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The Fad Is Not Your Friend—How Large Should You Go?

April 17, 2017
position sizing
Fredrik Broden

The market in 2017 won’t be like the market in 2016, which wasn’t like the market in 2015. Sure, there might be similarities. But what makes each market true to itself is perpetual uncertainty. To handle this ride as a trader, you need to keep learning, investigating, and evolving. Acquire as much knowledge as you can. And most of all, learn to apply that knowledge correctly.

Like all card players worth their salt, traders are forever on the hunt for the next hip “something” to give them an edge. Streaming quotes? Got ’em. Split-second order executions? Check. Customized market and account information updated in real time? Love it. Beyond that, traders are happy to poke around in whatever newfangled financial or statistical theories come down the pike. And one theory that routinely pops up in trading circles is the Kelly Criterion.

What Happens In Vegas …

Back in the 1950s, a super smart guy, John L. Kelly at Bell Labs, turned his attention to Las Vegas. For mathematicians, games of chance have long been a focus of study and source of inspiration. Kelly devised a new strategy for bet-sizing in blackjack and poker. Instead of betting $10 on every hand, he suggested a different amount, say, $5 or $20, depending on the difference between the theoretical probability of winning the hand versus the probability of success you think the hand has.

For example, consider a single deck of cards in a blackjack game. There are 16 cards with a value of 10 or higher (10, jack, queen, king) and four aces. If 12 of those “10” cards and three of the aces have already been played, you might adjust your strategy and bet according to a perceived increase in the probability of winning that hand. The Kelly Criterion therefore represents a percentage of your total “stake” that the theory suggests you wager. It goes like this:

Kelly % to bet = (prob of winning * payout – (1 – prob of winning)) / payout

Payout is the amount of money you’d get if you win a bet that costs $1. So, if you bet $1 to make $2, and you win, that’s a $2 payout on a $1 bet (i.e., 2:1 odds). And the probability of winning is what you estimate the likelihood of winning to be. As an example, let’s say you think the probability of winning a bet that pays $2 on a $1 bet is 40%:

Kelly % = (40% * 2 – (1 – 40%)) / 2 = 10%

The Kelly Criterion suggests you bet 10% of your stake on that single wager. If you have a $500 stake, you’d wager $50 on that bet. But what if you thought the probability of winning was only 20%?

Kelly % = (20% * 2 – (1 – 20%)) / 2 = -20%

If the Kelly Criterion gives you a negative result, you wouldn’t wager any amount on that bet.

Some curious traders found out about Kelly. They thought his ideas might help determine how many contracts they should buy or sell for a particular trade. Kelly, they deduced, might suggest one contract in one situation, or five contracts in another. Hey, if it’s good enough for Las Vegas, it’s good enough for trading, right? Well, as always, there’s a little fine print.

… Stays In Vegas

The formula compares the probability derived from the odds (win $2/bet $1) to how you perceive the probability of making a winning bet (40%, 20%, etc.). To derive probability from the odds, divide the cost of the bet, by the cost plus the payout. So, 2:1 odds would have a 1 / (2+1) = 33% probability of winning that $2 payout; 3:1 odds would have a 1 / (3+1) = 25% probability of winning that $3 payout.

In the 2:1 odds example, the odds say there’s a 33% probability you’ll win, but you think you have a 40% probability of winning. That’s the rationale for placing a 10% wager on that bet. Now let’s say you think you have a 50% probability of winning that 2:1 bet:

Kelly % = (50% * 2 – (1- 50%)) / 2 = 25%

Yikes! A 10% increase in your estimate of probability increases the Kelly Criterion percentage by 2.5. See the problem? If you incorrectly estimate the probability of making money, the amount you would wager (read “risk”) can vary widely. Some traders might estimate the probability of making money on a trade by looking at their history of making similar trades. If eight of the past 10 of those types of trades—say, short calls—have been profitable, then wouldn’t the next short call have an 80% probability of winning?

Not so fast. It’s possible to have strings of winning or losing trades that don’t necessarily reflect the future potential performance of the strategy. As you’ve often heard, past performance is never an indication of the future.

Now, this is not an exhaustive treatment of Kelly, but the point’s still the same. The “market” says there’s a 33% probability you’ll make money on that 2:1 bet. But you think you have a 40% or 50% probability of making money. The higher you go, the bigger your bet.

It takes a lot of guts and ego to think that your probability estimate for winning on a bet or trade is more accurate than everyone else’s. And if you trade too big based on assumptions, and you’re wrong, and the trade loses money, it can cost you a big chunk of capital.

It’s not that the Kelly Criterion is mathematically incorrect. When it comes to trading, there are so many variables that fixed odds for a single trade aren’t possible. Moreover, the market has thousands of participants driving stocks and options prices to an equilibrium that might represent a theoretical fair value. I’m not picking on the Kelly Criterion. There are options pricing models that use stochastic volatility inputs. It sounds great, until you try to come up with a predictive volatility model.

But the motivation for using the Kelly Criterion can be valid: You want some sort of method to determine how much you might risk on a given trade. Start with a more reasonable and safe assumption. Unlike card games, there are no “edges” in trading. Arbitrages don’t exist for retail traders. Guaranteed profits beyond simple risk-free interest rates don’t exist, either.

With all that out of the way, there are a couple of approaches to position sizing you could consider.

Position Sizes: Beyond Vegas

Capital Requirements. One approach suggests you can balance positions by capital requirements and/or risk. The amount of money required to put on a trade is determined by your broker, the clearing firm, and regulatory agencies. And that amount is typically tied to a position’s level of risk.

Riskier positions can have larger capital requirements. It doesn’t assume anything about the probability of making money or whether it’s a good or bad trade. But that assessment of risk can tell you something. If you don’t pick favorites, no position should require more capital or risk than others. This means the risk might be roughly balanced across positions in your portfolio. For example, if the other positions in your portfolio have $100 capital requirements or max losses, you might consider a trade with a capital requirement or max loss of $25. If a trade has a capital requirement or max loss of $200, maybe you pass.

Beta-Weighting. The second approach is similar to the first, but considers the beta-weighted deltas of your positions. Delta is a measure of market risk, and beta-weighting your position deltas to a common index, like SPX, basically lets you turn grapes and bananas into apples, then compare apples. For example, a position in ABCD might show a delta of +200, and a position in XYZ might show a delta of +50. But ABCD’s SPX beta-weighted deltas might be +75, and XYZ’s SPX beta-weighted deltas might be +100. You could say that the XYZ position is riskier than the ABCD position because XYZ could theoretically act like +100 deltas in SPX, versus +75 deltas in ABCD.

To see the beta-weighted deltas of your portfolio, hop on to your thinkorswim® platform by TD Ameritrade, select the Monitor tab, and look under the Position Statement section. If the beta-weighted deltas are roughly the same across the positions in your portfolio, the risk might be roughly balanced.

Now, to figure this out before you place a trade, you can see the beta-weighted deltas on the Analyze page, too. You can enter a simulated trade and see how its beta-weighted delta compares to the others in your portfolio (Figure 1). If it’s smaller, you might consider increasing the size of the trade. If it’s larger, you might consider trading fewer shares or contracts, or passing on the trade completely because it’s too risky.

analyze tab positions


From the Analyze tab, enter a simulated trade, select the beta-weighting option, and see how the delta of the trade stacks up against others in your portfolio. Source: thinkorswim by TD Ameritrade. For illustrative purposes only.

Gangsters Are a Mirage

Good position sizing can help keep your trading account out of trouble. Bad position sizing can destroy you. And any approach to position sizing can be misused. Luckily for you, you have the tools on thinkorswim to help analyze potential trades and your portfolio so you don’t rely on dangerous assumptions. Market uncertainty can threaten you all it wants with its Vegas-style tough talk. At the closing bell, put on a Frank Sinatra record, kick your feet up, and revel in your superior trading brain. After all, size matters.