Part II. Problems 1. You have a portfolio that you have carefully crafted to carry a beta of 1.60 in relation to the S&P 500. However, to hedge some of that risk, you try to buy call options on the SPY (a S&P 500 tracking ETF) that only go up half as much as the market (S.50 for every S1). You are rebalancing everything right now and are looking at the following for your option overlap hedge. Which option should you choose to hedge with to get you as close to your hedging goal as possible. The current SPY is $467. (15 pts) Exercise Price Time (in days) Risk-free Rate Volatility Dividend Yield Option 1 455 55 2% 20% 1.75% Option 2 470 85 2% 22% 1.75% Option 3 485 48 2% 18% 1.75% 2. You are a bond trader. You currently hold a boud Portfolio made up of the following Bonds: Bond 2 45 Number Held CR Ps Years Left Face Value Bond 1 60 6.54% $1.068 15 $1.000 4,65% 5951 6 $1,000 Bond 3 75 1.0996 5918 12 $1.000 a. What is the Macmulay duration of your portfolio? (10 pts) b. If you believe that interest rates are going to increase by 1%, what will happen to your bond portfolio according to duration? (10 pts) c. What is the approximated convexity of Bond 1? (10 pts) 3. Consider the following options: You want to make a long strangle strategy with Options 1 and 2. The current stock price is $21.50. (15 pts) Exercise Price Premium Call $25 $5.50 Put $18 $3.20 What is the strategy profit at the following stock price points? Profit Stock Price 12 19 22 27 33 Part II. Problems 1. You have a portfolio that you have carefully crafted to carry a beta of 1.60 in relation to the S&P 500. However, to hedge some of that risk, you try to buy call options on the SPY (a S&P 500 tracking ETF) that only go up half as much as the market (S.50 for every S1). You are rebalancing everything right now and are looking at the following for your option overlap hedge. Which option should you choose to hedge with to get you as close to your hedging goal as possible. The current SPY is $467. (15 pts) Exercise Price Time (in days) Risk-free Rate Volatility Dividend Yield Option 1 455 55 2% 20% 1.75% Option 2 470 85 2% 22% 1.75% Option 3 485 48 2% 18% 1.75% 2. You are a bond trader. You currently hold a boud Portfolio made up of the following Bonds: Bond 2 45 Number Held CR Ps Years Left Face Value Bond 1 60 6.54% $1.068 15 $1.000 4,65% 5951 6 $1,000 Bond 3 75 1.0996 5918 12 $1.000 a. What is the Macmulay duration of your portfolio? (10 pts) b. If you believe that interest rates are going to increase by 1%, what will happen to your bond portfolio according to duration? (10 pts) c. What is the approximated convexity of Bond 1? (10 pts) 3. Consider the following options: You want to make a long strangle strategy with Options 1 and 2. The current stock price is $21.50. (15 pts) Exercise Price Premium Call $25 $5.50 Put $18 $3.20 What is the strategy profit at the following stock price points? Profit Stock Price 12 19 22 27 33
