Calculating the profit earned from a leveraged futures contract
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.
"The fact that dividends grow in perpetuity does not prevent one from calculating duration.  In fact, many academic papers look at exactly this problem, such as Lewin and Satchell.  This Wilmott thread discusses some of the pros and cons of the concept in some detail. PS: Although I was already broadly familiar with the literature and I use the duration of equities in some of my every-day work as a professional working in finance, I found the links above doing a simple google search for ""equity duration.""" In addition to the answer from CQM, let me answer your 'am I missing anything?' question. Then I'll talk about how your approach of simplifying this is making it both harder and easier for you. Last I'll show what my model for this would look like, but if you aren't capable of stacking this up yourself, then you REALLY shouldn't be borrowing 10,000 to try to make money on the margin. Am I missing anything? YES. You're forgetting (1) taxes, specifically income tax, and (2) sales commissions//transaction fees.  On the first: You have not considered anything in your financial model for taxes. You should include at least 25% of your expected returns going to taxes, because anything that you buy... and then sell within 12 months... is taxed as income. Not capital gains. On the second: you will incur sales commissions and/or transaction fees depending on the brokerage you are using for your plan. These tend to vary widely, but I would expect to spend at least $25 per sale. So if I were building out this model I would think that your break-even would have to at least cover: monthly interest + monthly principal payment income tax when sold commissions and broker's fees every time you sell holdings On over-simplifying: You have the right idea with thinking about both interest and principal in trying to sketch this out. But as I mentioned above, you're making this both harder and easier for yourself. You are making it harder because you are doing the math wrong. The actual payment for this loan (assuming it is a normal loan) can be found most easily with the PMT function in Excel: =PMT(rate,NPER,PV,FV)... =PMT(.003, 24, -10000, 0). That returns a monthly payment  (of principal + interest) of 432.47.  So you actually are over-calculating the payment by $14/month with your ballpark approach. However, you didn't actually have all the factors in the model to begin with, so that doesn't matter much.  You are making it artificially easier because you have not thought about the impact of repaying principal. What I mean is this--in your question you indicate:  I'm guessing the necessary profit is just the total interest on this loan = 0.30%($10000)(24) = $720 USD ? So I'll break even on this loan - if and only if - I make $720 from stocks over 24 months (so the rate of return is 720/(10000 + 720) = 6.716%). This sounds great-- all you need is a 6.716% total return across two years. But, assuming this is a normal loan and not an 'interest-only' loan, you have to get rid of your capital a little bit at a time to pay back the loan. In essence, you will pay back 1/3 of your principal the first year... and then you have to keep making the same Fixed interest + principal payments out of a smaller base of capital.  So for the first few months you can cover the interest easily, but by the end you have to be making phenomenal returns to cover it.  Here is how I would build a model for it (I actually did... and your breakeven is about 1.019% per month. At that outstanding 12.228% annual return you would be earning a whopping $4.) At least as far as the variables are concerned, you need to be considering: Your current capital balance (because month 1 you may have $10,000 but month 2 you have just 9,619 after paying back some principal).  Your rate of return (if you do this in Excel you can play with it some, but you should save the time and just invest somewhere else.) Your actual return that month (rate of return * existing capital balance).  Loan payment = 432 for the parameters you gave earlier.  Income tax = (Actual Return) * (.25). With this kind of loan, you're not actually making enough to preserve the 10,000 capital and you're selling everything you've gained each month.  Commission = ($25 per month) ... assuming that covers your trade fees and broker commissions. I guarantee you that this is not the deal breaker in the model, so don't get excited if you think I'm over-estimating this and you realize that Scottrade or somewhere will let you have trades at $7.95 each.   Monthly ending balance == next month's starting capital balance.  Stack it all up in Excel for 24 months and see for yourself if you like. The key thing you left out is that you're repaying each month out of capital that you'd like to use to invest with. This makes you need much higher returns.  Even if your initial description wasn't clear and this is an interest-only loan, you're still looking at a rate of about 7.6% annually that you need to hit in order to just break even on the costs of holding the loan and transferring your gains into cash. Damn, helpful Harry above me.   So, in general, when compounding the value of an investment, if you're seeing an annualized interest rate of 4%, and the interest compounds monthly (or n number of times per year), you're going to multiply the Principal P by the growth rate (the interest rate), adjusted for the number of periods that your investment grows in a year. P_end = P * (1 + 0.04/n)^(n * t), where n = number of periods, and t = number of years. If the interest compounds annually, you earn P *(1.04), if it compounds monthly, you earn (1 + 0.04/12)^(12 * 1).   Apply this logic to discounting future cash flows to their net present value. When discounting future cash flows, you're essentially determing the opportunity cost of now being unable to put your investment elsewhere and earning that corresponding interest (discount) rate.   Thus, you would discount $1000 by (1 + 0.08/12)^1, and $2000, $3000 in a similar fashion. Then, as icing on the cake, sum up to get your cumulative net present value.  Please let me know if any portion of my explanation is unclear; I would be happy to elaborate! "When margin is calculated as the equity percentage of an account, the point at which a broker will forcibly liquidate is typically called ""maintenance margin"". In the US, this is 25% for equities. To calculate the price at which this will occur, the initial and maintenance margin must be known.  The formula for a long with margin is: and for a short where P_m is the maintenance margin price, P_i is the initial margin price, m_i is the initial margin rate, and m_m is the maintenance margin rate.  At an initial margin of 50% and a maintenance margin of 25%, a long equity may fall by 1/3 before forced liquidation, a short one may rise by 50%. This calculation can become very complex with different asset classes with differing maintenance margins because the margin debt is applied to all securities collectively." "The other two folks here are right with the math and such, so I'll just throw some intuition out there for you.  The basis for this valuation model is really just tacking the Gordon growth model (which is really just a form of valuing a perpetuity) onto a couple of finite discounted cash flows. So that ending part is the Gordon growth model *at the future point* discounted back to the present.  The Gordon growth model uses a ""next period"" dividend for the very simple reason that it's the next one you'd get if you bought the stock.  Is that explanation clear enough, or were some of these points not adequately explained in your class? I'll help a bit more, if I can." leveraged etf's are killer to hold because they seek to return some multiple of the DAILY price movement in an index. so twm seeks to return 2x the daily move in the russell 2000 Let's trace this out assuming (just to make it easy) large daily moves, and that you start with $1000 and the russell 2000 starts at 100. start of first day rusell 2000 == 100 you have $1000 end of first day (up 10% nice!) rusell 2000 == 110 you have $1200 end of second day (~9.1% down) russell 20000 == 100 you have $981.60 so the russell 2000 can move nowhere and you have lost money! This doesn't apply to all etf's just leveraged etf's.  You would be better buying more of a straight inverse etf (RWM) and holding that for a longer time if you wanted to hedge. As Chris pointed out: If your expenses are covered by the income exactly, as you have said to assume, then you are basically starting with a $40K asset (your starting equity), and ending with a $200K asset (a paid for home, at the same value since you have said to ignore any appreciation). So, to determine what you have earned on the $40K you leveraged 5x, wouldn't it be a matter of computing a CAGR that gets you from $40K to $200K in 30 years? The result would be a nominal return, not a real return. So, if I set up the problem correctly, it should be: $40,000 * (1 + Return)^30 = $200,000 Then solve for Return. It works out to be about 5.51% or so. The owner of a long futures contract does not receive dividends, hence this is a disadvantage compared to owning the underlying stock. If the dividend is increased, and the future price would not change, there is an arbitrage possibility. For the sake of simplicity, assume that the stock suddenly starts paying a dividend, and that the risk free rate is zero (so interest does not play a role). One can expect that the future price is (rougly) equal to the stock price before the dividend announcment. If the future price would not change, an investor could buy the stock, and short a futures contract on the stock. At expiration he has to deliver the stock for the price set in the contract, which is under the assumptions here equal to the price he bought the stock for. But because he owned the stock, he receives the announced dividend. Hence he can make a risk-free profit consisting of the divivends. If interest do play a role, the argument is similar. Is the following correct?  The firm needs $20,000 for the investment. It borrows $6,000 @ 7%, and supplies $14,000 in equity.  The interest expense on the borrowing is $420 ($6,000 times 7%).  After one year, the firm receives $26,500 from its investment. Subtract $6,420 (return borrowings plus interest). The firm is left with $20,080. Divide by starting equity of $14,000. Subtract 1 from the ratio.  **Levered return on equity is 43.4%.** I have found a good explanation here: http://www.contracts-for-difference.com/Financing-charge.html Financing is calculated by taking the overall position size, and multiplying it by (LIBOR + say 2%) and then dividing by 365 x the amount of days the position is open. For instance, the interest rate applicable for overnight long positions may be 6% or 0.06. To calculate how much it would cost you to hold a long position for X number of days you would need to make this 'pro rata' meaning that you would need to divide the 0.06 by 365 and multiply it by X days and then multiply this by the trade size. So for example, for a trade size of $20,000, held for 30 days, the interest cost would be about $98.6. It is important to note that due to financing, long positions held for extended periods can reduce returns. I think you're missing the fact that the trader bought the $40 call but wrote the $45 call -- i.e. someone else bought the $45 call from him.  That's why you have to subtract 600-100.  At expiration, the following happens: So $600 + -$100 = $500 total profit. Note: In reality he would probably use the shares he gets from the first call to satisfy the shares he owes on the second call, so the math is even simpler: "Of course, which is why you need to have a scoring function / utility function for the ""filters"", i.e. Are you going to value it by rate of accuracy hor by a metric where wins = +2, losses = -1, such that it uses a criteria like that to decide whether or not a filter adds value, (some even use a compound effect i.e. wins = 2+e^(1+w) where w is the consecutive wins).  A metric like the above would capture the trade off between predictive power and profit. Also some traders watch their Max DD very carefully so they may be very risk averse." Ok so I used Excel solver for this but it's on the right track.  Latest price = $77.19  Latest div = $1.50  3-yr div growth = 28%  g = ???  rs = 14%  So we'll grow out the dividend 3 years @ 28%, and then capitalize them into perpetuity using a cap rate of [rs - g], and take the NPV using the rs of 14%. We can set it up and then solve g assuming an NPV of the current share price of $77.19.  So it should be:  NPV = $77.19 =   [$1.50 / (1+0.14)^0 ] +  [$1.50 x (1+0.28)^1 / (1+0.14)^1 ] +  ... +  [$1.50 x (1+0.28)^3 / (1+0.14)^3 ] +  [$1.50 x (1+0.28)^3 x (1+g) / (0.14-g) / (1+0.14)^4 ]  Which gives an implied g of a little under 9%. Let me know if this makes sense, and definitely check the work... The initial margin is $5940 and maintenance margin $5400.  A simple search of Comex Gold Margin gives the CME group site. You then need to specify CMX metals to see the margins.  Gold is currently about $1300. A gold future is 100 oz. So the full contract is worth $130K. You want to 'go long' so you enter into a contract for Dec '14. You put up $5940, and if gold rises, you gain $100 for each $1 it goes up. Likewise on the downside. If gold drops $5.40, you lost $540 and will get a call to end the position or to put up more money. It's similar to stock margin requirements, only the numbers are much lower, your leverage with futures is over 20 to 1. Profit after tax can have multiple interpretations, but a common one is the EPS (Earnings Per Share).  This is frequently reported as a TTM number (Trailing Twelve Months), or in the UK as a fiscal year number.  Coincidentally, it is relatively easy to find the total amount of dividends paid out in that same time frame. That means calculating div cover is as simple as:  EPS divided by total dividend.  (EPS / Div). It's relatively easy to build a Google Docs spreadsheet that pulls both values from the cloud using the GOOGLEFINANCE() function.  I suspect the same is true of most spreadsheet apps.  With a proper setup, you can just fill down along a column of tickers to get the div cover for a number of companies at once.