The Daily Workshop Report
by Robert Sheard (TMF Sheard)

LEXINGTON, KY. (August 13, 1997) -- In today's Foolish Four column, I wrote about the myths we live by in golf and investing when it comes to accountability. I want to use this companion column today to describe the formulas one needs to account for returns accurately. Take a peek at my Foolish Four column and then I'll meet you right back here.

Back already? Good. Let's talk about total return first since it's the easiest formula. By focusing on the total value of your portfolio, you get the best picture of your overall strategy. You can apply this formula to any individual stock, of course, but looking at the whole makes more sense than looking at the parts too closely.

The formula for total return requires only two numbers, the original value of the investment and the value now.

Total Return = (Value Now - Original Value) / Original Value

For example, if your Original Value is $50,000 and the Value Now is $64,000, your Total Return is 28%.

(64,000 - 50,000) / 50,000 = 0.28

That formula does not take into account the length of time of the investment. It simply measures total growth (positive or negative). What's nice about this accounting is that trading costs are already built into the formula because you're using the actual values from your brokerage statement. If you deposited $50,000, made a number of trades, paying commissions on each trade, and now your portfolio is worth $64,000, you've made 28% after all costs. Very simple, very accurate.

But perhaps a more relevant return is the annualized return, which takes the duration of the investment into account as well. For this calculation, you'll need one more piece of information -- the period of the investment (in years). The calculation is a little more complex, so you'll need a calculator that can handle exponents or a spreadsheet.

Annualized Return = (Value Now / Original Value) ^ (1 / Years) - 1

Using our same example, let's say you achieved this 28% growth in a very short time, only 9 months (or 0.75 years). Let's plug in the numbers:

(64,000 / 50,000) ^ (1 / 0.75) - 1 =

or

1.28 ^ 1.333 - 1 = 0.3898 (38.98%)

(Note: the ^ symbol denotes an exponent. You can plug the equation into a spreadsheet just as I've listed it here and the calculation should work correctly.)

In other words, your annualized return based on the nine months is roughly 39%. If it had taken two years to achieve that 28% total return, though, your annualized return would be significantly lower.

(64,000 / 50,000) ^ (1 / 2) - 1 = 0.1314 (13.14%)

The biggest accountability difficulty arises if you add or subtract money from your account during the course of the period that you wish to measure. Both of the previous equations assume a single deposit and no cash flow during the period being tested. If you add regularly to your account (as we hope you do) or withdraw money to pay for living expenses during retirement, etc., you need to use a much more complicated approach to measuring your annualized returns.

Fortunately, programs like Quicken and many spreadsheets include a function that can accommodate you (Internal Rate of Return). These functions measure the time value of the cash flows and generate an overall annualized return for all of the additions and withdrawals as a single portfolio. (You may have to hunt for the feature that works best in your spreadsheet software. The XIRR function in Excel is what I use, but it took some work to find it. It wasn't listed in the original group of functions, but going to the Tools menu, selecting Add-Ins, and then checking the box called Analysis ToolPak added the XIRR function to my financial functions options.)

With that function you simply set up a two-column spreadsheet. In the first column, list the dates of every cash deposit or withdrawal to your account. In the second column, list the amounts (make sure to include a negative sign for withdrawals). You don't have to list the dates and amounts of dividends because those are part of the portfolio growth, not new money you're adding. For your last entry, use today's date and your total portfolio value as the amount. (Enter this amount with a negative sign as if you were withdrawing everything.) The function wizard will ask you to select the cells for the values and then the dates, and voila, it automatically calculates your annualized return (in a decimal value that you can either translate yourself or format within the spreadsheet to print out as a percentage value).

Once you set one up a time or two, it's simple and extremely helpful if you make regular additions to a retirement fund. My wife's 403(b), for example, receives an automatic monthly deposit taken directly out of her paycheck. By listing those monthly deposits (which change by a few dollars every time her salary changes) and using the XIRR function, I'm able to tell immediately how her retirement account is doing relative to the S&P 500 over the same period. It only takes about five minutes to update each quarter when her new statement arrives. The same goes for our regular stock account, to which we add cash on a monthly basis.

No myths, no fudged numbers, full accountability, the Foolish way to keep track!

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