Starting with a hypothesis

What trades do you want to do? After you figure out what and how to trade, you can start setting forth what your strategy will be. Will you look for high-momentum, small-cap stocks? Seek price changes related to news events in agricultural commodities? Ride large-cap stocks within their ranges? Arbitrage stock index futures and their options?

After you do your research, you can lay out your strategy as a hypothesis, which may be something like this: “High-momentum, small-cap stocks tend to close up for the day, so I can buy them in the morning and make money selling them in the afternoon.” Or this: “News events take at least half an hour to affect corn prices, so I can buy or sell on the news and make a profit.” With this statement, you can move on to the test to see whether your hypothesis holds.

One of the most valuable parts about backtesting is that you have to be very specific about what your trading rule is. Computers cannot understand vague instructions, and if you find that your trading strategy is too complicated to write out and set into a backtesting program, it’s probably too complicated for you to follow.

Running the test

Say you start with something simple: Maybe you have reason to think that pharmaceutical companies that are moving down in price on decreasing volume will turn and close up for the day. The first thing you do is enter that into the software: the industry group and the buy pattern that you’re looking for. The results will show whether your hunch is correct and how often and for what time periods.

If you like what you see, you can add more variables. What happens if you add leverage (use borrowed money) in your trades? Leverage increases your risk of loss, but it also increases your potential return. How does that affect your trade? Suppose you increase the size of your trades, making fewer but larger ones. Would that help you make more money or less? By playing around with the system, you can get a good sense of the best way to make money with your trade ideas. You can also get a sense of when your rule won’t work, which can help you avoid problems.

If your strategy doesn’t work in testing, you want to ask yourself why not. Is your theory not as good as you thought, or are the markets different now? And if they are different now, how are they different? Unless you can answer those questions, you’re just engaging in wishful thinking, and wishful thinking will destroy any trader, no matter what the test results may be.

Most backtesting software allows for optimization, which means that it can come up with the leverage, position, holding period, and other parameters that will generate the best risk-adjusted return given the data on hand. You can then compare this result to your trading style and your capital position to see whether it works.

Backtesting is subject to something that traders call over-optimization, mathematicians call curve-fitting, and analysts call data mining. All these terms mean that the person performing the test looks at a past time where the market performed well and then identifies all the variables and specifications that generated that performance. Although over-optimization sounds great, what often happens is that the test generates a model that includes unnecessary variables and that makes no logical sense in practice. If you find a strategy that works when the stock closes up one day, down two days, then up a third day, followed by four down days when it hits an intra-day high, you probably haven’t made an amazing discovery; you’ve just fit the curve.

If the Chicago Cubs get in the World Series again, I know exactly what I will do: Everything I did in 2016, because if I do it wrong, they won’t win. Right? I’m not the only sports fan with weird superstitions. Human beings have evolved to see patterns, even when no pattern exists. It’s the same with the market. It’s entirely possible that, although the results of your test look great, they only show a random event that happened to work once. Maybe my choice of bar to watch Game 7 had nothing to do with the Cubs victory, as hard as that’s to imagine. That’s why you need to keep testing, even after you start trading.

Comparing the results with market cycles

The markets change every day in response to new regulations, interest rate fluctuations, economic conditions, nasty world events, and run-of-the-mill news events. (It’s like the joke about weather: If you don’t like it now, wait a minute, and it’ll change.) Different securities and strategies do better in some market climates than in others.

When you backtest, be sure to do so over a long enough period of time so that you can see how your strategy would work over different market conditions. Here are some things to check:

• How did the strategy do in periods of inflation? Economic growth? High interest rates? Low interest rates?
• What was happening in the markets during the time that the strategy worked best? What was happening when it worked worst? How likely is either of those to happen again?
• How does market volatility affect the strategy? Is the security more volatile than the market, less volatile, or does it seem to be removed from the market?
• Have major changes occurred in the sector over the period of the test? Examples of these types of changes include new technologies that increase demand for certain commodities or changes in regulation that make industries obsolete. Does this mean that past performance still applies?
• Have there been changes in the way that the security trades? For example, the bulk of trading in most commodities used to take place in open-outcry trading pits. Now, trading is almost entirely electronic. How do your test results look given current trading technologies?

In the capital assets pricing model, which is a key part of academic finance theory, the market risk is known as beta. The value that a portfolio manager adds to investment performance is known as alpha. In the long run, conventional finance theory says that the return on a diversified portfolio comes from beta; alpha doesn’t exist, so investors can’t beat the market in the long run. In the short run, where day traders play, this relationship may not be so strong.

Remember the maximum maxim in finance: Past performance is not indicative of future results. A strategy may test perfectly, but that doesn’t mean it will continue to work. Backtesting is an important step to successful day trading, but it is only one step.

AmiBroker

AmiBroker (www.amibroker.com) offers a robust backtesting service at a relatively low price. For that reason, it’s a popular choice with people who are getting started in day trading and who don’t have more expensive services. It also allows users to make sophisticated technical charts that they can use to monitor the markets. One drawback is that you may have to pay extra for the market-price-quote data, depending on what securities and time periods you want to test.

Investor/RT

Developed by a company called Linn Software (www.linnsoft.com), Investor/RT allows you to develop your own tests and create your own programs. It has packages for Macs, which makes it popular with traders who prefer Apple computers. Its users tend to be sophisticated about their trading systems and backtesting requirements; this software isn’t really for beginners.

MetaStock

As the name implies, MetaStock (www.metastock.com) is designed for traders who work in stocks, although a MetaStock package is available especially for currency traders, and the regular packages include capabilities for futures and commodities traders. It defines traders as end-of-day (those who make decisions about trading tomorrow based on numbers at the end of today’s trading) and as real-time (those who make decisions during the trading day). Most day traders are real-time traders. The company is owned by Thomson Reuters, a major financial-information services company.

NinjaTrader

NinjaTrader (www.ninjatrader.com) is a popular software package used for managing and programming traders. It includes great backtesting capabilities, too. The platform works with many different brokerage firms, for a fee, but the charting and trade testing capabilities are free. That may be why it’s become one of the most popular services for backtesting.

OptionVue

If you trade options, you may want to check out OptionVue (www.optionvue.com), which offers a range of analytical tools on the options markets. The software’s BackTrader module, an add-on feature, helps you learn more about options markets, test new strategies, and examine relationships between options and the underlying stocks — really useful information for people working in equity markets.

Tradecision

Tradecision’s (www.tradecision.com) trade-analysis software package is a little pricier than most retail trading alternatives, but it offers more advanced capabilities, including an analysis of the strengths and weaknesses of different trading rules. It can incorporate advanced money-management techniques and artificial intelligence to develop more predictions about performance in different market conditions. The system may be overkill for most new day traders, but it can come in handy for some.

TradeStation

TradeStation (www.tradestation.com) is an online broker that specializes in services for day traders. Its strategy testing service lets you specify different trading parameters, and then it shows you where these trades would have taken place in the past, using price charts. That way, you can see what would have happened, which is helpful if you’re good at technical analysis. It also generates a report of the strategy, showing dollar, percentage, and win-loss performance over different time periods. It doesn’t have a trade-simulation feature.

Trading Blox

The Trading Blox software system (www.tradingblox.com) was developed by professional traders who needed to test their own theories and who didn’t want to do a lot of programming to do it. It comes in three versions (and price levels), ranging from basic to sophisticated, and the company boasts that it works with some commercial trading firms. Of course, some of its capabilities may be more than you need when you’re starting out.

Income

When investors talk about income returns, they mean regular payments from their investments, usually in the form of dividends from stock or interest payments on bonds. As a day trader, you may earn income on the cash balance in your brokerage account but probably not from your trading activities.

Capital gains

A capital gain is the price appreciation in an asset — a stock, a bond, a house, or whatever it is that you’re investing in. You buy it at one price, sell it at another, and the difference is a capital gain. (Unless, of course, you sell the asset for less than you paid, and then you have a capital loss.)

For tax purposes, capital gains are classified as either long-term or short-term. Under the current tax law, any capital gain on an asset held for less than one year is considered to be a short-term gain, and if the asset is owned for one year or more before it’s sold, then it’s considered to be a long-term capital gain. The difference isn’t semantic; long-term capital gains are taxed at lower rates than short-term capital gains. You can read all about that and then some in Chapter 17.

Income in tax terms is different from income in financial terms. Much of what an investor would consider to be a capital gain, such as the short-term capital gains that day traders generate, the IRS considers to be income.

Calculating compound average rate of return (CAGR)

The most common way to calculate investment returns is to use a time-weighted average. This method is perfect for traders who start with one pool of money and don’t add to it or take money out. This is also called the compound average rate of return (CAGR). If you are looking at only one month or one year, it’s a simple percentage. To calculate performance on a percentage basis, you use this equation:

EOY represents the end of year asset value, and BOY represents the beginning of year value. The result is the percentage return for one year, and to calculate it, you use simple arithmetic.

Now if you want to look at your return over a period of several years, you need to look at the compound return rather than the simple return for each year. The compound return shows you how your investment is growing. You are getting returns on top of returns, and that’s a good thing. But the math gets a little complicated because now you have to use the root function on your calculator. The equation for compound annual growth looks like this:

EOP represents the end of the total time period, BOP represents the beginning of the total time period, and N is the number of years that you’re looking at.

The basic percentage rate of return is great; it’s an accurate, intuitive measure of how much gain you’re generating from your trading activities. As long as you don’t take any money out of your trading account or put any money into it, you’re set.

Calculating performance when you make deposits and withdrawals

You may be putting money into your account. Maybe you have a salaried job and are day trading on the side, or maybe your spouse gives you a percentage of his income to add to your trading account. You may also be taking money out of your day trading account to cover your living expenses or to put into other investment opportunities. All that money flowing into and out of your account can really screw up your performance calculation. You need a way to calculate the performance of your trading system without considering the deposits and withdrawals to your trading account.

Here’s an example: You start day trading on January 1 with $100,000 in your account. On May 1, your income tax refund from last year arrives, and you add $1,000 of the money to your account and start trading with it. On December 1, you take out $5,000 to buy holiday presents. At the end of the year, your account is worth $115,000. How did you do?

As a day trader, you have a few methods at your disposal for calculating your performance when you make withdrawals and deposits:

• The Modified Dietz method loses a little accuracy but makes up for it with simplicity.
• The time-weighted rate of return isolates investment and trading performance from the rest of the account.
• The dollar-weighted rate of return has many flaws but gives a sense of what the account holder has.

Read on to see the return that would be calculated using each of these methods.

MODIFIED DIETZ METHOD

The Modified Dietz method is related to the simple percent change formula, but it adjusts the beginning and ending period amounts for the cash inflows and cash outflows. The equation for the Modified Dietz method looks like this:

If you plug in the numbers from the example, you get

Do the math and you see that the result is 19.8 percent.

The advantage of the Modified Dietz method is that it’s so easy to do. You can use it when you want a rough idea of how you are doing with your trading but you don’t have the time to run a more detailed analysis. The key disadvantage is that it doesn’t consider the timing of the deposits and withdrawals. It would generate the same answer if you took out $5,000 in May and put in $1,000 in December, even though the amount of money you would have to trade between May 1 and December 1 would be very different.

TIME-WEIGHTED RATE OF RETURN

The time-weighted rate of return shows the investment performance as a percentage of the assets at hand to trade. This method is the standard of trader evaluation, but the math is much more complicated than with the basic percentage change or the Modified Dietz method. You need to calculate the CAGR for each time period and then do a second calculation to incorporate each of those over a longer period. Using the preceding example, you’d calculate one return for the first four months of the year, another for the next seven months, and then a third return for the month of December. These three returns would then be multiplied to generate a return for the year.

The general equation you use to figure the time-weighted rate of return looks like this:

N is the total number of time periods that you are looking at, and rpn is the return for that particular time period. To make the calculations easier, you can do it in a spreadsheet. Figure 13-4 shows the time-weighted return for this example. As you can see, the result is 18.78 percent, a little below the Modified Dietz return.

If you plan on adding to or taking money out of your account, you can make your return calculations much easier by setting a regular schedule and sticking to it. Otherwise, you have to do calculations for fractional time periods. It’s not impossible, but it’s kind of a hassle.

The time-weighted rate of return gives you the best sense of your trading performance, and its precision more than offsets the complexity of the calculation. You want to look at this number when you are deciding whether to change or refine your strategy.

DOLLAR-WEIGHTED RETURNS

The dollar-weighted return, also called the money-weighted return, is the rate that makes the net present value of a stream of numbers equal to zero. That calculation is also called the internal rate of return or IRR, and it is used for other things than just return calculations. You can use it to determine what the return is for a stream of numbers over time and to calculate returns when you’re putting money into or taking money out of your trading account. And if you have a financial calculator such as the Hewlett-PackardHP17BII+ or the Texas Instruments BA2+, the calculations are pretty easy.

Ah, but there’s a catch! Although useful, the dollar-weighted method can misstate returns and occasionally shows nonsensical results if too many negative returns appear in a series. And yes, day traders often have negative returns. If you get a result showing a ridiculously large positive or a ridiculously small negative return (like –15,989.9 percent, for example), you may want to try another calculation.

Figure 13-5 shows the dollar-weighted rate of return using the same data used in the two preceding examples.

The result is 12.1 percent, lower than the other two examples because the dollar-weighted return overstates the withdrawal and the loss in the last month of the year. The withdrawals affect the account’s spending power, offsetting the investment performance. But the overall account balance is up more than 12.1 percent, even considering the deposit at the beginning of May. The weight of the cash flows threw off this calculation.

Because of the problems with dollar-weighted returns, professional investors who analyze investment returns usually prefer the time-weighted, compound average approach. Still, the dollar-weighted return has some value, especially for an investor who wants to know how the asset value has changed over time. Because a day trader is usually both an investor and an account owner, the dollar-weighted rate of return can show whether the investment performance is affecting spending power. This measure is particularly useful if you are trying to decide whether to continue day trading.

Just as you have alternatives in calculating your performance, so too does anyone trying to sell you a trading system or training course. Ask questions about the performance calculation method and how cash flows and expenses are handled. The numbers may not look so great once you grade the math behind them.

Batting average — er, win-loss percentage

Baseball players are judged by how often they hit the ball. After all, they can’t score until they get on base, and they can't get on base without a hit or a walk. The number of hits relative to the number of times at bat is the batting average. It's a simple, beautiful number.

Day traders often calculate their batting average, too, although they may call it their win-loss percentage or win ratio. It's the same: the number of successful trades to the total number of trades. Not all trades have to work out for you to make money, but the more often the trades work for you, the better your overall performance is likely to be. If you have both good performance and a high batting average, then your strategy may have less risk than one that relies on just a handful of home run trades amidst a bunch of strikeouts.

Standard deviation

Want something harder than your batting average? Turn to standard deviation, which is tricky to calculate without a spreadsheet but forms the core of many risk measures out there.

The standard deviation calculation starts with the average return over a given time period. This is the expected return, the return that, on average, you get if you stick with your trading strategy. But any given week, month, or year, the return may be very different from what you expect. The more likely you are to get what you expect, the less risk you take. Insured bank savings accounts pay a low interest rate, but the rate is guaranteed. Day trading offers the potential for much higher returns but also the possibility that you could lose everything any one month — especially if you can’t stick to your trading discipline.

The explanation is a lot easier to understand after you take a gander at Figure 13-6.

As this figure shows, you calculate standard deviation through a series of steps:

1. Take every return over the time period and then find the average.

   A simple mean will do. Here, there are 12 months, so I added all 12 returns and then divided by 12.

2. Subtract the average from each of the 12 returns.

   This calculation shows how much any one return differs from the average, to give you a sense of how much the returns can go back and forth.

3. Square the differences you found in Step 2 (multiply them by themselves) to get rid of the negative numbers.

   When you add those up, you get a number known in statistics as the sum of the squares.

4. Find the average of the sum of the squares.

5. Calculate the square root of the average of the sum of the squares.

   That square root from this step is the standard deviation, the magic number you’re looking for.

Of course, you don’t have to do all of this math. Almost all trading software calculates standard deviation automatically, but at least you now know where the calculation comes from.

The higher the standard deviation, the riskier the strategy. This number can help you determine how comfortable you are with different trading techniques you may be backtesting, as well as whether you want to stick with your current strategy.

In academic terms, risk is the likelihood of getting any return other than the return you expect. To most normal human beings, there’s no risk in getting more than you expect; the problem is in getting less of a return than you were counting on. This is a key limitation of risk evaluation. Of course, a few periods of better-than-expected returns are often followed by a run of worse-than-expected returns as performance reverts to the mean.

The truism that past performance is no indicator of future results applies to risk as well as to return.

Performance relative to an index

The most common way to think about investment performance is relative to a market index. These are the measures of the overall market that are quoted all the time in the news, such as the Standard & Poor’s 500 and the Dow Jones Industrial Average. Not only are these widely watched, but many mutual funds and futures contracts also are designed to mimic their performance. That means investors can always do at least as well as the index itself, if their investment objectives call for exposure to that part of the broad investment market.

One big problem is that day traders often look at the wrong index for the type of investment that they have. They’ll compare the performance of trading in agricultural commodities to the Standard & Poor’s 500 when a commodities index would be a better measure. And the indexes assume that the assets in question are held for the long haul rather than traded every few minutes or every few hours.

If you aren’t sure what index to use, check a financial website such as Yahoo! Finance (http://finance.yahoo.com/indices) or check out the Market Lab section of Barron’s (www.barrons.com), a weekly financial publication put out by Dow Jones & Company, the same people who publish The Wall Street Journal and the Dow Jones Industrial Average. Both of these have lengthy lists of different stock, bond, and commodity indexes covering the United States and the world. You can find the one that best matches your preferred markets and use it to compare your performance.

In some cases, your trading practices may overlap more than one index. If so, pick the indexes that are appropriate and compare them only to those trades that match. If you trade 40 percent currencies and 60 percent metals, then you should create your own hybrid index that’s 40 percent currencies and 60 percent metals.

Performance relative to your time

In the earlier section “Pulling everything into a profit and loss statement,” where I talk about tracking your trades and doing a profit and loss statement, I say that you should calculate your hourly wage. There’s a reason for that. Instead of day trading, you could put your money in a nice, simple index mutual fund and take a regular job. If your hourly wage is less than what you can earn elsewhere, you may want to consider doing just that.

Of course, there are benefits to working on your own that don’t often show up in your bank account. I say this as someone who left finance to be a financial writer. If you enjoy day trading and if you make enough money to suit your lifestyle, by all means, don’t let the relative numbers stop you.

Performance relative to other traders

You probably want to know how you’re doing relative to other people who are trading. However, you’ll probably never know. No central repository of trading returns exists (although wouldn’t it be interesting if the brokerage firms or exchanges could report that?). Some academics have done studies of day trading returns, but they’re working with historic data stripped of customer information.

On message boards and at get-togethers, you may hear other traders talk about their returns. Take this information with an entire box of salt. Some people lie. Others exaggerate or obfuscate. Someone who has average or poor returns may want to lie to try to impress others, while those with great returns may not want to call attention to their prowess.

Ignore whatever other traders tell you about their returns. If you are satisfied with your performance relative to your risk and your time, nothing else matters.