To evaluate their performance accurately, it’s necessary for stock traders to calculate their rate of return. This is simple when there have been no external changes to the account, such as deposits or withdrawals, and all income and losses are due to trading.

The equation is:

However, external changes such as deposits or withdrawals complicate the calculations, as these must be accounted for and their influence removed from the computation. This is done by dividing the trading year into sections around the changes, computing the rate of return for each of those sections, and then combining them, to give the final overall rate of return.

First, break the year into sections. If one deposit was made into the account and later in the year one withdrawal taken from it, the trading year would be divided into three sections, e.g.:

•    the trading year before the changes;
•    the trading year beginning with the date of the deposit and extending to the day before the withdrawal; and
•    the trading year beginning with the date of the withdrawal and extending to the year’s close.

The equation above is used to calculate the rate of return for each of these sections of the trading year. Note that the ending balance for each section does not include the external change, e.g., the deposit or withdrawal, but the beginning balance of the next section does.

These sections are then chain-linked together, utilising the following equation:

R1 is the rate of return for trading undertaken in the first section of the year, R2 is the rate for the second, and so on. The number of sections and therefore the number of calculations required will of course vary from trader to trader, and from year to year.

Also note that percentages must be converted to decimals for the purpose of chain-linking. This is done by moving the decimal two positions to the left. Following the calculations, the decimal place is shifted back to its original position, to reflect percentages again.

Most importantly, don’t forget to subtract 1 at the end of the calculation.

As an example, Trader Vic began the trading year with a mini-account of $5,000. On 1 May, with his balance standing at $5,635, he deposited another $5,000 into the account. On 1 September, with his balance now at $12,225, he withdrew $5,000. At the end of the trading year, his balance was $8,125.

The trading year is divided into three around the deposit and withdrawal, and the rates of return, calculated for each, equal 12.7%, 14.9%, and 12.5%. The equation becomes:

A respectable rate of return in any market.

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