Calculating Your Return: Pay Attention, Ladies

When the Beardstown Ladies revealed last week that the return on their stock portfolio was far less than previously touted, the revelation no doubt left many individual investors scratching their heads.

If the authors of five well-known investment books can’t calculate the return on their portfolio--thinking they had earned 23.4% a year when they really made only 9.1%--how are you supposed to figure your performance?

Indeed, it’s tough for amateur investors to calculate their exact returns because doing so is time-consuming and complex.

But don’t despair. Small investors can quickly and easily get a close approximation of their returns, either by hand or with the help of a computer and spreadsheet program. And for most investors, that’s more than good enough.

“I don’t know that a totally accurate figure is all that important,” said Maria Crawford Scott, editor of the Chicago-based American Assn. of Individual Investors’ monthly newsletter. “Getting it down to the hundredths of a percentage point isn’t going to make you a better investor. Your time is better spent on other financial matters.”

To show how to do the numbers by hand, let’s start with a formula from the AAII that can be used to calculate the annual return on a brokerage account.

Before you start, you’ll need to know the value of the account at the beginning of the year and at the end. You also must know how much you added to, and subtracted from, the account through the year.

In basic terms, here’s how the formula works: You’ll take the ending value of the account and adjust it by half of your total net additions or withdrawals. You’ll make a similar adjustment to the beginning value. (We’ll explain this half-of-the-total business later.)

Then, you’ll get the return by dividing the ending value by the beginning value.

You must pay special attention to dividends or interest payments you received from the account if you did not automatically reinvest them.

Why keep track of that unreinvested income? Because interest and dividends are part of the account’s total return. If you kept them in the account, you don’t have to worry about them in this tabulation. But if you didn’t reinvest them--in other words, they were paid out to you--you technically withdrew that money from your account and must remember to figure it back in when assessing your return.

Let’s take a hypothetical account worth $35,000 at the start of the year and $50,000 at the end. The investor added $5,000 in new money through the year but also had $2,000 in dividends mailed to him.

What was the portfolio return? Using the formula above, start by adding that unreinvested income to the ending value of the account. In our example, add $2,000 to $50,000, giving you $52,000.

Then, separately, subtract money you’ve taken out of the account from any money you’ve put in, such as regular contributions. In our example, we have net additions of $5,000. Multiply that amount by 0.5 for a result of $2,500.

Why do you multiply by 0.5? Because, for ease of calculation, you’re assuming that half of your net additions came in the first six months of the year and the other half in the second six months.

The approximation method works best when you make regular contributions and withdrawals. It would be skewed, however, if you put in, or took out, large amounts at irregular intervals.

If you wanted to figure your exact return, you’d have to know the precise timing of every contribution and withdrawal. That in itself is laborious, not to mention that you’d have to do many different calculations to account for the sums involved and their timing. The effort is probably not worth it.

Next, subtract the $2,500 in adjusted net additions from the $52,000 arrived at earlier. That leaves $49,500, which is the numerator.

Now, let’s calculate the denominator.

Add the account value at the beginning of the period, $35,000, to the adjusted net additions, $2,500. That gives us $37,500.

Here’s the grand finale: Divide the numerator, $49,500, by the denominator, $37,500. That leaves 1.32. Subtract 1 to reach 0.32 and, to switch it from a decimal to a percentage, multiply by 100. That gives the final result: a return of 32%.

This formula also would work for an investor’s overall portfolio.

Say someone had a brokerage account, a few mutual funds and a 401(k) retirement account. Instead of doing the calculations for just one account at a time, you can do them for the entire portfolio at once.

To get as accurate a return as possible for any account, do this calculation frequently, such as quarterly, Scott advises.

Here’s another formula you may need:

Say you figure your returns quarterly using the example above. You’ll naturally want to know your annual return. Once you have the four quarterly numbers, you can easily get that annual figure.

Imagine that a stock portfolio returns 2.5% in the first quarter, 5% in the second, 7.5% in the third and 10% in the fourth. Turn those figures into decimals and add 1 to each: 1.025, 1.05, 1.075 and 1.10. Multiply them in that order, subtract 1 and multiply by 100. The answer: a return of 27.3%.

If you have a computer and the Microsoft Excel spreadsheet program, it’s even easier to calculate the return on your portfolio.

Consider an example calculated with the help of Olivier Ledoit, a finance professor at the Anderson School at UCLA.

Your account has $5,000 at the start of the year and $7,500 at the end. The investor adds a net $1,515 through the year. What’s the return?

Within the Excel spreadsheet, type 5,000 in the first box, or cell, in column A. That’s the money in the account at the beginning of the year. In each cell below that, type in these amounts, in order, as per Ledoit’s example: 600; -380; -100; 325; 325; 200; -405; 300; 1,000; -300; -50.

Those are the net amounts that were either added to, or withdrawn from, the account each month.

In the 13th cell, type in -7,500. The account has $7,500 but the program requires the information be entered this way.

In the cell below that, type in this formula: +(1+IRR(A1:A13))

Then hit the “shift” and “6” keys together and type in 12-1. That spews out the return: 17.1%.

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By the Numbers

An investor has $35,000 in his brokerage account at the start of the year and $50,000 at the end. Assuming he invested $5,000 in new cash during the year and took out $2,000 in dividends, here’s how he would calculate the portfolio’s return:

The Basic Formula

For Example ...

$50,000 + $2,000 -- [0.5 x ($5000)]

$35,000 + [0.5 x ($5,000)]

... Becomes ...

$52,000 -- $2,500*

$35,000 + $2,500*

... and Finally

$49,500

$37,500

= 1.32 -- 1 = 0.32 x 100 = 32%

*Assumes net additions to account. If the account had net withdrawals, the figure reached after multiplying by 0.5 would be added in the numerator and subtracted in the denominator (the reverse of the example above).

Source: American Assn. of Individual Investors