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Overview of Performance Metrics

Performance Metrics Types

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 section presents four type of investment performance metrics:

  • The first type 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 sharpe to calculate the ratio for one or more asset return series. To compute the information ratio and associated tracking error, use inforatio to calculate these quantities for one or more asset return series.

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

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

Performance Metrics

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

    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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