1 Options and risk management (a) You have $10,000, which you want to invest in XYZ stock and options. The stock price of XYZ is So = $40, and the price of a six-month call on XYZ with strike X = $40 is Co = $1. Consider the following three portfolios: (1) Invest all your wealth in XYZ stock; (2) invest all your wealth in call options on XYZ stock; (3) buy 100 calls and put the rest of your wealth in a bank-account that carns a six-month riskfree return of R; = 1%. In a table, compute the payoff of all three portfolios when Sr, the price of XYZ six months from now is $30, $40, $50 and $60. Use rows for these states of the world and columns for the payoffs of the three investments. Which portfolio appears to be the most risky? Which portfolio appears to be the safest? People sometimes say that call options are "safe", because the investor is protected when the price of the underlying asset falls. Does portfolio (2) confirm or contradict this reasoning? Are call options really safe? What happens when you use calls in combination with a bank account, as in portfolio (3): can calls reduce risk relative to a pure stock investment then? (b) Suppose you sell (write) a European put option on XYZ with strike $50 and expiration 7. Draw the payoff of your position as a function of Sr, the price of XYZ, in a payoff diagram. In the same diagram, draw the payoff of selling 2 put options. Now draw the payoff of selling ten put options. What happens to the slope of the payoff function in the range where ST