Can you help me solve this brainteaser about allocation?
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Can you help me solve this brainteaser about allocation?
[I posted a similar question recently but it went off in a different direction, so trying again here with a narrower framing of the problem.]
You have $100 million. You want to grow it as much as possible for heirs and charities. But, in the case of extreme catastrophe, you still want to have $5 million left over for yourself. You define "extreme catastrophe" as a 95% decline in Total World Stock Market.
A first stab at this would be to say that you should put $5 million in "safe" assets and then $95 million in "risky" assets. However, I am positing that that is too conservative given the goal. If your "risky" asset is, for example, a total world stock fund, then it's not going to go to 0 unless all of the world's companies become valueless. So even if we assume a 95% loss, you're still going to end up with more than $5 million in the catastrophic case.
This may seem like splitting hairs when the starting number is $100 million, but pretend it's $1 billion. Now your "risky" asset is still worth $50 million in the event of a 95% loss, and it's even clearer that you've invested too conservatively for your goals.
Instead, it seems fair to say that the right approach is to allocate your portfolio between "risky" and "safe" assets such that you still have $5 million remaining even if you experienced a 95% decline in your "risky" portfolio. For the round numbers I picked above, that happens to equate to a 100% "risky" / 0% "safe" portfolio. It maximizes gains while still ensuring your $5 million in the event of extreme catastrophe.
However, when you define the asset allocation like this, then a funny thing happens that I have trouble getting my head around: The more the market goes up, the riskier you make your portfolio. And the more the market goes down, the more conservative you make it.
For example, say your assets increased to $110 million. Now, in order to preserve the constraint of "maximum growth with $5 million left in a 95% loss", you'd want to (based on some quick math) borrow $555K on margin and invest that in risky assets.
On the other hand, say your assets decreased to $80 million. Now, in order to preserve the constraint of "maximum growth with $5 million left in a 95% loss", you'd want to put about $79 million in risky assets and $1 million in safe assets.
This feels intuitively wrong, because it seems to imply buying high and selling low. Can someone help me break this mental logjam?
Here's another way to put it: The conventional wisdom says to choose your stock allocation such that you'd be comfortable losing 50% of it for a decade or more. However, the conventional wisdom also says to rebalance on the way down. This almost seems like a paradox. Say you choose to put 50% of your $100K in stocks on the basis that you can withstand a $50K loss. Then stocks fall 30%, bringing your portfolio down to $85,000 (35% stocks, 65% bonds). Now you rebalance back to 50% stocks, such that $42,500 of your money is in stocks and the other $42,500 is in bonds. Are you still prepared to lose 50% of your stock allocation at this point? No, of course not...because that would represent a total decline of 72.5% of your original stock allocation, not 50%. Yet if the "be prepared to lose 50% rule" doesn't mean "be prepared at any given moment", then what does it mean?
You have $100 million. You want to grow it as much as possible for heirs and charities. But, in the case of extreme catastrophe, you still want to have $5 million left over for yourself. You define "extreme catastrophe" as a 95% decline in Total World Stock Market.
A first stab at this would be to say that you should put $5 million in "safe" assets and then $95 million in "risky" assets. However, I am positing that that is too conservative given the goal. If your "risky" asset is, for example, a total world stock fund, then it's not going to go to 0 unless all of the world's companies become valueless. So even if we assume a 95% loss, you're still going to end up with more than $5 million in the catastrophic case.
This may seem like splitting hairs when the starting number is $100 million, but pretend it's $1 billion. Now your "risky" asset is still worth $50 million in the event of a 95% loss, and it's even clearer that you've invested too conservatively for your goals.
Instead, it seems fair to say that the right approach is to allocate your portfolio between "risky" and "safe" assets such that you still have $5 million remaining even if you experienced a 95% decline in your "risky" portfolio. For the round numbers I picked above, that happens to equate to a 100% "risky" / 0% "safe" portfolio. It maximizes gains while still ensuring your $5 million in the event of extreme catastrophe.
However, when you define the asset allocation like this, then a funny thing happens that I have trouble getting my head around: The more the market goes up, the riskier you make your portfolio. And the more the market goes down, the more conservative you make it.
For example, say your assets increased to $110 million. Now, in order to preserve the constraint of "maximum growth with $5 million left in a 95% loss", you'd want to (based on some quick math) borrow $555K on margin and invest that in risky assets.
On the other hand, say your assets decreased to $80 million. Now, in order to preserve the constraint of "maximum growth with $5 million left in a 95% loss", you'd want to put about $79 million in risky assets and $1 million in safe assets.
This feels intuitively wrong, because it seems to imply buying high and selling low. Can someone help me break this mental logjam?
Here's another way to put it: The conventional wisdom says to choose your stock allocation such that you'd be comfortable losing 50% of it for a decade or more. However, the conventional wisdom also says to rebalance on the way down. This almost seems like a paradox. Say you choose to put 50% of your $100K in stocks on the basis that you can withstand a $50K loss. Then stocks fall 30%, bringing your portfolio down to $85,000 (35% stocks, 65% bonds). Now you rebalance back to 50% stocks, such that $42,500 of your money is in stocks and the other $42,500 is in bonds. Are you still prepared to lose 50% of your stock allocation at this point? No, of course not...because that would represent a total decline of 72.5% of your original stock allocation, not 50%. Yet if the "be prepared to lose 50% rule" doesn't mean "be prepared at any given moment", then what does it mean?
- backpacker
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Re: Can you help me solve this brainteaser about allocation?
That sounds right. Imagine that I have only $10. If I want to make sure to have no more than $10 in a crisis, I don't have to do anything. I can just hold cash. If I have $1,000,000 and don't want to have more than $10 in a crisis, I need to put that money in some seriously risky investments.
Think about it this way. Suppose I offer you 2:1 odds on a fair coin and will keep giving you those odds on future flips. You should make boat loads of money! But you adjust your bets so that whenever you lose, you will have no more than $10. Your "portfolio" will go through wild swings, but you will be almost certainly never have much more than $10. This because one bad flip at any point sets you back to $10.
Since the odds of a 95% crash are a lot lower, the situation with stocks is a bit different. But over a long enough time frame, the situation is similar. Over the next 1,000 years, I bet there will be a 95% world stock crash at some point. Setting up a 1,000 year portfolio that is guaranteed to have no more than $5 million in a crash like that virtually guarantees that it will be worth only $5 million at some point.
Think about it this way. Suppose I offer you 2:1 odds on a fair coin and will keep giving you those odds on future flips. You should make boat loads of money! But you adjust your bets so that whenever you lose, you will have no more than $10. Your "portfolio" will go through wild swings, but you will be almost certainly never have much more than $10. This because one bad flip at any point sets you back to $10.
Since the odds of a 95% crash are a lot lower, the situation with stocks is a bit different. But over a long enough time frame, the situation is similar. Over the next 1,000 years, I bet there will be a 95% world stock crash at some point. Setting up a 1,000 year portfolio that is guaranteed to have no more than $5 million in a crash like that virtually guarantees that it will be worth only $5 million at some point.
Re: Can you help me solve this brainteaser about allocation?
The "resolution" is just the realization that you're looking at conflicting advice. A static, rebalanced percentage-based asset allocation follows a different strategy than liability matching or some kind of safe/risky strategy.
On a related topic, Wade Pfau has talked about retirement income strategies as a kind of continuum between those based on probability and those focused on safety. It makes more sense to read for yourself, so check here:
http://retirementresearcher.com/the-yin ... losophies/
On a related topic, Wade Pfau has talked about retirement income strategies as a kind of continuum between those based on probability and those focused on safety. It makes more sense to read for yourself, so check here:
http://retirementresearcher.com/the-yin ... losophies/
- Maynard F. Speer
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Re: Can you help me solve this brainteaser about allocation?
If you know you'll need a set "emergency" amount, it makes more sense to just keep that $5m as a cash buffer .. leave it untouched .. Seeing as you don't want to raid it (therefore it's no use for rebalancing) and you don't need to grow it -> seems obvious to compartmentalise it like that
But of course .. we've got inflation to worry about .. So that $5m probably does want some risk/growth-exposure .. In which case you could have a separate low-risk portfolio in cash-like assets
Most people think of risk in terms of percentage loss .. and perhaps with inflation it makes more sense to do so
But of course .. we've got inflation to worry about .. So that $5m probably does want some risk/growth-exposure .. In which case you could have a separate low-risk portfolio in cash-like assets
Most people think of risk in terms of percentage loss .. and perhaps with inflation it makes more sense to do so
"Economics is a method rather than a doctrine, an apparatus of the mind, a technique of thinking, which helps its possessor to draw correct conclusions." - John Maynard Keynes
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Re: Can you help me solve this brainteaser about allocation?
OK, but how do you then resolve the point raised at the end, wherein people are simultaneously instructed to pick a percentage-based stock/bond asset allocation wherein they could tolerate a 50% drop in stocks, while also instructed to rebalance during a crash to maintain that percentage (thereby apparently exposing them to a larger potential loss than originally conceived when picking the stock/bond allocation)?lack_ey wrote:The "resolution" is just the realization that you're looking at conflicting advice. A static, rebalanced percentage-based asset allocation follows a different strategy than liability matching or some kind of safe/risky strategy.
On a related topic, Wade Pfau has talked about retirement income strategies as a kind of continuum between those based on probability and those focused on safety. It makes more sense to read for yourself, so check here:
http://retirementresearcher.com/the-yin ... losophies/
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Re: Can you help me solve this brainteaser about allocation?
But this does not meet the constraints of the question, which is to grow the amount as aggressively as possible. This has lower expected return.Maynard F. Speer wrote:If you know you'll need a set "emergency" amount, it makes more sense to just keep that $5m as a cash buffer .. leave it untouched .. Seeing as you don't want to raid it (therefore it's no use for rebalancing) and you don't need to grow it -> seems obvious to compartmentalise it like that
But of course .. we've got inflation to worry about .. So that $5m probably does want some risk/growth-exposure .. In which case you could have a separate low-risk portfolio in cash-like assets
Most people think of risk in terms of percentage loss .. and perhaps with inflation it makes more sense to do so
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Re: Can you help me solve this brainteaser about allocation?
Also, I'm curious to hear what you would actually do in this situation with this strategy during a decline, given the objectives above.lack_ey wrote:The "resolution" is just the realization that you're looking at conflicting advice. A static, rebalanced percentage-based asset allocation follows a different strategy than liability matching or some kind of safe/risky strategy.
On a related topic, Wade Pfau has talked about retirement income strategies as a kind of continuum between those based on probability and those focused on safety. It makes more sense to read for yourself, so check here:
http://retirementresearcher.com/the-yin ... losophies/
Re: Can you help me solve this brainteaser about allocation?
If there is a 95% loss (total loss in your example) in the "risky" asset, then it is likely there will be no such "risk free" left at that point. I believe the only time, last 100 years, when the market (USA) had a compounded loss was during great depression - 80%. Other places like Germany, Japan etc folks may have lost all 100%. Your scenario is very drastic and pessimistic.
Having freedom, food and roof is being 90% lucky in life and so is index investing. So, don't let the remaining 10% bother you.
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Re: Can you help me solve this brainteaser about allocation?
Well it's intended as the last bastion of conservatism in what is overall a very aggressive strategy of investing 100% or more of your portfolio in risky assets. You could change it to say that you want $5 million in an 80% loss, etc., but the point is to be pretty damn sure that you'll end up with $5 million in any conceivable outcome.paper200 wrote:If there is a 95% loss (total loss in your example) in the "risky" asset, then it is likely there will be no such "risk free" left at that point. I believe the only time, last 100 years, when the market (USA) had a compounded loss was during great depression - 80%. Other places like Germany, Japan etc folks may have lost all 100%. Your scenario is very drastic and pessimistic.
(And my understanding is that the loss during the great depression was 89%.)
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Re: Can you help me solve this brainteaser about allocation?
Is it so bad to have $5 million "at some point" though? The presumption here is that you're able to ride out the volatility and that you'll eventually reach new heights, even though you will inevitably need to suffer through valleys along the way.backpacker wrote:That sounds right. Imagine that I have only $10. If I want to make sure to have no more than $10 in a crisis, I don't have to do anything. I can just hold cash. If I have $1,000,000 and don't want to have more than $10 in a crisis, I need to put that money in some seriously risky investments.
Think about it this way. Suppose I offer you 2:1 odds on a fair coin and will keep giving you those odds on future flips. You should make boat loads of money! But you adjust your bets so that whenever you lose, you will have no more than $10. Your "portfolio" will go through wild swings, but you will be almost certainly never have much more than $10. This because one bad flip at any point sets you back to $10.
Since the odds of a 95% crash are a lot lower, the situation with stocks is a bit different. But over a long enough time frame, the situation is similar. Over the next 1,000 years, I bet there will be a 95% world stock crash at some point. Setting up a 1,000 year portfolio that is guaranteed to have no more than $5 million in a crash like that virtually guarantees that it will be worth only $5 million at some point.
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Re: Can you help me solve this brainteaser about allocation?
Typically "drops of x%" are defined peak to trough. So maybe you could set your asset allocation so that you'd have $5 million so long as you didn't drop more than 95% from the all-time market peak.
I've encountered a similar problem when contemplating using margin (and how much margin to use). Let's say you decide you want to be (100 + x)% in equities, and you use margin to accomplish this. In a bull market, your leverage ratio decreases and decreases, so you use more and more margin to maintain the (100 + x)% allocation, buying stock at higher and higher prices on the way up. But if you keep this up, you'll run into a bubble eventually and suddenly all that margin and all that stock you bought on margin at progressively higher prices looks like a bad idea. On the other hand, during market downturns, your leverage ratio skyrockets, and you have to choose between allowing your leverage ratio to skyrocket and selling equities to maintain (100 + x)%. But this amounts to selling low (why use margin if you're just going to sell the stocks you bought on borrowed money at a loss?).
I don't think this problem has a solution per se. The issue you describe is a direct, inevitable consequence of wanting to maintain a position that at all times would be worth EXACTLY $5 million after a 95% drop in equities. "EXACTLY" requires you to take more and more risk by buying stock on margin when stock prices rise (if you don't take more and more risk when prices rise, then you would be left with > $5 million after a 95% drop, which according to your reasoning means that you are leaving money on the table. So with your strategy you have to buy more and more as prices rise so that you would have exactly $5 million after the drop). Likewise, "EXACTLY" requires you to sell more and more as prices fall. So if you want to solve this "problem," you should revise your requirement. One way to revise this requirement is something that others have suggested: maintain a position that at all times would be worth AT LEAST $5 million after a 95% drop in equities. "AT LEAST" doesn't require you to leverage more and more on the way up, which saves you from painful deleveraging at a loss on the way down.
I've encountered a similar problem when contemplating using margin (and how much margin to use). Let's say you decide you want to be (100 + x)% in equities, and you use margin to accomplish this. In a bull market, your leverage ratio decreases and decreases, so you use more and more margin to maintain the (100 + x)% allocation, buying stock at higher and higher prices on the way up. But if you keep this up, you'll run into a bubble eventually and suddenly all that margin and all that stock you bought on margin at progressively higher prices looks like a bad idea. On the other hand, during market downturns, your leverage ratio skyrockets, and you have to choose between allowing your leverage ratio to skyrocket and selling equities to maintain (100 + x)%. But this amounts to selling low (why use margin if you're just going to sell the stocks you bought on borrowed money at a loss?).
I don't think this problem has a solution per se. The issue you describe is a direct, inevitable consequence of wanting to maintain a position that at all times would be worth EXACTLY $5 million after a 95% drop in equities. "EXACTLY" requires you to take more and more risk by buying stock on margin when stock prices rise (if you don't take more and more risk when prices rise, then you would be left with > $5 million after a 95% drop, which according to your reasoning means that you are leaving money on the table. So with your strategy you have to buy more and more as prices rise so that you would have exactly $5 million after the drop). Likewise, "EXACTLY" requires you to sell more and more as prices fall. So if you want to solve this "problem," you should revise your requirement. One way to revise this requirement is something that others have suggested: maintain a position that at all times would be worth AT LEAST $5 million after a 95% drop in equities. "AT LEAST" doesn't require you to leverage more and more on the way up, which saves you from painful deleveraging at a loss on the way down.
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Re: Can you help me solve this brainteaser about allocation?
Thanks! This is exactly the kind of analysis I was looking for. So you said you were contemplating this as well when using margin. What did you ultimately decide to do?aaaaaaabbbbbbbbbb wrote:Typically "drops of x%" are defined peak to trough. So maybe you could set your asset allocation so that you'd have $5 million so long as you didn't drop more than 95% from the all-time market peak.
I've encountered a similar problem when contemplating using margin (and how much margin to use). Let's say you decide you want to be (100 + x)% in equities, and you use margin to accomplish this. In a bull market, your leverage ratio decreases and decreases, so you use more and more margin to maintain the (100 + x)% allocation, buying stock at higher and higher prices on the way up. But if you keep this up, you'll run into a bubble eventually and suddenly all that margin and all that stock you bought on margin at progressively higher prices looks like a bad idea. On the other hand, during market downturns, your leverage ratio skyrockets, and you have to choose between allowing your leverage ratio to skyrocket and selling equities to maintain (100 + x)%. But this amounts to selling low (why use margin if you're just going to sell the stocks you bought on borrowed money at a loss?).
I don't think this problem has a solution per se. The issue you describe is a direct, inevitable consequence of wanting to maintain a position that at all times would be worth EXACTLY $5 million after a 95% drop in equities. "EXACTLY" requires you to take more and more risk by buying stock on margin when stock prices rise (if you don't take more and more risk when prices rise, then you would be left with > $5 million after a 95% drop, which according to your reasoning means that you are leaving money on the table. So with your strategy you have to buy more and more as prices rise so that you would have exactly $5 million after the drop). Likewise, "EXACTLY" requires you to sell more and more as prices fall. So if you want to solve this "problem," you should revise your requirement. One way to revise this requirement is something that others have suggested: maintain a position that at all times would be worth AT LEAST $5 million after a 95% drop in equities. "AT LEAST" doesn't require you to leverage more and more on the way up, which saves you from painful deleveraging at a loss on the way down.
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Re: Can you help me solve this brainteaser about allocation?
Also, since you seem to understand exactly what I'm getting at here, I'm curious to hear your take on whether or not the strategy I'm describing is in fact the one with the highest expected return, even though it seems counterintuitive due to the buy-high / sell-low conundrum. Is that what you were implying by putting "problem" in quotes?aaaaaaabbbbbbbbbb wrote:Typically "drops of x%" are defined peak to trough. So maybe you could set your asset allocation so that you'd have $5 million so long as you didn't drop more than 95% from the all-time market peak.
I've encountered a similar problem when contemplating using margin (and how much margin to use). Let's say you decide you want to be (100 + x)% in equities, and you use margin to accomplish this. In a bull market, your leverage ratio decreases and decreases, so you use more and more margin to maintain the (100 + x)% allocation, buying stock at higher and higher prices on the way up. But if you keep this up, you'll run into a bubble eventually and suddenly all that margin and all that stock you bought on margin at progressively higher prices looks like a bad idea. On the other hand, during market downturns, your leverage ratio skyrockets, and you have to choose between allowing your leverage ratio to skyrocket and selling equities to maintain (100 + x)%. But this amounts to selling low (why use margin if you're just going to sell the stocks you bought on borrowed money at a loss?).
I don't think this problem has a solution per se. The issue you describe is a direct, inevitable consequence of wanting to maintain a position that at all times would be worth EXACTLY $5 million after a 95% drop in equities. "EXACTLY" requires you to take more and more risk by buying stock on margin when stock prices rise (if you don't take more and more risk when prices rise, then you would be left with > $5 million after a 95% drop, which according to your reasoning means that you are leaving money on the table. So with your strategy you have to buy more and more as prices rise so that you would have exactly $5 million after the drop). Likewise, "EXACTLY" requires you to sell more and more as prices fall. So if you want to solve this "problem," you should revise your requirement. One way to revise this requirement is something that others have suggested: maintain a position that at all times would be worth AT LEAST $5 million after a 95% drop in equities. "AT LEAST" doesn't require you to leverage more and more on the way up, which saves you from painful deleveraging at a loss on the way down.
And, you said "according to your reasoning" -- but isn't it a fact that if you do not need more than $5 million in the catastrophic case, then you are indeed leaving money on the table if you don't leverage?
Last edited by johnanglemen on Sun Apr 19, 2015 4:46 pm, edited 1 time in total.
Re: Can you help me solve this brainteaser about allocation?
johnanglemen wrote: You have $100 million. You want to grow it as much as possible for heirs and charities. But, in the case of extreme catastrophe, you still want to have $5 million left over for yourself. You define "extreme catastrophe" as a 95% decline in Total World Stock Market.
Based on the language of this premise putting 100% in stocks meets the requirements. What question is there about this? But, see below.
A first stab at this would be to say that you should put $5 million in "safe" assets and then $95 million in "risky" assets. However, I am positing that that is too conservative given the goal. If your "risky" asset is, for example, a total world stock fund, then it's not going to go to 0 unless all of the world's companies become valueless. So even if we assume a 95% loss, you're still going to end up with more than $5 million in the catastrophic case.
The first stab is above -- 100% in stocks. In the case of setting aside $5M you wish to protect against even more than an extreme catastrophe, so you have changed the premise, as you admit yourself at the end of the paragraph. That said, the difference in aggressiveness between 95% stocks and 100% stocks is too small to worry about.
One objection to your terms is that apparently "grow it as much as possible" is actually a code word in your mind for 100% Total World Stock Market, and your only question is whether or not you should set aside the $5M. We already answered that you should not set aside the $5M because you already assume you don't need to. You didn't want the conversation to go off track, which is fine. But, would it be off track to suggest the investment should be all in small cap value. Or, would doing that mean that you would no longer be comfortable with the 95% downside limit. On that tangent, why not set aside the $5M and then invest the rest in small cap value for more return?
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Re: Can you help me solve this brainteaser about allocation?
How have I changed the premise? I didn't follow your logic here. 100% stocks only leaves you with $5 million in the 95% case on day 1, when you have a $100 million portfolio. But the second it grows at all, which it would be expected to do, then now a 95% decline in a 100% stock portfolio leaves you with more than $5 million. And the second it shrinks at all, then now a 95% decline leaves you with less than $5 million. And the question is about what to do in those scenarios.dbr wrote:johnanglemen wrote: You have $100 million. You want to grow it as much as possible for heirs and charities. But, in the case of extreme catastrophe, you still want to have $5 million left over for yourself. You define "extreme catastrophe" as a 95% decline in Total World Stock Market.
Based on the language of this premise putting 100% in stocks meets the requirements. What question is there about this? But, see below.
A first stab at this would be to say that you should put $5 million in "safe" assets and then $95 million in "risky" assets. However, I am positing that that is too conservative given the goal. If your "risky" asset is, for example, a total world stock fund, then it's not going to go to 0 unless all of the world's companies become valueless. So even if we assume a 95% loss, you're still going to end up with more than $5 million in the catastrophic case.
The first stab is above -- 100% in stocks. In the case of setting aside $5M you wish to protect against even more than an extreme catastrophe, so you have changed the premise, as you admit yourself at the end of the paragraph. That said, the difference in aggressiveness between 95% stocks and 100% stocks is too small to worry about.
Last edited by johnanglemen on Sun Apr 19, 2015 4:56 pm, edited 2 times in total.
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Re: Can you help me solve this brainteaser about allocation?
The only reason I have been using Total World Stock is because I figured that if I instead referred abstractly to a "risky asset", then people would start talking about how all sorts of risky assets have gone to 0. So I wanted to clarify that I'm not suggesting that you put the portfolio in Apple stock or something, because that would lead to the straw man argument of "You can't assume that 95% loss is the upper bound!" So I picked something that is risky but still diversified enough that it could not truly go to 0 in any feasible outcome.dbr wrote:One objection to your terms is that apparently "grow it as much as possible" is actually a code word in your mind for 100% Total World Stock Market, and your only question is whether or not you should set aside the $5M. We already answered that you should not set aside the $5M because you already assume you don't need to. You didn't want the conversation to go off track, which is fine. But, would it be off track to suggest the investment should be all in small cap value. Or, would doing that mean that you would no longer be comfortable with the 95% downside limit. On that tangent, why not set aside the $5M and then invest the rest in small cap value for more return?
Whether the risky asset is Total World or Small Cap Value or anything else that can't go to 0, you still run into the issue that as soon as the portfolio grows above $100M, a 95% loss now leaves you with more than $5M, and is therefore "too conservative" by the standards of the question.
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Re: Can you help me solve this brainteaser about allocation?
The underlying issue is the mistaken assumption that allocation decisions are ultimately mathematically solvable.
Allocation decisions need to be based on human, not mathematical, criteria. In this case we have conflict between two goals: maximizing expected return (presumably risk-adjusted returns) and keeping a margin of safety, no matter what happens in the market. You can't resolve this with math, you simply have to decide which of the two criteria is more important.
Allocation decisions need to be based on human, not mathematical, criteria. In this case we have conflict between two goals: maximizing expected return (presumably risk-adjusted returns) and keeping a margin of safety, no matter what happens in the market. You can't resolve this with math, you simply have to decide which of the two criteria is more important.
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Re: Can you help me solve this brainteaser about allocation?
Thank you for weighing in, but I don't understand how this can't be solved by math provided you're willing to accept the assumption that "no matter what happens in the market" is defined as "there will not be greater than a 95% loss in the stock market" (which I am). How can there not exist a mathematically optimal solution?Alex Frakt wrote:The underlying issue is the mistaken assumption that allocation decisions are ultimately mathematically solvable.
Allocation decisions need to be based on human, not mathematical, criteria. In this case we have conflicting criteria between maximizing expected return (presumably risk-adjusted returns) and keeping a margin of safety, no matter what happens in the market. You can't resolve this with math, you simply have to decide which of the two criteria is more important.
Re: Can you help me solve this brainteaser about allocation?
The changed premise was in the conversation about setting aside the $5M and the change in premise was to worry about a more than 95% decline. You then rejected that change in premise anyway. It makes no sense to set aside the $5M unless you are worried about a worse than 95% decline from the original amount, the original premise being a 95% decline from some amount larger or the same as the original. In any case, setting aside anything has already been shown to not be the desired choice.johnanglemen wrote:How have I changed the premise? I didn't follow your logic here. 100% stocks only leaves you with $5 million in the 95% case when you have a $100 million portfolio. But the second it grows at all, which it would be expected to do, then now a 95% decline in a 100% stock portfolio leaves you with more than $5 million.dbr wrote:johnanglemen wrote: You have $100 million. You want to grow it as much as possible for heirs and charities. But, in the case of extreme catastrophe, you still want to have $5 million left over for yourself. You define "extreme catastrophe" as a 95% decline in Total World Stock Market.
Based on the language of this premise putting 100% in stocks meets the requirements. What question is there about this? But, see below.
A first stab at this would be to say that you should put $5 million in "safe" assets and then $95 million in "risky" assets. However, I am positing that that is too conservative given the goal. If your "risky" asset is, for example, a total world stock fund, then it's not going to go to 0 unless all of the world's companies become valueless. So even if we assume a 95% loss, you're still going to end up with more than $5 million in the catastrophic case.
The first stab is above -- 100% in stocks. In the case of setting aside $5M you wish to protect against even more than an extreme catastrophe, so you have changed the premise, as you admit yourself at the end of the paragraph. That said, the difference in aggressiveness between 95% stocks and 100% stocks is too small to worry about.
As to the fact that a 95% decline leaves you with more than the $5M if the portfolio has grown, then since you are already at 100% TWSM, the only solution is to invest in something more risky than that when you arrive at that point. The question then is whether it is a premise that the only choices are 95% or 100% TWSM.
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Re: Can you help me solve this brainteaser about allocation?
I am still not quite following the first point, but we definitely agree that setting aside an amount is not optimal, so I will leave it there.dbr wrote:The changed premise was in the conversation about setting aside the $5M and the change in premise was to worry about a more than 95% decline. You then rejected that change in premise anyway. It makes no sense to set aside the $5M unless you are worried about a worse than 95% decline from the original amount, the original premise being a 95% decline from some amount larger or the same as the original. In any case, setting aside anything has already been shown to not be the desired choice.johnanglemen wrote:How have I changed the premise? I didn't follow your logic here. 100% stocks only leaves you with $5 million in the 95% case when you have a $100 million portfolio. But the second it grows at all, which it would be expected to do, then now a 95% decline in a 100% stock portfolio leaves you with more than $5 million.dbr wrote:johnanglemen wrote: You have $100 million. You want to grow it as much as possible for heirs and charities. But, in the case of extreme catastrophe, you still want to have $5 million left over for yourself. You define "extreme catastrophe" as a 95% decline in Total World Stock Market.
Based on the language of this premise putting 100% in stocks meets the requirements. What question is there about this? But, see below.
A first stab at this would be to say that you should put $5 million in "safe" assets and then $95 million in "risky" assets. However, I am positing that that is too conservative given the goal. If your "risky" asset is, for example, a total world stock fund, then it's not going to go to 0 unless all of the world's companies become valueless. So even if we assume a 95% loss, you're still going to end up with more than $5 million in the catastrophic case.
The first stab is above -- 100% in stocks. In the case of setting aside $5M you wish to protect against even more than an extreme catastrophe, so you have changed the premise, as you admit yourself at the end of the paragraph. That said, the difference in aggressiveness between 95% stocks and 100% stocks is too small to worry about.
As to the fact that a 95% decline leaves you with more than the $5M if the portfolio has grown, then since you are already at 100% TWSM, the only solution is to invest in something more risky than that when you arrive at that point. The question then is whether it is a premise that the only choices are 95% or 100% TWSM.
On the second point, that's not the only option...you can also start investing on margin at Interactive Brokers at < 60bps, such that you're now more than 100% invested in equities. Which makes sense to me, until you consider the point that I and aaaaaaabbbbbbbbbb were discussing above, which is that you're de facto buying more as the market rises and selling more as the market declines.
So I guess the purest distillation of the question at this point is: Does this allocation strategy have the highest expected return, given the $5 million / 95% constraint? Intuitively it does not seem like it could, because it implies buying high (when your portfolio increases above $100M) and selling low (when your portfolio decreases below $100M). But intuitively it also seems like it has to, because it's the highest risk / highest reward of all the options (setting aside $5M, etc). And these two opposing intuitions are what I cannot reconcile.
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Re: Can you help me solve this brainteaser about allocation?
Well, I haven't decided on anything yet, but I have some ideas.johnanglemen wrote:Thanks! This is exactly the kind of analysis I was looking for. So you said you were contemplating this as well when using margin. What did you ultimately decide to do?
One solution is to use very small amounts of margin, and never sell to deleverage. It seems reasonable to assume that for some value of x, a (90 + x)% drop in a globally diversified equities portfolio will never occur, short of the apocalypse (and in the event of the apocalypse, your TIPs won't be any safer than my equities). So you would use a tiny amount of margin for a tiny leverage ratio (for whatever value of x you choose). Whenever your leverage ratio would fall below your target, you would increase your ratio back up to your target. Whenever your leverage ratio would rise above your target, you would do nothing. So you leverage more when the stock market goes up, but you don't deleverage when it goes down. Since you use so little leverage, you will never have a margin call unless the apocalypse occurs.
But the gains here would be minimal, and we're greedy, aren't we?
If you have a very reliable income/credit line you could amp the previous strategy up a bit and rely on cashflow from income/credit to deleverage a bit during a crash. But maybe this is too risky. (You wouldn't want to be forced to turn tricks to supplement your income and thereby avoid a margin call.)
Another idea is to base your leverage ratios on fundamentals. If you're facing a CAPE of 5 then maybe leverage isn't such a bad idea. But if it's 1989 and you're investing in Japan and looking at CAPE's of around 100 then it's probably a bad idea to leverage. Of course if you follow this line of reasoning then maybe you should just buy value stocks. Plus, it's hard to time the market - there have been periods where inflated P/E ratios have been sustained for years on end (until they weren't).
A third idea is to "dollar cost average" with your margin. Every month, buy $x of equities on margin. This protects you from over-leveraging yourself during a bubble. The strategy you propose could conceivably result in you taking out a bajillion dollar margin loan during a sufficiently large bubble (and only during a bubble). No such problem if you do $x every month. The usual DCA benefit of buying more shares when prices are low and fewer when prices are high applies. The tricky question is: how do we choose $x? You would want to choose it so that buying $x on margin each month keeps you near some long-run leverage ratio target, without getting too far away from the target. But you still need to allow for the flexibility to deviate from the target (we have already discussed the problems inherent to maintaining a fixed leverage ratio in the face of volatility).
A fourth idea is to use non-callable debt. E.g.: I buy a diverse collection of real estate. Every month I issue $x in mortgage-backed bonds that have long maturities, and dollar cost average my loans into the stock market. If the term on the bonds is sufficiently long, and if your leverage is sufficiently conservative, then maybe you would be able to ride out market volatility and realize that juicy arbitrage (stock market return - interest rate). Although probably this wouldn't work, else it would have been done already. Plus, there's a chance that the markets will behave irrationally for longer than the term of the bonds.
Re: Can you help me solve this brainteaser about allocation?
Yes, a property of your postulated investment is that cases are possible when a 95% catastrophe leaves you with more than $5M. In that case when the investment grows you can change it out for an investment that can plunge by more than 95%. At the same time, if the investment shrinks below the original amount, you are going to have to change it out for one that cannot decline by as much as 95%. Otherwise, you have postulated requirements that do not have a solution. However, not having a solution is as valid an answer as any other answer. This sort of thing happens all the time in mathematical problems.johnanglemen wrote:
Whether the risky asset is Total World or Small Cap Value or anything else that can't go to 0, you still run into the issue that as soon as the portfolio grows above $100M, a 95% loss now leaves you with more than $5M, and is therefore "too conservative" by the standards of the question.
Re: Can you help me solve this brainteaser about allocation?
The problem is not with mathematics. The problem is modeling. There are many good portfolio models out there where you can plug in your numbers and get a answer. For your particular example, almost all of the models are going to suggest taking a very high level of risk. Higher than 100% equities. lever up your portfolio 4:1 using margin and most models would still consider your portfolio very safe in meeting a 5m minimum goal.johnanglemen wrote:Thank you for weighing in, but I don't understand how this can't be solved by math provided you're willing to accept the assumption that "no matter what happens in the market" is defined as "there will not be greater than a 95% loss in the stock market" (which I am). How can there not exist a mathematically optimal solution?Alex Frakt wrote:The underlying issue is the mistaken assumption that allocation decisions are ultimately mathematically solvable.
Allocation decisions need to be based on human, not mathematical, criteria. In this case we have conflicting criteria between maximizing expected return (presumably risk-adjusted returns) and keeping a margin of safety, no matter what happens in the market. You can't resolve this with math, you simply have to decide which of the two criteria is more important.
Which takes us back to the models. Economies and markets are not static. Models tend to fall apart under times of stress. Conservative models designed to minimize portfolio losses during times of stress tends to fail during times of stress. We know all sorts of ways that models differ from real life. fat tails is a classic example. I have lived through 3 market crashes that where, mathematically speaking (assuming a normally shaped bell curve), 1 in a 1000 year events.
On a more realistic note, I will point to you towards "Value at Risk" and "Immunized Portfolios". Both of these are traditional methods used to measure and limit downside risk. They are not prefect but it is the best that we have got.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
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Re: Can you help me solve this brainteaser about allocation?
I can't comment on whether your strategy (or any other) has the highest expected return. Given a model of how markets behave, we can discuss what strategy has the highest expected return. But no model has been specified. And if we focus on actual markets rather than models, it is of course impossible to identify the strategy with the highest expected return in advance. I can speculate that your strategy will have lackluster returns unless prices only go up. As soon as prices drop, you start selling at a low price the stocks you bought with margin at a high price. The bigger the drop, the bigger the losses. 50%+ drops like we have seen before would have clobbered your strategy.johnanglemen wrote:Also, since you seem to understand exactly what I'm getting at here, I'm curious to hear your take on whether or not the strategy I'm describing is in fact the one with the highest expected return, even though it seems counterintuitive due to the buy-high / sell-low conundrum. Is that what you were implying by putting "problem" in quotes?
And, you said "according to your reasoning" -- but isn't it a fact that if you do not need more than $5 million in the catastrophic case, then you are indeed leaving money on the table if you don't leverage?
I put "problem" in quotes because in my opinion the problem you described is not a problem per se. It's a necessary consequence of the strategy you describe. Instead, I would call it a property or a consequence of your strategy.
I said according to your reasoning because you are only leaving money on the table if you decide that your degree of leverage is desirable, even despite the downsides. Most investors use no leverage at all (except for maybe a mortgage or revolving credit line), but they are not necessarily leaving money on the table (although I think many of them are). What if your friend Bob were to leverage 1000000000000000:1 and then ask you why you are leaving money on the table by having such a puny leverage ratio. How would you respond?
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Re: Can you help me solve this brainteaser about allocation?
Also, my list of margin strategies could be done with futures/options instead of margin.
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Re: Can you help me solve this brainteaser about allocation?
Well I think if you take the question within the very narrow parameters it's allowing - then keeping $5m risk-free means you've simply de-risked $5m, and cut your potential returns correspondingly (which would be some fraction of a percent - and an entirely sensible thing to do)johnanglemen wrote:But this does not meet the constraints of the question, which is to grow the amount as aggressively as possible. This has lower expected return.Maynard F. Speer wrote:If you know you'll need a set "emergency" amount, it makes more sense to just keep that $5m as a cash buffer .. leave it untouched .. Seeing as you don't want to raid it (therefore it's no use for rebalancing) and you don't need to grow it -> seems obvious to compartmentalise it like that
But of course .. we've got inflation to worry about .. So that $5m probably does want some risk/growth-exposure .. In which case you could have a separate low-risk portfolio in cash-like assets
Most people think of risk in terms of percentage loss .. and perhaps with inflation it makes more sense to do so
I agree it's conflating a mathematical issue with a human issue .. I think that's a very elegant way to put it
My solution would always be the endowment solution: to avoid concentrating capital in any one sector, so you're not conceivably exposed to a 95% loss .. and if you test endowment-style asset allocations (such as Swensen's Yale portfolio at portfolio visualiser, you see it generally appears to beat pure stock/bond allocations on a risk-adjusted basis)
Many would say the large allocation to Absolute Return funds is giving away quite a bit in management fees, but it's one of the few sectors which tends to stand up when other assets are in meltdown
MFUTS = Managed futures
https://www.portfoliovisualizer.com/bac ... allocation
"Economics is a method rather than a doctrine, an apparatus of the mind, a technique of thinking, which helps its possessor to draw correct conclusions." - John Maynard Keynes
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Re: Can you help me solve this brainteaser about allocation?
Then the answer is trivial, but depends on what "there will not be greater than a 95% loss in the stock market" really means. If it means that the stock market has an absolute floor of 5% of its current price, then you keep 100% in the stock market always. If it means that is can lose 95% and then there is some sort of pause after which it can lose a further 95%, then you keep 100% in the market until it hits your 5% and then go to 100% safe assets.johnanglemen wrote:Thank you for weighing in, but I don't understand how this can't be solved by math provided you're willing to accept the assumption that "no matter what happens in the market" is defined as "there will not be greater than a 95% loss in the stock market" (which I am). How can there not exist a mathematically optimal solution?Alex Frakt wrote:The underlying issue is the mistaken assumption that allocation decisions are ultimately mathematically solvable.
Allocation decisions need to be based on human, not mathematical, criteria. In this case we have conflicting criteria between maximizing expected return (presumably risk-adjusted returns) and keeping a margin of safety, no matter what happens in the market. You can't resolve this with math, you simply have to decide which of the two criteria is more important.
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Re: Can you help me solve this brainteaser about allocation?
1) Keep in mind that there is a difference between maximizing expected returns and maximizing the returns you are most likely to get. If you invest $100 and the expected returns are about $750 over 30 years at 7%. But the median returns (i.e. the returns that you get at least 50% of the time) will be much lower than that. More like $400. Your odds of getting $750 are only about 30%. Mean returns (i.e. expected returns) are always higher than median returns (i.e. the returns you will probably get). See this great blog post for more.
2) If you care about maximizing the returns you will probably get, the Kelly criterion is your new best friend. Because it has been mathematically proven to do that.
Suppose (for simplicity) that the stock market returns 5% on good years and loses 95% on bad years. Suppose that it has a bad year 1 out of every 200 years. The Kelly criterion then tells you to put 94.7% in stocks.
That's just an estimate, because the stock market has more than two outcomes. Really, the Kelly criterion is just an expected utility calculation for an investor who values money logarithmically. So any distribution of stock market returns could easily be plugged in.
2) If you care about maximizing the returns you will probably get, the Kelly criterion is your new best friend. Because it has been mathematically proven to do that.
Suppose (for simplicity) that the stock market returns 5% on good years and loses 95% on bad years. Suppose that it has a bad year 1 out of every 200 years. The Kelly criterion then tells you to put 94.7% in stocks.
That's just an estimate, because the stock market has more than two outcomes. Really, the Kelly criterion is just an expected utility calculation for an investor who values money logarithmically. So any distribution of stock market returns could easily be plugged in.
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Re: Can you help me solve this brainteaser about allocation?
Bob's allocation leaves him in debt in the case of extreme catastrophe (as defined here). Mine doesn't. Why would I want to follow Bob?aaaaaaabbbbbbbbbb wrote:I can't comment on whether your strategy (or any other) has the highest expected return. Given a model of how markets behave, we can discuss what strategy has the highest expected return. But no model has been specified. And if we focus on actual markets rather than models, it is of course impossible to identify the strategy with the highest expected return in advance. I can speculate that your strategy will have lackluster returns unless prices only go up. As soon as prices drop, you start selling at a low price the stocks you bought with margin at a high price. The bigger the drop, the bigger the losses. 50%+ drops like we have seen before would have clobbered your strategy.johnanglemen wrote:Also, since you seem to understand exactly what I'm getting at here, I'm curious to hear your take on whether or not the strategy I'm describing is in fact the one with the highest expected return, even though it seems counterintuitive due to the buy-high / sell-low conundrum. Is that what you were implying by putting "problem" in quotes?
And, you said "according to your reasoning" -- but isn't it a fact that if you do not need more than $5 million in the catastrophic case, then you are indeed leaving money on the table if you don't leverage?
I put "problem" in quotes because in my opinion the problem you described is not a problem per se. It's a necessary consequence of the strategy you describe. Instead, I would call it a property or a consequence of your strategy.
I said according to your reasoning because you are only leaving money on the table if you decide that your degree of leverage is desirable, even despite the downsides. Most investors use no leverage at all (except for maybe a mortgage or revolving credit line), but they are not necessarily leaving money on the table (although I think many of them are). What if your friend Bob were to leverage 1000000000000000:1 and then ask you why you are leaving money on the table by having such a puny leverage ratio. How would you respond?
Also, how does 50% clobber this allocation? In the example given above, after a 10% gain in your portfolio (to $110M), you borrow just $555K (0.5%) to maintain the constraint.
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Re: Can you help me solve this brainteaser about allocation?
If Bob deleverages on the way down in the same manner you do, then he will not end up in debt (nor will he be wiped out). I say "according to you" you're leaving money on the table because there's a risk involved if you use significant leverage. Yes, your strategy insures you won't drop below $5 million. In that sense it is not risky. But what about the other 95 million? That portion is subject to additional risk because of the leverage. Furthermore, because your strategy involves buying higher and higher as the market rises and selling lower and lower as the market drops, it's questionable whether you're getting any additional return (nevermind having good risk-adjusted return). Suppose the market moves in the following manner. Every odd-numbered day it goes up 10%. Every even-numbered day it drops 9.05%. (Assume all months have 30 days). The guy whose portfolio is 100% equities gains 8.6% annually. Your strategy underperforms. Now look at http://www.google.com/finance?q=INDEXSP:.INX Zoom in on a short timescale (1 month or less). In the event of even minor volatility, your commitment to deleveraging means that your use of leverage loses you money. The risk you take is that even if there is only minor volatility you do worse than 100% equities. So there really isn't any money on the table at all (unless you happen to live in an alternate universe where the S&P 500 doesn't move like it does in our universe).
10 years later your portfolio is up to $1 bil. At this point you take a margin loan equal to about 5.26% of your portfolio, roughly an order of magnitude greater in percentage terms. Also, what I meant is that the gains you got from using margin during the bull market would have been clobbered. It's true that your portfolio wouldn't have been clobbered very much more than the other guy's. But this is only because you use very little margin. In absolute terms, the downside of your leverage when you force yourself to sell during the 50% crash is fairly low (but a lot more significant at 105.26% equities than at 100.55% equitiies). But the gains you had from margin were also proportionally small, so any benefit you got from using margin gets clobbered. If my portfolio consists of a million in cash plus a $1000 bet that the S&P 500 will only rise, then my bet will get clobbered, even if my portfolio does not. The fact that my portfolio comes out OK doesn't mean my bet didn't get clobbered - it only means that my bet was a small one.
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Really you need to relax the requirement to deleverage as the market falls. Otherwise you commit to buying high and selling low, which only works if there is no volatility. You have to endure the greater risk you face when prices drop and your leverage ratio increases if you want to enjoy the benefit of additional gains from leverage. By deleveraging on the way down you attempt to escape the greater risk you assumed by leveraging in the first place. But there is no free lunch, as we have both realized: deleveraging on the way down amounts to buying high and selling low. I really think you need to relax the requirement to deleverage. If you do, the questions become "how (and how much) do I leverage" and "when (if ever) do I deleverage when the market falls."
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Let me bring options to your attention. A call option gives the buyer the right (but not the obligation) to buy a security at a predetermined price for a period of time. A put option gives the buyer the right to sell. Let's say Microsoft stock is at $100. For $50, I buy a call option that allows me to buy a share of Microsoft for $50. Suppose Microsoft goes up to $101. What is my option worth now? At $101, the right to buy for $50 is worth $51. So a 1% rise in Microsoft results in a 2% rise in the value of my option. But my downside is also multiplied by 2. (In the real world, I would have to pay more than $50 for a call option that lets me buy Microsoft at $50, to compensate the seller of the option for the service he is providing me.)
10 years later your portfolio is up to $1 bil. At this point you take a margin loan equal to about 5.26% of your portfolio, roughly an order of magnitude greater in percentage terms. Also, what I meant is that the gains you got from using margin during the bull market would have been clobbered. It's true that your portfolio wouldn't have been clobbered very much more than the other guy's. But this is only because you use very little margin. In absolute terms, the downside of your leverage when you force yourself to sell during the 50% crash is fairly low (but a lot more significant at 105.26% equities than at 100.55% equitiies). But the gains you had from margin were also proportionally small, so any benefit you got from using margin gets clobbered. If my portfolio consists of a million in cash plus a $1000 bet that the S&P 500 will only rise, then my bet will get clobbered, even if my portfolio does not. The fact that my portfolio comes out OK doesn't mean my bet didn't get clobbered - it only means that my bet was a small one.
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Really you need to relax the requirement to deleverage as the market falls. Otherwise you commit to buying high and selling low, which only works if there is no volatility. You have to endure the greater risk you face when prices drop and your leverage ratio increases if you want to enjoy the benefit of additional gains from leverage. By deleveraging on the way down you attempt to escape the greater risk you assumed by leveraging in the first place. But there is no free lunch, as we have both realized: deleveraging on the way down amounts to buying high and selling low. I really think you need to relax the requirement to deleverage. If you do, the questions become "how (and how much) do I leverage" and "when (if ever) do I deleverage when the market falls."
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Let me bring options to your attention. A call option gives the buyer the right (but not the obligation) to buy a security at a predetermined price for a period of time. A put option gives the buyer the right to sell. Let's say Microsoft stock is at $100. For $50, I buy a call option that allows me to buy a share of Microsoft for $50. Suppose Microsoft goes up to $101. What is my option worth now? At $101, the right to buy for $50 is worth $51. So a 1% rise in Microsoft results in a 2% rise in the value of my option. But my downside is also multiplied by 2. (In the real world, I would have to pay more than $50 for a call option that lets me buy Microsoft at $50, to compensate the seller of the option for the service he is providing me.)
Re: Can you help me solve this brainteaser about allocation?
Yes, and there are other variations as well. This "puzzler" is flawed because the premises have not completely defined the situation and there are variations where the solution to the problem changes depending on what was assumed. In some variations not all the requirements of the solution can be met. When the solution exists it appears to be trivial in most examples.Alex Frakt wrote:Then the answer is trivial, but depends on what "there will not be greater than a 95% loss in the stock market" really means. If it means that the stock market has an absolute floor of 5% of its current price, then you keep 100% in the stock market always. If it means that is can lose 95% and then there is some sort of pause after which it can lose a further 95%, then you keep 100% in the market until it hits your 5% and then go to 100% safe assets.johnanglemen wrote:Thank you for weighing in, but I don't understand how this can't be solved by math provided you're willing to accept the assumption that "no matter what happens in the market" is defined as "there will not be greater than a 95% loss in the stock market" (which I am). How can there not exist a mathematically optimal solution?Alex Frakt wrote:The underlying issue is the mistaken assumption that allocation decisions are ultimately mathematically solvable.
Allocation decisions need to be based on human, not mathematical, criteria. In this case we have conflicting criteria between maximizing expected return (presumably risk-adjusted returns) and keeping a margin of safety, no matter what happens in the market. You can't resolve this with math, you simply have to decide which of the two criteria is more important.
It might be helpful to understand what the purpose of the question is -- in terms of leading to some actual investment strategy for a real case.
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Re: Can you help me solve this brainteaser about allocation?
Well, the goal is to help devise an actual investment strategy. Numbers have been changed to protect the innocent, the strategy will not be devised based solely on an Internet message board, yada yada. But there is a real sense that not enough risk is being taken / not enough reward is being generated given that the safe number is already being preserved in even the extreme downside cases.dbr wrote:Yes, and there are other variations as well. This "puzzler" is flawed because the premises have not completely defined the situation and there are variations where the solution to the problem changes depending on what was assumed. In some variations not all the requirements of the solution can be met. When the solution exists it appears to be trivial in most examples.Alex Frakt wrote:Then the answer is trivial, but depends on what "there will not be greater than a 95% loss in the stock market" really means. If it means that the stock market has an absolute floor of 5% of its current price, then you keep 100% in the stock market always. If it means that is can lose 95% and then there is some sort of pause after which it can lose a further 95%, then you keep 100% in the market until it hits your 5% and then go to 100% safe assets.johnanglemen wrote:Thank you for weighing in, but I don't understand how this can't be solved by math provided you're willing to accept the assumption that "no matter what happens in the market" is defined as "there will not be greater than a 95% loss in the stock market" (which I am). How can there not exist a mathematically optimal solution?Alex Frakt wrote:The underlying issue is the mistaken assumption that allocation decisions are ultimately mathematically solvable.
Allocation decisions need to be based on human, not mathematical, criteria. In this case we have conflicting criteria between maximizing expected return (presumably risk-adjusted returns) and keeping a margin of safety, no matter what happens in the market. You can't resolve this with math, you simply have to decide which of the two criteria is more important.
It might be helpful to understand what the purpose of the question is -- in terms of leading to some actual investment strategy for a real case.
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Re: Can you help me solve this brainteaser about allocation?
Thanks for your patience on this. I'm getting there. It's just a learning curve for me because previously my approach to investing was based on two (what I thought were) axioms: (1) the higher the exposure to equity, the higher the likely return; and (2) you should evaluate your market/risk exposure at any given moment in a vacuum, as if you had just entered the market, rather than in relation to previously experienced/arbitrary high watermarks [which I thought was a rationality trap].aaaaaaabbbbbbbbbb wrote:If Bob deleverages on the way down in the same manner you do, then he will not end up in debt (nor will he be wiped out). I say "according to you" you're leaving money on the table because there's a risk involved if you use significant leverage. Yes, your strategy insures you won't drop below $5 million. In that sense it is not risky. But what about the other 95 million? That portion is subject to additional risk because of the leverage. Furthermore, because your strategy involves buying higher and higher as the market rises and selling lower and lower as the market drops, it's questionable whether you're getting any additional return (nevermind having good risk-adjusted return). Suppose the market moves in the following manner. Every odd-numbered day it goes up 10%. Every even-numbered day it drops 9.05%. (Assume all months have 30 days). The guy whose portfolio is 100% equities gains 8.6% annually. Your strategy underperforms. Now look at http://www.google.com/finance?q=INDEXSP:.INX Zoom in on a short timescale (1 month or less). In the event of even minor volatility, your commitment to deleveraging means that your use of leverage loses you money. The risk you take is that even if there is only minor volatility you do worse than 100% equities. So there really isn't any money on the table at all (unless you happen to live in an alternate universe where the S&P 500 doesn't move like it does in our universe).
10 years later your portfolio is up to $1 bil. At this point you take a margin loan equal to about 5.26% of your portfolio, roughly an order of magnitude greater in percentage terms. Also, what I meant is that the gains you got from using margin during the bull market would have been clobbered. It's true that your portfolio wouldn't have been clobbered very much more than the other guy's. But this is only because you use very little margin. In absolute terms, the downside of your leverage when you force yourself to sell during the 50% crash is fairly low (but a lot more significant at 105.26% equities than at 100.55% equitiies). But the gains you had from margin were also proportionally small, so any benefit you got from using margin gets clobbered. If my portfolio consists of a million in cash plus a $1000 bet that the S&P 500 will only rise, then my bet will get clobbered, even if my portfolio does not. The fact that my portfolio comes out OK doesn't mean my bet didn't get clobbered - it only means that my bet was a small one.
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Really you need to relax the requirement to deleverage as the market falls. Otherwise you commit to buying high and selling low, which only works if there is no volatility. You have to endure the greater risk you face when prices drop and your leverage ratio increases if you want to enjoy the benefit of additional gains from leverage. By deleveraging on the way down you attempt to escape the greater risk you assumed by leveraging in the first place. But there is no free lunch, as we have both realized: deleveraging on the way down amounts to buying high and selling low. I really think you need to relax the requirement to deleverage. If you do, the questions become "how (and how much) do I leverage" and "when (if ever) do I deleverage when the market falls."
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Let me bring options to your attention. A call option gives the buyer the right (but not the obligation) to buy a security at a predetermined price for a period of time. A put option gives the buyer the right to sell. Let's say Microsoft stock is at $100. For $50, I buy a call option that allows me to buy a share of Microsoft for $50. Suppose Microsoft goes up to $101. What is my option worth now? At $101, the right to buy for $50 is worth $51. So a 1% rise in Microsoft results in a 2% rise in the value of my option. But my downside is also multiplied by 2. (In the real world, I would have to pay more than $50 for a call option that lets me buy Microsoft at $50, to compensate the seller of the option for the service he is providing me.)
I'm wondering if I have complicated the issue by introducing leverage. I did not expect that to become a focal point of the discussion, as the difference between 100% and 101% always seemed a bit arbitrary to me.
You said "because your strategy involves buying higher and higher as the market rises and selling lower and lower as the market drops, it's questionable whether you're getting any additional return (nevermind having good risk-adjusted return)." However, it seems like this applies even if we declare that 100% equities is the upper bound. After all, when the portfolio drops to $80M, you still (in the original framing) are expected to move from 100% equities to something more conservative that would preserve the $5M in a catastrophe. So when you said "Really you need to relax the requirement to deleverage as the market falls", I am wondering if you meant "Really you need to relax the requirement to become more conservative as the market falls."
(Likewise, in the example you give at the beginning, I wonder if the issue is actually leverage vs non-leverage, or if it's that the first guy is shifting his allocation on the way down and the second is remaining at 100% equities. Just want to make sure we've got one variable at a time.)
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Re: Can you help me solve this brainteaser about allocation?
Yeah, you're right. I got fixated on the use of leverage. Probably because in my own portfolio I have 100% equities as my baseline and am contemplating how I might go beyond 100%. If we replace "deleverage on the way down" with "sell riskier assets and buy safer assets on the way down" the same analysis applies. If you were to repeatedly switch between 100/0 equities bonds and 95/5 bonds in the hypothetical "up on odd days, down on even days" scenario, then you'd experience the same sort of losses as with leverage. Also, if you think of margin loans as a negative allocation to bonds (e.g. you sold someone else a bond instead of buying one from someone else), then we have a unified framework where going from 130% equities to 110% equities is tantamount to buying bonds to cancel out some of your negative bonds, just like going from 100% equities to 80% equities involves buying bonds.
From a practical perspective though, if you set 100% equities as the ceiling, then it is likely that you will soon reach a point where you portfolio has grown to the point where it is almost unthinkable that you will ever have to adopt a safer asset allocation to protect against a 95% drop. E.g. after a few decades you have $500 million and you'd have to have an 80% drop and then another 95% drop immediately after to fall down to $5M.
From a practical perspective though, if you set 100% equities as the ceiling, then it is likely that you will soon reach a point where you portfolio has grown to the point where it is almost unthinkable that you will ever have to adopt a safer asset allocation to protect against a 95% drop. E.g. after a few decades you have $500 million and you'd have to have an 80% drop and then another 95% drop immediately after to fall down to $5M.
Re: Can you help me solve this brainteaser about allocation?
In your original $100 million case, why not simply invest the profits in excess of $100 million in a higher risk / higher reward asset that would go to zero in an extreme catastrophe?
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Re: Can you help me solve this brainteaser about allocation?
I'm not sure what aaaaaaabbbbbbbbbb's answer would be, but mine would be that just because I'm willing to take more risk doesn't mean I want to take stupid/unsystematic risk. I still believe in the efficiency of markets, so I still want the excess to be invested in something that has a sensible risk/return ratio.CFM300 wrote:In your original $100 million case, why not simply invest the profits in excess of $100 million in a higher risk / higher reward asset that would go to zero in an extreme catastrophe?
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Re: Can you help me solve this brainteaser about allocation?
Exactly! This is why I'm trying to find a scalable strategy early on, because an outcome like this (with smaller numbers) seems inevitable.aaaaaaabbbbbbbbbb wrote:From a practical perspective though, if you set 100% equities as the ceiling, then it is likely that you will soon reach a point where you portfolio has grown to the point where it is almost unthinkable that you will ever have to adopt a safer asset allocation to protect against a 95% drop. E.g. after a few decades you have $500 million and you'd have to have an 80% drop and then another 95% drop immediately after to fall down to $5M.
So you said you've already set 100% equities as your baseline. Does that mean that you currently keep your allocation as 100% equities rain or shine, bust or boom?
Re: Can you help me solve this brainteaser about allocation?
So an investment in which you could lose $95 million of $100 million is "sensible," but one in which you could lose everything is "stupid" -- even though you're only investing "stupidly" the profits from your initial "sensible" $100 million investment?johnanglemen wrote:just because I'm willing to take more risk doesn't mean I want to take stupid/unsystematic risk. I still believe in the efficiency of markets, so I still want the excess to be invested in something that has a sensible risk/return ratio.
And yet you're also going to fret over investing too conservatively if you invest everything (the initial $100 million and the profits from that investment) in the "sensible" investment, because, if the investment doubled, then you'd be left with $10 million rather than $5 million if a financial apocalypse occurred?
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Re: Can you help me solve this brainteaser about allocation?
I don't think we're saying the same thing, and I didn't mean to imply that your suggestion itself was "stupid."CFM300 wrote:So an investment in which you could lose $95 million of $100 million is "sensible," but one in which you could lose everything is "stupid" -- even though you're only investing "stupidly" the profits from your initial "sensible" $100 million investment?johnanglemen wrote:just because I'm willing to take more risk doesn't mean I want to take stupid/unsystematic risk. I still believe in the efficiency of markets, so I still want the excess to be invested in something that has a sensible risk/return ratio.
And yet you're also going to fret over investing too conservatively if you invest everything (the initial $100 million and the profits from that investment) in the "sensible" investment, because, if the investment doubled, then you'd be left with $10 million rather than $5 million if a financial apocalypse occurred?
My point is that I see no reason to abandon the efficient market hypothesis and the principles of this board with the excess money. If you think that investing in an individual stock is an uncompensated risk with smaller dollars, then you also think it's an uncompensated risk with large dollars. Why would you take the uncompensated risk in the latter case just because you can afford to?
It's not "stupid" because it can go to zero, it's "stupid" because (according to the principles we all subscribe to) it's uncompensated.
Re: Can you help me solve this brainteaser about allocation?
Because, apparently, you're worried about having more than some minimum amount of money remaining should a financial apocalypse occur. In your own words, you don't want to invest "too conservatively", which you initially explained by saying that the investment wouldn't go to zero given an extreme catastrophe. Your own words:johnanglemen wrote:My point is that I see no reason to abandon the efficient market hypothesis and the principles of this board with the excess money. If you think that investing in an individual stock is an uncompensated risk with smaller dollars, then you also think it's an uncompensated risk with large dollars. Why would you take the uncompensated risk in the latter case just because you can afford to?
"However, I am positing that that is too conservative given the goal. If your "risky" asset is, for example, a total world stock fund, then it's not going to go to 0 unless all of the world's companies become valueless."
The upshot seems to be that yes, as your portfolio grows you're going to have to take more risk (via leverage or investing in higher risk assets) if you want to ensure that you'll only have X amount of dollar remaining should the maximum risk materialize.
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Re: Can you help me solve this brainteaser about allocation?
(2) is definitely true. Nothing about the portfolio you hold today should hinge on the portfolio you held yesterday.johnanglemen wrote: It's just a learning curve for me because previously my approach to investing was based on two (what I thought were) axioms: (1) the higher the exposure to equity, the higher the likely return; and (2) you should evaluate your market/risk exposure at any given moment in a vacuum, as if you had just entered the market, rather than in relation to previously experienced/arbitrary high watermarks [which I thought was a rationality trap].
(1) depends on what you mean. Suppose that I offer you a bet at 1000:1 odds that a pair of fair dice comes up 12. Betting $95 million on that maximizes your expected returns. Your expected return (return in each outcome weighted by probability of that outcome) is about $2.5 billion. The expected return of declining the bet is $0. Taking the bet is also "safe" in the sense that you are guaranteed to still have $5 million left over. But of course, you're almost certainly going to lose $95 because the odds of rolling a 12 are so small.
Stock returns over long periods of time are like that. They are "positively skewed". Using leverage increases the expected returns and increases the positive skew. So there are a few outcomes where you turn into Bill Gates. Those outcomes drag up the average of returns across all possible outcomes. But most likely, you'll do worse than you would have done without all that risk.
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Re: Can you help me solve this brainteaser about allocation?
Yes, we agree on that. That isn't really the question though. The question is how to do this in such a way that you're not just buying high and selling low, which is what aaaabbb and I are discussing.CFM300 wrote:Because, apparently, you're worried about having more than some minimum amount of money remaining should a financial apocalypse occur. In your own words, you don't want to invest "too conservatively", which you initially explained by saying that the investment wouldn't go to zero given an extreme catastrophe. Your own words:johnanglemen wrote:My point is that I see no reason to abandon the efficient market hypothesis and the principles of this board with the excess money. If you think that investing in an individual stock is an uncompensated risk with smaller dollars, then you also think it's an uncompensated risk with large dollars. Why would you take the uncompensated risk in the latter case just because you can afford to?
"However, I am positing that that is too conservative given the goal. If your "risky" asset is, for example, a total world stock fund, then it's not going to go to 0 unless all of the world's companies become valueless."
The upshot seems to be that yes, as your portfolio grows you're going to have to take more risk (via leverage or investing in higher risk assets) if you want to ensure that you'll only have X amount of dollar remaining should the maximum risk materialize.
I gather from the way you're talking about this that you think the objective is a little bit silly, but to me it seems no different than what everyone does in determining their asset allocation strategy: you're trying to identify the strategy that properly fulfills your objectives relative to your risk tolerance. If a 20 year old showed up here and said he was investing for his retirement and was thinking of putting 90% in bonds, everyone would say "that's way too conservative for your goals!" Well, the use case here is investing for maximum growth for heirs and charities, without bankrupting oneself.
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Re: Can you help me solve this brainteaser about allocation?
But some of the ideas discussed in this thread seem to fail that test. For instance, people have discussed holding an allocation that could withstand a "95% decline from X" (where X = the market's recent high or something of that nature) rather than a "95% decline from your current position." Indeed, this board's approach to asset allocation in general seems to fail that test, doesn't it? Because people say to pick an allocation where they'd feel comfortable losing 50% or more of their equities, yet people also advise to rebalance on the way down. So that tolerance of "losing 50%" is relative to your starting point, and not to your position at any given moment. (Sorry to keep harping on that, but I'm still a bit confused by it.)backpacker wrote:(2) is definitely true. Nothing about the portfolio you hold today should hinge on the portfolio you held yesterday.johnanglemen wrote: It's just a learning curve for me because previously my approach to investing was based on two (what I thought were) axioms: (1) the higher the exposure to equity, the higher the likely return; and (2) you should evaluate your market/risk exposure at any given moment in a vacuum, as if you had just entered the market, rather than in relation to previously experienced/arbitrary high watermarks [which I thought was a rationality trap].
I get the dice example but I don't quite follow how investing is equities is analogous to betting on a 12? You conclude that "most likely, you'll do worse than you would have done without all that risk"... how are you likely to do worse by putting 95% of your money in stocks than by putting it in cash or bonds? If you were more likely to make money by investing in safe assets than risky assets, than wouldn't we all just invest in safe assets? Apologies, I'm probably missing something obvious about the point you're making.backpacker wrote:(1) depends on what you mean. Suppose that I offer you a bet at 1000:1 odds that a pair of fair dice comes up 12. Betting $95 million on that maximizes your expected returns. Your expected return (return in each outcome weighted by probability of that outcome) is about $2.5 billion. The expected return of declining the bet is $0. Taking the bet is also "safe" in the sense that you are guaranteed to still have $5 million left over. But of course, you're almost certainly going to lose $95 because the odds of rolling a 12 are so small.
Stock returns over long periods of time are like that. They are "positively skewed". Using leverage increases the expected returns and increases the positive skew. So there are a few outcomes where you turn into Bill Gates. Those outcomes drag up the average of returns across all possible outcomes. But most likely, you'll do worse than you would have done without all that risk.
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Re: Can you help me solve this brainteaser about allocation?
The problem with this strategy is that you are restricting your options by compartmentalizing your assets into an ultra-safe bucket and an ultra-risky bucket. The universe of possible strategies includes many that do not require you to make this strict compartmentalization, and to adopt your suggestion is to dismiss all these other strategies without even considering them. Furthermore, considering the incredibly high risk tolerance and ability to take risk of the scenario in the OP, you'd be leaving a lot of money on the table if you were to put your entire $100M principal in a safe investment and invest only the earnings in a risky way.CFM300 wrote:In your original $100 million case, why not simply invest the profits in excess of $100 million in a higher risk / higher reward asset that would go to zero in an extreme catastrophe?
I see a lot of people advocate "mental accounting" strategies along these lines, e.g. you divide your retirement portfolio into a portion you absolutely can't afford to lose and then put it in TIPS or annuities, and then invest the rest more aggressively. But the fact of the matter is that it is possible to construct a portfolio with the same riskiness as this two-bucket portfolio by putting all your money into a single bucket - a single bucket filled with investments that have a riskiness that lies in between the riskiness of TIPS and stocks. And such a portfolio might be better in other ways, so we need to consider it.
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Re: Can you help me solve this brainteaser about allocation?
I've been 100%+ equities since I started investing 11 years ago. Fortunately for me I held steadfast during the last crash. My employment held steadfast too. I'm a man of very simple tastes, pretty high income, and 11 years of massive savings/investment returns, so I can afford to take on the risk. As for whether I need to take it, well, I want to see the number go really big! Currently I'm at 105% equities (using a small, safe amount of margin and a bit of options) while I figure out if and how I can take on more risk safely.johnanglemen wrote:Exactly! This is why I'm trying to find a scalable strategy early on, because an outcome like this (with smaller numbers) seems inevitable.
So you said you've already set 100% equities as your baseline. Does that mean that you currently keep your allocation as 100% equities rain or shine, bust or boom?
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Re: Can you help me solve this brainteaser about allocation?
You and I are in very similar situations. Would like to stay in touch as we work through this. Curious to hear about your process for figuring this out in the future, and even the process you used to get to 105%. It seems like you've more or less decided on the strategy I originally outlined, except without the de-risking on the way down. So you've essentially decided that the market won't ever fall more than X% from the point at which you began investing, and therefore you're comfortable with 105% right now. I'm tempted to follow suit, but without some specific preordained strategy, it feels arbitrary to me. Without hardcoded logic of "if A then B, but if C then D," I know I'll just end up greeting greedy and quietly dialing up my margin in good times.aaaaaaabbbbbbbbbb wrote:I've been 100%+ equities since I started investing 11 years ago. Fortunately for me I held steadfast during the last crash. My employment held steadfast too. I'm a man of very simple tastes, pretty high income, and 11 years of massive savings/investment returns, so I can afford to take on the risk. As for whether I need to take it, well, I want to see the number go really big! Currently I'm at 105% equities (using a small, safe amount of margin and a bit of options) while I figure out if and how I can take on more risk safely.johnanglemen wrote:Exactly! This is why I'm trying to find a scalable strategy early on, because an outcome like this (with smaller numbers) seems inevitable.
So you said you've already set 100% equities as your baseline. Does that mean that you currently keep your allocation as 100% equities rain or shine, bust or boom?
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Re: Can you help me solve this brainteaser about allocation?
105% isn't really the result of a perfected strategy, it's just a holding pattern to maintain while I figure things out. Also, the 105% is even safer than you might think. Consider the following two ways to attain 105% leverage: 1) you leverage your entire portfolio at 1.05:1; 2) you put 95% of your portfolio in an unleveraged bucket, and leverage the rest 2:1.johnanglemen wrote:Curious to hear about your process for figuring this out in the future, and even the process you used to get to 105%.
Here's what I have: a margin loan equal to 2% of my portfolio, and 3% of my portfolio is call options that provide 2:1 leverage. Compared to a portfolio with 5% margin and no options, this portfolio does worse in the event of a minor drop but better in the event of a massive (say 90%+) drop. Why do I buy options that give (say) 2:1 leverage rather than (say) 1.05:1? Well, the deeper in the money the option is, the lower the time value of the option. And I don't want to pay for the time value of the option, I just want the leverage.
Well, with a leveraged strategy it's more like "you've decided that the market won't ever fall more than f(x)% from its current value," where x is your leverage at the present moment. After all, with leverage you risk either being wiped out or forced to deleverage at a massive loss at every point in time.johnanglemen wrote:So you've essentially decided that the market won't ever fall more than X% from the point at which you began investing, and therefore you're comfortable with 105% right now.
Yes, this is a big concern with strategies that use leverage. There's a huge risk of downfall from leveraging during a bubble and then being crushed when it pops.johnanglemen wrote:I know I'll just end up greeting greedy and quietly dialing up my margin in good times.
One partial solution: DCA with your margin/options/whatever. Every month, add $x of borrowed money (or equivalent leverage from options/futures). Note that this perpetual borrowing won't necessarily cause your leverage ratio to go to infinity because 1) you're making regular contributions from your earned income (at least I am) 2) as the market rises, you automatically deleverage.
Another partial solution: take out loans/options with a long term. We can think of a margin loan as a loan with an infinitesimal term. (I.e., it's like the brokerage is constantly re-loaning the money to you, and at any point it can issue a margin call and decide to not re-loan you the money at the end of the next infinitesimally long term). So in the event of a crash, you're boned. But suppose that instead you take out loans with a long term, or buy LEAPS (long-term calls). Then you're probably fine unless the loan/call expires during the nadir of a crash. Another possibility: stagger the loans/LEAPS temporally.
Another partial solution: rather than leverage your entire portfolio, leverage only a portion of it at a higher ratio. This has major downsides, but you're forced to do this anyway if you use extremely deep in the money call options.
Another partial solution: have earned income. Infusions of your income into your portfolio during a market crash will go a long way toward deleveraging without selling at a loss. The one good thing about having a high leverage ratio sprung onto you during a crash is that the ratio rapidly decreases as you add money.
Another partial solution: credit cards/other revolving credit lines. Not quite as bad an idea as you might think. When a crash pushes you to a dangerously high leverage ratio, even a bit of borrowed money from your revolving credit line will deleverage you a lot (just like with infusions of income). I have great credit, tons of credit available, and could get 0% for 12-18 months balance transfer cards.
Last edited by aaaaaaabbbbbbbbbb on Mon Apr 20, 2015 5:38 pm, edited 2 times in total.
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Re: Can you help me solve this brainteaser about allocation?
Ah, nice point. You've convinced me. Bogleheads sometimes talk as though you lack moral fiber if you have an 80/20 portfolio, stocks drop by half, and you don't rebalance all the way back to 80/20. But rebalancing back to 80/20 no matter what may violate the "do today whatever you would do if you were investing for the first time" test. Because if you have less to lose, you may reasonably want to take less risk.johnanglemen wrote: But some of the ideas discussed in this thread seem to fail that test. For instance, people have discussed holding an allocation that could withstand a "95% decline from X" (where X = the market's recent high or something of that nature) rather than a "95% decline from your current position." Indeed, this board's approach to asset allocation in general seems to fail that test, doesn't it? Because people say to pick an allocation where they'd feel comfortable losing 50% or more of their equities, yet people also advise to rebalance on the way down. So that tolerance of "losing 50%" is relative to your starting point, and not to your position at any given moment. (Sorry to keep harping on that, but I'm still a bit confused by it.)
Here's the chart for the distribution of returns on an all-stock portfolio over 30 years. As you can see, the median (what you probably get) is a lot lower than the expectation (average over all scenarios).backpacker wrote: I get the dice example but I don't quite follow how investing is equities is analogous to betting on a 12? You conclude that "most likely, you'll do worse than you would have done without all that risk"... how are you likely to do worse by putting 95% of your money in stocks than by putting it in cash or bonds? If you were more likely to make money by investing in safe assets than risky assets, than wouldn't we all just invest in safe assets? Apologies, I'm probably missing something obvious about the point you're making.
[Edit: Fixed obnoxiously large chart. The x axis is return on $100. They y axis is number of trials, out of 100,000, where that result was achieved.]
My thought was that adding leverage can push up the mean while pushing down the median. That would be one reason why aggressively adding leverage as your portfolio grows and you have more to lose might both (a) increase expected returns and (b) be an insane thing to do. I'll have to think about it more though...
Last edited by backpacker on Tue Apr 21, 2015 7:52 am, edited 3 times in total.
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Re: Can you help me solve this brainteaser about allocation?
Yeah, but I don't see how you'd ever come up with that value without in some way--consciously or subconsciously--factoring in recent market performance. If you're going to come up with it in a vacuum, it seems like you have to pick something in the neighborhood of 80-90%, given what happened in the 1920s. And if you're always assuming that large of a drop, then you're never really going to feel comfortable leveraging, as we've discussed. Otherwise, if you pick something lower (like 50%) on the basis that "the market has already fallen so much lately," then you're not living purely in the present.aaaaaaabbbbbbbbbb wrote:Well, with a leveraged strategy it's more like "you've decided that the market won't ever fall more than f(x)% from its current value," where x is your leverage at the present moment. After all, with leverage you risk either being wiped out or forced to deleverage at a massive loss at every point in time.johnanglemen wrote:So you've essentially decided that the market won't ever fall more than X% from the point at which you began investing, and therefore you're comfortable with 105% right now.
Right. Of course, then you have the opportunity cost of all that time where you weren't leveraged even though you "could have been". My mind starts to glaze over at this point. How did you get so fluent in this stuff? Was it all just on-the-side learning? Any references that were particularly helpful?aaaaaaabbbbbbbbbb wrote:Yes, this is a big concern with strategies that use leverage. There's a huge risk of downfall from leveraging during a bubble and then being crushed when it pops. My proposed solution to this is to DCA with your margin/options/whatever. Every month, add $x of borrowed money (or equivalent leverage from options/futures). Note that this perpetual borrowing won't necessarily cause your leverage ratio to go to infinity because 1) you're making regular contributions from your earned income (at least I am) 2) as the market rises, you automatically deleverage.johnanglemen wrote:I know I'll just end up greeting greedy and quietly dialing up my margin in good times.
Last edited by johnanglemen on Mon Apr 20, 2015 5:42 pm, edited 1 time in total.
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Re: Can you help me solve this brainteaser about allocation?
Agree with you completely here. The problem is most apparent during a bubble - if the peak of the bubble was sufficiently high, then you could have lost 50% and still have a long way to go. The saner approach I think is to look at fundamentals (value investors agree). If you're at a PE of 100, then buckle in and prepare for a record drop. If you're at a PE of 5, then even if further drops occur, you'll do okay from dividends alone. I don't claim that fundamentals are some ultimate compass that will help you navigate volatility effortlessly, but looking at fundamentals seems a lot saner than anchoring to a valuation at a certain point in time - a valuation that can be (and has been) arbitrarily inflated.johnanglemen wrote:But some of the ideas discussed in this thread seem to fail that test. For instance, people have discussed holding an allocation that could withstand a "95% decline from X" (where X = the market's recent high or something of that nature) rather than a "95% decline from your current position." Indeed, this board's approach to asset allocation in general seems to fail that test, doesn't it? Because people say to pick an allocation where they'd feel comfortable losing 50% or more of their equities, yet people also advise to rebalance on the way down. So that tolerance of "losing 50%" is relative to your starting point, and not to your position at any given moment. (Sorry to keep harping on that, but I'm still a bit confused by it.)
By the way, I edited my last post with some stuff since you read it.