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Risk, Reward, Coin Flipping
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Years ago, I started asking questions that seemed like gambling to help understand how others viewed risk. I would ask, "If I offered you the chance to flip a fair coin, but I'd put up $2 and you'd only have to put up $1, would you play?" And then the follow on questions had to do with how much money and the nature of the bets, e.g. one taker said he'd like to bring $100, but make $10 bets, figuring that was the fastest path to wealth. As long as he won 1/3 of the flips, he'd at least break even.
I spent some more time tinkering with this idea, until I read "The Intelligent Asset Allocator" by William Bernstein who introduced the spin on this which was for me the 'missing link'. Instead of having a coin flip represent a gain of $2 or loss of $1, he suggests the gain as return of 30% and loss of 10%.
This was the difference between a purely hypothetical question, and something that more accurately reflect the stock market.
Let's look at the outcomes for one coin;
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| H |
.9 |
| T |
1.3 |
| Ave |
1.1 |
| STD |
.283 |
| Annualized Ret |
1.082 |
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| So far, so good, or "so what?" you may say. First, note that while the average of .9 and 1.3 is 1.1, if you have these returns one year after the next, your annual return is (1.3*.9)^.5 = 1.082, only 8.2%/year. But look what happens by "splitting the bet", half your money on one coin, then half on the next; |
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What do we gain by flipping two coins? If both show heads, or both tails, the result is still -10% or +30%, but in the two cases where there are both a head and tail, the return is +10%. The chance of loss has gone from 50% to 25%, the Standard Deviation of returns (risk) dropped, and the annualized return has gone up.
Continued |
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| H |
H |
.9 |
| H |
T |
1.1 |
| T |
H |
1.1 |
| T |
T |
1.3 |
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Ave |
1.1 |
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STD |
.163 |
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Ann |
1.091 |
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