Question

1.You are contemplating investing in a portfolio made up of two stocks, A and B. The beta of Stock A is 1.4, and the beta of Stock B is -1.3. Assume you plan to invest X% in Stock A, and the rest of your capital (that is, 1-X) in Stock B. What should X be so that the beta of the resulting portfolio is zero?

2. Consider an amortizing loan. The amount borrowed initially is $89202, the interest rate is 6% APR, and the loan is to be repaid in equal monthly payments over 13 years. As we know, while each monthly payment will be the same, the amounts of interest and principle paid will change from payment to payment. How much of the very first payment is interest?

3. The index model has been estimated for stocks A and B with the following results:

R(A) = 0.02 + 1.1Rm

R(B) = 0.02 + 1.2Rm

Additionally, the standard deviation of the market index is 16%.

What is the covariance between stocks A and B?

Answer 1

1.

Resulting portfolio Beta is Zero

0 = 1.40 × X - 1.30 × (1 - X)

0 = 1.40 × X - 1.30 + 1.30 × X

1.30 = 2.70 × X

X = 48.15%

Value of X is 48.15%.

2.

Monthly payment on loan is calculated in excel and screen shot provided below:

Monthly Payment on loan is $824.87.

Interest on first month payment = $89,202 × 6% / 12

= $446.01

Interest on first payment is $446.01.