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Defining Exposure for Daily P&L in a Rolling Short-Call Strategy

Article Quant Q&A · Author: Vladimir Nabokov
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Summary

The document considers how to calculate daily performance for a strategy that continually sells call options and replaces them at expiry. It points out that holding one contract is not a stable measure of portfolio exposure: the option’s dollar exposure changes as its value changes, and the same position can become a smaller share of a growing portfolio. Daily mark-to-market P&L for a short option is the prior day’s value minus its current value, but converting that P&L into a return requires a meaningful denominator.

The proposed approach is to define position size relative to portfolio value, such as keeping the premium sold or option notional at a constant portfolio proportion. The follow-up asks whether dividing P&L by strike is sensible, but the excerpt does not resolve that question or prescribe a complete return calculation. It also does not provide performance results or discuss margin, transaction costs, or realized payoff handling.

Key ideas

  • A fixed count of short options does not imply fixed portfolio exposure.
  • Option dollar exposure changes as the underlying option value changes.
  • Daily short-option mark-to-market P&L equals the previous option value minus the current value.
  • A return series needs a denominator tied to a defined capital or exposure base.
  • Sizing premium or notional as a constant fraction of portfolio value can make exposure more consistent.

Tags

OptionsRisk managementPosition sizingBacktesting
Full text
# P&L Calculation of Option Strategy


# P&L Calculation of Option Strategy












I have designed a call writing option strategy, where I am rolling the options upon expiry, i.e., my portfolio consists of one short call position at any given time.

I have a time series of the value of the option for each day. At expiry, I have a 0 if the option ends OTM and my payoff liability otherwise.

What is the correct approach for calculation my daily P&L time series?

How do I then summarise the performance of this strategy? Do I simply annualise this daily return time series?

TIA

## Answer by hjw (score 1)

https://quant.stackexchange.com/a/41558

The main problem with your description is that one option is not a consistent quantity when it comes to a portfolio strategy.

- The $ exposure of your option changes as the underlying price of the option changes.

- If you look at it from a portfolio basis. Assuming your strategy makes money, the value of the option you sell will become less and less significant in comparison to the portfolio value.

To compute a daily time series, I would suggest redefining your strategy to either sell premium that is a constant proportion of your portfolio, or sell a number of options whose notional is a constant proportion of your portfolio.

## Answer by Vladimir Nabokov (score 0)

https://quant.stackexchange.com/a/41626

I think I could've been more specific with my question. I'm just selling call options on the same stock with price $S$, and at every point in time, I never have more than one short call position in my book.

The option is always written on $1$ share of the underlying.

So everyday (except $T_0$) I can mark-to-market my short call option position with the Black-Scholes formula, with the current $S, r, \sigma \text{ and } \tau$. My P&L on day $t$, $PnL_t$, $PnL_t = V_{t-1}-V_{t}$ (if I was long call It'd be $PnL_t = V_{t}-V_{t-1}$). I have a daily P&L time series but this is not my daily return.

This is where I'm stuck, I've seen examples where people taking this daily P&L time series and divide by the strike of the current option, so their return on day $t$, $r_t$, is $r_t=\frac{PnL_t}{K}$. Does this make sense?

Thanks

VB

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