Sharpe ratio

The Sharpe ratio compares the return on a portfolio to the risk on a benchmark. It is:

d/σd where d = rp - rb

where rp is the return on a portfolio and
rb is the return on a benchmark
d is called the relative return and
σd is the standard deviation of d.

A very simple case of this is where the benchmark is a risk free investment, in which case the Sharpe ratio is the excess return on the portfolio divided by the standard deviation of the return on the portfolio.

The Sharpe ratio is interesting because it is a measure of the relationship between risk and return, a concept that is central to financial theory. It can be applied to both ex-ante (expected) returns (to assess an investment) and to ex-poste (historical) returns (to test the relationship between risk and reward).

One useful property of the Sharpe ratio is that the Sharpe ratio of a portfolio does not depend on the time over which it is measured. It will change with time period depending on the actual historic data, but there is no correlation between the Sharpe ratio and the length of time period. This is because the return and the standard deviation both increase with time. Sharpe ratios calculated over different periods of time are directly comparable.

The best source for further information is William F Sharpe's website, and this paper on the Sharpe ratio in particular.

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