Diversifying with a zero-correlation, zero-return volatile asset

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Diversifying with a zero-correlation, zero-return volatile asset

Post by nisiprius » Tue Oct 09, 2018 8:51 pm

You and a friend have roughly equal portfolios. You agree to meet once a week for at least twenty years, and bet $1,000 on the flip of a coin. Assume that the coin is fair, has exactly 50% probability of landing heads or tails, and your friend is honest and will keep the agreement.

Each of you has now made a long-term commitment of a portion of your portfolio to an asset consisting of the $1,000/week coin-flip bet. This asset has an expected long-term return of zero, an expected zero correlation with the rest of your portfolio, and an expected weekly standard deviation of $1,000.

Which of the following is true?

a) Long-term, the coin-flip "asset" adds valuable diversification to both portfolios, and improves the risk-adjusted return for both of you. It is mutually beneficial to enter into this arrangement, and you should seriously try to find a partner willing to do it.

b) The coin-flip has exactly no effect on your long-term risk, return, or risk-adjusted return. Of course, over any short period of time, or even over the entire twenty years, one or the other of you will be an overall winner and the other will be an overall loser, by sheer luck, but over twenty years the law of averages applies and the overall win or loss will almost certainly be very small.

c) The coin-flip adds risk without adding any return, and reduces the risk-adjusted return for both of you.

For extra credit, calculate the amount of diversification the coin-flip provides, using whatever measure of diversification you like.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by whodidntante » Tue Oct 09, 2018 9:03 pm

Is this about managed futures? :happy

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by HEDGEFUNDIE » Tue Oct 09, 2018 9:07 pm

How about a zero-correlation, positive return volatile asset, like EDV?

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by nisiprius » Tue Oct 09, 2018 9:09 pm

Arguably you can do better than a coin-flip agreement with a friend. But I still want to know whether, according to peoples' analysis, the coin-flip agreement is mutually beneficial, neutral, or mutually harmful.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by vineviz » Tue Oct 09, 2018 9:11 pm

Did I miss it: the coin flip is one asset, but what’s the portfolio it’s supposed to diversify (or not)?
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by lack_ey » Tue Oct 09, 2018 9:15 pm

Ex-ante both sides are adding more risk (more volatility) while not changing expected return. So harmful, unless the non-coinflip assets are negative expected return. As for realized returns, one would come out ahead in terms of earning money at the expense of the other, though with higher vol than not entering the agreement.

Or wait, I'm unclear on the wording. If this money is actually a "commitment of a portion of your portfolio" as in not available for investment in something else, then there's a cash drag that's reducing expected return.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by grkmec » Tue Oct 09, 2018 9:16 pm

Is this a serious question or are you looking for someone to help you with your MBA homework :D

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by Rowan Oak » Tue Oct 09, 2018 9:18 pm

c) The coin-flip adds risk without adding any return, and reduces the risk-adjusted return for both of you.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by nisiprius » Tue Oct 09, 2018 9:20 pm

vineviz wrote:
Tue Oct 09, 2018 9:11 pm
Did I miss it: the coin flip is one asset, but what’s the portfolio it’s supposed to diversify (or not)?
I didn't specify. Let's say both you and your friend hold similar portfolios, and to keep the thought experiment simple, assume 60% Vanguard Total Stock Market Index Fund, 40% Vanguard Total Bond Market Index Fund, rebalanced monthly. If you think some other portfolio is more interesting, use it. Assume that there is no casual connection between the coin flip and the rest of the portfolio and that the expected long-term correlation between the coin flip and the rest of the portfolio is zero.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by columbia » Tue Oct 09, 2018 9:24 pm

Buying a mix of 50% stocks/50% short term treasuries for 50 years is a perfectly rational and reasonable tactic.

You could do a lot worse, probably including engaging in the above (thought) exercise.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by HEDGEFUNDIE » Tue Oct 09, 2018 9:27 pm

Isn’t this basically gold? In which case, the answer should be A.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by venkman » Tue Oct 09, 2018 9:29 pm

If you factor in taxes, it's a net loss. If you come out ahead in a given year, you owe taxes on the amount you won; but if you come out negative for the year, you can't deduct the losses. So, after-tax, your expected return is negative. After inflation, it's even worse.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by Nate79 » Tue Oct 09, 2018 10:24 pm

I would guess C.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by nyclon » Tue Oct 09, 2018 10:30 pm

Guessing C.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by whodidntante » Tue Oct 09, 2018 10:31 pm

I have flipped coins (in the poker sense) for $1,000 plenty of times. I don't recommend it as a diversifier. LOL

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by bogglizer » Tue Oct 09, 2018 10:52 pm

I remember many years ago, having an argument about whether lottery tickets are a hedge for a portfolio. They are uncorrelated and highly volatile, but with negative return. Seems to be a similar question as above.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by AlphaLess » Tue Oct 09, 2018 11:16 pm

nisiprius wrote:
Tue Oct 09, 2018 8:51 pm
c) The coin-flip adds risk without adding any return, and reduces the risk-adjusted return for both of you.
P: random variable (portfolio)
B: random variable (bet).

Var (P + B) = Var ( P ) + 2 * Cov ( P,B) + Var ( B)

By the design of the problem, Cov ( P,B) = 0 {let's say we can muster up an iPhone app to throw a random coin, and it is truly random and does not use any known asset returns for randomness generation},

Var(B) > 0

So Var (P + B) > Var (P).

Also, notice that Std (P+B) = Sqrt ( Var (P+B)).

Thus, the risk of the (P+B) combo is higher, in variance and standard deviation terms.

E [ P + B ] = E [ P ] + E [ B ] {as expectation is additive}.
By design, E [ B ] = 0.

Thus, E [ P + B] = E [ P ]

If we use a simplest form of risk-adjusted return, ignoring interest rates:

Sharpe (P+B) = E [ P + B ] / Std (P + B) < E [ P ] / Std ( P) = Sharpe (P) , because
: numerators are equal,
: denominator Std ( P + B) is larger.

However, let me ask you this problem:
- you and a friend (let's call your friend Warren 'GEICO' Buffet) decided to meet up once a month,
- you give your friend $100 / M, for twenty years, maybe more,
- your friend Warren cashes that check, with a smirk,
- occasionally, when you have trouble with your car, of accident variety, Warren reluctantly writes a check to you, covering some part of the expenses resulting from the accident,
- it is known that the total dollar value of the checks that Warren might write to you is strictly lower than the total value of checks that you write to Warren.

Do you play this game with Warren?

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by triceratop » Wed Oct 10, 2018 12:49 am

AlphaLess wrote:
Tue Oct 09, 2018 11:16 pm
Do you play this game with Warren?
Yes: my Uncle, let's call him "Sam", told me to. Persuasive fellow.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by PaulF » Wed Oct 10, 2018 8:32 am

AlphaLess wrote:
Tue Oct 09, 2018 11:16 pm

- it is known that the total dollar value of the checks that Warren might write to you is strictly lower than the total value of checks that you write to Warren.
But why add this condition? I was with you right up until that point.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by JoMoney » Wed Oct 10, 2018 9:13 am

nisiprius wrote:
Tue Oct 09, 2018 8:51 pm
...

c) The coin-flip adds risk without adding any return, and reduces the risk-adjusted return for both of you.

For extra credit, calculate the amount of diversification the coin-flip provides, using whatever measure of diversification you like.
If the gambler has zero edge, i.e. if b = q / p, then the criterion recommends the gambler bets nothing.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by afan » Wed Oct 10, 2018 9:30 am

PaulF wrote:
Wed Oct 10, 2018 8:32 am
AlphaLess wrote:
Tue Oct 09, 2018 11:16 pm

- it is known that the total dollar value of the checks that Warren might write to you is strictly lower than the total value of checks that you write to Warren.
But why add this condition? I was with you right up until that point.
This condition is not true of insurance. For a company to be profitable it is not even necessary that the total of all premiums collected exceeds all benefits paid out. Insurance companies invest the premiums and expect to earn a positive return. They know that MOST policies will pay more in premiums than they collect in benefits. For SOME policies the totals will be close. For a small number of policies the payout will exceed all premiums by a large amount.

The company is betting they estimated the risks and priced the policy such that the line is profitable over all.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by afan » Wed Oct 10, 2018 9:33 am

The usual pitch for expensive alternative investments is positive expected return and negative correlation with other assets.

Some have claimed that zero or negative expected return can be useful if the negative correlation is strong enough.

And of course, you should pay a lot of money for someone to provide you with this great opportunity.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by Nate79 » Wed Oct 10, 2018 9:42 am

When do we get the answer?

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by HEDGEFUNDIE » Wed Oct 10, 2018 9:45 am

Nate79 wrote:
Wed Oct 10, 2018 9:42 am
When do we get the answer?
Just like everything else on BH, there is no answer, only interminable debate and backtesting

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by Misenplace » Wed Oct 10, 2018 9:59 am

Nate79 wrote:
Wed Oct 10, 2018 9:42 am
When do we get the answer?
Alphaless’ proof convinced me.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by bgf » Wed Oct 10, 2018 10:04 am

nisiprius wrote:
Tue Oct 09, 2018 8:51 pm
Which of the following is true?

b) The coin-flip has exactly no effect on your long-term risk, return, or risk-adjusted return. Of course, over any short period of time, or even over the entire twenty years, one or the other of you will be an overall winner and the other will be an overall loser, by sheer luck, but over twenty years the law of averages applies and the overall win or loss will almost certainly be very small.
there is no rebalancing between the "coin flip asset" and the rest of your portfolio, so it is as simple as saying you are setting aside a certain amount of cash ($5,000, $10,000, or whatever you think is sufficient to cover a really bad run at coin flips, i guess this is a personal decision based on how conservative you are) and letting it just sit there for twenty years. this amounts to about 1000 flips so i would feel fairly confident that it will not gain or lose much at all ( + or - 1% or so over the entire 20 year period).

because i can with almost mathematical certainty determine what i will gain or lose on the coin flip asset, i do not think it adds much risk at all, at least no more than an equivalent allocation to cash.

the volatility, standard deviation, correlation, and whatever else you want to throw in there are just red herrings. in practice, you have a cash allocation that will with near certainty be about the same amount of money in 20 years as it is today. as there is no rebalancing, it cannot provide you any benefit unless it outperforms the rest of your portfolio over the 20 year period, in which case, you are a horrible investor.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by David Jay » Wed Oct 10, 2018 10:38 am

I suspect this discussion is about "A" - does non-correlation alone, by definition, improve the performance of a portfolio. For instance, does adding less than perfectly correlated sector funds improve portfolio performance compared to simply holding Total Stock.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by rkhusky » Wed Oct 10, 2018 11:13 am

bgf wrote:
Wed Oct 10, 2018 10:04 am
there is no rebalancing between the "coin flip asset" and the rest of your portfolio, so it is as simple as saying you are setting aside a certain amount of cash ($5,000, $10,000, or whatever you think is sufficient to cover a really bad run at coin flips, i guess this is a personal decision based on how conservative you are) and letting it just sit there for twenty years. this amounts to about 1000 flips so i would feel fairly confident that it will not gain or lose much at all ( + or - 1% or so over the entire 20 year period).
It was stated that the other portfolio was 60/40 Total Stock/Total Bond. So, if you lose a few bets in a row, you have to sell some of the other portfolio. If you win a few bets in a row, you can buy more of the other portfolio.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by bgf » Wed Oct 10, 2018 12:21 pm

rkhusky wrote:
Wed Oct 10, 2018 11:13 am
bgf wrote:
Wed Oct 10, 2018 10:04 am
there is no rebalancing between the "coin flip asset" and the rest of your portfolio, so it is as simple as saying you are setting aside a certain amount of cash ($5,000, $10,000, or whatever you think is sufficient to cover a really bad run at coin flips, i guess this is a personal decision based on how conservative you are) and letting it just sit there for twenty years. this amounts to about 1000 flips so i would feel fairly confident that it will not gain or lose much at all ( + or - 1% or so over the entire 20 year period).
It was stated that the other portfolio was 60/40 Total Stock/Total Bond. So, if you lose a few bets in a row, you have to sell some of the other portfolio. If you win a few bets in a row, you can buy more of the other portfolio.
in the OP, there was no mention of rebalancing. in the clarification post, the rebalancing refers to within the 60-40 split, performed monthly. this is why I specifically stated that the investor had to choose and set aside an amount, at the outset, sufficient to cover the back and forth payments for the coin flips.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by vineviz » Wed Oct 10, 2018 12:48 pm

nisiprius wrote:
Tue Oct 09, 2018 8:51 pm
Which of the following is true?

a) Long-term, the coin-flip "asset" adds valuable diversification to both portfolios, and improves the risk-adjusted return for both of you. It is mutually beneficial to enter into this arrangement, and you should seriously try to find a partner willing to do it.

b) The coin-flip has exactly no effect on your long-term risk, return, or risk-adjusted return. Of course, over any short period of time, or even over the entire twenty years, one or the other of you will be an overall winner and the other will be an overall loser, by sheer luck, but over twenty years the law of averages applies and the overall win or loss will almost certainly be very small.

c) The coin-flip adds risk without adding any return, and reduces the risk-adjusted return for both of you.

For extra credit, calculate the amount of diversification the coin-flip provides, using whatever measure of diversification you like.
The answer, it turns out, is "none of the above".

I'm not sure if the answers were intentionally designed this way, or if they turned out that way due to a misunderstanding about what "diversification" means (hint: has nothing to do with risk-adjusted return).

a) is false because the coin flip DOES have an impact on risk-adjusted return (it lowers it).

b) is false because the coin flip DOES have an effect on all three criteria (long-term risk, return, or risk-adjusted return): it lowers all three.

c) is false because it lowers risk AND return for both parties, with a net effect of reducing risk-adjusted return.

The answer is "none of the above", in short, because the asset both improves diversification and reduces risk-adjusted return.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by Nate79 » Wed Oct 10, 2018 1:13 pm

vineviz wrote:
Wed Oct 10, 2018 12:48 pm
nisiprius wrote:
Tue Oct 09, 2018 8:51 pm
Which of the following is true?

a) Long-term, the coin-flip "asset" adds valuable diversification to both portfolios, and improves the risk-adjusted return for both of you. It is mutually beneficial to enter into this arrangement, and you should seriously try to find a partner willing to do it.

b) The coin-flip has exactly no effect on your long-term risk, return, or risk-adjusted return. Of course, over any short period of time, or even over the entire twenty years, one or the other of you will be an overall winner and the other will be an overall loser, by sheer luck, but over twenty years the law of averages applies and the overall win or loss will almost certainly be very small.

c) The coin-flip adds risk without adding any return, and reduces the risk-adjusted return for both of you.

For extra credit, calculate the amount of diversification the coin-flip provides, using whatever measure of diversification you like.
The answer, it turns out, is "none of the above".

I'm not sure if the answers were intentionally designed this way, or if they turned out that way due to a misunderstanding about what "diversification" means (hint: has nothing to do with risk-adjusted return).

a) is false because the coin flip DOES have an impact on risk-adjusted return (it lowers it).

b) is false because the coin flip DOES have an effect on all three criteria (long-term risk, return, or risk-adjusted return): it lowers all three.

c) is false because it lowers risk AND return for both parties, with a net effect of reducing risk-adjusted return.

The answer is "none of the above", in short, because the asset both improves diversification and reduces risk-adjusted return.
Can you clarify how adding the coin flip lowers risk?

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by vineviz » Wed Oct 10, 2018 2:01 pm

Nate79 wrote:
Wed Oct 10, 2018 1:13 pm
Can you clarify how adding the coin flip lowers risk?
Because the expected gain/loss from the coin flip is $0 each week and the expected gain/loss from the stock & bond portfolio is some positive number, the coin flip must reduce the magnitude of the expected gain/loss of the combination. The amount of risk reduction depends on the ratio of the stock/bond portfolio value and the notional value of the coin flip bet.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by rkhusky » Wed Oct 10, 2018 4:15 pm

bgf wrote:
Wed Oct 10, 2018 12:21 pm
in the OP, there was no mention of rebalancing. in the clarification post, the rebalancing refers to within the 60-40 split, performed monthly. this is why I specifically stated that the investor had to choose and set aside an amount, at the outset, sufficient to cover the back and forth payments for the coin flips.
The OP does not mention a cash account. Therefore, if you lose a weekly bet, you have to withdraw stocks or bonds to pay the bet. If you win the weekly bet, you have to buy stocks or bonds.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by rkhusky » Wed Oct 10, 2018 4:20 pm

I choose (b) no effect, especially in the limit that the portfolio value is much greater than the size of the bet.

If you consider the two portfolios in combination, then there is no real effect from moving money back and forth between the two portfolios. The effect on the two players is symmetric, so neither player will realize an advantage on average.

If I had two similar accounts at Vanguard, I don't see how I could change risk or return of either of the accounts by moving $1000/week between the two accounts based on a coin flip.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by Oicuryy » Wed Oct 10, 2018 5:41 pm

My answer is b) no effect.

You have a contract with your friend. The contract cost you nothing. It has an expected value of zero. It will not come due and be settled for at least twenty years.

I calculate that there is only about a 6% chance that you will end up owing, or winning, more than $25,000. (But don't trust my calculations.)

Enjoy your weekly get-together with your friend. But don't expect this contract to make any difference in your retirement savings.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by bgf » Wed Oct 10, 2018 6:20 pm

rkhusky wrote:
Wed Oct 10, 2018 4:15 pm
bgf wrote:
Wed Oct 10, 2018 12:21 pm
in the OP, there was no mention of rebalancing. in the clarification post, the rebalancing refers to within the 60-40 split, performed monthly. this is why I specifically stated that the investor had to choose and set aside an amount, at the outset, sufficient to cover the back and forth payments for the coin flips.
The OP does not mention a cash account. Therefore, if you lose a weekly bet, you have to withdraw stocks or bonds to pay the bet. If you win the weekly bet, you have to buy stocks or bonds.
that is never mentioned either.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by nisiprius » Wed Oct 10, 2018 7:45 pm

rkhusky wrote:
Wed Oct 10, 2018 4:15 pm
...The OP does not mention a cash account. Therefore, if you lose a weekly bet, you have to withdraw stocks or bonds to pay the bet. If you win the weekly bet, you have to buy stocks or bonds...
Something like this is a good exercise in the difficulty of formulating a precise questions.

Yes, as I'd conceived it, neither participant is in cash for very long. The bet is settled quickly. The loser sells $1,000 worth of portfolio assets, proportionately to allocation, and instantly conveys it to the winner, who buys $1,000 of portfolio assets, proportionately to allocation. Both hold the same portfolio composition. Settling the bet makes change at all in the combined portfolio. The loser owns a smaller percentage of the combined portfolio than before, the winner owns a larger percentage. If you imagine they each start with equal amounts of VBINX (60/40 balanced index), worth exactly $100,000 at the time of the bet, then after the bet is settled one of them owns $99,000 worth of VBINX and the other owns $101,000 worth.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by rnitz » Wed Oct 10, 2018 7:57 pm

This is an easy one. The answer is C. I don't need to know any statistics, math, finance, or other factors. I only need to have read Nisiprius posts for the last 10 years to know this is driving one of his points about how, unless it adds value, that adding randomness can't be improving your situation (unless you're dithering a signal :) ).

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by bgf » Wed Oct 10, 2018 8:13 pm

nisiprius wrote:
Wed Oct 10, 2018 7:45 pm
rkhusky wrote:
Wed Oct 10, 2018 4:15 pm
...The OP does not mention a cash account. Therefore, if you lose a weekly bet, you have to withdraw stocks or bonds to pay the bet. If you win the weekly bet, you have to buy stocks or bonds...
Something like this is a good exercise in the difficulty of formulating a precise questions.

Yes, as I'd conceived it, neither participant is in cash for very long. The bet is settled quickly. The loser sells $1,000 worth of portfolio assets, proportionately to allocation, and instantly conveys it to the winner, who buys $1,000 of portfolio assets, proportionately to allocation. Both hold the same portfolio composition. Settling the bet makes change at all in the combined portfolio. The loser owns a smaller percentage of the combined portfolio than before, the winner owns a larger percentage. If you imagine they each start with equal amounts of VBINX (60/40 balanced index), worth exactly $100,000 at the time of the bet, then after the bet is settled one of them owns $99,000 worth of VBINX and the other owns $101,000 worth.
sounds like something one could very easily program and model, running 10000 trials and telling us the breakdown.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by stlutz » Wed Oct 10, 2018 8:30 pm

If you're talking expectations, the answer would be (a). The coin flip either slightly increases or decreases your return and it and reduces your standard deviation. Result is that you end up with a higher Sharpe ratio.

If you're talking actual returns, it completely depends, as your expected zero return asset could lose a lot of money (i.e. the coin flip comes up wrong a lot) which hurts your overall returns and Sharpe ratio. The reverse can happen as well.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by longinvest » Wed Oct 10, 2018 8:49 pm

Let's consider portfolio returns.

We know that both friends have their portfolio invested in the same allocation; the time-weighted returns* of their portfolios will be identical. I am, of course, assuming that all of the money is invested in the market at all time, never lying aside as cash. I'll explain how, below.

* Time-weighted returns are, by definition, unaffected by buy and sell transactions. They are the returns of the underlying market.

Now, let me simplify things further. Let's assume that both investors own the entire market. Maybe the market is a single company with N shares. At the beginning, both investors own N/2 shares. Every week, the loser gives $1000 in shares to the winner. (No cash lying around in the portfolio, see?)

Now, you see me coming. There will be a transaction cost. Both will pay it to a third party (for accounting). So, the collective returns, earned by both friends, will be lower than that of the entire market, because it will be equal to the market return minus the fees** to transact the weekly $1,000.

** They'll have to pay the fees from their own pockets; the fee payments are portfolio contributions that are immediately lost as fees. No share is created or destroyed, nor sold to a third party.

As for the money-weighted returns of each of the two friends, it might be higher, equal, or lower than their collective after-fee returns, but the outperformance of one friend can only come at the expense of an underperformance of the other. It cannot be otherwise.

OK, I know, I haven't answered the initial question (a, b, or c), as I have no idea what the OP means by diversification and risk. Both words have many definitions. I don't care. All I care about is that this game is collectively costly to both. They would collectively do better not to play it.

P.S. Readers interested to learn more about time-weighted and money-weighted returns, and how to calculate their personal returns, can read our wiki's Calculating personal returns page.
P.P.S. My answer was inspired by William Sharpe's theorem: The Arithmetic of Active Management.
Last edited by longinvest on Thu Oct 11, 2018 10:38 pm, edited 3 times in total.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by AlphaLess » Wed Oct 10, 2018 9:52 pm

PaulF wrote:
Wed Oct 10, 2018 8:32 am
AlphaLess wrote:
Tue Oct 09, 2018 11:16 pm

- it is known that the total dollar value of the checks that Warren might write to you is strictly lower than the total value of checks that you write to Warren.
But why add this condition? I was with you right up until that point.
Easy! Because Warren is making money.
Put another way: if Warren stops making money, he will jack up your insurance rates.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by AlphaLess » Wed Oct 10, 2018 9:57 pm

afan wrote:
Wed Oct 10, 2018 9:30 am
PaulF wrote:
Wed Oct 10, 2018 8:32 am
AlphaLess wrote:
Tue Oct 09, 2018 11:16 pm

- it is known that the total dollar value of the checks that Warren might write to you is strictly lower than the total value of checks that you write to Warren.
But why add this condition? I was with you right up until that point.
This condition is not true of insurance. For a company to be profitable it is not even necessary that the total of all premiums collected exceeds all benefits paid out. Insurance companies invest the premiums and expect to earn a positive return. They know that MOST policies will pay more in premiums than they collect in benefits. For SOME policies the totals will be close. For a small number of policies the payout will exceed all premiums by a large amount.

The company is betting they estimated the risks and priced the policy such that the line is profitable over all.
I respectfully disagree. If insurance company can invest it, so can you.
I made a simplifying assumption to separate the mechanism of insurance from the mechanism of investments earning returns.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by AlphaLess » Wed Oct 10, 2018 9:59 pm

triceratop wrote:
Wed Oct 10, 2018 12:49 am
AlphaLess wrote:
Tue Oct 09, 2018 11:16 pm
Do you play this game with Warren?
Yes: my Uncle, let's call him "Sam", told me to. Persuasive fellow.
Are you sure it is Uncle Sam, and not Uncle Harris(burg) of the Pennsylvania fame?

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by triceratop » Wed Oct 10, 2018 10:16 pm

AlphaLess wrote:
Wed Oct 10, 2018 9:59 pm
triceratop wrote:
Wed Oct 10, 2018 12:49 am
AlphaLess wrote:
Tue Oct 09, 2018 11:16 pm
Do you play this game with Warren?
Yes: my Uncle, let's call him "Sam", told me to. Persuasive fellow.
Are you sure it is Uncle Sam, and not Uncle Harris(burg) of the Pennsylvania fame?
It's a strange abbreviation -- Uncle Sa(cre)m(ento).
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by PaulF » Thu Oct 11, 2018 7:05 am

AlphaLess wrote:
Wed Oct 10, 2018 9:52 pm
PaulF wrote:
Wed Oct 10, 2018 8:32 am
AlphaLess wrote:
Tue Oct 09, 2018 11:16 pm

- it is known that the total dollar value of the checks that Warren might write to you is strictly lower than the total value of checks that you write to Warren.
But why add this condition? I was with you right up until that point.
Easy! Because Warren is making money.
Put another way: if Warren stops making money, he will jack up your insurance rates.
I don't think you are correctly stating how insurance works. In aggregate, Warren will make money. Whether an individual gets more or less from Warren than the individual puts in can vary.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by randomizer » Thu Oct 11, 2018 7:10 am

If it's not inflation adjusted, then I guess I won't really care 20 years from now anyway.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by AlphaLess » Thu Oct 11, 2018 8:38 am

PaulF wrote:
Thu Oct 11, 2018 7:05 am
AlphaLess wrote:
Wed Oct 10, 2018 9:52 pm
PaulF wrote:
Wed Oct 10, 2018 8:32 am
AlphaLess wrote:
Tue Oct 09, 2018 11:16 pm

- it is known that the total dollar value of the checks that Warren might write to you is strictly lower than the total value of checks that you write to Warren.
But why add this condition? I was with you right up until that point.
Easy! Because Warren is making money.
Put another way: if Warren stops making money, he will jack up your insurance rates.
I don't think you are correctly stating how insurance works. In aggregate, Warren will make money. Whether an individual gets more or less from Warren than the individual puts in can vary.
Ex-post, sure, some individuals will make money.
Ex-ante, you need to take expectations.
In expectation, a typical customer will LOSE money.

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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by David Jay » Thu Oct 11, 2018 8:49 am

AlphaLess wrote:
Thu Oct 11, 2018 8:38 am
In expectation, a typical customer will LOSE money.
And gladly, in most cases.

Can you imagine "improving your return"? I'll schedule a major accident every year so the insurance company doesn't "make money" off of me.
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Re: Diversifying with a zero-correlation, zero-return volatile asset

Post by bgf » Thu Oct 11, 2018 9:06 am

David Jay wrote:
Thu Oct 11, 2018 8:49 am
AlphaLess wrote:
Thu Oct 11, 2018 8:38 am
In expectation, a typical customer will LOSE money.
And gladly, in most cases.

Can you imagine "improving your return"? I'll schedule a major accident every year so the insurance company doesn't "make money" off of me.
insurance underwriting is not as profitable as many make it seem on this board. it is highly competitive, low barrier to entry, and a consistently profitable underwriter is a rare thing.

https://www.naic.org/documents/topic_in ... eports.pdf

https://www.valuepenguin.com/2017/05/au ... ikely-2018

look to the combined ratio metric. under 100% means underwriting was profitable for the period. over 100% means that they actually lost money on the underwriting operations.

it takes a lot of discipline for an underwriter to issue fewer policies when they don't think the premiums compensate the risk. this leads to a shrinking of the float which is where the majority of the value of an insurance operation is derived.

i own shares in both Markel and Berkshire Hathaway. Their insurance operations, while not always, are consistently profitable. They've managed this while consistently growing their written premiums and float. most can't do this.

i say this only because i often see posts that make it seem like the insurer is screwing over their insureds. in many years, the insurer actually loses money to its insureds, in the aggregate.
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