How do you calculate the rate of return (ROR) when buying and selling put options?
"RoR for options you bought is fairly easy: (Current Value-Initial Cost)/Initial Cost gives you the actual return. If you want the rate of return, you need to annualize that number: You divide the return you got above by the number of days the investment was in place, and then multiply that number by the number of days in a year. (365 if you're using calendar days, about 255 if you're using trading days.) RoR for options you sold is much more complex: The problem is that RoR is basically calculating the size of your return relative to the capital it tied up to earn it.   That's simple when you bought something; the capital tied up is the money you put up.   It's more complex on a position like a short option, where the specific transaction in question generates cash when it's put on.    The correct way to deal with this is to A) Bundle your strategy (options, stock and collateral) into one RoR where appropriate, and B) include any needed collateral to support the short option in the calculation. So, if you sell a ""cash-secured"" put, where you have to post the money that you'd need to take delivery of the shares if they were put to you, the initial cost is the total amount you'd need to put the trade on:   in this case, it's the cash amount, less the premium you collected for selling the put.  That's just one example.    But the approach holds more broadly:  if you're using covered calls, your original cost is the cost of the stock less the premium generated by the sale of the call." What Jaydles said. I think of each strategy in terms of Capital at Risk (CaR). It's a good thing to know when considering any position. And then conveniently, the return is always profit / CaR. With covered calls it's pretty easy. Pay $1000 for stock, receive $80 in premium, net CaR is $920.  If you own the stock and write calls many times (that expire worthless, or you that you buy back), there are two measurements to consider. First, treat every covered call as a buy-write. Even if you already own the stock, disregard the real cost basis, and calculate from the moment you write the call, using the stock price at that time. The second measure is more complicated, but involves using something like the XIRR function in a spreadsheet. This tracks the series as a whole, even accounting for times where there is no written call outstanding. For the written put, even though your broker may only require 30% collateral in a margin account, mentally treat them as cash-secured. Strike less premium is your true CaR. If the stock goes to zero by expiration, that's what you're on the hook for. You could just compute based on the 30% collateral required, but in my view that confuses cash/collateral needs with true risk. Note: a written put is exactly identical to a covered call at the same strike. If you tend to favor puts over CCs, ask yourself why. Just like a loaded gun, leverage isn't inherently bad, but you sure want to know when you're using it. Rate of return is (Current value - initial value) divided by initial value. Buy $10,000 worth of put options and sell them for $15,000, and your rate of return is 0.5, or 50%.
There are different perspectives from which to calculate the gain, but the way I think it should be done is with respect to the risk you've assumed in the original position, which the simplistic calculation doesn't factor in. There's a good explanation about calculating the return from a short sale at Investopedia.  Here's the part that I consider most relevant: [...] When calculating the return of a short sale, you need to compare the amount the trader gets to keep to the initial amount of the liability.   Had the trade in our example turned against you, you (as the short   seller) would owe not only the initial proceeds amount but also the   excess amount, and this would come out of your pocket. [...] Refer to the source link for the full explanation. Update: As you can see from the other answers and comments, it is a more complex a Q&A than it may first appear.  I subsequently found this interesting paper which discusses the difficulty of rate of return with respect to short sales and other atypical trades: Excerpt: [...]   The problem causing this almost uniform omission of a percentage   return on short sales, options (especially writing), and futures, it   may be speculated, is that the nigh-well universal and conventional   definition of rate of return involving an initial cash outflow   followed by a later cash inflow does not appear to fit these   investment situations. None of the investment finance texts nor   general finance texts, undergraduate or graduate, have formally or   explicitly shown how to resolve this predicament or how to justify the   calculations they actually use. [...] Ok, so disregarding passivity, could you help me through a simplified example?   Say I only had two assets, SPY and TLT, with a respective weight of 35 and 65% and I want want to leverage this to 4x.  Additionally, say daily return covar is:  * B/B .004% * B/S -.004% * S/S .02%   Now, if I read correctly, I should buy ATM calls xxx days in the future.  Which may look like: Ticker, S, K, Option Price, Delta, Lambda  * TLT  $126.04  $126.00  $4.35  0.50  14.5 * SPY  $134.91  $134.00  $6.26  0.55  11.8  ^ This example is pretty close but some assets are far off.   I feel like I'm on the wrong track so I'll stop here.    I just want to lever up my risk-parity. Margin rates are too high and I'm docked by Reg-T. "You'd need to know the delta and the theta of the option. You can either calculate them yourself using a model like Black-Scholes (assuming you have a market price and can imply a volatility, and know the other factors that go into the model) or, you can see if your broker quotes ""greeks"" as well (mine does). The delta is the sensitivity (rate of change in value) to the underlying stock price, and the theta is the sensitivity to time passing (usually expressed in $/day).  So if your option has a delta of .5 and a theta of -.04, when one day passes and the underlying stock goes up $3, the option will gain roughly $1.50 due to the underlying stock price and lose $0.04 due to time passing." I asked a friend and he gave me a good explanation, so I'm just gonna paste it here for others: There is a simple and a complex answer depending on how much you want to understand the pricing dynamic of options.  LEAPs don't react 1:1 with a stock move because the probability of your option being in the money at expiry is still very much up in the air so you basically don't get full credit for a move in the stock this far out from expiry. The more complex answer involves a discussion of option 'greeks'.  Delta, Gamma, Theta, Vega, and Rho are variables that affect the pricing of all options.  The key greek in this case is Delta because it describes mathematically the expected move of an option as a ratio vs changes in stock price.  For put options the ratio is -1 to 0 where -1 is direct correlation between stock price and option price and 0 is no correlation.  The Delta increases as an option gets deeper in the money and also as it gets closer to expiry and reflects the probability of the option expiring in the money.  For your option contract the current Delta is -0.5673  so -3.38 * -0.5673 = 1.9 which is close.  Also keep in mind that that strike price had a last trade at 12:03 when the stock was at 13.3 and the current ask price is 22.30 so the last price isn't a true reflection of the market value.   As for the other greeks, Gamma is a reflection of volatility in the sense that it affects the rate of change of Delta as price and time changes.  Theta is the value of the time component of the option and is expressed as the expected time decay per day.  The problem is that the time premium is really some arbitrary number that the market maker seems to be able to change at will without justification and it can fluctuate wildly over short periods of time and I think this may explain some of the discrepancy.   If you bought the options when AAPL was $118.68 a couple weeks ago (option price of $18.85) and now AAPL is at $112.34 and the Delta over that time averaged at -0.55 then your expected option price would be $22.34 (($118.68 - $112.34) * 0.55 + 18.85 = $22.34) so you lost around $0.24 in time premium or 'Theta burn' over the last 2 weeks assuming it opens trading around 22.1 on Monday. Your broker should have information about the option contract greeks somewhere.  For my platform I have to put the cursor over top of the option contract for it to show me the greeks.  If your broker doesn't have this then you can get it from nasdaq.com. This is another reason that I only invest in deep in the money LEAPs because the time premium is much much lower than near the money and also because delta is much higher so if I want to trade out of it early I don't feel like I'm getting ripped off not getting paid for a stock price move.  For example look at the Jan 17 175 put.  The Delta is -0.9 and the time premium is only $0-1 depending if you are looking at the bid or ask.  The only downside is expected returns are lower for deep in the money contracts and they are expensive to buy. "Re. question 2 If I buy 20 shares every year, how do I get proper IRR? ... (I would   have multiple purchase dates) Use the money-weighted return calculation: http://en.wikipedia.org/wiki/Rate_of_return#Internal_rate_of_return  where t is the fraction of the time period and Ct is the cash flow at that time period. For the treatment of dividends, if they are reinvested then there should not be an external cash flow for the dividend.  They are included in the final value and the return is termed ""total return"".  If the dividends are taken in cash, the return based on the final value is ""net return"". The money-weighted return for question 2, with reinvested dividends, can be found by solving for r, the rate for the whole 431 day period, in the NPV summation. Now annualising And in Excel" For this, the internal rate of return is preferred. In short, all cash flows need to be discounted to the present and set equal to 0 so that an implied rate of return can be calculated. You could try to work this out by hand, but it's practically hopeless because of solving for roots of the implied rate of return which are most likely complex. It's better to use a spreadsheet with this capability such as OpenOffice's Calc. The average return on equity is 9%, so anything higher than that is a rational choice. Example Using this simple tool, the formula variables can easily be input. For instance, the first year has a presumed cash inflow of $2,460 because the insurance has a 30% discount from $8,200 that is assumed to be otherwise paid, a cash inflow of $40,000 to finance the sprinklers, a cash outflow of $40,000 to fund the sprinklers, a $400 outflow for inspection, and an outflow in the amount of the first year's interest on the loan. This should be repeated for each year.  They can be input undiscounted, as they are, for each year, and the calculator will do the rest. To calculate any daily return, all one need do is divide the final value by the initial value, subtract 1, and multiply by 100%: This can be applied to either the futures alone, the investments used as margin collateral alone, or all together. Margin collateral as a factor of a derivative's return Collateral can take many forms. Many suggest that cost and revenue for a derivative trade should also take into account margin requirements.  This can become problematic. If a futures position moved against the trader, yet the margin was secured with equities at the maximum, and the equities moved with the trader, the futures trade could be interpreted as less of a loss because the collateral, which is probably totally disassociated with the futures position, increased in value. Then again, if a futures position moved with the trader, yet the margin collateral moved against the trader then taken together, the futures trade would look less profitable. Furthermore, most likely the result of a futures position and its collateral would never produce the same result, so extrapolation would become ever more difficult. For ease of analysis, a position's cost and revenue should be segmented from another unless if those positions are meant to hedge each other.  Margin is not a cost, but it is a liability, so margin will affect the balance sheet of a futures trade but not its income statement, again unless if the collateral is also used to hedge such futures position. "I work at a mid market investment bank and while we don't usually use required rates of return (when we do it's typically in ranges based on previous experience in the market e.g. PE firms will look at IRR of 25%+ on mezz deals etc...) I can offer some insight into how you can think about it.   ""Required rate of return"" is a fairly arbitrary concept and literally is whatever you define it to be. Typically, the required rate of return is a function of risk i.e. the higher the riskiness of a project, the higher the return must be to compensate you for taking on that risk (this view is as per Markowitz's modern portfolio theory). This is easier said than done however as ""risk"" is tricky to define (The general, though somewhat outdated, rule is that risk = variability of returns).  To your questions:  1. How is rate of return determined: In my field of work (fairly niche) required rate of returns aren't usually an exact science and are typically based on i) financial leverage in the business ii) operating risk (seasonality, management team strength etc...) iii) type of security (e.g. for debt deals, what is the investment secured by)  2. Am I correct in thinking a firm will just choose a rate of return that they are already receiving? No, you are not correct, UNLESS the risk profile of the investment opportunity matches your current business. E.g. if you're a shoe manufacturer earning 15% on your capital and are looking to acquire another manufacturer in the same business with the same risk profile, then you can use your current rate of return as the requirement. If for e.g. you're a shoe manufacturer contemplating opening a new fully automated plant which will cost half your current net worth but allow you to triple your production, you will need to use a different (higher) required rate of return to compensate your firm for the additional risk it's taking on. E.g. if your shiny new plant only gets you a 15% return, you might as well deploy your capital in your current business at a much lower risk and earn the same amount of money.   Disclaimer: I have simplified. Significantly." I was typing up a long response and lost it to a backspace.. so, I apologize but I don't intend on rewriting it all.  You'll have to use a method called bootstrapping to get the forward rates.  Essentially you're looking at the spot rate today, and the forward rates, then filling in what must be the rate to make them equal out in the end.  Sorry I'm not more help! I'll just copypasta out of the book for the sake of clarity:   * If you think about it, you see that the only brokers who touch the switch for light bulb number 64 are those whose numbers are divisors of 64. That is, light bulb 64 has its state changed by brokers whose numbers are factors of 64. This means brokers 1, 2, 4, 8, 16, 32, 64. Because light bulb 64 is originally off, it must be after this odd number of switches that it is on.   * You want to be short a put if you expect a price rise. In this case, you expect to keep the option premium when the option expires worthless.   There are a few pages worth of questions for the options, so the explanation for the IBM one is somewhat limited. I'm not entirely sure about some of the details in your question, since I think you meant to use $10,000 as the value of the futures contract and $3 as the value of the underlying stock. Those numbers would make more sense. That being said, I can give you a simple example of how to calculate the profit and loss from a leveraged futures contract. For the sake of simplicity, I'll use a well-known futures contract: the E-mini S&P500 contract. Each E-mini is worth $50 times the value of the S&P 500 index and has a tick size of 0.25, so the minimum price change is 0.25 * $50 = $12.50.  Here's an example. Say the current value of the S&P500 is 1,600; the value of each contract is therefore $50 * 1,600 = $80,000. You purchase one contract on margin, with an initial margin requirement1 of 5%, or $4,000. If the S&P 500 index rises to 1,610, the value of your futures contract increases to $50 * 1,610 = $80,500. Once you return the 80,000 - 4,000 = $76,000 that you borrowed as leverage, your profit is 80,500 - 76,000 = $4,500.  Since you used $4,000 of your own funds as an initial margin, your profit, excluding commissions is 4,500 - 4,000 = $500, which is a 500/4000 = 12.5% return. If the index dropped to 1,580, the value of your futures contract decreases to $50 * 1,580 = $79,000. After you return the $76,000 in leverage, you're left with $3,000, or a net loss of (3,000 - 4000)/(4000) = -25%. The math illustrates why using leverage increases your risk, but also increases your potential for return. Consider the first scenario, in which the index increases to 1,610. If you had forgone using margin and spent $80,000 of your own funds, your profit would be (80,500 - 80,000) / 80000 = .625%. This is smaller than your leveraged profit by a factor of 20, the inverse of the margin requirement (.625% / .05 = 12.5%). In this case, the use of leverage dramatically increased your rate of return.  However, in the case of a decrease, you spent $80,000, but gained $79,000, for a loss of only 1.25%. This is 20 times smaller in magnitude than your negative return when using leverage. By forgoing leverage, you've decreased your opportunity for upside, but also decreased your downside risk. 1) For futures contracts, the margin requirements are set by the exchange, which is CME group, in the case of the E-mini. The 5% in my example is higher than the actual margin requirement, which is currently $3,850 USD per contract, but it keeps the numbers simple. Also note that CME group refers to the initial margin as the performance bond instead. yes, you are double counting. Your profit is between ($7.25 and $8) OR ($7.75 and $8.50). in other words, you bought the stock at $7.75 and sold at $8.00 and made $0.50 on top. Profit =  $8.00-$7.75+$0.50 (of course all this assumes that the stock is at or above $8.00 when the option expires. If it's below, then your profit = market price - $7.75 + $0.50 by the way the statement  won't call me away until the stock reaches $8.50 is wrong. They already paid $0.50 for the right to buy the stock at $8.00. If the stock is $8.01 on the day of expiration your options will be executed(automatically i believe). A bullish (or 'long') call spread is actually two separate option trades.  The A/B notation is, respectively, the strike price of each trade. The first 'leg' of the strategy, corresponding to B, is the sale of a call option at a strike price of B (in this case $165).  The proceeds from this sale, after transaction costs, are generally used to offset the cost of the second 'leg'. The second 'leg' of the strategy, corresponding to A, is the purchase of a call option at a strike price of A (in this case $145). Now, the important part: the payoff.  You can visualize it as so. This is where it gets a teeny bit math-y.  Below, P is the profit of the strategy, K1 is the strike price of the long call, K2 is the strike price of the short call, T1 is the premium paid for the long call option at the time of purchase, T2 is the premium received for the short call at the time of sale, and S is the current price of the stock.  For simplicity's sake, we will assume that your position quantity is a single option contract and transaction costs are zero (which they are not). P = (T2 - max(0, S - K2)) + (max(0, S - K1) - T1) Concretely, let's plug in the strikes of the strategy Nathan proposes, and current prices (which I pulled from the screen).  You have: P = (1.85 - max(0, 142.50 - 165)) - (max(0, 142.50 - 145)) = -$7.80 If the stock goes to $150, the payoff is -$2.80, which isn't quite break even -- but it may have been at the time he was speaking on TV. If the stock goes to $165, the payoff is $12.20. Please do not neglect the cost of the trades!  Trading options can be pretty expensive depending on the broker.  Had I done this trade (quantity 1) at many popular brokers, I still would've been net negative PnL even if NFLX went to >= $165. Simple math. Take the sale proceeds (after trade expenses) and divide by cost. Subtract 1, and this is your return. For example, buy at 80, sell at 100, 100/80 = 1.25, your return is 25%. To annualize this return, multiply by 365 over the days you were in that stock. If the above stock were held for 3 months, you would have an annualized return of 100%.  There's an alternative way to annualize, in the same example above take the days invested and dive into 365, here you get 4. I suggested that 25% x 4 = 100%. Others will ask why I don't say 1.25^4 = 2.44 so the return is 144%/yr. (in other words, compound the return, 1.25x1.25x...) A single day trade, noon to noon the next day returning just 1%, would multiply to 365% over a year, ignoring the fact there are about 250 trading days. But 1.01^365 is 37.78 or a 3678% return. For long periods, the compounding makes sense of course, the 8%/yr I hope to see should double my money in 9 years, not 12, but taking the short term trades and compounding creates odd results of little value. But an axiomatic approach only works in a deterministic environment, it does not work in a probabilistic environment. By your own arguments, because humans have free will so economics cannot be equated with a deterministic branch like physics. At this point now you are just contradicting yourself over and over.   And it depends entirely on how accurate the axioms are. If observations do not match equation outcomes, then while the mathematics of the equation might be sound, the obvious conclusion is that the axioms themselves are faulty.