FM for Actuaries

138 CHAPTER 4
Expected return
Standard deviation
US 16% 21%
Germany 20% 25%
Japan 17% 27%
The correlation matrix of the three stock indices is as follows:
US Germany Japan
US 100%
Germany 37% 100%
Japan 26% 33% 100%
You construct a portfolio of the three markets with 15% weight in US, 40%
weight in Germany and 45% weight in Japan. Calculate the expected return
and standard deviation of the return of the portfolio.
4.24 The value of Ms Sweetheart Company is sensitive to the price of cocoa. If the
cocoa crop fails due to bad weather, the price of cocoa rises and the company
suffers losses. The following shows the three scenarios of the company:
Bearish market Bullish market Crop failure
Rate of return 13% 20% −15%
Probability 40% 50% 10%
Kenny has a portfolio of risk-free bonds and Ms Sweetheart stock. The riskfree
interest rate is 5% per annum. The expected return of Kenny’s portfolio
is 9%. Calculate the standard deviation of the return of Kenny’s portfolio.
4.25 The values of Ms Sweetheart Company and Mr Sugar Company are sensitive
to the price of cocoa. If the cocoa crop fails due to bad weather, Ms Sweetheart
suffers from huge losses while Mr Sugar generates more profit. The
following shows the three scenarios of Mr Sugar (refer to Exercise 4.24 for
Ms Sweetheart):
Bearish market Bullish market Crop failure
Rate of return 8% 13% 20%
Probability 40% 50% 10%