1. Let the information on your portfolio be given as follows. You have three funds in the basket. The "beta's" among them that are estimated by using S&P 500 index are given as follows; = 1.22, = 1.03 = 0.85. Answer the following questions;
a) Why do we need these "beta's" to construct the portfolio?
They help us understand the risk between each beta and gives us the ability to calculate the weight for each beta.
b) If the risk-free rate is given as 2%, what are the required returns for fund 1 and fund 2 if the market rate of return is expected to have 12%?
E(R1) = .02 + 1.22(.12 - .02) = 14.2%
E(R2) = .02 + 1.03(.12 - .02) = 12.3%
c) Is it possible to construct a risk-free (or zero-beta) portfolio by combining asset 1 and asset 2? If yes, what is the required return for this portfolio? If the transaction cost for this portfolio requires 0.5% of commission, will you do it?
Yes, B = w(B1) + w(B2)
0 = 1.22w1 + 1.03w2
-1.22w1 = 1.03w2
w1 = -0.844w2
-.844w2 + w2 = 1
.156w2 = 1
w2 = 6.410, w1 = 5.410
Expectation: (12.3%)(6.410) + (14.2%)(5.410) = .78843 + .76822 = 1.55665
Yes it is possible to construct a risk-free (or zero-beta) portfolio by combining asset 1 and asset 2. If the transaction cost for this portfolio requires 0.5% of commission, then I will not construct such a Portfolio since overall return would be negative.
d) If you'd like to form a portfolio with fund 1 and fund 2 that replicates fund 3's beta, what are the weights of this portfolio? What are the assumptions needed for the construction of such portfolio?