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Calculating Returns for Stock, Call, and Cash Strategies

Article Quant Q&A · Author: 1190
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Summary

The document explains how to distinguish payoff, profit, and return across three six-month investments: shares, long calls, and calls combined with a money market fund. It uses a stock that falls below the call’s strike at expiration to illustrate that an out-of-the-money call expires worthless. The option holder loses the premium paid, so the return is calculated by comparing the position’s ending value with its initial cost; the stock strategy is assessed in the same way using its ending value and purchase price.

For the combined strategy, the ending portfolio value includes both the option payoff and the accumulated cash investment. The answers mention continuous compounding for interest and logarithmic returns, but do not fully reconcile the compounding convention with the example or show a complete calculation for all three strategies. The discussion is therefore a conceptual guide to setting up the calculations, rather than a worked comparison with a single consistent return convention.

Key ideas

  • Option payoff at expiration is the greater of zero or the difference between spot and strike.
  • Profit accounts for the premium paid, while payoff alone does not.
  • A call that expires out of the money has zero terminal value and loses its premium.
  • Portfolio return compares ending value with the initial investment, including accumulated cash when applicable.

Tags

OptionsEquitiesDerivatives pricingRisk management
Full text
# How can I calculate returns for three investment strategy?


# How can I calculate returns for three investment strategy?












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.

## Answer by JazKaz (score 1, accepted)

https://quant.stackexchange.com/a/53253

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.

## Answer by Mehdi Zare (score 1)

https://quant.stackexchange.com/a/53247

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.