Page 326 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 13: Portfolio Performance Evaluation

Where, Notes
r p = Expected portfolio return
r = Risk free rate
f
= Portfolio standard deviation
p
The Sharpe ratio tells us whether the returns of a portfolio are due to smart investment decisions
or a result of excess risk. This measurement is very useful because although one portfolio or
fund can reap higher returns than its peers, it is only a good investment if those higher returns
do not come with too much additional risk. The greater a portfolio’s Sharpe ratio, the better its
risk-adjusted performance will be.
A variation of the Sharpe ratio is the Sortino ratio, which removes the effects of upward price
movements on standard deviation to instead measure only the return against downward price
volatility.

Example: Consider two portfolios A and B. On the basis of information given below,
compare the performance of portfolios A and B.

Portfolio Return Risk-free Excess Portfolio risk
I (R M) rate (R F) return (R F – R M) (SD)
A 21 8 13 10
B 17 8 9 8

Solution:
A = 13/10 = 1.3
B = 9/8 = 1.125
Reward per unit of risk in case of Portfolio A is relatively higher. Hence its performance is said
to be good.

Treynor Portfolio Performance Measure (aka: reward to volatility ratio)

This measure was developed by Jack Treynor in 1965. Treynor (helped developed CAPM) argues
that, using the characteristic line, one can determine the relationship between a security and the
market. Deviations from the characteristic line (unique returns) should cancel out if you have a
fully diversified portfolio.
Treynor’s Composite Performance Measure: He was interested in a performance measure that
would apply to all investors regardless of their risk preferences. He argued that investors would
prefer a CML with a higher slope (as it would place them on a higher utility curve). The slope of
this portfolio possibility line is:
R M R F
T =
i
1
Where, R = Market Return
RFR = Risk Free return, and

= SD
1
A larger T value indicates a larger slope and a better portfolio for all investors regardless of
i
their risk preferences. The numerator represents the risk premium and the denominator represents
the risk of the portfolio; thus the value, T, represents the portfolio’s return per unit of systematic
risk. All risk-averse investors would want to maximize this value.

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