24. If you own a stock, buying a put option on thestock will greatly reduce your risk. This is the ideabehind portfolio insurance. To illustrate, consider astock that currently sells for $56 and has an annualvolatility of 30%. Assume the risk-free rate is 8%,and you estimate that the stock’s annual growthrate is 12%.a. Suppose you own 100 shares of this stock. Usesimulation to estimate the probability distributionof the percentage return earned on this stock duringa one-year period.b. Now suppose you also buy a put option (for $238)on the stock. The option has an exercise price of$50 and an exercise date one year from now. Usesimulation to estimate the probability distributionof the percentage return on your portfolio over aone-year period. Can you see why this strategy iscalled a portfolio insurance strategy?c. Use simulation to show that the put option should,indeed, sell for about $238.
24. If you own a stock, buying a put option on the
stock will greatly reduce your risk. This is the idea
behind portfolio insurance. To illustrate, consider a
stock that currently sells for $56 and has an annual
volatility of 30%. Assume the risk-free rate is 8%,
and you estimate that the stock’s annual growth
rate is 12%.
a. Suppose you own 100 shares of this stock. Use
simulation to estimate the probability distribution
of the percentage return earned on this stock during
a one-year period.
b. Now suppose you also buy a put option (for $238)
on the stock. The option has an exercise price of
$50 and an exercise date one year from now. Use
simulation to estimate the probability distribution
of the percentage return on your portfolio over a
one-year period. Can you see why this strategy is
called a portfolio insurance strategy?
c. Use simulation to show that the put option should,
indeed, sell for about $238.
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