# How to calculate return on investment for an adjustment to a complex options position?

Say I currently hold a set of options positions with the same symbol/expiry that collectively have a net present value based on the estimated value at expiration of +10. I could also liquidate the positions now at a value of +6.

I am considering a set of multiple transactions with the same symbol/expiry. If I executed these transactions, I would net +8 including commissions. The estimated present value at expiration for the resulting positions would decline by -3 to 7. I could also liquidate the entire position after the transactions at a value of +5.

How to I determine the ROI of executing these transactions?

My gut says its 8 / 3 = 266%, I 'invested' that -3 that I lost in value to gain an immediate value of $8. But that does not seem to work for all the different scenarios, such as when a set of transactions results in both an increase in estimated NPV and a net benefit to the execution. If there a general purpose equation that will allow me to measure ROI consistently across these scenarios? How do I account for the reduction in the liquidation value since only one of the two scenarios will occur (either the liquidation value will matter or the value at expiration)? • You did not tell us how much you invested to build up your position, so we can not calculate ROI. Since you say it has an npv of 10 we can assume you invested 10, but You say that you would eliminate it at 6. That seems to suggest that the market does not think its worth 10, or its illiquide. I assume you think its worth 10 on average, but there is a considerable risk and the actual return is uncertain. Not knowing the return makes ROI calculation difficult too. Maybe you can calculate an average/expected return. – Ami44 Sep 17 '16 at 16:13 • I didn't consider the initial investment to establish the position because I'm trying to estimate the ROI of the adjustment transaction itself instead of the change in ROI for the entire history of the position. – user548084 Sep 17 '16 at 17:08 • Also I didn't mean that I would liquidate it for 6, I meant I could liquidate it for 6 (but I wouldn't because I think its worth 10 to keep it). But these numbers are illustrative because I'm looking for a general purpose solution to the problem. – user548084 Sep 17 '16 at 17:10 • I'm going to ask this question in a different way, if that gets answered I'll mark this one as answered as well – user548084 Sep 20 '16 at 3:32 ## 4 Answers My instinct is to compute the expected value of the options right now. In a black-scholes framework, you simply recompute your put / call value with current time to expire and underlying price(s), and add up the values, then compare to the cost in the market of closing these positions. Note that if you use the market IV to calculate this, you will get back from this that both are exactly the same expected value. Like most things with options, determining the best course of action depends on your view of volatility vs the rest of the market. • Perhaps you looking instead for relative risk / reward? ie, why risk \$2.00 to make the last \$.10 on an option while leaving myself open to gamma risk? – pyrex Sep 17 '16 at 22:58 • Yes, relative risk / reward is where I'm trying to get to. This math is very simple if the option is a net debit and the expected value is positive. What I can't figure out is how to choose between two options that both have a net credit and a positive increase in expected value. – user548084 Sep 20 '16 at 3:01 I certainly see a problem in the fact, that you say that your position has a npv of 7, but you can not sell your position at 7 right now. I assume you're position has a considerable risk. That means you do not know your actual return. On average it might be 7, but it might be more or less in the end. That means you can only calculate an average ROI not the actual one. But let's assume your npv's are real market values at which you could sell your position at any time. Since the ROI is simply your profit divided by the capital you used to generate that profit, it would be in your case 5/3 = 166%, since you invested a value of 3 to make a profit of 5. If your transactions result in an immediate increase in cash and value of your position than you have an arbitrage opportunity and you should try to do as much of these transactions as possible. The ROI would be infinite. Addendum: I think ROI is not usefull in your situation. You can use it at the end, when all positions are eliminated. Before that I doubt its usefullness. I assume that your transactions are changing the risk of your position. Otherwise it seems impossible to me to create a cash and npv increase simultanously. That means you need a measure of success that also takes your risk into considerations like Sharpe ratio et. al. • I looked at the Sharpe ratio, but investopedia.com/terms/s/sharperatio.asp says its not applicable to options. – user548084 Sep 20 '16 at 2:41 • The immediate increase in cash and the increase in expected/npv value are what troubles me the most. But even in that situation, there must still be a way of comparing two alternate transactions that both increase cash and expected value. Is the answer to that is the standard deviation of returns i.e. "risk"? – user548084 Sep 20 '16 at 2:46 • Think about what stops you to make a billion of that transactions. It's the possibility that the expected value will not realize, right. I think you need to quantify that risk and than use something like your return divided by that risk as your measure of success. – Ami44 Sep 20 '16 at 17:12 • Sure, that's my thought as well. With a net credit and a positive ROI there must be another factor at play, which is obviously risk. My challenge is how to control for that risk, or, exactly what metric to use in combination with EV/NPV and the net credit. – user548084 Sep 23 '16 at 2:58 It's fairly straightforward to calculate ROI for a long only options portfolio, since what pay can be considered principal. For a net short position, however, ROI may be undefined since their is no principal and net loss if theoretically not defined. In cases where principal is not defined, it is standard to use value-at-risk for the denominator since this represent a best-estimate of principal at stake. The standard cut-off values for VaR are 1%, 2%, and even just 2 sigmas. In instances where you cannot compute VaR, it may be acceptable to use required maintenance margin as designated by your broker or clearing house. For example, the CME Group used to use a margin system called SPAN, which was basically a complex VaR model. Brokerages which cleared under the CME broadly adopted this model for risk reporting. To your example, you assume you have a net expected return of 8. If your broker/clearing house requires you to have 10 in your account to maintain the position, then the net expected ROI would be$\frac{8}{10}$or 80%. As a caveat, margin requirements are in flux and tend to increase when volatility increases or correlations break down (thus margin call). So if your broker suddenly decides you need 16 in your account to maintain said position, then expected ROI would decrease to$\frac{8}{16}\$ or 50%.

P&L calculations can get complex when dealing with derivatives. From a traders/portfolio managers prospective ROI/NPV/EV are irrelevant for calculating returns/risk on a book of positions. The options might be ITM now, but looking at current expiration value is making the assumption that the asset will either stay ITM or become further ITM. Ultimately, a position is worth whatever the current spread shows, not the expiration value. If you are concerned about the expiration value, the current market for the position, should encompass the likelihood that it will expire ITM, hence the price will be higher, but I digress .

If use are using this for risk calcs you should look do calcs with mark-to-market/bid/mid/ask. You are correct to calculate the returns using bid price less commission. There are two simple way to calculate the returns in this case. One in context of the portfolio and one in the context of the position only.

Calcs for Long

$$\ Weighted Position Return = \frac{ ( (Price_T - Entry Price - Commission) * Contracts * Multiplier )}{Portfolio Money Value}$$

$$\ Position Return = \frac{( Price_T - Commission )}{(Entry Price + Commission)} -1$$

Calcs for Short

These require a little logic. I will use calls for this example:

$$\ If\ Strike > Price_T$$

$$\ Then \frac{Net\ Premium}{Portfolio\ Money\ Value}$$

$$\ Else\ \frac{Net\ Premium\ -\ (Price_t\ -\ Strike)\ *\ Contracts\ *\ Multiplier\ -\ Commission }{Portfolio\ Money\ Value}$$

Let me know if the explanation is useful to you.

Also one note, is your goal risk management or portfolio analytics?