PORTFOLIO EVALUATION
Portfolio evaluation is the process of measuring and comparing the returns (actually) earned on a
portfolio with the returns (estimates) for a benchmark portfolio. In other words, the portfolio
evaluation identifies whether the performance of a portfolio has been superior or inferior to other
portfolios. It may be noted that the returns of the portfolio includes both the capital gain and the
revenue income.
MEASURES OF PORTFOLIO PERFORMANCE
There are several measures suggested for evaluation of portfolio performance. Some of these are
based on pure returns.
I. Return per unit of Risk: An obvious way to look at the performance of the
portfolio is to find out the reward per unit of risk undertaken. A risk-free security
earns only risk-free return. However, the return earned over and above the risk-free
security is the risk-premium and is earned for bearing risk. The risk-premium may be
divided by the risk factor to find out the reward per unit of risk undertaken. This is
also known as reward to risk ratio. There are two method of measuring reward to
risk ratio as follows:
(a). Sharpe Ratio: This ratio is also called Reward to variability Ratio. In this ratio,
the risk is measured in terms of standard deviation. The ratio is:
I
R p – RF
Sharpe Ratio = -----------------
σp
In this ratio, σp is the standard deviation of the portfolio and shows total risk
of the portfolio. The Sharpe Index measures the risk premium of the portfolio
relative to the total amount of risk in the portfolio. The index measures the
slope of the risk-return line. The Sharpe Index helps summarizing the risk
and return of a portfolio in a single measure that categorises the performance
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on risk adjusted basis. The larger the index value, the better the portfolio has
performed.
(b). Treynor Ratio: This ratio is called Reward to Volatility Ratio. In this
ratio, the risk is measured by the β of the portfolio. The ratio is:
I
R p – RF
Treynor Ratio = -----------------
βp
In this equation, β p is the β of the portfolio. The Treynor Index
measures the risk premium of the portfolio where the risk
premium is the difference between the return and the risk-free
rate. The risk premium is related to the amount of systematic risk
present in the portfolio.
It may be noted that the numerator in both the Sharpe ratio and
Treynor Ratio is same i.e., the risk premium. However the two
differ with respect to the denominator. In Sharpe Ratio, the risk is
measured by σ (i.e., total risk), while in case of Treynor Ratio, the
risk is measured by β (i.e., the systematic risk). The β measure
assumes that the portfolio is well diversified and there is no
remaining diversifiable risk, however, Sharpe Ratio considers the
total risk. It assumes that if the portfolio is not well diversified,
then the portfolio return be adjusted for diversifiable risk also. So,
the Sharpe Ratio adjusts the portfolio return for adjusted as well
as unsystematic risk.
If the portfolio is well diversified, Treynor Ratio is appropriate for
evaluating the performance of a portfolio. However if the portfolio
is not well diversified, Sharpe Ratio should be used.
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II. Differential Returns: Michael Jensen has developed another
method for evaluation of performance of a portfolio. This
measure is based on differential returns and is known as
Jensen’s Ratio or Jensen’s Index. The Jenson’s Ratio measures
the difference between the actual return of a portfolio and
expected return of a portfolio in view of the risk of the portfolio.
It is n\based on the CAPM where
RS = IRF + (RM – IRF) β
CAPM gives the expected return of security or a portfolio in view of its
β, i.e., its systematic risk. The differential return gives an indication, how
well the portfolio has performed. The differential return is Alpha factor
and is stated as αp as follows:
αp = R p – Exp. Return of the portfolio
If αp is positive, it shows that the portfolio has performed better and it
has out-performed the market. If the αp negative, it means that the
portfolio has underperformed as compared to the market. If αp is zero,
it indicated that the portfolio has just performed what it is expected to.
In this case, the expected return and the actual return of the portfolio ,
both would be on the SML. Jensen’s measures, α is based on the
systematic risk and requires β and SML. It measures the distance
between the portfolio return and the SML. For example, the risk-free
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rate is 8% and the market return RM is 14%. Portfolio X has a β of 1.2
and Portfolio Y has a β of 0.5. The actual returns of these two
portfolios are 13% and 12% respectively. Jensen’s Index for these
portfolios can be measured as follows:
Expected return as per CAPM
Portfolio X = .8 + (.14 - .08) 1.2
= 15.2%
Portfolio Y = .08 + ( .14- .08) .5
= 11%
Jensen’s Ratio:
α x = R p – Exp. Return of a portfolio
= ( 13% - 15.2%)
= - 2.2%
α y = R p – Exp. Return of a portfolio
= ( 12% - 11%)
= 1%
Portfolio x has a negative α. It means that its performance is less
than what it should be in view of its risk. The α of portfolio Y is
positive which means that is performance is better than
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what it should be in view of its risk. So Portfolio Y is better
managed than Portfolio X. It may be noted that the
Treynor and Sharpe indices provide measures of relative
performance of portfolios on a risk-adjusted basis. Jenson’s
index attempts to construct a measures of absolute
performance.
