Taking Short-Term Risk for Long-Term Reward

Here’s an interesting passage from David Aldous’ review of The Black Swan. Aldous is a stats professor at Berkeley.

I am always puzzled that writers on financial mathematics (Taleb included) tend to ignore what strikes me as the most important insight that mathematics provides. Common sense and standard advice correctly emphasize a trade-off between short term risk and long term reward, but implicitly suggest this spectrum goes on forever. But it doesn’t. At least, if one could predict probabilities accurately, there is a “Kelly strategy” which optimizes long-term return while carrying a very specific (high but not infinite) level of short term risk, given by the remarkable formula

with chance 50% [or 25% or 10%] your portfolio value will sometime drop below 50% [or 25% or 10%] of its initial value.

Now actual stock markets are less volatile, and consequently the best (fixed, simple) investment strategy for a U.S. investor over the last 50 years has been to invest about 140% of their net financial assets in stocks (by borrowing money). It is easy to say [p. 61] The sources of Black Swans today have multiplied beyond measurability and imply this is a source of increased market volatility, but it is equally plausible or implausible to conjecture that mathematically-based speculative activity is pushing the stock market toward the “Kelly” level of volatility.

Here’s what he means by a “Kelly strategy.”

Posted by on May 11th, 2014 at 8:08 pm


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