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The ex-post Sharpe ratio uses the same equation as the one above but with realized returns of the asset and benchmark rather than expected returns; see the second example below. The information ratio is a generalization of the Sharpe ratio that uses as benchmark some other, typically risky index rather than using risk-free returns.
The Sharpe ratio is awkward to interpret when it is negative. Further, it is difficult to directly compare the Sharpe ratios of several investments. For example, what does it mean if one investment has a Sharpe ratio of 0.50 and another has a Sharpe ratio of −0.50? How much worse was the second portfolio than the first?
If at any time there is an investment that has a higher Sharpe ratio than another then that return is said to dominate. When there are two or more investments above the spectrum line, then the one with the highest Sharpe ratio is the most dominant one, even if the risk and return on that particular investment is lower than another.
When a risk-free asset is introduced, the half-line shown in the figure is the new efficient frontier. It is tangent to the hyperbola at the pure risky portfolio with the highest Sharpe ratio. Its vertical intercept represents a portfolio with 100% of holdings in the risk-free asset; the tangency with the hyperbola represents a portfolio with ...
Broadly speaking, in business enterprises, risk is traded off against benefit. RAROC is defined as the ratio of risk adjusted return to economic capital. The economic capital is the amount of money which is needed to secure the survival in a worst-case scenario, it is a buffer against unexpected shocks in market values.
The SFRatio has a striking similarity to the Sharpe ratio. Thus for normally distributed returns, Roy's Safety-first criterion—with the minimum acceptable return equal to the risk-free rate—provides the same conclusions about which portfolio to invest in as if we were picking the one with the maximum Sharpe ratio.
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