George Pearson thinks he had a pretty good year last year. He saw his portfolio grow from $260,000 at the beginning of the year to $356,714 by year-end. But part of that growth was due to a fairly large addition to his portfolio—$50,000 he received from a small inheritance mid-year. He also made a series of withdrawals—$1,200 each quarter—and he added $5,000 to his portfolio toward the end of the year.

So, how did he really do? What George needs to do is to figure out the return on his portfolio.

What’s in a Return?

An investor’s total portfolio return consists of the change in value of the portfolio, plus any income provided by the portfolio during the investment period. Translating this into an equation, assuming no additions or withdrawals, is relatively simple; it compares the ending value to the beginning value to determine a percentage change in value:

Using the equation for George’s portfolio results in a 37% increase in value. But for George’s situation, this is misleading—although his portfolio did increase 37% last year, a good part of that was due to his own cash infusion into the portfolio. This equation, then, does not answer his question concerning how well his invested assets performed.

The most accurate measure of portfolio performance is the internal rate of return, also known as the compound return. This provides the actual return that the portfolio received over a certain time period, taking into consideration all “cash flows” and their timing. How do cash flows affect the return?

Money added to the original investment is not part of the investment’s return, but anything the addition earns is part of the return. For example, if you add $1,000 to a portfolio at the beginning of the year, it works for you (or against you, if the investment sours) for a longer time than if you were to put it in at the end of the year; yet in both situations, you have added the same amount—$1,000—to the same original portfolio value.

The formula for determining a compound total return is too complex to do by hand. Instead, a financial calculator or computer is needed; many financial software programs exist to help investors accurately determine their return.

George, however, doesn’t have a computer or financial calculator. How can he measure his portfolio return? There are several measures George can use to determine an approximate return on his portfolio.

The Approximation Method

One approach is to use the approximation formula. It is relatively simple and reasonably accurate—close enough to make an informed decision. The information needed to perform the calculation is contained in brokerage and mutual fund statements.

The return calculation compares ending values to beginning values and adjusts for net additions or withdrawals by subtracting 50% of net additions from the ending value and adding 50% to the beginning value. The 50% adjustment to both the beginning and ending values creates a midpoint average for the cash flows no matter when they were actually made. The equation is more accurate when additions and withdrawals are relatively periodic and are not large (greater than 10%) relative to total portfolio value.

Table 1 illustrates the equation for George’s portfolio: Half of his net additions of $50,200 are subtracted from the $356,714 ending value, and half are added to the $260,000 beginning value; dividing the adjusted ending value by the adjusted beginning value and subtracting 1.0 results in a portfolio return of 16.3%. That compares to an internal rate of return (IRR) for the portfolio of 16.5% (the IRR calculation was performed using Captool, a popular portfolio management program).

In this example, George’s net additions of $50,200 represent a substantial portion of his total portfolio value. However, the bulk of the addition—$50,000—occurred mid-year, so the approximate return equation is relatively close to the more accurate internal rate of return figure. If George’s $50,000 addition had occurred at a different time, the approximation equation would be less accurate.

Time-Weighted Returns

Another measure of portfolio performance, particularly useful when large additions or withdrawals are made, is to determine the time-weighted return.

This method is relatively straightforward: Returns are determined for each subperiod up to the point in time when the addition or withdrawal occurs, and for the subperiod after the addition or withdrawal. These subperiod returns are then linked together (compounded) to produce a total return for the overall period. To link together the subperiod returns, you simply add 1.0 to each subperiod return (in decimal form), and multiply all the subperiod factors. This approach is illustrated in Table 1.

• If cash inflows and outflows are substantial, and you want to determine how well your invested assets performed—in other words, how much your money earned for you during the year—you should use a calculator or computer program that can perform an internal rate of return calculation. 

• If cash inflows and outflows are substantial and you want to measure your success as a decision-maker—how well did your selection of assets perform relative to a benchmark portfolio or another manager—use the time-weighted return equation, or its approximation, the weighted portfolio return. 

• If you want to brag to friends about how well your portfolio did—use whichever return is higher. 

This article was written by Maria Crawford Scott for the April 1998 issue of the AAII Journal. At the time, Crawford Scott was editor of the AAII Journal.