Sharpe Single Index Model:Portfolio Optimisation maximise return -given risk level

This model assumes that the one macroeconomic factor that causes systematic risk affecting all stock returns can be represented by the rate of return on a market index e.g. the FTSE 100. This relationship is considered to be linear. This differs fundamentally from the Markowitz Model, which requires rigorous analysis to calculate expected returns,variance, standard deviation and covariance of each individual security to every other security in the portfolio. The advantages are clear. The need to construct matrix calculation models is avoided and, in theory at least, all regularly traded securities with relatively large volumes will be represented.The return on any share can be itemised into the expected excess return of an individual firm , represented by its Alpha coefficient,the return on macroeconomic events and unexpected microeconomic events that affect that particular firm.

This exposition goes through the solver procedure required to maximise return for a given level of risk using the solver tool. Image One shows the situation after solver has been run and a solution arrived at. After completion of the procedure we have a variance of 0.000456802 and a level of return of -0.025607152. Image Three shows the original state of the model, with each share allocation being set at 20%. We can see that after solver 97.77% of the portfolio is alocated to Vodafone. Clearly we may not choose to implement this particular portfolio because of the low level of return in relation to variance (Risk Level)

Image One

 

Image Two

 

 

Image Three