MOCK EXAM for 21th November 2013
Group 4
1. Sir Gawain and the Green advisor
Sir Gawain can invest in three assets: A, B and C. These assets have
the same standard deviation, 50%. Their expected rates of return
are: 15% (A), 20% (B) and 30% (C). The correlation between each
pair is 0.20. Since Sir Gawain is the owner of one hundred banks,
no one of them bankrupt, he can not only lend money at the risk
free interest rate, but also borrow at this rate (5%).
At first sight he has decided to invest his whole budget in asset C,
because he likes a risk level as high as 50% volatility, and, for this
volatility, asset C has the highest expected rate of return.
Nevertheless, before investing, he asks the opinion of Mrs. Green,
the most successful financial advisor of the galaxy. Mrs. Green
makes the following portfolio for Sir Gawain:
▲Portfolio of risky assets:
•10% in A
•27.50% in B
•62.50% in C
▲Borrow the 31.91% of your budget and invest your 131.91% in
the portfolio of risky assets.
Standard
deviation (σ)
Expected rate of
return E(Rj)
%
investment
(Xj
)
Corr
A
Corr
B
Corr C
Stock A 50% (0.5) 15% (0.15) 10% (0.1) 1 0.2 0.2
Stock B 50% (0.5) 20% (0.15) 27.5%
(0.275)
0.2 1 0.2
Stock C 50% (0.5) 30% (0.15) 62.5%
(0.625)
0.2 0.2 1
Risk-free
interest rate
5% (0.05)
Questions:
a) Which are the expected rate of return and the standard deviation
of the portfolio of risky assets?