Investment Theory and Portfolio Development - Performance Measures

These adjust portfolio performance for risk. The higher the ratio, the more that the performance is worth the risk, ceteris paribus. An understanding of their inputs and the differences between the metrics is critical.

Performance measurement is important in the ongoing evaluation of client portfolios and circumstances. Know these ratios:

  1. Sharpe Ratio - measures the average return on a portfolio minus the average return on a risk free asset (the difference being the excess return over the risk free asset) divided by the standard deviation of the portfolio. The ratio measures the risk-adjusted performance of a portfolio or the extra reward received for the extra risk assumed. The formula appears below.


    Sp=Rp-Rf/σ


    where Sp= the risk-adjusted portfolio return, Rp= the portfolio return in excess of the risk-free rate, Rf= the risk-free rate and σ=t he standard deviation of return on the portfolio.

    The limitations of the ratio are two. First, standard deviation as a risk measure is most appropriate for portfolio strategies with roughly symmetric return distributions. For portfolio strategies with asymmetric returns attributable to some form of optionality, the measure may be a less than accurate barometer of risk-adjusted
    performance. Second, negative Sharpe ratios will tend to increase with an increase in risk (e.g. from -1 to -.5), whereas with positive ratios, the increase in risk produces a lower number. With the negative ratio, one should not automatically infer better risk-adjusted performance. A longer evaluation period may be necessary, as well as the possible use of an alternative risk-adjusted return metric.
  2. Treynor Ratio - measures the average return on a portfolio, minus the average return on a risk free asset (the difference being the excess return over the risk free asset), divided by the beta of the portfolio. The ratio measures the risk-adjusted performance of a portfolio or the extra reward received for the extra risk assumed. The formula appears below:


    Tp=Rp-Rf/β


    where Tp= the risk-adjusted portfolio return, Rp= the portfolio return in excess of the risk-free rate, Rf= the risk-free rate and β= the beta of return on the portfolio.
  3. Jensen Ratio - is an absolute measure of performance, in contrast to the Sharpe and Treynor ratios which are relative measures. Stated below, the formula determines whether the portfolio adds alpha, the difference between the portfolio's actual return versus its expected return.


    ?p=Rp-{Rf+β(Rm-Rf)}

  4. Information Ratio - the ratio attempts to determine the ability of an investment manager to add return adjusted for risk. The formula is written as follows. Information Ratio=Average Excess Return (average of the difference between portfolio and benchmark returns)/Standard deviation of excess return. The ratio measures return and risk relative to a benchmark which the analyst needs to choose with care. Additionally, a sufficient number of time periods need to be chosen over which to observe the ratio. The ratio can be manipulated and a strong past information ratio is no guarantee of a similar one in the future.
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