Question

3. 26% 20:29 Today 19:16 Edit 02 (a) Using the relevant formulas and diagrams, distinguish between the following performance measures: (1) Jensen's alpha and (ii) Sharpe measure; (ii) Treynor measure (10 marks)

Answer 1

Jensons Alpha is the excess return the portfolio provides over and above the theoretical return calculated as per CAPM (capital asset pricing model). It is represented as:

Jensons Alphs = Rp- R(Ex)

Rp= Portfolio return

R(Ex)= Expected return of portfolio as per CAPM

Thus Jensons Alpha = Rp- (Rf +  β(Rm-Rf))

Where Rf= Risk free rate

Rm= Return on market

  β= measure of relative volatility of stock/portfolio relative to market. Thus beta greater than 1 means it's more volatile than market and if less than 1, it's less volatile when compared to market.

Sharpe ratio is the return in excess of the risk free rate per unit of total risk of portfolio which is represented by the volatility of the portfolio.

Thus Sharpe ratio = ( Rp-Rf )/σ p

Where Rp= Return of portfolio

Rf= Risk free rate

σ p= Standard deviation of portfolio which is the measure of volatility in returns used to represent the total risk of portfolio.

Treynor ratio is similar to Sharpe ratio and measures the return in excess of the risk free rate per unit of risk of the portfolio but the risk here is the systematic risk of the portfolio represented as beta β of the portfolio (unlike Sharpe ratio where the risk is the total risk including systematic and nonsystematic represented as standard deviation of portfolio)

Thus treynor ratio = ( Rp-Rf )/β

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