Question 1

Consider investing in three different bonds. All maturity values are $100. All interest rates are expressed per annum with semi-annual compounding and coupons are paid semi-annually as in the US Treasury bond market.

Bond A: a 6-month zero-coupon bond. The current price is $95.50

Bond B: a 2-year coupon bond with 7 % coupon.

Bond C: a 4-year zero-coupon bond.

The yield curve is currently flat.

1. Compute the yield to maturity on these bonds.

1. What must the price of the 2-year coupon bond (Bond B) be?

1. What is the price of the Bond C?

1. Compute the Modified durations of the three bonds.

1. Suppose you want to find a portfolio of bonds A and B with the same D^m as that of Bond C, what should the portfolio weights be?

1. You expect interest rates to increase by 25 bp (0.25%). What percentage price change does the D^m concept predict for the three bonds?

1. Given these percentage price changes, is there any advantage to being invested in Bond C, as compared to being invested in the portfolio of Bonds A and B as computed in part (5)?

Question 2

Assume that CAPM is a good representation of the risk-return relationship. You are holding a portfolio of stocks. The portfolio's standard deviation is 40% and its correlation with "M" is 0.8. The risk free rate is 2.5%, the expected market return is 12%, and the standard deviation of the market return is 17.6%.

1.What is the expected return on your portfolio?

2.Is this portfolio efficient? How can you tell?

3.If this portfolio is not efficient, how much risk reduction could you achieve, at no sacrifice in expected return, by making your portfolio an efficient one?

4.Now suppose that you are comfortable with the overall risk of your current portfolio, but want to improve your return by making your portfolio efficient. What would be the return on the efficient portfolio with the same overall risk as your current portfolio?

Question 3

Your goal is to estimate the cost of capital of a small software company, Codestart, using CAPM and the Fama-French 3-Factor Model. The risk-free rate is 4% and the excess expected return on the market index is 8.6%.

(a)According to the CAPM the beta of Codestart is 2.3. What is the CAPM expected return of Codestart?

(b)What would be the expected return on Codestart if the covariance of returns between Codestart and "M" doubles?

(c)Estimating the factor loadings for the Fama-French model, you find that Codestart's b_m = 1.58, b_SMB=1.19 and b_HML= -0.15. Given that the expected return on the SMB factor is 5.2%, and the expected return on the HML factor is 4.8%, what is the expected return of Codestart according to the Fama-French 3-Factor Model?

Using the Fama-French model, what is the systematic volatility (standard deviation) of Codestart stock given that the volatility of the market index is 16%, the volatility of the SMB factor is 15% and the volatility of HML factor is 13%?

Question 4

Consider the following data on the S&P 500, FTSE and Nikkei indices:

s

S&P 500

0.1

0.16

FTSE

0.08

0.09

Nikkei

0.05

0.05

Risk Free asset

0.02

The correlation matrix is given by:

S&P 500

FTSE

Nikkei

S&P 500

1

FTSE

0.6

1

Nikkei

0.4

0.5

1

1.Construct the Minimum Variance Efficient (MVE) portfolio, consisting of these three indexes and report the weights of each of these three indexes in the MVE pf. If you used Solver, please explain how you set it up.

2.What are the mean and standard deviation of the MVE portfolio?

3.Find the portfolio with the maximum .