Question
5. (27pts) An insurance company collects 100 million USD from insurance premiums and needs to decide how to invest the money. Suppose there is a
5. (27pts) An insurance company collects 100 million USD from insurance premiums and needs to decide how to invest the money. Suppose there is a bond fund (B), a stock fund (S) and a risk-free asset to consider. Their statistics are given below.
Table 3: Mean returns, volatilies, correlation and the risk-free rate (rf )
Bond Stock
mean volatility 4% 10% 12% 25%
correlation 0.15 rf 1%
-
(1) (10pts) Find the optimal risky portfolio for the insurance company.
-
(2) (7pts) Suppose the insurance company cannot invest more than 20% in the stock fund and it hopes to achieve a mean return as high as possible. What is the complete portfolio?
-
(3) (5pts) Suppose the bond fund invests in two bonds: a 1-year zero coupon bond and a 4-year coupon bond (annual coupon with 5% coupon rate). The current YTM for both equals 6% and the pro- portions of the two bonds are 30% and 70%, respectively. What is the duration of the bond fund?
-
(4) (5pts) Suppose the yield suddenly increases 1% and there is no change in the stock fund value and in the value of the risk-free asset. What is the approximate change in the value of the complete portfolio held by the insurance company?
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started