Assignment:
Problem
A pension fund can invest its money into two types of bonds. Type A bonds have high average annual return, but also high return volatility, i.e. they are high-risk bonds. Type B bonds have lower average annual return, but also have lower volatility of their return, i.e. they are low-risk bonds.
The fund offers its clients two types of investment plans: "Be Safe!" plan and "Feeling Lucky?" plan. "Feeling Lucky?" plan includes 5 bonds of type A, "Be Safe!" plan includes 5 bonds of type
Suppose that a single type A bond has its return ra distributed normally with mean ja = 24 and standard deviation o A = 16, while a single type B bond has its return to distributed normally with mean jb = 12 and standard deviation ob = 9. It is also known that returns of these two bonds have a correlation of 0.4.
1. Calculate the probability that a single type A bond yields
(a) less than $0
(b) more than $9
(c) more than $4, but less than $8
2. Calculate the probability that a single type B bond yields
(a) less than $0
(b) more than $9
(c) more than $5, but less than $15
3. Let X be the return of the "Be Safe!" plan. Calculate
(a) expected value of X
(b) standard deviation of X
4. Let Y be the return of the "Feeling Lucky?" plan. Calculate
(a) expected value of Y
(b) standard deviation of Y
5. Suppose that a new investment plan "Fifty-fifty" has been offered to clients. The new plan includes 10 bonds of type A and 10 bonds of type B. The fund claims that this new plan will offer higher return than "Be Safe!" plan and lower risk than "Feeling Lucky!" plan. Let Z be the return of the new plan "Fifty-fifty". Calculate
(a) expected value of Z
(b) standard deviation of Z