Asset Management
Question 1 (Diversification 0.5pt)
Consider the following:
1. Strategy I: Suppose that you invest $100 in a stock. There is a 60% chance that the stock
will go up in value by $10 at by the end of this year. There is a 40% chance that the stock
will go down in value by $5 by the end of the year.
2. Strategy II: Suppose that you invest $10 in 10 separate stocks. Each of these stocks also has a 60% chance of going up by 10% and a 40% chance of going down by 5% by the end of the year, and the performance of each of them is independent from the performance of the others.
The rate of return on each of these investment strategy can be described as
Money at end of year
Money at beginning of year − 1
Calculate the expectation and variance of rates of return for these two strategies.
Question 2
There are two assets in the market A and B.A has an expected return of 8% and a standard devi- ation of 10%. B has an expected return of 10% and a variance of 0.01. The correlation between A and B is 0.25. You cannot short.
1. What is the standard deviation of B ?
2. What is the minimum standard deviation of a portfolio consisting of A and B ? Describe that portfolio for K dollars to invest. What is the expected return of this portfolio?
3. What is the minimum standard deviation for a portfolio with expected return of 10%?
Hint: If there is only one portfolio that can achieve the target return of 10%, then it has automat- ically the largest standard deviation.
Question 3
Suppose there are three states of the world, which are all equally likely, and two different financial assets. In the first state of the world, the first asset returns 8% and the second asset returns −5%.
In the second state, the first asset returns −4% and the second asset returns 15%. In the third state, the first asset returns 12% and the second asset returns 6%.
– What is the mean return on each asset? What is the variance and standard deviation of the return on each asset? Use natural units, not percentages .
– What is the covariance of the returns of the two assets? What is the correlation between the two returns?
