Trading: Getting Position Size Right

I often mention that the most important – and easiest – risk management technique is choosing the initial position size for any trade. The tradeoff comes from owning a position that allows us to earn sufficient profit, without taking on too much risk. This is a topic that I approach from a ‘keep it simple’ method. However, there are always some traders who appreciate a more detailed mathematical analysis of how a trader makes this decision. This post is for such readers.

There is one important point to keep in mind. The discussion below provides a formula for choosing investment size. There are many reasons why an individual trader may be uncomfortable with this statistical approach. For one, the math may be correct, but we often have a bias based on our previous experience (I call that ‘evidence’) that suggests a specific trade may offer a better (or worse) opportunity than comparable trades. Ignoring that evidence is not prudent. As option traders we must recognize that each bet is not identical to the others because we are not in a casino with a freshly shuffled deck of cards, or fresh turn of a wheel. Instead we are in the marketplace where we can observe many items that influence the market. Even when we cannot predict direction, it may be clear that today’s (name the strategy) trade is vastly different from a similar trade occurring in another time slot. As a simple example, would anyone truly want to make the same standard-sized trade when facing the market debacle in Nov 2008 vs. making a similar trade today? I know that I wouldn’t. I’d do something differently: smaller size, lower deltas for my short options…

Beyond that, this system was designed for casino wagering, when each spin of the wheel is identical in probability to every other spin of the wheel (assuming that there is no cheating). When betting on roulette, we are unlikely to place a disproportionately large bet on a single roll. Contrast that with blackjack and a card-counting system. If you can get beyond the fact that casinos no longer welcome card counters, when we were able to count cards and know when our odds of success against the dealer were much higher than normal, it was natural to increase our wager. Similarly, the option trader knows when it pays to reduce (or increase) risk because of circumstances that the mathematical model cannot know exist.

There should be a place in our investing arsenal of tools for a system that offers guidance, even if it comes with limitations. From that perspective, I offer this discussion. Do not be concerned if the math is beyond you.


Kelly’s strategy

If you have a specific cash bankroll, how much should you wager on each play to maximize the gain and minimize the loss? The goal: Increase that bankroll over the long term.

Kelly used the strategy of betting a fixed portion of the bankroll on each wager, discovered that when you bet a small fraction, you never go bankrupt. However, wealth grows quite slowly. When the fraction wagered is large, the chances of ruin are increased.

Kelly’s answer: The right balance is to bet the size of your advantage. In other words, when the bet is even money and your chances of winning/losing are 52/48, bet that difference, or 4% of your bankroll. To work, many bets are required. Thus, the long term.

From Wikipedia:

The Kelly criterion is a formula used to determine the optimal size of a series of bets. In most gambling scenarios, and some investing scenarios, the Kelly strategy will do better than any essentially different strategy – in the long run.

There is a big ‘however’:

As Kelly’s original paper demonstrates, the criterion is only valid when the investment or “game” is played many times over, with the same probability of winning or losing each time, and the same payout ratio.

When trading, the odds are almost never identical because each wager comes with a different set of market conditions.

For the mathematical details of how to plan the wager, see the Wikipedia article. Note: This is not for everyone.

Why Position-Sizing Is Critical to Options Success

This post is of interest. The version below is edited.

Jul 10, 2012 By Traders Reserve

The rally over the past few weeks has occurred at a blistering pace. Only 8 times in the past 60 years has the S&P 500, pushed lower by 10% or more one month, only to rally more than 10% in the following month. Each rally came in the middle of a bear market.

The strategy of most professional options traders is some variation of a credit spread.

Truth be told, the first few months of the year was tough for traders using credit spreads. Even those of us who trade out-of-the-money credit spreads took losses.

When asked by subscribers in Options Advantage how to handle extreme moves in the market, I tell them that the simplest and most effective method is appropriate position-sizing.

It is imperative that your account size and risk tolerance be taken into account when determining appropriate position-sizing.

Even if we use strategies intended to take advantage of huge moves, we can still lose. No trade is a lock. No guaranteed winners exist. Position-sizing is always important.

How do you know how much to trade? My favorite guideline is the Kelly Formula.

In probability theory the Kelly criterion/strategy is used to maximize the long-term growth rate of repeated plays of a given trade that has positive expected value.

The formula specifies the percentage of the current bankroll to be bet (invest/trade) at each iteration.

In addition to maximizing the profit, the Kelly strategy also includes the added benefit of having a zero risk of ruin; the formula will never allow for a loss of 100% of the bankroll on any trade.

If you want to be a successful trader/investor over the long term, then taking the time to figure out an appropriate position-sizing plan is imperative. Please, please, please do not overlook this important concept.

You will not regret it.

I concur. It’s key to keep it simple. For those who want a more reliable plan, give Kelly a try. My major complaint with the system is that we do not know the probability of winning and cannot easily adapt the system to our methods.

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