P

where:

Rp = average portfolio return

Rp= average risk-free rate

CTp = standard deviation of portfolio

Accounting for Performance

Portfolio performance can be compared against the benchmark portfolio using the Sharpe ratio. A portfolio Sharpe ratio higher than the benchmark ratio (if statistically significant) will offer evidence of superior performance. Statistical significance can be tested using the /■-statistic as follows:

MERp and MERB are mean excess returns of the portfolio, P, and the benchmark, B, respectively, and ap and aB are standard deviations of the total returns of P and B respectively. N is the number of observations (time periods).

A i-stat of two or greater would indicate presence of skill (and not luck) at a 95% confidence level. That is, the probability of achieving by chance the excess returns (per unit of total risk) on the portfolio greater than the excess returns (per unit of the total risk) on the benchmark is only 5%.

Accounting for Risk

The Sharpe ratio accounts for risk by incorporating the standard deviation of total returns in the denominator. As discussed earlier, Sharpe is a measure of excess returns per unit of risk, so a higher ratio offers evidence of better performance compared to a lower ratio.

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