Lifecycle Investing - Leveraging when young

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Ben Mathew
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Re: Lifecycle Investing - Leveraging when young

Post by Ben Mathew » Sun Mar 10, 2019 11:32 am

Lifecycle investing would have helped in both your friends' cases.
dknightd wrote:
Sun Mar 10, 2019 10:54 am
A few years ago I was talking with some older friends about retirement savings. Lets pretend it was 2009. I think it was about then.
One was all in the market. He said he was ready to retire, then the market crashed, and he did not have enough money yet.
Lifecycle investing involves reducing stock exposure when you are closer to retirement (because you took more exposure early). So unlike with traditional asset allocation, you are not as susceptible to a few bad years around retirement age when your portfolio is overweight.
dknightd wrote:
Sun Mar 10, 2019 10:54 am
The other took a very conservative approach, and he did not have enough to retire yet either.
Since lifecycle investing reduces overall lifetime portfolio risk for a given return, you might be able to tolerate more stock exposure over a lifetime --i.e. take some of the benefits of lifecycle investing as higher return instead of lower risk.
dknightd wrote:
Sun Mar 10, 2019 10:54 am
It sounds like you have family money to support what I would call gambling. You are shooting for the moon. It could work out really well. Or not.
Lifecycle investing is the opposite of gambling. It's more conservative than traditional asset allocation because it's spreading the risks more. If someone bets all their money on one coin toss with a positive expected return, that's a gamble. If they spread their bets across fifty coin tosses, it's less risky.

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Re: Lifecycle Investing - Leveraging when young

Post by dknightd » Sun Mar 10, 2019 12:18 pm

Ben Mathew wrote:
Sun Mar 10, 2019 11:32 am
Lifecycle investing would have helped in both your friends' cases.
dknightd wrote:
Sun Mar 10, 2019 10:54 am
A few years ago I was talking with some older friends about retirement savings. Lets pretend it was 2009. I think it was about then.
One was all in the market. He said he was ready to retire, then the market crashed, and he did not have enough money yet.
Lifecycle investing involves reducing stock exposure when you are closer to retirement (because you took more exposure early). So unlike with traditional asset allocation, you are not as susceptible to a few bad years around retirement age when your portfolio is overweight.
dknightd wrote:
Sun Mar 10, 2019 10:54 am
The other took a very conservative approach, and he did not have enough to retire yet either.
Since lifecycle investing reduces overall lifetime portfolio risk for a given return, you might be able to tolerate more stock exposure over a lifetime --i.e. take some of the benefits of lifecycle investing as higher return instead of lower risk.
dknightd wrote:
Sun Mar 10, 2019 10:54 am
It sounds like you have family money to support what I would call gambling. You are shooting for the moon. It could work out really well. Or not.
Lifecycle investing is the opposite of gambling. It's more conservative than traditional asset allocation because it's spreading the risks more. If someone bets all their money on one coin toss with a positive expected return, that's a gamble. If they spread their bets across fifty coin tosses, it's less risky.
I can not redo what I have already done. Although I did wake up at 8am, then go into the kitchen and find out it was really 7am. Was like living in a time machine. But not a big enough difference for investment timelines.
I know the past. I can not predict the future.

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Re: Lifecycle Investing - Leveraging when young

Post by dknightd » Sun Mar 10, 2019 12:26 pm

The OP is essentially leveraging family money. At least that is the way I read this thread. So really nothing to loose.

edit: if you were starting with nothing you would have to be very brave to go with 150% stock allocation

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Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Sun Mar 10, 2019 12:49 pm

Ben Mathew wrote:
Wed Mar 06, 2019 10:13 am

Yes, it's not widely recognized, but lifecycle investing and the sequence of return risk problem are really one and the same.
I've given this further thought and I can talk a bit more intelligently about it. I've gone through some of the math from the Samuelson and Merton papers and here are my thoughts:

It's true that borrowing X money, investing it as a lump sum, and then not touching it at all for the rest of your life has no sequence of return risk. But this isn't quite what lifecycle investing is.

Lifecycle investing assumes a constant, relative risk aversion (RRA) (like Merton and Samuelson). That means the proportion invested in the risky asset does not depend on wealth or time. But the dollar amount will certainly change.

To determine that proportion, they use equation 25 from the Merton paper "LIFETIME PORTFOLIO SELECTION UNDER UNCERTAINTY: THE CONTINUOUS-TIME CASE". That equation tells the optimal proportion of wealth to be invested in the risky asset as a function of the risky asset premium over the riskless asset, volatility and relative risk aversion.

The RRA is obtained by first finding out your own personalized utility function (done very elegantly and with all the math in the background, via the "New Job" question of the book), and RRA just flows out of that personalized utility function. This isn't relevant to this post but thought I should mention it.


Here's why it matters and why I have the feeling that this method is superior to the lump sum:
None of these equations are dependent on the past. Equation 25 doesn't have a term to the extent of "did you hit your allocation correctly before? Then in that case, do not modify buy/sell any stocks".

From this I gather that perhaps investing a lump sum is the perfect time diversification as measured by sequence of return risk (since it has none of it). But lifecycle investing does not do that; it rebalances the dollar amount in stocks to hit the optimal stock proportion as calculated by Merton. In this sense, they are not "one and the same" IMO. It's close and along the same veins, but they fundamentally do different things. Here's an issue of nomenclature: If you define "time diversification" your way, the lump sum method wins. If you define it as "always having the Samuelson share exposure", then obviously lifecycle investing, by definition, wins.


Having gone through the math I gotta say I feel more attracted to the lifecycle investing model. It feels to me like it's the lump sum model, but improved because you make decisions after every result of your bet, rebalancing back to the optimal proportion exposure. I think the lump sum model is ideal if you're not allowed to make decisions based on the results year after year (i.e. you're only allowed to buy/sell X dollars and you make that decision years in advance). But if you are allowed to see the results (which you are in real life) and make modifications, instinct is telling me that the approach that rebalances back to the optimal proportion is more effective.

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Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Sun Mar 10, 2019 12:54 pm

dknightd wrote:
Sun Mar 10, 2019 12:26 pm
The OP is essentially leveraging family money. At least that is the way I read this thread. So really nothing to loose.

edit: if you were starting with nothing you would have to be very brave to go with 150% stock allocation
Nothing to lose if I was the heir to that money. Which I'm not.

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Re: Lifecycle Investing - Leveraging when young

Post by dknightd » Sun Mar 10, 2019 1:20 pm

Do what feels right for you.

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Re: Lifecycle Investing - Leveraging when young

Post by bobcat2 » Sun Mar 10, 2019 1:53 pm

I think 305pelusa should continue his reading and thinking on life-cycle investing. At a minimum I would suggest he or she read and think about the following paper and article, both on life-cycle investing.

Bodie, Zvi and Merton, Robert C. and Samuelson, William F., Labor Supply Flexibility and Portfolio Choice in a Life-Cycle Model (January 1992) NBER Working Paper No. w3954, January 1992. Note that the Samuelson in this paper is Bill, Paul Samuelson's son.
https://www.nber.org/papers/w3954


Robert C. Merton
Applying Life-Cycle Economics - a retirement solution that integrates accumulation and payout phases
https://www.nestpensions.org.uk/schemew ... cs,PDF.pdf

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.

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Re: Lifecycle Investing - Leveraging when young

Post by Ben Mathew » Mon Mar 11, 2019 2:34 am

305pelusa wrote:
Sun Mar 10, 2019 12:49 pm
Ben Mathew wrote:
Wed Mar 06, 2019 10:13 am

Yes, it's not widely recognized, but lifecycle investing and the sequence of return risk problem are really one and the same.
I've given this further thought and I can talk a bit more intelligently about it. I've gone through some of the math from the Samuelson and Merton papers and here are my thoughts:

It's true that borrowing X money, investing it as a lump sum, and then not touching it at all for the rest of your life has no sequence of return risk. But this isn't quite what lifecycle investing is.

Lifecycle investing assumes a constant, relative risk aversion (RRA) (like Merton and Samuelson). That means the proportion invested in the risky asset does not depend on wealth or time. But the dollar amount will certainly change.

To determine that proportion, they use equation 25 from the Merton paper "LIFETIME PORTFOLIO SELECTION UNDER UNCERTAINTY: THE CONTINUOUS-TIME CASE". That equation tells the optimal proportion of wealth to be invested in the risky asset as a function of the risky asset premium over the riskless asset, volatility and relative risk aversion.

The RRA is obtained by first finding out your own personalized utility function (done very elegantly and with all the math in the background, via the "New Job" question of the book), and RRA just flows out of that personalized utility function. This isn't relevant to this post but thought I should mention it.


Here's why it matters and why I have the feeling that this method is superior to the lump sum:
None of these equations are dependent on the past. Equation 25 doesn't have a term to the extent of "did you hit your allocation correctly before? Then in that case, do not modify buy/sell any stocks".

From this I gather that perhaps investing a lump sum is the perfect time diversification as measured by sequence of return risk (since it has none of it). But lifecycle investing does not do that; it rebalances the dollar amount in stocks to hit the optimal stock proportion as calculated by Merton. In this sense, they are not "one and the same" IMO. It's close and along the same veins, but they fundamentally do different things. Here's an issue of nomenclature: If you define "time diversification" your way, the lump sum method wins. If you define it as "always having the Samuelson share exposure", then obviously lifecycle investing, by definition, wins.


Having gone through the math I gotta say I feel more attracted to the lifecycle investing model. It feels to me like it's the lump sum model, but improved because you make decisions after every result of your bet, rebalancing back to the optimal proportion exposure. I think the lump sum model is ideal if you're not allowed to make decisions based on the results year after year (i.e. you're only allowed to buy/sell X dollars and you make that decision years in advance). But if you are allowed to see the results (which you are in real life) and make modifications, instinct is telling me that the approach that rebalances back to the optimal proportion is more effective.
You shouldn't equate lifecycle investing with the constant relative risk aversion (CRRA) assumption. CRRA is a strong assumption about preferences that leads to a nice closed form solution. But its results should not be used as a prescription. CRRA assumes that you are equally willing to bet half your wealth on a gamble whether you have $100K or $100 million in wealth. Your preferences might well be different. Mine certainly are. Our attitudes towards risk is a complicated thing. Assuming a simple functional form for our utility will lead to results which, while illuminating in some ways, can't be taken literally.

Under CRRA, you're right that if you lose some money in stocks, you'll want to rebalance back into stocks to maintain the same fraction of wealth allocated to stocks. And if stocks gain, you'll rebalance back into bonds. But that's simply because you've assumed this utility function that says you'll want to do that. Let me give you an example where that won't be the case. A common way to think about the stock/bond AA is to say you'll hold bonds to cover your basic necessities and stocks to cover your the luxuries you can live without. Suppose you're 50 and stocks crash. Should you convert a large fraction of your bonds to stocks to maintain the same proportion of your wealth in stocks? No, because you still need those bonds to cover your basic necessities. Replenishing stocks will put your funding of basic necessities at risk, and that's not what you want to do. Such a person does not have CRRA preferences, and should not rebalance to maintain a constant proportion of wealth in stocks.

I think you also misunderstand how I'm suggesting the lump sum benchmark strategy be used--maybe because I wasn't clear about it. I don't think people should put $X lump sum in stocks in at age 25 then stick to it rigidly. Everything is financial planning is "until new information comes in." If you get a raise, or an inheritance, or become disabled, have an expensive divorce, or your investments do unexpectedly well or unexpectedly badly, of course, reevaluate what you should do in light of that new information. Presumably, there was a process whereby at age 25 you said, "Knowing what I know now, I think I should put $X in stocks and let it ride unless something unexpected happens" Well, at age 26, ask yourself that question again. Something unexpected probably did happen in the last twelve months. So now the answer is "Knowing what I know now, I think I should actually put $Y in stocks and let it ride, unless, of course, something unexpected happens again" Yes, that will mean extra contributions or withdrawals from the stock account. But you have to respond to new information. You can't leave something as-is just because that's what you decided when you were 25. The lump sum benchmark is not meant to be an inflexible strategy. It's just a benchmark to help you figure out how to act given what you know now.

If adopting the "stocks first" strategy of investing 100% stocks till age N, and sending all further contributions to 100% bonds, age N is subject to change. Early years should clearly be stocks. But towards the middle, it will be hard to know when to make the switch over to bonds. A person might decide at age 40 that it's time to switch to bonds, but then realize at age 41 that that was too early, and switch those contributions back to stocks. Maybe he or she switches again at age 43. But then realize that was too late, and change some existing stocks to bonds. I expect some back and forth like this to happen for a few years in the "in between" zone until one is clearly into the bond phase.

It's important to note also that risk minimization is only one of the important considerations of asset allocation. The other big consideration is that you want to find out the results of your bet early rather than late because that will give you more time to respond (work more and consume less if the portfolio performs poorly; loosen the belt and take vacations if portfolio performs well). This means you'll prefer to place your bets early, meaning more than even stock exposure when young.

So what I'm really saying is use the "lump sum and let it ride" version as a benchmark strategy to help you think about how much you should have in stocks. Re-evaluate every year (or two or three), and change your allocations if you need to. If you have CRRA preferences, yes, you will end up keeping a constant fraction of your wealth in stocks. Every year you will say, "Given that I know that I have this much wealth at this time, I will put 40% of it into stocks." But if you don't have those preferences, then you don't need to do that. Look at the distribution of returns, and decide what looks good to you.
Last edited by Ben Mathew on Mon Mar 11, 2019 9:59 am, edited 1 time in total.

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Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Mon Mar 11, 2019 3:57 am

Ben Mathew wrote:
Mon Mar 11, 2019 2:34 am
305pelusa wrote:
Sun Mar 10, 2019 12:49 pm
Ben Mathew wrote:
Wed Mar 06, 2019 10:13 am

Yes, it's not widely recognized, but lifecycle investing and the sequence of return risk problem are really one and the same.
I've given this further thought and I can talk a bit more intelligently about it. I've gone through some of the math from the Samuelson and Merton papers and here are my thoughts:

It's true that borrowing X money, investing it as a lump sum, and then not touching it at all for the rest of your life has no sequence of return risk. But this isn't quite what lifecycle investing is.

Lifecycle investing assumes a constant, relative risk aversion (RRA) (like Merton and Samuelson). That means the proportion invested in the risky asset does not depend on wealth or time. But the dollar amount will certainly change.

To determine that proportion, they use equation 25 from the Merton paper "LIFETIME PORTFOLIO SELECTION UNDER UNCERTAINTY: THE CONTINUOUS-TIME CASE". That equation tells the optimal proportion of wealth to be invested in the risky asset as a function of the risky asset premium over the riskless asset, volatility and relative risk aversion.

The RRA is obtained by first finding out your own personalized utility function (done very elegantly and with all the math in the background, via the "New Job" question of the book), and RRA just flows out of that personalized utility function. This isn't relevant to this post but thought I should mention it.


Here's why it matters and why I have the feeling that this method is superior to the lump sum:
None of these equations are dependent on the past. Equation 25 doesn't have a term to the extent of "did you hit your allocation correctly before? Then in that case, do not modify buy/sell any stocks".

From this I gather that perhaps investing a lump sum is the perfect time diversification as measured by sequence of return risk (since it has none of it). But lifecycle investing does not do that; it rebalances the dollar amount in stocks to hit the optimal stock proportion as calculated by Merton. In this sense, they are not "one and the same" IMO. It's close and along the same veins, but they fundamentally do different things. Here's an issue of nomenclature: If you define "time diversification" your way, the lump sum method wins. If you define it as "always having the Samuelson share exposure", then obviously lifecycle investing, by definition, wins.


Having gone through the math I gotta say I feel more attracted to the lifecycle investing model. It feels to me like it's the lump sum model, but improved because you make decisions after every result of your bet, rebalancing back to the optimal proportion exposure. I think the lump sum model is ideal if you're not allowed to make decisions based on the results year after year (i.e. you're only allowed to buy/sell X dollars and you make that decision years in advance). But if you are allowed to see the results (which you are in real life) and make modifications, instinct is telling me that the approach that rebalances back to the optimal proportion is more effective.
You shouldn't equate lifecycle investing with the constant relative risk aversion (CRRA) assumption. CRRA is a strong assumption about preferences that leads to a nice closed form solution. But its results should not be used as a prescription. CRRA assumes that you are equally willing to bet half your wealth on a gamble whether you have $100K or $100 million in wealth. Your preferences might well be different. Mine certainly are. Our attitudes towards risk is a complicated thing. Assuming a simple functional form for our utility will lead to results which, while illuminating in some ways, can't be taken literally.

Under CRRA, you're right that if you lose some money in stocks, you'll want to rebalance back into stocks to maintain the same fraction of wealth allocated to stocks. And if stocks gain, you'll rebalance back into bonds. But that's simply because you've assumed this utility function that says you'll want to do that. Let me give you an example where that won't be the case. A common way to think about the stock/bond AA is to say you'll hold bonds to cover your basic necessities and stocks to cover your the luxuries you can live without. Suppose you're 50 and stocks crash. Should you convert a large fraction of your bonds to stocks to maintain the same proportion of your wealth in stocks? No, because you still need those bonds to cover your basic necessities. Replenishing stocks will put your funding of basic necessities at risk, and that's not what you want to do. Such a person does not have CRRA preferences, and should not rebalance to maintain constant wealth in stocks.

I think you also misunderstand how I'm suggesting the lump sum benchmark strategy be used--maybe because I wasn't clear about it. I don't think people should put $X lump sum in stocks in at age 25 then stick to it rigidly. Everything is financial planning is "until new information comes in." If you get a raise, or an inheritance, or become disabled, have an expensive divorce, or your investments do unexpectedly well or unexpectedly badly, of course, reevaluate what you should do in light of that new information. Presumably, there was a process whereby at age 25 you said, "Knowing what I know now, I think I should put $X in stocks and let it ride unless something unexpected happens" Well, at age 26, ask yourself that question again. Something unexpected probably did happen in the last twelve months. So now the answer is "Knowing what I know now, I think I should actually put $Y in stocks and let it ride, unless, of course, something unexpected happens again" Yes, that will mean extra contributions or withdrawals from the stock account. But you have to respond to new information. You can't leave something as-is just because that's what you decided when you were 25. The lump sum benchmark is not meant to be an inflexible strategy. It's just a benchmark to help you figure out how to act given what you know now.

If adopting the "stocks first" strategy of investing 100% stocks till age N, and sending all further contributions to 100% bonds, age N is subject to change. Early years should clearly be stocks. But towards the middle, it will be hard to know when to make the switch over to bonds. A person might decide at age 40 that it's time to switch to bonds, but then realize at age 41 that that was too early, and switch those contributions back to stocks. Maybe he or she switches again at age 43. But then realize that was too late, and change some existing stocks to bonds. I expect some back and forth like this to happen for a few years in the "in between" zone until one is clearly into the bond phase.

It's important to note also that risk minimization is only one of the important considerations of asset allocation. The other big consideration is that you want to find out the results of your bet early rather than late because that will give you more time to respond (work more and consume less if the portfolio performs poorly; loosen the belt and take vacations if portfolio performs well). This means you'll prefer to place your bets early, meaning more than even stock exposure when young.

So what I'm really saying is use the "lump sum and let it ride" version as a benchmark strategy to help you think about how much you should have in stocks. Re-evaluate every year (or two or three), and change your allocations if you need to. If you have CRRA preferences, yes, you will end up keeping a constant fraction of your wealth in stocks. Every year you will say, "Given that I know that I have this much wealth at this time, I will put 40% of it into stocks." But if you don't have those preferences, then you don't need to do that. Look at the distribution of returns, and decide what looks good to you.
I agree with everything and will simply clarify one thing. I'm not equating CRRA to the book's Lifecycle Investing strategy. But it is a fact that they assume CRRA when they make their recommendation for the stock share.

All the data simulations were run with that assumption. Their Monte Carlos were done that way. Their tests with Japanese and UK markets also assumed proportions of stocks based on CRRA.

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Re: Lifecycle Investing - Leveraging when young

Post by AnonJohn » Mon Mar 11, 2019 9:29 am

inbox788 wrote:
Sat Mar 09, 2019 3:28 pm
Ben Mathew wrote:
Sat Mar 09, 2019 3:06 pm
(So in a sense we are leveraged using our mortgage loan.) Now that we are in our 40s, the imperative to leverage is going away anyway. We have plenty of stock exposure now. If I was not confident that retirement would be fully funded, I might consider switching new contributions to bonds for a few years at the end to get closer to the lifecycle model. But it won't make sense in our case since I believe that our retirement consumption will be well funded anyway, and so the risk is not falling on us, but on our heirs.
A home/mortgage is a wonderful leverage when you're young, deleverage as you age passive strategy. You typically begin with a 5:1 or 10:1 (10-20% down payment) and over a course of 15 or 30 years, delevage as you pay it off. I'm unaware of a similar passive strategy using equities. If someone crafted some sort of fund like target date funds, would there be sufficient interest?
+1. Came here to say the same thing. If one takes out a 30 year mortgage and pays it off per schedule while otherwise investing for retirement, you are leveraging when young. The mortgage is a negative bond that is much larger than the portfolio for most early-stage investors. Many people ignore the mortgage and set their AA at something over 2:1 stocks : bonds. I wonder how this compares to the explicit leverage strategies discussed in this thread?

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Re: Lifecycle Investing - Leveraging when young

Post by pezblanco » Mon Mar 11, 2019 5:53 pm

Just some more data on the expected returns to be followed by leveraging and having a regular contribution stream figured in. This is not the authors' system .... just some data about leveraging with an income stream.

Assumptions:

1) The last 51 years of real stock, real long term bonds, and real 1-month T-bill rates are what we sample from to get future returns.

2) The borrow rate is assumed to be 1-month T-bill + 1.5%

3) We assume that we start off in year one with an initial capital of 1. Then every year after that we add R amounts of additional capital.

4) If we are leveraged and lose more than what we have invested, we assume that our fortune resets to zero. I.e. we don't ever actually loses that drive us into a negative regime. If we achieved leverage by option contracts for example (as the authors recommend) that would be case.

Image

Remarks:

1) From the simulations, there are some interesting behaviors of the annual return vs. leverage especially for short time periods ... the returns go up to a peak, then go down, then go back up. See blue line on graph below for a 5 year investment horizon. With short time periods, you get so much gain from leveraging up that the disasters (reset to zero) don't happen enough to wipe out the advantages of huge leverage. The one year investment horizon of course is just a monotonically increasing graph ....

2) The author's choice of 2 for leverage is looking reasonable. If you start off with a large fortune (R=.03 ... see yellow line on graph below ... this might be if you are given $500,000 and you had say a 100K/year job that allowed you to invest 15K/year), then you should use a lower leverage value (closer to the 1.5 that optimizes the Kelly Criterion). If you just start off with no fortune and put in the same quantity every year (see red line on graph), then you should leverage a bit more (about 1.8). Both the yellow and red lines are for 30 year investment horizons.

3) The graphs bounce around a bit .... I was simulating 1 million outcomes per point on each line (20 points/line) and my little laptop was getting very tired.

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Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Mon Mar 11, 2019 6:21 pm

pezblanco wrote:
Mon Mar 11, 2019 5:53 pm
Just some more data on the expected returns to be followed by leveraging and having a regular contribution stream figured in. This is not the authors' system .... just some data about leveraging with an income stream.

Assumptions:

1) The last 51 years of real stock, real long term bonds, and real 1-month T-bill rates are what we sample from to get future returns.

2) The borrow rate is assumed to be 1-month T-bill + 1.5%

3) We assume that we start off in year one with an initial capital of 1. Then every year after that we add R amounts of additional capital.

4) If we are leveraged and lose more than what we have invested, we assume that our fortune resets to zero. I.e. we don't ever actually loses that drive us into a negative regime. If we achieved leverage by option contracts for example (as the authors recommend) that would be case.

Image

Remarks:

1) From the simulations, there are some interesting behaviors of the annual return vs. leverage especially for short time periods ... the returns go up to a peak, then go down, then go back up. See blue line on graph below for a 5 year investment horizon. With short time periods, you get so much gain from leveraging up that the disasters (reset to zero) don't happen enough to wipe out the advantages of huge leverage. The one year investment horizon of course is just a monotonically increasing graph ....

2) The author's choice of 2 for leverage is looking reasonable. If you start off with a large fortune (R=.03 ... see yellow line on graph below ... this might be if you are given $500,000 and you had say a 100K/year job that allowed you to invest 15K/year), then you should use a lower leverage value (closer to the 1.5 that optimizes the Kelly Criterion). If you just start off with no fortune and put in the same quantity every year (see red line on graph), then you should leverage a bit more (about 1.8). Both the yellow and red lines are for 30 year investment horizons.

3) The graphs bounce around a bit .... I was simulating 1 million outcomes per point on each line (20 points/line) and my little laptop was getting very tired.
That looks like Matlab to me yes? Any chance I could get a copy of your code and just kind of verify/run some of these results myself (maybe even with more individualized parameters)?

I get it if it's your secret sauce that you've been working on and developing so I totally get it if you'd rather not

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Re: Lifecycle Investing - Leveraging when young

Post by pezblanco » Mon Mar 11, 2019 6:35 pm

No problem ... it's just that I'm embarrassed by my cringingly bad Matlab code .... people used to laugh at me for it. :D

I'll send it to you via PM ....

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Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Wed Mar 13, 2019 9:24 pm

I guess just to conclude, here's the plan I settled on:

The one thing I dislike about lifecycle investing is the "buy high, sell low" attitude when leveraging in Phase 1. It adds a feedback mechanism to the strategy that makes you invest more/less based on market conditions (not a fan of this).

So instead, I will opt for a range of leverage allowed (similar to rebalancing bands). My ideal leverage level will be 1.5:1. That way, even if stocks drop a massive 50% and I don't contribute any savings that year, the leverage will only rise to ~3:1 (which I feel comfortable with). I do expect to save significantly though.

This way, I believe I can keep the leverage controlled to levels that I think are very reasonable, purely with savings contributions (without a need to sell during market downturns). I accept this might be less ideal than 2:1 with rebalancing to sell at losses (the true lifecycle investing strategy of the book). I also accept it will take me longer to hit my lifetime stock allocation by targeting 1.5:1 leverage instead. But the upside is that by keeping the leverage much more conservative than 2:1, I have a much wider range of higher leverage such that I don't have to sell during extreme market downturns. Feels like a good blend between lifecycle investing and something I feel comfortable with.

I appreciate the help from everyone here. Perhaps I'll update/bump the thread in the future.

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Re: Lifecycle Investing - Leveraging when young

Post by vineviz » Thu Mar 14, 2019 11:11 am

305pelusa wrote:
Wed Mar 13, 2019 9:24 pm
The one thing I dislike about lifecycle investing is the "buy high, sell low" attitude when leveraging in Phase 1. It adds a feedback mechanism to the strategy that makes you invest more/less based on market conditions (not a fan of this).
Lifecycle investing is form of diversification, like any rebalancing strategy, not a strategy for maximizing returns. If you care about how much risk you are taking with your portfolio, rebalancing at least occasionally is going to be required.

That said, rebalancing a lifecycle investing strategy is just like rebalancing any other: it's more akin to "buy low, sell high" than to "buy high, sell low". And although a leveraged equity strategy is probably going to require more frequent rebalancing than an unleveraged strategy you can manage it using the same kinds of rebalancing rules you might otherwise use (for instance using rebalancing bands instead of hard targets). This will keep your portfolio risk within a reasonable range without incurring too much turnover of any sort.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

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Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Thu Mar 14, 2019 1:13 pm

vineviz wrote:
Thu Mar 14, 2019 11:11 am
305pelusa wrote:
Wed Mar 13, 2019 9:24 pm
The one thing I dislike about lifecycle investing is the "buy high, sell low" attitude when leveraging in Phase 1. It adds a feedback mechanism to the strategy that makes you invest more/less based on market conditions (not a fan of this).
That said, rebalancing a lifecycle investing strategy is just like rebalancing any other: it's more akin to "buy low, sell high" than to "buy high, sell low".
During phase 1, you haven't achieved your lifetime equity exposure yet. The recommendation is to use 2:1 leverage and maintain that. If the market rises, your leverage drops, and you can borrow more money to invest and get back to 2:1. When the market drops, your leverage increases so you are supposed to sell to bring the leverage back to 2:1. That's "buy high, sell low".

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Re: Lifecycle Investing - Leveraging when young

Post by vineviz » Thu Mar 14, 2019 2:22 pm

305pelusa wrote:
Thu Mar 14, 2019 1:13 pm
During phase 1, you haven't achieved your lifetime equity exposure yet. The recommendation is to use 2:1 leverage and maintain that. If the market rises, your leverage drops, and you can borrow more money to invest and get back to 2:1. When the market drops, your leverage increases so you are supposed to sell to bring the leverage back to 2:1. That's "buy high, sell low".
I think you've got something mixed up.

In the early years of a lifecycle investment strategy you own only stocks. The only reason you'd ever sell any of your leveraged or unleveraged stocks during this phase would be if they rose in value precipitously, in which case you'd be selling high not low.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

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Re: Lifecycle Investing - Leveraging when young

Post by koolmelee » Thu Mar 14, 2019 3:19 pm

I used leverage buying my first duplex at age 23. Cheapest leverage out there. 5 years later, the property has gone up 40% in value and gives me $700/mo income.

Only thing i would ever use a margin account for is day trading. Interest rates are too high otherwise.

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Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Thu Mar 14, 2019 5:18 pm

vineviz wrote:
Thu Mar 14, 2019 2:22 pm
305pelusa wrote:
Thu Mar 14, 2019 1:13 pm
During phase 1, you haven't achieved your lifetime equity exposure yet. The recommendation is to use 2:1 leverage and maintain that. If the market rises, your leverage drops, and you can borrow more money to invest and get back to 2:1. When the market drops, your leverage increases so you are supposed to sell to bring the leverage back to 2:1. That's "buy high, sell low".
I think you've got something mixed up.

In the early years of a lifecycle investment strategy you own only stocks. The only reason you'd ever sell any of your leveraged or unleveraged stocks during this phase would be if they rose in value precipitously, in which case you'd be selling high not low.
Nothing mixed up on my end. Not sure what lifecycle strategy you're referring to. But "lifecycle investing" as per the book I'm talking about in this thread (by the two Yale Prof.) is very clear. During the first phase, you can't hit your equity exposure yet because you don't have enough savings. Best you can do is 2:1 leverage. And you're not adviced to let it get higher than that either.

When the market drops, your leverage increases as a result. To keep the leverage under control, you sell.

Once you're past phase 1 and can reach your desired equity exposure, THEN increases in the market dictate you sell while decreases in the market dictate you buy.

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Re: Lifecycle Investing - Leveraging when young

Post by vineviz » Thu Mar 14, 2019 5:52 pm

305pelusa wrote:
Thu Mar 14, 2019 5:18 pm

When the market drops, your leverage increases as a result. To keep the leverage under control, you sell.
This is where I think you're confused: your leverage doesn't increase when the market drops.

Let's work a simple example: say you have $50k in savings and you want 200% equity exposure (i.e. 2x leverage) on that $50k.

You buy $50k worth of SSO (ProShares Ultra S&P500), a 2x leveraged ETF.

The S&P 500 drops 10%.

Now you have $40k worth of SSO, a 2x leveraged ETF. Your leverage hasn't changed at all.

Different example. say you have $50k in savings and you want 150% equity exposure (i.e. 1.5x leverage) on that $50k.

You buy $25k worth of SSO and $25k worth of VOO (Vanguard S&P 500 ETF), to get 1.5x leverage. The S&P 500 drops 10%.

Your SSO is now worth $20k, and your VOO is worth $22.5k. Your overall equity exposure is ($20k x 2)+($22.5k x 1) = $62.5k.

On $42.5k of savings with $62.5k in equity exposure, your leverage is 1.47 instead of 1.50: it didn't increase, it fell.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

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Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Thu Mar 14, 2019 6:21 pm

vineviz wrote:
Thu Mar 14, 2019 5:52 pm
305pelusa wrote:
Thu Mar 14, 2019 5:18 pm

When the market drops, your leverage increases as a result. To keep the leverage under control, you sell.
This is where I think you're confused: your leverage doesn't increase when the market drops.
It absolutely does. Say you have 50k. You use margin to borrow another 50k. Invest the 100k in stocks. That's 2x leverage.
Say market drops 10%. You now have 90k in stocks. You still owe 50k so that means you only own 40k. That's 2.25x leverage.
vineviz wrote:
Thu Mar 14, 2019 5:52 pm
305pelusa wrote:
Thu Mar 14, 2019 5:18 pm

When the market drops, your leverage increases as a result. To keep the leverage under control, you sell.
Let's work a simple example: say you have $50k in savings and you want 200% equity exposure (i.e. 2x leverage) on that $50k.

You buy $50k worth of SSO (ProShares Ultra S&P500), a 2x leveraged ETF.

The S&P 500 drops 10%.

Now you have $40k worth of SSO, a 2x leveraged ETF. Your leverage hasn't changed at all.
You should read up on how these ETFs work. The reason the leverage stayed at x2 is that the funds themselves take care of selling when the market drops and buying when the market rises to ensure the leverage is constant.

From a quick google search:
https://money.usnews.com/investing/arti ... nvestments
"On top of this, since leveraged ETFs are rebalanced daily, they must buy additional exposure when the index goes up and rid themselves of it when it falls; they buy high and sell low."

vineviz wrote:
Thu Mar 14, 2019 5:52 pm

Different example. say you have $50k in savings and you want 150% equity exposure (i.e. 1.5x leverage) on that $50k.

You buy $25k worth of SSO and $25k worth of VOO (Vanguard S&P 500 ETF), to get 1.5x leverage. The S&P 500 drops 10%.

Your SSO is now worth $20k, and your VOO is worth $22.5k. Your overall equity exposure is ($20k x 2)+($22.5k x 1) = $62.5k.

On $42.5k of savings with $62.5k in equity exposure, your leverage is 1.47 instead of 1.50: it didn't increase, it fell.
If all your examples consist of leveraged ETFs that already sell during drops and buy during increases for you to maintain constant leverage, then you'll obviously not notice the effect.

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Re: Lifecycle Investing - Leveraging when young

Post by ThrustVectoring » Thu Mar 14, 2019 7:57 pm

I think there's a strong case to be made for using call options instead of straight leverage for the very early portion of lifecycle investing. By capping your maximum option losses to your monthly investment amount, you can afford significantly more leverage without risk of ruin.

For example, https://finance.yahoo.com/quote/SPY190517C00282000 is the two-month at-the-money call option on the S&P 500 at this point in time. Roughly speaking, it costs something like $500 to give you the right to whatever growth $28,200 of the S&P 500 does over the next two months. If you invest $500 per month, you can buy these options each month indefinitely and put the proceeds from them into equity index funds without ever risking going broke. As a small optimization, you probably want to sell them with one month remaining to expiration, rather than holding them all the way through.

Since these are at-the-money options, they're roughly half as sensitive to price changes in the underlying as you'd expect based off of multiplying the strike price by 100. So this means your overall leverage after you first invest money is roughly 14000 / 500 = 28. It'll drop in a hurry once you've started accumulating assets, though.
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Re: Lifecycle Investing - Leveraging when young

Post by DonIce » Fri Mar 15, 2019 1:38 am

I can't understand why everyone focuses on call options rather than futures for strategies like this? Futures are much cheaper.

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Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Fri Mar 15, 2019 7:21 am

ThrustVectoring wrote:
Thu Mar 14, 2019 7:57 pm
I think there's a strong case to be made for using call options instead of straight leverage for the very early portion of lifecycle investing. By capping your maximum option losses to your monthly investment amount, you can afford significantly more leverage without risk of ruin.

For example, https://finance.yahoo.com/quote/SPY190517C00282000 is the two-month at-the-money call option on the S&P 500 at this point in time. Roughly speaking, it costs something like $500 to give you the right to whatever growth $28,200 of the S&P 500 does over the next two months. If you invest $500 per month, you can buy these options each month indefinitely and put the proceeds from them into equity index funds without ever risking going broke. As a small optimization, you probably want to sell them with one month remaining to expiration, rather than holding them all the way through.

Since these are at-the-money options, they're roughly half as sensitive to price changes in the underlying as you'd expect based off of multiplying the strike price by 100. So this means your overall leverage after you first invest money is roughly 14000 / 500 = 28. It'll drop in a hurry once you've started accumulating assets, though.
The reason the authors discourage higher leverage is that it apparently gets very expensive.

If I understand the process correctly then:
Paying 500 bucks to "borrow" 28200 for 2 months is absurdly expensive. That's an annual interest of 500/28200x6x100%=10.6%.

That doesn't even account for the foregone dividends, which makes it even more expensive

Not really enticed by that personally

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Re: Lifecycle Investing - Leveraging when young

Post by grayfox » Fri Mar 15, 2019 9:55 am

305pelusa wrote:
Fri Mar 15, 2019 7:21 am
ThrustVectoring wrote:
Thu Mar 14, 2019 7:57 pm
I think there's a strong case to be made for using call options instead of straight leverage for the very early portion of lifecycle investing. By capping your maximum option losses to your monthly investment amount, you can afford significantly more leverage without risk of ruin.

For example, https://finance.yahoo.com/quote/SPY190517C00282000 is the two-month at-the-money call option on the S&P 500 at this point in time. Roughly speaking, it costs something like $500 to give you the right to whatever growth $28,200 of the S&P 500 does over the next two months. If you invest $500 per month, you can buy these options each month indefinitely and put the proceeds from them into equity index funds without ever risking going broke. As a small optimization, you probably want to sell them with one month remaining to expiration, rather than holding them all the way through.

Since these are at-the-money options, they're roughly half as sensitive to price changes in the underlying as you'd expect based off of multiplying the strike price by 100. So this means your overall leverage after you first invest money is roughly 14000 / 500 = 28. It'll drop in a hurry once you've started accumulating assets, though.
The reason the authors discourage higher leverage is that it apparently gets very expensive.

If I understand the process correctly then:
Paying 500 bucks to "borrow" 28200 for 2 months is absurdly expensive. That's an annual interest of 500/28200x6x100%=10.6%.

That doesn't even account for the foregone dividends, which makes it even more expensive

Not really enticed by that personally
So that's how it works.

SPY is showing 2814.10. (It changes every second.)
You buy about at-the-money CALL option: SPY May 2019 282.000 call. The last reported price is 5.27. (What is Bid-Ask?)
1 option = 100 shares SPY, so it costs you $527.00 + commission.
Now you have the right to buy 100 shares of SPY at 282.00 per share until May 17. Expiration calendar.
So it's like you bought 28,200 worth of SPY for $527.00 + commission.
Then pretend the option price was interest payment for 2 months. 527/28200 = 1.86879% for 2 months.
Also, you don't receive any SPY dividends because you don't actually own any SPY.

What about LEAPS which I am told are 3-year options.
What is the price for that? What is the "interest rate"

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Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Fri Mar 15, 2019 10:20 am

grayfox wrote:
Fri Mar 15, 2019 9:55 am
305pelusa wrote:
Fri Mar 15, 2019 7:21 am
ThrustVectoring wrote:
Thu Mar 14, 2019 7:57 pm
I think there's a strong case to be made for using call options instead of straight leverage for the very early portion of lifecycle investing. By capping your maximum option losses to your monthly investment amount, you can afford significantly more leverage without risk of ruin.

For example, https://finance.yahoo.com/quote/SPY190517C00282000 is the two-month at-the-money call option on the S&P 500 at this point in time. Roughly speaking, it costs something like $500 to give you the right to whatever growth $28,200 of the S&P 500 does over the next two months. If you invest $500 per month, you can buy these options each month indefinitely and put the proceeds from them into equity index funds without ever risking going broke. As a small optimization, you probably want to sell them with one month remaining to expiration, rather than holding them all the way through.

Since these are at-the-money options, they're roughly half as sensitive to price changes in the underlying as you'd expect based off of multiplying the strike price by 100. So this means your overall leverage after you first invest money is roughly 14000 / 500 = 28. It'll drop in a hurry once you've started accumulating assets, though.
The reason the authors discourage higher leverage is that it apparently gets very expensive.

If I understand the process correctly then:
Paying 500 bucks to "borrow" 28200 for 2 months is absurdly expensive. That's an annual interest of 500/28200x6x100%=10.6%.

That doesn't even account for the foregone dividends, which makes it even more expensive

Not really enticed by that personally
So that's how it works.

SPY is showing 2814.10. (It changes every second.)
You buy about at-the-money CALL option: SPY May 2019 282.000 call. The last reported price is 5.27. (What is Bid-Ask?)
1 option = 100 shares SPY, so it costs you $527.00 + commission.
Now you have the right to buy 100 shares of SPY at 282.000 until May 17. Expiration calendar.
So it's like you bought 28,200 worth of SPY for $527.00 + commission.
Then pretend the option price was interest payment for 2 months. 527/28200 = 1.86879% for 2 months.
Also, you don't receive any SPY dividends because you don't actually own any SPY.

What about LEAPS which I am told are 3-year options.
What is the price for that? What is the "interest rate"
At least I think that's how it works.

LEAPS aren't any different. The SPDR ETF is currently trading at ~280. You can find a LEAP with an expiration in Dec 2021 and a strike price of half of that like this one:
https://finance.yahoo.com/quote/SPY2112 ... 7C00140000

It costs 141. The strike price is 140. So you're effectively borrowing 140 dollars for ~2 years. What do you pay?

You pay 141 now and 140 later. The SPDR is already 280. So you're only paying one extra dollar overall vs just downright buying the SPDR.

The biggest cost are the dividends though. At a dividend yield of 1.9%, thats 10.64 dollars you lose out on over the two years for having the option instead of the actual ETF. And then you add commission as well.

Say it's commision-free for a second. That means you overpaid 11.64 dollars to have the chance to borrow 140 bucks for two years. That comes out to approximately an annualized rate of 4.1% to borrow. Which isn't terrible.

These are mostly back-of-the-envelope. You should be a bit more rigurous on the process. I'm no expert by any means so feel free to correct me here.

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Re: Lifecycle Investing - Leveraging when young

Post by Ben Mathew » Fri Mar 15, 2019 12:38 pm

305pelusa wrote:
Fri Mar 15, 2019 7:21 am
ThrustVectoring wrote:
Thu Mar 14, 2019 7:57 pm
I think there's a strong case to be made for using call options instead of straight leverage for the very early portion of lifecycle investing. By capping your maximum option losses to your monthly investment amount, you can afford significantly more leverage without risk of ruin.

For example, https://finance.yahoo.com/quote/SPY190517C00282000 is the two-month at-the-money call option on the S&P 500 at this point in time. Roughly speaking, it costs something like $500 to give you the right to whatever growth $28,200 of the S&P 500 does over the next two months. If you invest $500 per month, you can buy these options each month indefinitely and put the proceeds from them into equity index funds without ever risking going broke. As a small optimization, you probably want to sell them with one month remaining to expiration, rather than holding them all the way through.

Since these are at-the-money options, they're roughly half as sensitive to price changes in the underlying as you'd expect based off of multiplying the strike price by 100. So this means your overall leverage after you first invest money is roughly 14000 / 500 = 28. It'll drop in a hurry once you've started accumulating assets, though.
The reason the authors discourage higher leverage is that it apparently gets very expensive.

If I understand the process correctly then:
Paying 500 bucks to "borrow" 28200 for 2 months is absurdly expensive. That's an annual interest of 500/28200x6x100%=10.6%.

That doesn't even account for the foregone dividends, which makes it even more expensive

Not really enticed by that personally
This calculation does not take into account the downside protection offered by call options (you get the gains, but not the losses). Much of the premium for an at-the-money call option (like this one) would be a payment for that protection. To calculate the implicit interest rate of leveraging using options, you can start by recreating the stock position with options using the put-call parity relationship:

- buy a call at strike price Z, expiring at time t
- sell a put at strike price Z, expiring at time t
- buy a bond that pays out Z at time t

Using strike price Z = $282, and time t = may 17 (2 months), we get
- buy call: $5.92
- sell put: $4.91
- buy bond: $282/(1+.0245)^(63/365)= $280.82

(It doesn't look like there's dividends expected on SPY before the May 17 expiry. When dividends are expected, you would have to include that in the bond payout.)

Total cost via options = $5.92 - $4.91 + 280.82 = $281.83
Current price of stock = $281.93

The prices are about the same, so options are not costlier than directly owning stocks.

So far, there's no leverage. To leverage using options, you simply reduce the amount of bonds that you are buying above. So the implicit interest rate of leveraging is the interest rate of the bonds that you give up, which is around 2.45% per year in this example. So you are actually leveraging at about the treasury rate of 2.45% per year.

I'm not a big fan of leveraging using just call options (i.e. without selling puts as well) because that involves taking a position not just on the long term growth of stocks, but also on volatility. If stocks go up slowly and steadily over 30 years, short term call options will lose money. If stocks go down over 30 years, but with lots of ups and down along the way, short term call options will pay out handsomely. Volatility is even more important for call options than the long term growth rate of stocks. I feel fairly confident about the long term growth rate of stocks, but have no strong position on the volatility. So leveraging using only call options is not a good fit for me.

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Re: Lifecycle Investing - Leveraging when young

Post by ThrustVectoring » Fri Mar 15, 2019 2:03 pm

Ben Mathew wrote:
Fri Mar 15, 2019 12:38 pm
I'm not a big fan of leveraging using just call options (i.e. without selling puts as well) because that involves taking a position not just on the long term growth of stocks, but also on volatility. If stocks go up slowly and steadily over 30 years, short term call options will lose money. If stocks go down over 30 years, but with lots of ups and down along the way, short term call options will pay out handsomely. Volatility is even more important for call options than the long term growth rate of stocks. I feel fairly confident about the long term growth rate of stocks, but have no strong position on the volatility. So leveraging using only call options is not a good fit for me.
If you're buying a call and selling a put at the same strike, you may as well open up a futures contract instead. It'll probably wind up being cheaper - it's what your counter-party is doing to hedge things anyhow after you make the trade.

Paying for convexity somehow is necessary for levering up to this extent based off your free cash flow. You want to cap your losses attributable to levered positions to your contribution rate. Otherwise, market moves can and will wipe out any progress you've been making. There's likely some kind of short volatility strategy you can add, I'm not expert enough to recommend anything specific for this situation and don't really want to dive down that rabbit hole at the moment. Possibly you could limit the effect of extreme moves by doing a synthetic long + collar (or another way of thinking about it: bull call spread + bull put spread).
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Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Fri Mar 15, 2019 6:40 pm

Ben Mathew wrote:
Fri Mar 15, 2019 12:38 pm
305pelusa wrote:
Fri Mar 15, 2019 7:21 am
ThrustVectoring wrote:
Thu Mar 14, 2019 7:57 pm
I think there's a strong case to be made for using call options instead of straight leverage for the very early portion of lifecycle investing. By capping your maximum option losses to your monthly investment amount, you can afford significantly more leverage without risk of ruin.

For example, https://finance.yahoo.com/quote/SPY190517C00282000 is the two-month at-the-money call option on the S&P 500 at this point in time. Roughly speaking, it costs something like $500 to give you the right to whatever growth $28,200 of the S&P 500 does over the next two months. If you invest $500 per month, you can buy these options each month indefinitely and put the proceeds from them into equity index funds without ever risking going broke. As a small optimization, you probably want to sell them with one month remaining to expiration, rather than holding them all the way through.

Since these are at-the-money options, they're roughly half as sensitive to price changes in the underlying as you'd expect based off of multiplying the strike price by 100. So this means your overall leverage after you first invest money is roughly 14000 / 500 = 28. It'll drop in a hurry once you've started accumulating assets, though.
The reason the authors discourage higher leverage is that it apparently gets very expensive.

If I understand the process correctly then:
Paying 500 bucks to "borrow" 28200 for 2 months is absurdly expensive. That's an annual interest of 500/28200x6x100%=10.6%.

That doesn't even account for the foregone dividends, which makes it even more expensive

Not really enticed by that personally
This calculation does not take into account the downside protection offered by call options (you get the gains, but not the losses). Much of the premium for an at-the-money call option (like this one) would be a payment for that protection. To calculate the implicit interest rate of leveraging using options, you can start by recreating the stock position with options using the put-call parity relationship:

- buy a call at strike price Z, expiring at time t
- sell a put at strike price Z, expiring at time t
- buy a bond that pays out Z at time t

Using strike price Z = $282, and time t = may 17 (2 months), we get
- buy call: $5.92
- sell put: $4.91
- buy bond: $282/(1+.0245)^(63/365)= $280.82

(It doesn't look like there's dividends expected on SPY before the May 17 expiry. When dividends are expected, you would have to include that in the bond payout.)
.
My understanding is you still account for it. In a perfect market, the price of the stock slowly rises every day until ex-dividend day. Then after that, it drops by the dividend amount. And so it continues.

You don't see that extremely neatly because it is hidden by the volatility of the stock. But it's definitely there.

So if buying an option through a period where no dividends are expected, you still have to account for it because there is an intrinsic increase in the stock value as dividend day approached.

You know more than me in econ but that was my understanding

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Re: Lifecycle Investing - Leveraging when young

Post by pezblanco » Fri Mar 15, 2019 7:33 pm

Ben Mathew wrote:
Fri Mar 15, 2019 12:38 pm
305pelusa wrote:
Fri Mar 15, 2019 7:21 am
ThrustVectoring wrote:
Thu Mar 14, 2019 7:57 pm
I think there's a strong case to be made for using call options instead of straight leverage for the very early portion of lifecycle investing. By capping your maximum option losses to your monthly investment amount, you can afford significantly more leverage without risk of ruin.

For example, https://finance.yahoo.com/quote/SPY190517C00282000 is the two-month at-the-money call option on the S&P 500 at this point in time. Roughly speaking, it costs something like $500 to give you the right to whatever growth $28,200 of the S&P 500 does over the next two months. If you invest $500 per month, you can buy these options each month indefinitely and put the proceeds from them into equity index funds without ever risking going broke. As a small optimization, you probably want to sell them with one month remaining to expiration, rather than holding them all the way through.

Since these are at-the-money options, they're roughly half as sensitive to price changes in the underlying as you'd expect based off of multiplying the strike price by 100. So this means your overall leverage after you first invest money is roughly 14000 / 500 = 28. It'll drop in a hurry once you've started accumulating assets, though.
The reason the authors discourage higher leverage is that it apparently gets very expensive.

If I understand the process correctly then:
Paying 500 bucks to "borrow" 28200 for 2 months is absurdly expensive. That's an annual interest of 500/28200x6x100%=10.6%.

That doesn't even account for the foregone dividends, which makes it even more expensive

Not really enticed by that personally
This calculation does not take into account the downside protection offered by call options (you get the gains, but not the losses). Much of the premium for an at-the-money call option (like this one) would be a payment for that protection. To calculate the implicit interest rate of leveraging using options, you can start by recreating the stock position with options using the put-call parity relationship:

- buy a call at strike price Z, expiring at time t
- sell a put at strike price Z, expiring at time t
- buy a bond that pays out Z at time t

Using strike price Z = $282, and time t = may 17 (2 months), we get
- buy call: $5.92
- sell put: $4.91
- buy bond: $282/(1+.0245)^(63/365)= $280.82

(It doesn't look like there's dividends expected on SPY before the May 17 expiry. When dividends are expected, you would have to include that in the bond payout.)

Total cost via options = $5.92 - $4.91 + 280.82 = $281.83
Current price of stock = $281.93

The prices are about the same, so options are not costlier than directly owning stocks.

So far, there's no leverage. To leverage using options, you simply reduce the amount of bonds that you are buying above. So the implicit interest rate of leveraging is the interest rate of the bonds that you give up, which is around 2.45% per year in this example. So you are actually leveraging at about the treasury rate of 2.45% per year.

I'm not a big fan of leveraging using just call options (i.e. without selling puts as well) because that involves taking a position not just on the long term growth of stocks, but also on volatility. If stocks go up slowly and steadily over 30 years, short term call options will lose money. If stocks go down over 30 years, but with lots of ups and down along the way, short term call options will pay out handsomely. Volatility is even more important for call options than the long term growth rate of stocks. I feel fairly confident about the long term growth rate of stocks, but have no strong position on the volatility. So leveraging using only call options is not a good fit for me.

This is a great post. I learned a lot reading this. Thank you, Ben. So, as for the purposes of this thread: Ayres and Nalebuff advocate buying deep in the money LEAPS. So basically, you don't sell the put and you don't buy the bonds (the put is basically worthless anyway ... so you won't be able to sell it?). You manipulate the leverage by the strike price.

My main question here is that you claim (and your numbers match up with that claim) that the interest rate is basically the 2 month T-bill rate. The 2 month Libor would actually be 15 cents off instead of the 10 you calculated with the T-bill. Interesting no? I think that you will find with the deep in the money LEAPS that you will definitely not be getting T-bill rates .... so something is not explained here (at least in my untutored in this field's mind)

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Re: Lifecycle Investing - Leveraging when young

Post by Ben Mathew » Sat Mar 16, 2019 10:02 am

ThrustVectoring wrote:
Fri Mar 15, 2019 2:03 pm
Ben Mathew wrote:
Fri Mar 15, 2019 12:38 pm
I'm not a big fan of leveraging using just call options (i.e. without selling puts as well) because that involves taking a position not just on the long term growth of stocks, but also on volatility. If stocks go up slowly and steadily over 30 years, short term call options will lose money. If stocks go down over 30 years, but with lots of ups and down along the way, short term call options will pay out handsomely. Volatility is even more important for call options than the long term growth rate of stocks. I feel fairly confident about the long term growth rate of stocks, but have no strong position on the volatility. So leveraging using only call options is not a good fit for me.
If you're buying a call and selling a put at the same strike, you may as well open up a futures contract instead. It'll probably wind up being cheaper - it's what your counter-party is doing to hedge things anyhow after you make the trade.

Paying for convexity somehow is necessary for levering up to this extent based off your free cash flow. You want to cap your losses attributable to levered positions to your contribution rate. Otherwise, market moves can and will wipe out any progress you've been making. There's likely some kind of short volatility strategy you can add, I'm not expert enough to recommend anything specific for this situation and don't really want to dive down that rabbit hole at the moment. Possibly you could limit the effect of extreme moves by doing a synthetic long + collar (or another way of thinking about it: bull call spread + bull put spread).
Yes, a futures contract would probably be the way to go if you are looking for a linear payout that avoids a position on volatility. It would come down to transaction costs, and I'm guessing a thickly traded futures contract would be cheaper than buying a call and selling a put.

Deep in the money calls can also reduce the volatility exposure and give more of a one-for-one movement with stocks. But even then, I don't think the volatility exposure is trivial over the long run. You're basically paying a small fee every time to avoid the risk of a market crash. That premium will probably add up to something large over a lifetime, and deviate significantly from the benchmark of simply leveraging stocks using a long term non-callable loan.

The product that I probably would have been interested in when I was younger, if it existed, is a very long term call option that expires in 30 years or more. That would be much more of a bet on long term growth than on short term volatility. LEAPS are only 2 to 3 years out, which is still too short for me.

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Re: Lifecycle Investing - Leveraging when young

Post by Ben Mathew » Sat Mar 16, 2019 10:17 am

305pelusa wrote:
Fri Mar 15, 2019 6:40 pm
Ben Mathew wrote:
Fri Mar 15, 2019 12:38 pm
305pelusa wrote:
Fri Mar 15, 2019 7:21 am
ThrustVectoring wrote:
Thu Mar 14, 2019 7:57 pm
I think there's a strong case to be made for using call options instead of straight leverage for the very early portion of lifecycle investing. By capping your maximum option losses to your monthly investment amount, you can afford significantly more leverage without risk of ruin.

For example, https://finance.yahoo.com/quote/SPY190517C00282000 is the two-month at-the-money call option on the S&P 500 at this point in time. Roughly speaking, it costs something like $500 to give you the right to whatever growth $28,200 of the S&P 500 does over the next two months. If you invest $500 per month, you can buy these options each month indefinitely and put the proceeds from them into equity index funds without ever risking going broke. As a small optimization, you probably want to sell them with one month remaining to expiration, rather than holding them all the way through.

Since these are at-the-money options, they're roughly half as sensitive to price changes in the underlying as you'd expect based off of multiplying the strike price by 100. So this means your overall leverage after you first invest money is roughly 14000 / 500 = 28. It'll drop in a hurry once you've started accumulating assets, though.
The reason the authors discourage higher leverage is that it apparently gets very expensive.

If I understand the process correctly then:
Paying 500 bucks to "borrow" 28200 for 2 months is absurdly expensive. That's an annual interest of 500/28200x6x100%=10.6%.

That doesn't even account for the foregone dividends, which makes it even more expensive

Not really enticed by that personally
This calculation does not take into account the downside protection offered by call options (you get the gains, but not the losses). Much of the premium for an at-the-money call option (like this one) would be a payment for that protection. To calculate the implicit interest rate of leveraging using options, you can start by recreating the stock position with options using the put-call parity relationship:

- buy a call at strike price Z, expiring at time t
- sell a put at strike price Z, expiring at time t
- buy a bond that pays out Z at time t

Using strike price Z = $282, and time t = may 17 (2 months), we get
- buy call: $5.92
- sell put: $4.91
- buy bond: $282/(1+.0245)^(63/365)= $280.82

(It doesn't look like there's dividends expected on SPY before the May 17 expiry. When dividends are expected, you would have to include that in the bond payout.)
.
My understanding is you still account for it. In a perfect market, the price of the stock slowly rises every day until ex-dividend day. Then after that, it drops by the dividend amount. And so it continues.

You don't see that extremely neatly because it is hidden by the volatility of the stock. But it's definitely there.

So if buying an option through a period where no dividends are expected, you still have to account for it because there is an intrinsic increase in the stock value as dividend day approached.
You are right that the price of stock includes the dividend and then drops by the dividend amount on the ex-dividend day. Pricing of options would have to take these price dynamics into account. But here we are not pricing options, just using options to recreate a synthetic stock position. Buying a call + selling a put + buying a bond will create a position that pays out precisely the price of the stock at expiry (assuming no early exercise). This price would not include dividends paid out. So to recreate exactly the position of owning a stock, you would have to buy some extra bonds to cover the dividend if the stock will pay dividend. (There is a potential complication involving whether a dividend will prompt early exercise. I'm not an options expert, so I don't know how that will play out. But in the case of this example, there was no dividend expected, so the calculation would not be affected.)
Last edited by Ben Mathew on Sat Mar 16, 2019 10:32 am, edited 1 time in total.

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Re: Lifecycle Investing - Leveraging when young

Post by Ben Mathew » Sat Mar 16, 2019 10:31 am

pezblanco wrote:
Fri Mar 15, 2019 7:33 pm
Ayres and Nalebuff advocate buying deep in the money LEAPS. So basically, you don't sell the put and you don't buy the bonds (the put is basically worthless anyway ... so you won't be able to sell it?). You manipulate the leverage by the strike price.
Deep in the money calls will get you closer to the benchmark of holding stocks on margin. The longer the term, the better. So given what's out there, deep in the money LEAPS will get you closest to a position where the bet is more on long term growth and less on short term volatility. But even with deep in the money calls, you'll still be paying a small premium for the crash protection. Over the long term, your outcome will probably be significantly different from the benchmark of leveraging using a long term non-callable loan.
pezblanco wrote:
Fri Mar 15, 2019 7:33 pm
I think that you will find with the deep in the money LEAPS that you will definitely not be getting T-bill rates .... so something is not explained here
If you replicate the stock using deep in the money LEAPS -- i.e buy call+sell put+buy bond, you will likely find that you are getting rates comparable to the other options. (Otherwise there would be an arbitrage opportunity.)

If you buy only the call, the reason the rates look high is that you are also paying for the downside protection. It's less than for at-the-money calls, but it's still there.

Another issue might be more that the further away you go from at-the-money, the less thickly traded it is, so the bid-ask spread might be unacceptable.

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Re: Lifecycle Investing - Leveraging when young

Post by ThrustVectoring » Sat Mar 16, 2019 1:40 pm

Ben Mathew wrote:
Sat Mar 16, 2019 10:02 am
ThrustVectoring wrote:
Fri Mar 15, 2019 2:03 pm
Ben Mathew wrote:
Fri Mar 15, 2019 12:38 pm
I'm not a big fan of leveraging using just call options (i.e. without selling puts as well) because that involves taking a position not just on the long term growth of stocks, but also on volatility. If stocks go up slowly and steadily over 30 years, short term call options will lose money. If stocks go down over 30 years, but with lots of ups and down along the way, short term call options will pay out handsomely. Volatility is even more important for call options than the long term growth rate of stocks. I feel fairly confident about the long term growth rate of stocks, but have no strong position on the volatility. So leveraging using only call options is not a good fit for me.
If you're buying a call and selling a put at the same strike, you may as well open up a futures contract instead. It'll probably wind up being cheaper - it's what your counter-party is doing to hedge things anyhow after you make the trade.

Paying for convexity somehow is necessary for levering up to this extent based off your free cash flow. You want to cap your losses attributable to levered positions to your contribution rate. Otherwise, market moves can and will wipe out any progress you've been making. There's likely some kind of short volatility strategy you can add, I'm not expert enough to recommend anything specific for this situation and don't really want to dive down that rabbit hole at the moment. Possibly you could limit the effect of extreme moves by doing a synthetic long + collar (or another way of thinking about it: bull call spread + bull put spread).
Yes, a futures contract would probably be the way to go if you are looking for a linear payout that avoids a position on volatility. It would come down to transaction costs, and I'm guessing a thickly traded futures contract would be cheaper than buying a call and selling a put.

Deep in the money calls can also reduce the volatility exposure and give more of a one-for-one movement with stocks. But even then, I don't think the volatility exposure is trivial over the long run. You're basically paying a small fee every time to avoid the risk of a market crash. That premium will probably add up to something large over a lifetime, and deviate significantly from the benchmark of simply leveraging stocks using a long term non-callable loan.

The product that I probably would have been interested in when I was younger, if it existed, is a very long term call option that expires in 30 years or more. That would be much more of a bet on long term growth than on short term volatility. LEAPS are only 2 to 3 years out, which is still too short for me.
The volatility exposure is necessary for hedging the risk of a short-term rise in equity prices when you cannot afford to buy up the equity position today on margin. Downside volatility hits you with a margin call. Upside volatility makes buying up your desired equity more expensive. An early investor using leverage is already short volatility.

Long-term non-callable loans are uhh, not really available at competitive costs.
Current portfolio: 60% VTI / 40% VXUS

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Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Sat Mar 16, 2019 2:16 pm

Question for those who seem much more knowledgeable on the subject.

What about the tax implications of LEAPS and futures in taxable accounts? The one thing I like about just getting a loan or maybe margin is that I buy VGD funds that I know are extremely diversified and very tax efficient.

My understanding is that things like futures and LEAPS get taxed with the 60/40 rule. Isn't it possible this increased tax liability could offset the time diversification benefit?

I'm not familiar with derivatives enough that such options might complicate the portfolio enough for me to offset the advantage of time diversification.

On that note, any good books/guides on long-term leveraged strategies I could read are highly appreciated, from taxes, to recommended brokerages, etc. I'm kinda clueless on the topic haha.

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