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.

a)Compute the yield to maturity on these bonds.

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

c)What is the price of the Bond C?

d)Compute the Modified durations of the three bonds.

[Note: bonds pay semiannual coupons and period of time is 6 months. You will calculate duration in half-years first, and then divide the result by 2 to find D in years. To find Modified Duration, divide Duration (in years) by (1+rate per year/2).]

e)Suppose you would like to build a portfolio of bonds A and B with the same D^m as that of Bond C, what should the portfolio weights be?

f)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?

g)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 (e)?

Question 2 Consider the following data on the S&P 500, FTSE and Nikkei indices: Er OF 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 Nikkei 0.4 0.5 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 Sharpe Ratio = And-Question 3 Consider a put option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free rate is 5%, the volatility is 25% per annum, and the time to maturity is four months. a. Use a 2-period binomial model to price this same option. b. Use Black-Scholes formula to value this option c. How much the European call option on this stock with the same strike (E) and time to maturity (T) will cost? d. How much the American call with the same E and T will cost