Assume that the price of DF stock went from a price of $104 on March 2 to 146 on April 1.

With a current stock price of 146, there is a call option available on the DF stock with an exercise price of 146, an expiration in six months and a price of 7.30

And there are 3 different investment strategy

(1) Invest all of your amount 14,600 in the DF stock (buy 100 shares)

(2) Invest all of your 14,600 in the DF call options (buy 2,000 call options)

(3) Buy 100 calls for 730 and invest the remaining 13,870 for the next six months in a money market fund that pays 8% annual interest.

Calculate the payoff and 6-month return for this investment alternative by assuming that the stock price is observed to be 50 on 6 months later.

—- (1) For the first strategy ,

I calculate payoff as follows

$$\pi = 100* ( 50- 146)= - 9600$$

I calculated the 6-month investment = $\frac{S_{final}-S_{initial}}{S_{initial}}$

(2) For the second strategy

The payoff $ \pi = 2000[max(0, 50-146) -7.3]=-14600$

But how can I calculate the return of this second strategy (long call)?

(3) For the Third strategy

The payoff $ \pi = 100[max(0, 50-146) -7.3]+ 13870 * e^{(1/2)*0.08}$

And for that, how can I calculate the 6-month return?


Summary: my question is how can I calculate the 6- month return for three investment strategy? Please tell me what is the formula?

Thanks a lot.


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