Exercise 1. With the portfolio that we talked about in class composed by SPY ETF shares, a call option, a (risky) bond, and cash. The objective is to simulate returns to the portfolio based on certain probability distribution assumptions and compute the risk measures discussed in class.

(a) With the assumption that the log-returns of the stock index are normally distributed, a particular way of simulating the returns is S = S t + Z t in which S is todays price, t the time step were considering, a mean return or drift value, and the standard deviation. Z represents a normal distribution. Assuming the drift term is = 4% and the volatility is 12%, use Excel to simulate 5,000 returns using the formula above.

For example, if you draw a random number 1 from the normal distribution, say .1, then the updated stock price a month from now is such that S = 2, 340 0.04 1 12 + .12 .1 r 1 12! = 15.90 which leads to Snew = 2, 340 + 15.90 = 2355.90.