve Reading »

NixoN94 wrote: Mon Mar 09, 2020 2:49 pm
305pelusa wrote: Mon Mar 09, 2020 2:47 pm
NixoN94 wrote: Mon Mar 09, 2020 2:28 pm
305pelusa wrote: Mon Mar 09, 2020 10:16 am
NixoN94 wrote: Mon Mar 09, 2020 8:37 am Extremely interested in this concept and the way of dealing with it.

I am currently 25 years old and have been investing for 7 years.
2013: 1K invested
2019: 5K invested
2020: 25K invested

As you can see my returns were very positive percentagewise but I now have a negative end result if you would look at 2013-2020 moneywise as I had one of the most negative market timings to invest the 20K I got after buying a house.

That's why I opened a topic on this forum to see how people dealt with it. Leveraging seems like an extreme option to me personally but it also seems like there is no alternative to it (I haven't read too much on it though).

What are some alternatives to leveraging? One way I could think of was a less extreme version where one would invest 100% when younger and only about 50% at age 50 instead of leveraging to e.g. 200% at age 25.

I don't see alternatives to reducing the risk of putting more money in the market at later stages in life but would like to hear them if anyone knows them.
What occurred to you describes the problem perfectly. Had you gotten more exposure back in the good years (more even exposure through time), you would be well in positive territory. But it is having little money in good years and lots in bad that lead to the worst outcomes.

The only way to gain more exposure to stocks when you don’t have the money is through leverage, plain and simple. It’s not extreme with the right mindset. To me it’s extreme NOT to use it; you’re really putting most of your eggs on your near-retirement year baskets.

In any case, if you’re unwilling to use leverage, then get as close as you can. That means 100% in stocks, see if you can use 0% APR credit cards, don’t pay off mortgage or auto loans if the rates are reasonable, etc.

William Bernstein argues a way to mimic leverage is to factor tilt strongly to small and value. This is another avenue. I don’t feel as confident about the value premium (and certainly not the size premium) as the equity premium but it’s a reasonable idea nonetheless. I personally use it and tilt strongly to value, quality and investment to try to increase the risk of the portfolio as a form of pseudo-leverage.

Every bit counts and if the most you’re comfortable with is 100% stocks, then that’s ok too :)
The thing I'm not sure about yet, is how to decide how much to invest. I can kind of measure what I'm going to make with my job in the next 40 years but the costs are a bit harder. I will probably have kids and am not sure what the costs of living will be in the future.

Also, what about inflation ? Should I count it in already when investing now that money will be worth less in 40 years ?
Do you have the book? It does a reasonable job at answering some of these questions.

Long story short, with 40 years to retirement, you probably don’t have to calculate any of this. Chances are you should leverage 2:1 (the max they recommend) because even then you won’t even be close to the ideal amount of exposure.
I'll be reading the book first indeed.
One last question I have to you for now, what is a reasonable rate for a margin ? Cheapest I could find by now is 3,5% which still seems like a lot to me.
Amazon audible lets you get one free book with their free trial in case you want to start reading (listening?) it already by the way.

I think 3.5% is reasonable. A leveraged ETF might be OK as well since at the beginning of the strategy, you’re supposed to use constant leverage so they fit very well. They do have high fees and might borrow expensively so you’llhave to consider that.

Other forms of leverage are options and futures. I can only imagine these are also possibilities to a European investor. If you have doubts about how to calculate borrowing rates or using these products, just ask. The book explains it any ways though.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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