Better Than Sharpe

[nodoodahs]

The Sharpe ratio has four big problems. First, it penalizes upside volatility equally to downside volatility. Second, it ignores higher moments of the distribution. Third, it is extremely sensitive to the ratio of standard deviation to the average return, which, in practice, tends to prefer low-standard-deviation, low-return strategies, which exacerbates the second point. Fourth and final, it ignores the compounding rate of the return stream.

Assume the risk-free rate is 4% and you are evaluating three return streams, A, B, and C.

A has an average of 20% and a standard deviation of 10%.
B has an average of 10% and a standard deviation of 5%.
C has an average of 25% and a standard deviation of 25%.

A has a Sharpe ratio of 1.60.
B has a Sharpe ratio of 1.20.
C has a Sharpe ratio of 0.84.

The problem is that their compounding rates are wildly different!

A will compound at about 19.5%.
B will compound at about 9.9%.
C will compound at about 22.0%.

Which of these gives you the better return over the risk-free rate?

Sharpe would say the ranking is A, B, C.

I would consider that a better ranking would be C, A, and B, with C and A almost equivalent, and B being by far the worst return stream.

The ranking should be based on something Better Than Sharpe (BTS). BTS = the compounding rate above and beyond the risk-free rate.

Annual compounding can be estimated as the average annual return minus the one-half of the variance of the annual return. If done on a monthly timeframe, this would be 12 times the monthly average minus six times the monthly variance.

Then just subtract the risk-free rate and you have a metric that is BTS (Better Than Sharpe).
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I haven’t seen a beatin’ like that since somebody stuck a banana in my pants and turned a monkey loose.

[nodoodahs]

I find it sad that matching the return of an index while reducing the vol level is preferred to accepting the vol level of that index and proceeding to out-perform it by a large margin.
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I haven’t seen a beatin’ like that since somebody stuck a banana in my pants and turned a monkey loose.

[rffrydr]

Does alpha hide in spikes? Does anybody in money management care?

The "Sharpe Ratio" was just one more symptom of "The Greed Born of Fear" bull run.

Matching an index with less volatility than that index is what it's all about these days. That led to some funny expressions in "value" funds back at the 2000 spinner, loaded up with Cisco and AOL.

Funny what doesn't matter.
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Today is the Tomorrow you worried about Yesterday!