Overview of Performance Metrics

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Performance Metrics Classes Performance Metrics Example

Performance Metrics Classes

Sharpe first proposed a ratio of excess return to total risk as an investment performance metric. Subsequent work by Sharpe, Lintner, and Mossin extended these ideas to entire asset markets in what is called the Capital Asset Pricing Model (CAPM). Since the development of the CAPM, a variety of investment performance metrics has evolved.

This chapter presents four classes of investment performance metrics:

• The first class of metrics are absolute investment performance metrics that are called "classic" metrics since they are based on the CAPM. They include the Sharpe ratio, the information ratio, and tracking error. To compute the Sharpe ratio from data, use the function sharpe to calculate the ratio for one or more asset return series. To compute the information ratio and associated tracking error, use the function inforatio to calculate these quantities for one or more asset return series.

• The second class of metrics are relative investment performance metrics to compute risk-adjusted returns. These metrics are also based on the CAPM and include Beta, Jensen's Alpha, the Security Market Line (SML), Modigliani and Modigliani Risk-Adjusted Return, and the Graham-Harvey measures. To calculate risk-adjusted alpha and return, use portalpha.

• The third class of metrics are alternative investment performance metrics based on lower partial moments. To calculate lower partial moments, use the functions lpm for sample lower partial moments and elpm for expected lower partial moments.

• The fourth class of metrics are performance metrics based on maximum drawdown and expected maximum drawdown. To calculate maximum or expected maximum drawdowns, use the functions maxdrawdown and emaxdrawdown.

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Performance Metrics Example

To illustrate the functions for investment performance metrics, you will work with three financial time series objects using performance data for:

• An actively managed, large-cap value mutual fund

• A large-cap market index

• 90-day Treasury bills

The data is monthly total return prices that cover a span of 5 years.

The following plot illustrates the performance of each series in terms of total returns to an initial $1 invested at the start of this 5-year period:

load FundMarketCash
plot(TestData)
hold all
title('\bfFive-Year Total Return Performance');
legend('Fund','Market','Cash','Location','SouthEast');
hold off

The mean (Mean) and standard deviation (Sigma) of returns for each series are

Returns = tick2ret(TestData);
Assets
Mean = mean(Returns)
Sigma = std(Returns, 1)

which gives the following result:

Assets = 
    'Fund'    'Market'    'Cash'
Mean =
    0.0038    0.0030    0.0017
Sigma =
    0.0229    0.0389    0.0009

In this chapter, you will work with this data to demonstrate that the example fund has done well in absolute, relative, and risk-adjusted terms with respect to the investment performance metrics.

Note   Functions for investment performance metrics use total return price and total returns. To convert between total return price and total returns, use ret2tick and tick2ret.

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Investment Performance Metrics

Using the Sharpe Ratio

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