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Calculating ROI for a Rolled Short Put Using Cash Flows

Article Quant Q&A · Author: professorDante
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Summary

The document considers how to calculate return on investment for a margin-backed short put that is closed and replaced with a new put. The example tracks the initial premium, margin posted, closing cost, returned margin, and the new trade’s premium and margin requirement. It questions whether transaction-level percentage returns can be combined by weighting them against the latest margin.

The answer treats the initial opening and closing as a completed position: the premium received and margin posted imply an initial net cash outlay, while closing the option returns margin less the buyback cost. It calculates ROI from the resulting cash balance relative to the initial outlay. The newly opened put is still active, so its eventual return cannot be determined from the supplied information; the answer excludes it from the realized ROI. The calculation assumes margin is unchanged while the first position is open and does not address alternative conventions for defining capital at risk or portfolio-level performance.

Key ideas

  • A rolled option position contains realized cash flows from the closed trade and an open replacement trade.
  • The example computes realized ROI from the initial net cash outlay and cash returned at closure.
  • The new short put’s premium and margin do not establish its eventual ROI while the trade remains open.
  • The calculation assumes the original margin is returned unchanged when the position closes.

Tags

OptionsRisk management
Full text
# Return on Investment for rolled options position on margin


# Return on Investment for rolled options position on margin












I'm trying to calculate my return on investment (ROI) for an options position on margin that has been rolled. I'll give an example:

- Sell to Open (STO) a naked put position, for which I collect 100 premium, and the margin put up is 1000, for example. I have 1 contract.

- Roll the position by Buying to Close (BTC) the short, which costs me 50, and then STO another naked put for 150, with a new margin requirement of 1750.

I know each transactional ROI:

- STO 100/1000 = 10%

- BTC 50/1000 = -5%

- STO 150/1750 = 8.6%

My question is, what is the overall positional ROI, calculated from these transactional ROIs? How to weight each ROI?

Is it weighted according to the latest margin, so:

10.1000/1750 - 5.1000/1750 + 8.6.1750/1750 = 11.45%?

## Answer by ZRH (score 0)

https://quant.stackexchange.com/a/43762

I would argue that it makes no sense to include 3)in the calculation, since that position can only be valued at the point of inception, given the info you have provided.

For 1) and 2), you get the ROI as follows: on the STO, you collect a premium of 100 and pay a margin of 1000, i.e. net cash outlay of 900. When you do the BTC, you pay a premium of 50 and collect 1000 margin (assuming no moves on margin account). Thus you collect 950.

So with an initial investment of 900 which turns into 950, you get a ROI of 950/900=5.56%

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.