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Risk and Reward
A look at Standard Deviation

by Ann Coleman
([email protected])

Alexandria, VA (November 23, 1998) -- No one can say you don't have choices here in Foolish Four Land. Our three basic strategies, the High Yield 10, the Foolish Four, and the RP Variation, all have their own variations. It can get confusing. With renewal/best investment season coming up for many people, let's look at factors that you may want to consider when choosing among our many variations.

I did a quick rundown on our various strategies in September, so if you aren't clear on what the strategies and variations are, you might want to review the following articles:

High Yield 10
Foolish Four
RP Variation
Variations on the basic strategies (This article includes average annual returns for all strategies.)

Returns are obviously one thing to consider -- but what about risk factors? Standard deviation is one useful way to assess the riskiness of an investment. I know, I know, standard deviation is a statistics term, but don't break out in hives. It's not that tough, and it is extremely useful when choosing among strategies.

Disclaimer: Bear in mind that the kind of risk we are talking about here is not the risk that you will lose everything in a catastrophic crash, but the risk that at some specific point, your money may not be at the level you expect. It addresses the year-to-year variations in the returns. That's a very useful thing to look at, but it doesn't encompass every aspect of risk.

First concept: The smaller the standard deviation, the closer each year's returns will be to the average return. In other words, the less volatile and risky the strategy. We quote returns all the time, but that is only part of the picture. Knowing the standard deviation can give you a feel for how close each year's returns are likely to come to the expected return.

Here is a mini-example: 

       Strategy 1  Strategy 2
Year 1    24%         44%
Year 2    32%         24%
Year 3    75%          6%
Year 4   -13%         32%

CAGR      26%         26%
Avg.      30%         27%
SD        36%         16%

Both of the above strategies have compound annual growth rates (CAGR) of 26% per year. No matter which strategy you picked, $10,000 invested at the beginning of year one would have grown to around $25,000 at the end of year 4. (Nice strategy, eh?) But the arithmetic averages are different, and one strategy provided much more uniform returns.

[NOTE: The arithmetic average (mean) is not the proper average to use when quoting returns, but it is the one around which your yearly returns will cluster. Sorry, I wish it were easier, but thems the numbers. In most cases the mean will be fairly close to the CAGR, so in this case you can think of them as roughly the same.]

Essentially, the standard deviation describes a range. It tells you how close the sample data (our yearly returns) cluster around the average return.

Strategy 1 has a very wide range. The standard deviation tells us that 68% of the returns should fall within a range of plus or minus 36 percentage points of the arithmetic average and 95% should fall within plus or minus 70 percentage points. Here's how that looks:

Strategy 1
68% of returns will fall within the range -6% to 66%.
95% of returns will fall within the range -42% to 102%
and 5% of the time the returns will fall beyond that range, meaning they could be less than -42% or greater than 102%.

Strategy 2 has the more uniform returns and a much lower standard deviation.

68% of returns will fall within the range 11% to 43%.
95% of returns will fall within the range -5% to 59%
and 5% of the time the returns will fall beyond that range, meaning they could be less than -5% or greater than 59%.

Someone once said, "Statistics are a statement of the obvious." It should have been obvious that Strategy 1 was a more volatile strategy and that Strategy 2 was much more stable. The standard deviation is just a quick way of quantifying that. It makes it easier to compare strategies -- which is exactly what TMF Sandy, Mr. Data himself, will be doing tomorrow.

Fool on and prosper!

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Current Dow Order | 1998 Dow Returns

11/23/98 Close
Stock  Change   Last
--------------------
UK   +   1/4   44.75
IP   -  15/16  45.06
MO   +2  7/16  58.19
EK   -1  1/16  75.63

                   Day   Month    Year
        FOOL-4   +0.44%   5.99%  17.55%
        DJIA     +2.34%   9.10%  18.54%
        S&P 500  +2.12%   8.15%  22.44%
        NASDAQ   +2.55%  11.63%  25.92%

    Rec'd   #  Security     In At       Now    Change

 12/31/97  276 Philip Mor    45.25     58.19    28.59%
 12/31/97  206 Eastman Ko    60.56     75.63    24.87%
 12/31/97  289 Int'l Pape    43.13     45.06     4.49%
 12/31/97  291 Union Carb    42.94     44.75     4.22%


    Rec'd   #  Security     In At     Value    Change

 12/31/97  276 Philip Mor 12489.00  16059.75  $3570.75
 12/31/97  206 Eastman Ko 12475.88  15578.75  $3102.88
 12/31/97  289 Int'l Pape 12463.13  13023.06   $559.94
 12/31/97  291 Union Carb 12494.81  13022.25   $527.44


               Dividends Paid YTD  $1092.81
                            TOTAL  $58776.62

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