AN INVESTMENT ADVISOR IS ANALYZING THE RANGE OF POTENTIAL EXPECTED...
8.
An investment advisor is analyzing the range of potential expected returns of a new fund designed to repli-
cate the directional moves of the BSE Sensex Index but with twice the volatility of the index. The Sensex has
an expected annual return of 12.3% and volatility of 19.0%, and the risk free rate is 2.5% per year. Assuming
the correlation between the fund’s returns and that of the index is 1, what is the expected return of the fund
using the capital asset pricing model?
a.
18.5%
b.
19.0%
c.
22.1%
d.
24.6%
Correct Answer: c
Rationale:
If the CAPM holds, then R
i
= R
f
+
β
i
x (R
m
– R
f
), which is maximized at the greatest possible beta value
which implies a correlation of 1 between the fund’s return and the index return. Since the volatility of the fund is twice
that of the index, a correlation of 1 implies a maximum beta
β
i
of 2. Therefore: R
i
(max) = 2.5% + 2 x (12.3% - 2.5%) = 22.1%.
Section:
Foundations of Risk Management
Reference:
Edwin J. Elton, Martin J. Gruber, Stephen J. Brown and William N. Goetzmann, Modern Portfolio Theory
and Investment Analysis, 9th Edition
(Hoboken, NJ: John Wiley & Sons, 2014). Chapter 13, “The Standard Capital
Asset Pricing Model.”
Learning Objective:
Apply the CAPM in calculating the expected return on an asset.