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# Expectancy

Expectancy - What is it, and why is it important?

Expectancy is one of the performance metrics that MCI uses to assess the overall profitability of our trading strategies. Very simply, it is a statistical measure of a strategy’s profit (or loss) potential, determined over a period of time sufficiently long enough to include a meaningful representation of trading outcomes.

The formula for Expectancy is:

$$E = (P_w \cdot \overline{R_w}) – (P_l \cdot \overline{R_l})$$

where $P_w$ is the probability of a winning trade, $P_l$ is the probability of a losing trade, $\overline{R_w}$ is the average return of a winning trade, and $\overline{R_l}$ is the average return of a losing trade.

If $\overline{R_w}$ and $\overline{R_l}$ are expressed in dollar amounts, then the expectancy will be expressed in dollars as well, and will represent – on the average, the amount of dollars gained (or lost) per dollar invested. If $\overline{R_w}$ and $\overline{R_l}$ are expressed as percentages, then the expectancy will also be a percentage value, and will represent – on the average, the percent gain (or loss) of a trade.

Regardless of how the formula is used, several important points should be noted:

1. Expectancy is a statistical measure. It cannot and does not predict with 100% accuracy, the future potential of any trading strategy.
2. If the expectancy is a positive number, the strategy will likely be profitable in the long-term.
3. Conversely, if expectancy is a negative number, the strategy will likely NOT be profitable in the long-term.
4. A high $P_w$ (> 50%) does not guarantee a profitable strategy. Nor does a low $P_w$ ( < 50%) guarantee an unprofitable strategy.

The reason expectancy is important stems primarily from #4 above. A strategy may be advertised as having an “Extremely high $P_w$”. In fact, most of our strategies do have very high $P_w$ values. However, that doesn’t tell the whole story. A couple of examples will help to illustrate this point more clearly:

Example #1 – High $P_w$, but not a profitable strategy In this example, a strategy has a $P_w$ of 60%, so the $P_l$ is 40%. The average win is $300, and the average loss is$500.

We calculate the expectancy, $E$, as:

$$E = (0.6 \cdot 300) – (0.4 \cdot 500)$$

This results in an expectancy of -$20 So we see that even though the strategy has winning trades more than half of the time, the expectancy is negative, and will likely produce losses of$20 per trade, on the average, over the long term.

In the next example, we look at a strategy that produces winning trades less than half of the time, but is more likely to be profitable.

Example #2 – Low $P_w$, but still a profitable strategy

In this example, a strategy has a $P_w$ of 45%, so the $P_l$ is 55%. The average win is $250, and the average loss is$140.

We calculate the expectancy as:

$$E = (0.45 \cdot 250) – (0.55 \cdot 140)$$ This results in an expectancy of $35.50 So here we see that even though the strategy has winning trades less than half of the time, the expectancy is positive, and will likely produce profits of$35.50 per trade, on the average, over the long term.

Two methods we use at MCI to help improve expectancy are:

1. Extensive backtesting over a long period of time and a variety of market conditions, utilizing optimization techniques such as MonteCarlo analysis, which allows us to fine-tune strategy parameters to produce more reliable entry and exit triggers, leading to a higher $P_w$ and Average Win values.
2. Prudent use of stop-losses helps to limit Average Loss to a risk-appropriate value

All of our products are engineered to produce exceptional return potential while maintaining a reasonable downside risk profile. Read more about our products here.