Page 269 - DCOM304_INDIAN_FINANCIAL_SYSTEM

Indian Financial System

Notes In this expression,  m = 1.

Example: Assume that you are an administrator of a large pension fund (i.e. Terry
Teague of Boeing) and you are decide whether to renew your contracts with your three money
managers. You must measure how they have performed. Assume you have the following results
for each individual's performance: Market return 14%, Risk-free 8% and Beta 1.
Solution:
We can calculate the T values for each investment manager:

Tm (0.14-0.08)/1.00 = 0.06
TZ (0.12-0.08)/0.90 = 0.044
TB (0.16-0.08)/1.05 = 0.076
TY (0.18-0.08)/1.20 = 0.083

These results show that Z did not even "beat-the-market." Y had the best performance, and both
B and Y beat the market. [To find required return, the line is: 0.08 + 0.06(Beta)].
You can achieve a negative T value if you achieve very poor performance or very good
performance with low risk. For instance, if you had a positive beta portfolio but your return was
less than that of the risk-free rate (which implies you weren't adequately diversified or that the
market performed poorly) then you would have a (–) T value. If you have a negative beta
portfolio and you earn a return higher than the risk-free rate, then you would have a high T-
value. Negative T values can be confusing, thus you may be better off plotting the values on the
SML or using the CAPM [in this case, 0.08 + 0.06(Beta)] to calculate the required return and
compare it with the actual return. i.e. realised portfolio return (R ) in excess of risk-free rate (R )
p f
divided by the beta of the portfolio. Both these measures provide a way of ranking the relative
performance of various portfolios on a risk-adjusted basis. For investors whose portfolio is a
predominant representation in a particular asset class, the total variability of return as measured
by standard deviation is the relevant risk measure.

Example:
Fund Return Risk-free Rate Excess Return SD Beta
1 20 10 10 8 0.80
2 30 10 20 15 1.10
Calculate of Sharpe and Treynor ratios for two hypothetical funds.
Solution:

Sharpe Ratio Fund 1 = (20 – 10)/8 = 1.23
Sharpe Ratio Fund 2 = (30 – 10)/1.5 = 1.33
Treynor Ratio Fund1 = (20 – 10)/0.80 = 12.50

Treynor Ratio Fund 2 = (30 – 10)/1.10 = 18.18
The ranking on both these measures will be identical when both the funds are well diversified.
A poorly diversified fund will rank lower according to the Sharpe measure than the Treynor
ratio. The less diversified fund will show greater risk when using standard deviation.
Treynor Measure vs. Sharpe Measure: The Sharpe measure evaluates the portfolio manager on
the basis of both rate of return and diversification (as it considers total portfolio risk in the

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