Which of the following statements are wrong (Hint: three are wrong) A. You can construct a...

Which of the following statements are wrong (Hint: three are wrong)

A. You can construct a Principal Protected investment by buying zero coupon bonds and put options

B. -S = -B-C+P

C. Stock returns are lognormally distributed and stock prices are normally distributed

D. A risk free portfolio can be constructed through a combination of stock and a certain number

of its options

E. Making a portfolio Gamma neutral requires the use of options

F. Buying a put is equivalent to selling a call

Solutions

Expert Solution

B) By rearraning the equation, C - P = S - B, where C is the price of a call option, P is the price of a put option, S is the value of stock and B is the value of bond. This is equation is not correct as it is not followed by the put-call parity.

The put-call parity states that C - P = S - Xe^ -rt, where Xe^ -rt is the present value of strike. The difference between the price of a call option and a put option should be equal to the price of the underlying stock minus the present value of the strike price at which the call and put options are bought and not the value of bond.

D) A risk free portfolio is a portfolio which has a near 0 beta in order to mitigate the systematic risk. If a portfolio is constructed with a combination of a stock and a certain number of it's options, delta and gamma risks can be mitigated, but the beta of the stock will still not be 0 and hence the beta of the portfolio is not 0. Thus, the portfolio is not a risk free portfolio. In order to create a risk free portfolio, a combination of different stocks and their options are needed so as to mitigate delta, gamma, and beta risk.

F) Buying a put option is not equivalent to selling a call option due to the limited profits that an investor can earn on selling the call option.

Eg: let the price of the stock and strike be $100. Investor A buys a put option for $3 and investor B sells a call option and recieves a premium of $2. Lets assume at the time of maturity, the price of the stock is $80. Investor A will get a return of $18 ( 100 - 80 - 2 ), while investor B will just keep the premium of $2. Hence, selling a call option has a cap on the max return while buying a put does not.

jeff jeffy answered 1 year ago

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