Optimising Asset Allocation by
Maximising the Sharpe Ratio
Samir Khan
Adept Scientific plc
Introduction
The Sharpe ratio quantifies how effectively a portfolio of risky assets utilises risk to maximise return. It is defined as follows.
The expected portfolio return is predicted from historic data, the standard deviation of the asset mix is traditionally used as a proxy for risk (or volatility) and the risk free return is the return that can be expected from a zero-risk investment (i.e. the interest on US Treasury Bills or the redemption yield on UK gilts). A higher Sharpe Ratio essentially signifies a more risk efficient portfolio.
This application calculates the optimum asset mix for a portfolio of stocks by maximising its Sharpe ratio.
Historic Returns and other Data
Number of stocks in the portfolio
The following vectors contain historic returns of the stocks over 12 time periods.
The risk free return.
Sharpe Ratio and Investment Constraints
Define a vector that contains the mean returns.
Define the covariance matrix.
For the three stocks under consideration the Sharpe ratio is defined as follows, where the arguments to the function is the fraction of capital invested in each stock.
Additionally, the fraction of capital invested in each stock must add up to 1.
The Sharpe Ratio is now maximised with respect to the constraint.
Hence the optimised portfolio contains the three stocks in the following fractions.
This asset mix has a Sharpe Ratio of
A value of 1 or higher is traditionally regarded as good while a value over 2 is considered very good.
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