Expectancy

I have mentioned the concept of “expectancy” a number of times on this site and a Platinum Member recently asked me for a reference to a post on the subject. The references are somewhere in the comments sections of various posts so I thought it might be more useful for me to dedicate a short, specific, post to the subject that is easier for members to find (through Search) in the future.

Expectancy refers to the expected return (relative to risk) that an investor might expect to generate from the use of a well-defined investment/trading “system” or Plan. It is therefore not specific to any particular “system” (Strategic Asset Allocation (SAA) Plan, Mean Variance Optimization (MVO) Methodology, Momentum System…etc) but is general and applicable to any/all “systems” and “ideas”.

To calculate expectancy we need 2 pieces of information:

1. The Win/Loss Ratio or % Winning Trades / % Losing Trades;
2. The Reward/Risk Ratio or size of Average Winning trade / size of Average Losing trade

We can then combine these two pieces of information to determine the Expectancy of our system:

Expectancy = (% Winning Trades x Average Winning Trade) – (% Losing Trades x Average Losing Trade)

For example, let’s assume that we have a “system” that has 60% winning trades and 40% losing trades and that when we win, we win $15 and when we lose, we lose $10. Then our “Expectancy” is:

(60% x $15) – (40% x $10) = $5

i.e. for every $10 (average loss) we risk we “expect” to make $5.

Obviously, for a system to be viable/profitable “expectancy” must be positive. Remember also that costs must be factored into this calculation.

This does not necessarily mean that our system must have more winning trades than losing trades to be profitable e.g. let’s assume we only have 45% winners and 55% losers in the above example, then we get:

Expectancy = (45% x $15) – (55% x $10) = $1.25

Clearly not as good as the first example, but still profitable. Obviously if our Reward/Risk ratio is higher we can afford to have a lower Win/Loss ratio and still remain profitable. Using the Reward/Risk ratio in the first example (1.5:1) our Win/Loss ratio can drop to 40%/60% before our “expectancy” drops to zero.

If our Reward/Risk ratio is small, then we need a high Win/Loss ratio to be profitable – this is why most investors prefer to “let profits run” and to manage risk.

Thus, if we want to “develop” a “system” that exits at a profit target this may result in a system that has a higher percentage of winning trades, but the average size of the winning trades may be smaller. Likewise, if we employ stops, we may have smaller losses but we may have more of them (some may have gone on to be winners if prices bounced – i.e have turned out to be winners).

No matter what “system” we choose to employ, we should always have the satisfaction of knowing that, over the long run, we have a positive “expectancy” of profit. This is often determined through back-testing.

David