1.

1. a) Derive an expression that relates the M² ratio to the Sharpe ratio and the market Treynor ratio.

1. b) A 5-year bond has face value $1,000 (paid at maturity) and annual coupon rate 5% (paid in arrears at the end of the year). The yield-to-maturity is 5.3%. What is the duration and convexity of the bond?

c) You wish to create a financial instrument that has a payoff in 6 months time equal to the maximum value of $1,000 and $1,000 + $0.3*(S&P Index in 6 months time 3,200). The current S&P 500 index are trading at 3,200, and the 6-month call and put options with strike price 3,200 is trading at 110 and 105, respectively. What is the cost of your instrument?