How a Short Call Changes the Value of a Stock Portfolio

Summary

The document resolves a portfolio valuation question by clarifying the option position’s direction. A portfolio holding shares plus a long call includes the call’s positive value; a portfolio that has sold the call must subtract the liability represented by that option. The stated example gives a stock price, share count, call strike, and expiry, then compares the portfolio values under these two positions.

The accepted answer explains that the lower quoted portfolio total is consistent with being short the call, while the higher total is consistent with owning it. The key lesson is to mark each position with its sign before adding component values: long assets contribute positively, and written options create liabilities. This is a basic mark-to-market accounting distinction, not a pricing method for determining the call’s value. The example assumes the option’s value at expiry follows from the stated stock price and strike, and does not discuss premiums paid, transaction costs, or portfolio risk.

Key ideas

• A long call contributes positively to the marked value of a portfolio.
• A short call is a liability and reduces the portfolio’s value by the option’s current value.
• Portfolio totals depend on whether the option position is owned or written.
• Position signs should be established before adding marked values across portfolio holdings.

Tags

# How to compute a portfolio value?


# How to compute a portfolio value?












I am learning fundamentals of option market and ran into an example I do not understand :

Let's assume I have a portfolio of 3 shares priced \$22, and a European call option to buy a share for \$21 in 3 months. If the stock price turns out to be \$22, the value of the option will be \$1. The text states that the value of my portfolio is $22*3-1 = \$65 $, why isn't is $22*3+1=\$67$ ? Thanks

## Answer by Valometrics.com (score 1, accepted)

https://quant.stackexchange.com/a/51168

If you are long the call option (you purchased it), the value will be as you said $22*3+1=67$.

If you are short the call option (you sold it), the value becomes: $22*3-1=65$

## Answer by user9875321__ (score 0)

https://quant.stackexchange.com/a/51173

As @Valometrics suggests, the only way you portfolio can be worth 65 is indeed that you are short that call. Otherwise it wouldn't make sense for it to be worth only 65 instead of 67

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