Performance evaluation

Fund performance can be compared to some benchmark or target as a way of ranking and assessing that fund. This is obviously useful to an investor who may be considering whether to invest with this fund, and can also be used internally as way of monitoring fund manager performance.

Investment results need to account for both return and risk, previously we have measured these separately using for example the holding period return and standard deviation as general measures of return and risk. It is also possible to combine return and risk either by showing return as a ratio of risk or by adjusting the ‘raw’ return for risk to produce a risk adjusted return.

There are a wide range of different investment performance measures, five of the most common are described below. Two purely measure risk, standard deviation and drawdown, two are risk adjusted ratios; Sharpe and Treynor and finally Jensen’s alpha gives a risk adjusted return.

Standard deviation

This a measure of the weighted average deviation from the mean, giving an indication of the volatility of a stock price. This includes both movements above the mean as well as movements below the mean. Many investors would not classify stock returns in excess of the average as a ‘risk’ (called upside risk) and only consider returns below average (called downside risk). Broadly however stock returns are symmetrical about the mean therefore the size of downside and upside risk are similar therefore standard deviation should be a good measure of both total risk as well as downside risk.

Drawdown

This is the maximum amount of loss compared to the initial investment during the period of the investment. For example £1m is invested, at some point during the year the value falls to £800k and then increases to £1.1m at the end of the year. Although the annual return is 10% there was a 20% drawdown during the period of the investment. Although this is a simple measure of risk it is important because drawdowns have a major impact on the long run performance of a portfolio. For example a 20% drawdown requires a 25% increase to restore the value of the fund. This gap between the impact of losses and profits gets worse the larger the drawdown, so in the extreme a loss of 50% needs a subsequent gain of 100% to restore value.

Sharpe ratio

The risk premium i.e. the return in excess of the risk free rate divided by the total risk given by the standard deviation:

Treynor ratio

The risk premium divided by the systematic risk:

Jensen’s alpha

The capital asset pricing model estimates the return an investment is expected to give based on its level of systematic risk. Therefore any return in excess of this can be regarded as a good risk adjusted result; Jensen’s alpha is simply the calculation of this excess return:

Selecting the right performance measure

Different performance measurements are appropriate for different situations, usually it is better to use a number of different measures at the same time. However do not combine these measures into one figure as this is likely to be misleading. The following points are relevant when choosing which measure to use:

Drawdown is the simplest measure, whilst Jensen’s alpha is also easily understandable, i.e. a simple risk adjusted return percentage.

The Sharpe ratio is good when assessing a portfolio as lack of diversification is penalised due to the use of standard deviation.

When assessing a new investment however the risk compared to the broad market is important. Therefore the Treynor and Jensen calculation which use beta as the risk measure are better in this situation.

Using standard deviation to forecast performance

Stock returns approximately follow a normal distribution, this makes it easy to predict the probability of different performance results. On average 68% of results should be within one standard deviation of the mean…