Tracking your portfolio
Another amazing insight from fooled by randomness. The essence of this is that if you are a passive investor, the more often you track your portfolio, the more your headache. Suppose you have invested in a portfolio where the expected annual return is R%, and the volatility is V%. The insight is that the more often you track your portfolio, the likelihood of the portfolio delivering a positive return between two observations falls extremely quickly.
In the example, given in the book, Taleb takes R to be 15% and V to be 10%. Note that on an annual basis, you are extremely unlikely to lose money on this. Taleb presents the following table in the book (not exactly; i remember bits of it and reconstructed it)
| Mean | 15% | ? | ? | ? | ? |
| S.D | 10% | ? | ? | ? | ? |
| ? | ? | ? | ? | ? | ? |
| Period | Multiple | Mean | S.D | Prob(-ve return) | Prob(return >0) |
| ? | ? | ? | ? | ? | ? |
| 1 year | 1 | 15.00% | 10.00% | 6.68% | 93.32% |
| 1 month | 12 | 1.25% | 2.89% | 33.25% | 66.75% |
| 1 week | 52 | 0.29% | 1.39% | 41.76% | 58.24% |
| 1 day | 365 | 0.04% | 0.52% | 46.87% | 53.13% |
| 1 hour | 8760 | 0.00% | 0.11% | 49.36% | 50.64% |
Note that although you are assured of making money in the “long term”, if you track the portfolio every hour, or even every day, the probability that you are disappointed is almost half!
Let me make a small change to the situation. Let me decrease the volatility to 2%. Now, over the long term, it’s guaranteed that you’ll make money. The table changes to:
| Mean | 15% | ? | ? | ? | ? |
| S.D | 2% | ? | ? | ? | ? |
| ? | ? | ? | ? | ? | ? |
| Period | Multiple | Mean | S.D | Prob(-ve return) | Prob(return >0) |
| ? | ? | ? | ? | ? | ? |
| 1 year | 1 | 15.00% | 2.00% | 0.00% | 100.00% |
| 1 month | 12 | 1.25% | 0.58% | 1.52% | 98.48% |
| 1 week | 52 | 0.29% | 0.28% | 14.92% | 85.08% |
| 1 day | 365 | 0.04% | 0.10% | 34.73% | 65.27% |
| 1 hour | 8760 | 0.00% | 0.02% | 46.81% | 53.19% |
Despite this “extremely strong” portfolio, if you look at it daily, you have a 35% chance of getting disappointed!
The main point to note here is that mean drops proportionally to the time. So the 1 month expected return is 1/12 of the annual expected return. However, standard deviation doesn’t behave the same way. If we assume returns in different time periods are independent (this is a fair assumption), it’s the variance that varies proportionally. Hence the standard variation drops only by a factor of the square root of the ratio of time periods.
So if you think you are a long term investor, don’t check that portfolio too often!
PS
If you want to play around with the numbers, I can send you the excel sheet. Mail me at skthewimp AT yahoo DOT com
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October 31st, 2009 at 11:38 am