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# A little quiz on trading returns

A book I’m currently reading (which will be reviewed later) presents a set of choices to the reader in terms of picking which sequences of market returns is the better choice. Let’s see how well you do.

1) Which set of returns produces the better final return?
A) -30%, +30%, -30%, +30%
or
B) -10%, +10%, -10%, +10%

2) What if we switch the sequence around?
A) +30%, -30%, +30%, -30%
or
B) +10%, -10%, +10%, -10%, +10%

3) How about adding an extra period?
A) -30%, +30%, -30%, +30%, +15%
or
B) -10%, +10%, -10%, +10%, 0%

4) What about if there are no negatives?
A) +10%, +10%, +10%, +10%
or
B) +20%, 0%, +20%, 0%

If you answered B, B, B, and A then congratulations!

If you did not, then you probably fell victim to thinking of the returns as being additive rather than multiplicative. By that I mean the final returns for question 1 are derived as follows:

A) 1 x (1-0.3) x (1+0.3) x(1-0.3) x (1+0.3) or 1 x 0.7 x 1.3 x.7 x 1.3 = 0.8281 or -17.19%
B) 1 x (1-0.1) x (1+0.1) x(1-0.1) x (1+0.1) or 1 x 0.9 x 1.1 x0.9 x 1.1 = 0.9801 or -1.99%

And because it doesn’t matter which order you do the multiplication in, the results for question 2 are exactly the same.

In the case of question 3, the added 15% return in period 5 isn’t enough to overcome the prior period’s ups and downs as 0.8281 x 1.15 only brings it back up to 0.9523.

For question 4 it’s again a simple pair of calculations

A) 1 x 1.1 x 1.1 x 1.1 x 1.1 = 1.4641 or +46.41%
B) 1 x 1.20 x 1 x 1.20 x 1 = 1.44 or 44%

The point the book authors are trying to make is the volatility impacts performance. The extension from there is that using risk management to at least reduce the size of your losers can increase your returns significantly.

## By John

Author of The Essentials of Trading

## 2 replies on “A little quiz on trading returns”

Maxsays:

Like anything else in life, the real answer that can’t be determined by simple math is; it all depends. In investing, it’s all about expectancy. Mathematically, it is the number of winning trades x the \$ average of the winning trades vs. the number of losing trades x the \$ aveage of the losing trades. The old saying of “cut your losses and let your winners run” will explain.

If you are a stock trader investing in a declining (bear) market and you set your stop at, say, 10%, one question is, “what do I do with my sale proceeds?” If your system calls for the purchase of another stock, you may also get another 10% loss. If your original stop was 20% rather than 10% you may be better off to have let the 10% loss run a little further.

Whatever you do, you’ve got to have done enough backtesting under various scenarios that you understand your system’s expectancy and you’ve adjusted your risk and money management plan accordingly to meet your objectives. Losses are part of investing and setting tight stops in a long-term investment plan can be counter-productive.

Well said Max. Too many traders/investors focus on the size of the stop and don’t give enough thought to the implications of its placement or how it fits within the context of the broader strategy.