Q1. Suppose your stock portfolio’s beta is 1.40 and it’s currently valued at $1 million. The S&P 500 index is currently at 2,000. The riskfree rate is 4% per annum and the dividend yield on both the index and your portfolio is 0%. What action is needed to provide protection against the value of your portfolio falling below $800,000 in 3 months?
If your answer involves options, be specific about (1) whether to buy or short, (2) call or put, (3) expiration, (4) strike price, and (5) how many option contracts are needed.
Hint: Example 15.2
On 5/30/2014, The Dow Jones Industrial Average (DJIA) closed at 16,717 and the price of the September 170 put was $6.10. Assume the riskfree rate is 1%, the dividend yield is 2%. Note that this put option is on DJIA level divided by 100, the strike price is 170 and expires on 9/20/2014.
Q2. Use Derivagem to calculate the implied volatility of the put option. For this homework, you can either use # of trading days/252 or # of calendar days/365 to calculate the time to expiration . Please include DG output.
Q3. Use putcall parity for European index options to find the arbitragefree price of a September 170 call.
Q4. Given the call price answered in Q3, use Derivagem to find the implied volatility of the call option.
Q5. Are the implied volatilities in Q2 and Q4 the same? What do you conclude about putcall parity and the implied volatility of European call and put options?
Q6. Would you expect the volatility of a stock index to be greater or less than the volatility of a typical stock? Explain your answer.
Q7. Does the cost of portfolio insurance increase or decrease as the beta of a portfolio increases? Explain your answer.