1. Bond Valuation
Consider three US Treasury securities that mature in 6, 12 and 18 months. Each of them has a face value of $1,000. Coupon payments are made semi-annually on these bonds, and the most recent coupon payment was made yesterday. The coupon rates (in annual terms) and current prices of these bonds are given in the table below.
Maturity Coupon Rate Current Price

Maturity	Coupon Rate	Current Price
6 Months	3.75%	$979.57
12 Months	3.50%	$922.90
18 Months	3.00%	$908.36

Using the 6 and 12 month maturities, compute the prices for which pure-discount bonds, with face values of $1,000, that mature in 6 and 12 months would sell. [Hint: If the pure discount bonds were traded, the 6 and 12 month Treasuries’ prices must be the same as the value of a portfolio of pure discount bonds that has the same stream of payments as the Treasury securities].

2. Portfolio Management

You are a portfolio manager and have been assigned a new client. Your client has her portfolio invested in two assets: a small stock fund and the market. The expected return on the small stock fund is 11% and its standard deviation is 33%. The market has an expected return of 8% and a standard deviation of 17%. The risk free rate is 3%. Currently, your client has a portfolio which is 90% in the small stock fund and 10% in the market. Assume the CAPM holds. Answer the Following Questions.

a.) What is the beta of the small stock fund?

b.) What is the beta of your client's current portfolio?

c.) What is the covariance between the small stock fund and the market?

d.) Calculate the expected return and standard deviation of your client's current portfolio.

e) You want to show your client that she can earn a higher expected rate of return without taking additional risk. Create an efficient portfolio that has the same standard deviation as your client’s initial portfolio. What is the expected return on the new portfolio? [Efficient portfolios are portfolios consisting of the market asset, i.e., S&P 500, and the Rf asset]. Hint: remember that the standard deviation of the Rf asset=0.