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.

  • $\begingroup$ I just want to know formulas to find these returns. And please check the payoff of the 3rd strategy. $\endgroup$
    – 1190
    Commented Apr 12, 2020 at 22:58

2 Answers 2


Note: with options contracts, payoff is different to profit. I think something is not correct with your formula (2) Secondly, sounds like this assignment question only requires payoff and return. Return is usually simple regarding options contracts such as 1 - this is what I have now divided by this is what I had before. Note: 1- is to make it into a percentage increase or decrease

Try this: if you had 26000 in shares at a price of 15.78 1 month ago, What would it be today if the price changed to 27.69 today?

With any question of return try drawing a timeline it may help.

  • $\begingroup$ N=number of calls, $S_T=$final stock price , X=exercise price, C=call premium, r=annual interest rate, T=time to expiration $\endgroup$
    – 1190
    Commented Apr 13, 2020 at 4:06
  • $\begingroup$ For the 2nd investment, the general formulas $$Profit = N*[max(0, S_T-X)-C]$$ $$Payoff = N* max(0, S_T-X)$$ $$ Return = 1- \frac{N*[max(0, S_T-X)-C]}{N*(X+C)}$$ $\endgroup$
    – 1190
    Commented Apr 13, 2020 at 4:08
  • $\begingroup$ In numerical, $$payoff = 2000 [max(0, 50-146)]$$ $$Return = 1- \frac{2000 [max(0, 50-146)]-7.3]}{2000(146+7.3)}$$ $\endgroup$
    – 1190
    Commented Apr 13, 2020 at 4:10
  • $\begingroup$ For the 3rd investment, the general formulas $$Profit = N*[max(0, S_T-X)-C]+ 13870 e^{r*T}$$ $$payoff = N*[max(0, S_T-X)]+ 13870 e^{r*T}$$ $\endgroup$
    – 1190
    Commented Apr 13, 2020 at 4:14
  • 1
    $\begingroup$ Yeah I think that’s right $\endgroup$
    – JazKaz
    Commented Apr 13, 2020 at 12:33

For the second strategy, your return is -100%. The call option will expire out of money, so it's worthless and you lost all of the money paid for the premium.

Value of a call option at expiration is easy:

P = Max(0, Spot - Strike)

If the option is out of money, meaning the spot is lower than the strike, the second term is negative and you get zero. Otherwise, it's simply the difference between strike and spot.

To find the profit, just deduct the premium paid to open this position.

For interest calculation, we usually use continuous compounding in finance. So, to get the rate of return, simply take the log of the final price to the starting price.

  • $\begingroup$ I just give the final stock price is 50 as an example. I have many final stock prices and I will calculate according to them. Please can you write the general return calculation formula for the 2nd and 3rd strategy. This is enough for me. Thank you for your reply dear Zare :) $\endgroup$
    – 1190
    Commented Apr 12, 2020 at 23:31

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