Least Understood Risk Management Concept: Coefficient of Likelihood

Wednesday, October 06, 2010

Normal Distribution
If you're still reading this after the title at least I haven't already bored you with the statistical jargon. The Coefficient of Likelihood is defined as the probability that an event will occur. In risk management, given a variety of possible future scenarios, each one can be assigned a percentage chance of happening. Most of us are not quantitative analysts with degrees in mathematics but the following is a framework for thinking about risk management and perhaps it will add an element to your decision-making process.

The understood side of the risk equation

Nearly every trader is taught from day one to measure the risk versus the reward of a trade before taking a position. Traders should and will typically focus on the risk first, the reward second. An important note: the risk is defined by the setup and should reflect the dynamics of the intended trade. This is a key initial point, the setup dictates the risk of loss per share, you dictate the P&L loss by your choice of size. Too many traders attempt to risk less by putting their stops at arbitrarily closer levels rather than respecting what the trade itself calls for. In order to put on a position, the trader should figure out the appropriate stop out level, then determine the dollar value they're willing to risk and back into the number of shares. But, not before considering probability as I explain below.

The reward side of the equation is often taught to be at least 2-to-1 versus risk. Some teach to look for scenarios with a much higher ratio but 2-to-1 is usually the accepted minimum. Reward can be measured in any variety of ways. Technicians will look at measured moves, Fibonacci extensions, subsequent support and resistance levels and the like. Fundamentalists will use valuation tools to forecast expected growth in earnings and possible expansions in multiples. Any way you slice it, calculating some idea about the possible reward is important for understanding whether the trade is a good bet relative to the assumed risk.

The poor approach to risk

Most traders understand the above concept in risk management and use it to their advantage by hunting around to discover the lowest risk/highest reward trade setups. They will let the trade's risk then dictate their position sizing based on the total dollar value they are willing to lose. The irony arises in that this is often the worst possible thing a trader could do! It is counter-intuitive yet without some deeper, more sophisticated analysis taking only the lowest risk/highest reward trades will likely lead to consistent losses. The reason for this derives from the Coefficient of Likelihood that too many traders ignore or never consider in their analysis.

The least understood side of the risk equation

The crucial component of the equation is the probability of each event: the stock hitting the stop or achieving the reward. The reason the counter-intuitive statement, that lowest risk/highest reward trades are often poor decisions, is true deals with the likelihood of the trade working out. In most cases, the seemingly lowest risk trade is trend-fighting. As the famous saying goes, "the trend is your friend" and as was later wisely added "until the bend at the end". The reason the extremely low risk/high reward trade may exist is because its probability of success is very low. Without accounting for the likelihood of success, the trader may be taking trades that actually have very poor expected returns.

Say a stock has rallied $5 and come off $1. A trader measuring risk/reward without probabilities thinks "if I short here, I'll risk $1 and if the stock reverses, I can make $4". So, the risk:reward is 1:4. But, say the stock has been trending higher for weeks, the broad market is very bullish and the stock is not extended. The probability of this trade working may be very low, say a 20% chance of it actually rolling over and achieving your measured reward. Therefore, using the Coefficient of Likelihood you find:

Expected risk: (80% x $1)= $0.80
Expected reward: (20% x $4)= $0.80

By considering the probability that your trade actually works out, you find that the risk/reward is actually equivalent and therefore not worth the trade as commissions will knock you into the red for the net expected outcome.

How to use this concept

It is my belief that the best traders do not simply find the lowest risk and highest reward trades and dictate their sizes accordingly. The best traders have a feel for the market and an intuition about probable future direction. Using this feel these traders know when the probabilities have shifted in their favor and only then put on larger position sizes. Most traders are not quants and so they do not precisely calculate the odds of success, and I doubt you even can do that. But under this framework, traders can begin to consider how probable a trade is. A very low risk trade that will probably not work out is often a terrible trade because it's virtually guaranteed to be a loser. At the same time, seemingly more risky trades that require larger stops may have the highest probabilities of success and, as such, be much less risky.

Many of the best trades require some of the largest risk in nominal terms because the probability of success is so high. These two go hand-in-hand because the broad market is all believing a trade will work and every trader is trying to get in. This scenario very often occurs with large gaps to the upside or downside. The novice trader will believe his risk is too great so he chooses not to put on a trade believing he missed the move and would be chasing prices. While the expert trader may have expected the gap and understands that the market is repricing stocks based on changed expectations. The gap is simply acting as confirmation that the trade to that direction is the correct trade and prices have moved away because so many others believe the same thing.

Amateur traders assume that every trade is 50/50 as far as probability goes. I think after years of experience and the development of a feel for the tape, most will know that many trades have much worse chances of success while others have much better. Considering trend is very important as it often increases your probability of success and will allow for greater risk-taking in terms of stock movement because the expected value is higher.

Brandon R. Rowley
"Chance favors the prepared mind."

*DISCLOSURE: Nothing relevant.
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