Exam 4: Security Analysis and Portfolio Theory

You are convinced that the next three months are going to be boom or bust months for IBM.Foreseeing a major increase or decrease in the stock price,you set up a position in options where you buy July 120 calls at $8.75 and you buy July 120 puts at $8.25.IBM is currently selling for $119. a. Draw the payoff diagram of cash flows on this position. b. What are the break-even points on the upside and downside of this position? c. Now assume that IBM has a variance of 0.08. Using the Black-Scholes model to value these two options, do you still think that you should take the above position? Why or why not? (Today is December 21, 2002; the options expire on July 18, 2003; the annualized riskless rate is 6%; ignore dividends.) d. What is the implied variance in the July 120 call?

Assume that you are a mutual fund manager with a total portfolio value of $100 million.You estimate the beta of the fund to be 1.25.You would like to hedge against market movements by using stock index futures.You observe that the S&P 500 June futures are selling for 260.15 and that the index is at 256.90. a. How many stock index futures would you have to sell to protect yourself against market risk? b. If the riskless rate is 6% and the market risk premium is 8%, what return would you expect to make on the mutual fund (assuming you don't hedge)? c. How much would you expect to make if you hedge away all market risk?

Is it possible for: a. a stock to have a standard deviation of return lower than the market portfolio if the stock's beta is greater than 1.0? b. all of the stockholders of XYZ Corporation to believe XYZ is undervalued? c. everyone to expect the stock market to go down in the next month? d. someone who sells stock short to make money even if the stock goes up? e. everyone to expect the Treasury 14s of 2011 to go down in price over the next month?

Assume that the yield curve is flat at 10% and that the expectations theory of the term structure holds.For a bond with 5 years to maturity,an annual coupon rate of 20%,and semi-annual coupon payments occurring at the middle and end of each year,what is the duration as of the beginning of year 3 just after a coupon payment?

Consider the following data for a stock and a call option on that stock: S₀ = $50,S₁ = $75 or $100,E = $50,and r = 1.10.Derive the hedge ratio ( )and the price of the call option.