# Return on Investment for rolled options position on margin [duplicate]

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:

1. 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.
2. 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:

1. STO 100/1000 = 10%
2. BTC 50/1000 = -5%
3. 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%?

## marked as duplicate by Lliane, skoestlmeier, amdopt, Helin, EzyFeb 5 at 10:01

• Not as I understand it - to my mind I should be able to calculate an ROI from a knowledge of the transactional ROIs, no? – professorDante Jan 29 at 5:41
• The problem is the way you define investment, the margin is not your investment. What happens if the margin change or you get margin called, you might end up with a ROI below -100%. That's also why ROI is a poor measure for long short portfolios (infinite ROI because net investment is 0). – Lliane Jan 29 at 9:36
• I would think it is your investment, for all intents and purposes, as you cannot use that margin for anything else. We could call it 'return on margin' for more clarity perhaps – professorDante Jan 29 at 18:01

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%

• So you say you can't know the ROI of the position until the position is closed from the BTC? Can't really use that! – professorDante Jan 29 at 16:56
• well it would still be 5.56%. if you close out trade #3 at the same terms u entered into it (u have not specified anything), that would be zero pnl there, so no impact to ROI – ZRH Jan 29 at 17:40