Tuesday, April 07, 1998

The Daily Workshop Report
by Robert Sheard (TMF Sheard)

LEXINGTON, KY. (April 7, 1998) -- In yesterday's column, I featured the Relative Strength Dozen model, which has been blazing through the first quarter of 1998. I promised I'd feature two more Dozens groups today, but I'm going to delay part of that promise until tomorrow because I received a request to explain the return calculations I make for these portfolios. Good idea, so let's do it today while looking at the Keystone Dozen.

The way these portfolio models are working, a new $1,000 is invested each month (it's all hypothetical money), which allows us to buy one additional stock each month. By the end of the first year, we'd have invested a total of $12,000 and will hold 12 stocks. But calculating the returns for such a portfolio are complicated by the fact that each new $1,000 was in the portfolio for a different length of time.

As of approximately 2:30 this afternoon (EDT), the Keystone Dozen portfolio looked like this:

Shares	Stock	Price	Cost	Now	Value	Return
12	FITB	81.75	989.00	86.38	1,036.50	4.8%
13	SGP	72.38	948.88	85.56	1,112.31	17.2%
11	PFE	88.50	981.50	101.50	1,116.50	13.8%
34	TCOMA	31.09	1065.19	31.88	1,083.75	1.7%
Cash		15.43
Total		4,364.49

The four stocks are listed in the order they were acquired, each one in successive months, so Fifth Third Bancorp <% if gsSubBrand = "aolsnapshot" then Response.Write("(Nasdaq: FITB)") else Response.Write("(Nasdaq: FITB)") end if %> has been in the portfolio for 97 days, Schering-Plough <% if gsSubBrand = "aolsnapshot" then Response.Write("(NYSE: SGP)") else Response.Write("(NYSE: SGP)") end if %> for 66 days, Pfizer <% if gsSubBrand = "aolsnapshot" then Response.Write("(NYSE: PFE)") else Response.Write("(NYSE: PFE)") end if %> for 38 days, and TCI <% if gsSubBrand = "aolsnapshot" then Response.Write("(Nasdaq: TCOMA)") else Response.Write("(Nasdaq: TCOMA)") end if %> for 7 days.

To account for the cash flow stream and the time value of those four deposits, I use the XIRR function in Microsoft Excel to get an annualized rate of growth for the entire portfolio. If you have Quicken or Microsoft Money, those programs will figure your annualized returns the same way Excel's XIRR function does. Using this function, we get an annualized rate of growth for the Keystone Dozen of 81.5%. The equivalent annualized rate of growth for the Standard & Poor's 500 since December 31 is 64.5%.

As the year's just barely more than one quarter old, though, annualized numbers can be very misleading. I don't know of anyone who really expects the S&P 500 Index to sustain this pace and score a 64.5% gain in 1998, do you? So to get a little more useful number, first we need to translate this annual rate of growth to a daily rate of growth so we can calculate the portion of that gain that applies to the number of days we've actually logged already in 1998.

Here we go. We need to use the equation for compounded growth for this exercise. (It really helps to have a financial calculator handy, however.)

(Future Value / Present Value) ^ (1 / Number of Periods) = Compound Growth Rate

So let's pick an arbitrary starting dollar amount of $100. Using our annualized rate of growth right now for the Keystone Dozen (81.5%), that $100 would turn into $181.50 after a year. So we know two of the variables:

Present Value = 100.00

Future Value = 181.50

If we want to get a daily growth rate equivalent, our number of periods has to be 365, so now we have all but one variable; let's fill in the blanks:

(181.50 / 100.00) ^ (1 / 365) - 1 = Daily Compound Growth Rate

If you want to do this by hand, enjoy. I'll plug it into my financial calculator. The daily growth rate equals 0.163444512%.

Now that we know the daily growth rate equivalent, we can apply that to the number of days we've actually logged in 1998 -- 97 days.

Using the same formula for compound growth, again choose an arbitrary Present Value of $100, and plug in the number of periods (97) and the interest rate (0.163444512%) and we can calculate the Future Value.

(Future Value / 100.00) ^ (1 / 97) - 1 = 0.163444512%

Dragging out my calculator quickly, that equals a Future Value of $117.16, which gives us a percentage gain from our starting value ($100.00) of 17.16%. Our growth rate for the first 97 days of the year, then, is 17.16%. Performing the same calculations on the S&P 500 Index's growth rate so far, we get a year-to-date equivalent of 14.14%. The Keystone Dozen model, then, is ahead of "the market" by three percentage points at this stage.

Now looking at the actual dollar and percentage gains for the four stocks in the model portfolio, the first question that pops into many people's minds is, how can the portfolio have gained 17.16% when the best performing stock of the four is only up 17.2%? Excellent question.

The answer lies in the time horizon for those two figures. Schering-Plough has risen 17.2% in only 66 days, which is a growth rate considerably higher than the 17.16% growth rate we calculated for the entire portfolio, which is based on a life-span of 97 days. So it doesn't help to compare raw numbers on the surface if they represent different time periods.

What this year-to-date equivalent return is good for is comparing it against another portfolio's returns beginning on January 1 and continuing through today. For example, if your stock-touting neighbor is bragging because his portfolio is up 10% already this year, you can smile knowing that both the S&P 500 and you are ahead of that pace.

I'll revisit these calculations again and again in the future because they can be confusing at first, but they're important for a regular saver to understand since adding new money to a portfolio will require the use of the XIRR function to get an accurate sense of your total returns. Fool on!

Check out the latest file updates for the Workshop:
New Rankings | 1998 Returns | New Database

[Robert Sheard is the author of the forthcoming book, The Unemotional Investor, due out from Simon & Schuster on May 12. To pre-order your copy, please visit Amazon.com, where it's available at a discounted price.]