b) Bandicoot Company has the following probability distribution of returns:
(i)
Calculate the expected return of Bandicoot Company
E(R) = [
0.2
*(0.05)] + (
0.3
*0) + (
0.3
*0.05) + (
0.2
*0.1) =
0.025
= 2.5%
(ii) Calculate the variance of Bandicoot Company
variance =
0.2
(0.05

0.025
)
2
+
0.3
(0

0.025
)
2
+
0.3
(0.05

0.025
)
2
+
0.2
(0.1

0.025
)
2
= 0.002625
(recall: variance is movement away from the mean squared, applying probability to each
possible occurrence: there is a 20% chance that the return of 0.05 will vary from the mean of
0.025 squared, 30% chance that the return of 0 will vary from the mean of 0.025 squared and
so on)
(iii) Calculate the coefficient of variation of Bandicoot Company
std dev = √(0.002625) = 0.051235
CV =std dev/mean return= 0.051235/0.025 = 2.05
(iv) If Alpaca Company has a CV of 1.75 which of the companiesBandicoot or Alpaca
would you choose as a risk averse investor?
Choose Alpaca as it has a lower CV which implies lower risk for each unit of return
(v) If the correlation coefficient between Bandicoot and Alpaca is 0.9787, would these two
shares (Bandicoot and Alpaca) offer good diversification? Why or why not?
No, 0.9787 is very close to 1 which is perfect positive correlation, hence very little
diversification is possible. (However, recall that as long as correlation is less than 1, there is
still possibility for diversification. In this case, it is just very little diversification being
possible, so not a good choice for diversification purposes).
Portfolio Theory
The table below presents the expected returns, betas and standard deviations for three assets
A, B and C. The expected return on the market is 14% and the riskfree return is 3%.
Asset
E(R)
Beta
Std deviation
A
8%
0.8
6%
B
10.5%
1.2
8%
C
23%
1.6
12%