Solution
Rs. lakhs

Portfolio Value as on 31.12.1991 28.50
Portfolio value as on 01.01.1991 25.00

Appreciation in value 3.50
Add interest and dividends withdrawn for
Personal use 1.50
Capital withdrawn for house construction 5.00

Total Return Earned 10.00

Percentage Return = 10.00/25.00 = 40%

The actual return has to be evaluated by comparison to a benchmark taking risk into
account. The benchmark rate of return is that of the market as a whole which represents
the average performance of all investors taken together. Superior performance then
means performing better than the market index after adjusting for risk. The different
methods of evaluating portfolio performance that we shall discuss below differ mainly in
the method used for adjusting for risk.

The total risk of a portfolio is measured by the variance or the standard deviation. We
have seen earlier in this book that this total risk can be broken up into systematic risk and
unsystematic risk. The unsystematic risk can be eliminated by holding a diversified
portfolio. On the other hand, the systematic risk measured by the beta cannot be
diversified away because it represents the vulnerability to market fluctuations.

Reward per Unit of Risk

One natural way of adjusting for risk is to look at the reward per unit of risk. This was
exactly what Sharpe and Treynor proposed in their pioneering work on evaluation of
portfolio performance. But, while Sharp chose the standard deviation (total risk) as the
measure of risk, Treynor used the beta (systematic risk) as his measure of risk.

We know that the risk-free rate of interest is the return that we can earn without bearing
any risk. The risk premium is the return earned over and above the risk-free rate and is
the reward earned for bearing risk. We can, therefore, divide the risk premium by a
measure of risk to get the risk premium per unit of risk. The higher this ratio, the better
the portfolio has done; if we compute the performance measure for a number of
portfolios, we can rank these portfolios according to their performance. The Sharpe and