Quantifying Risk

Foolish investors recognize that investments carry risk, but most of us don't really have a good idea of what that really means. The use of certain tools can help us analyze these risks. We've run some numbers to demonstrate the chances of losing money when investing in different asset classes over three different time periods.

By Ethan Haskel (TMF Cormend)
September 6, 2000

No sane investor would send a check to her broker if she knew she would lose money. But do we really have a good idea of how much risk we're taking when we invest in stocks?

Most well-informed Fools are aware that historically stocks have gained about 11% a year on average. But this 11% average doesn't mean that the value of our portfolio will steadily increase each and every year by that percent. Such an average merely represents a summary of all the gains and losses that have occurred over the many years since we have been measuring stock market returns. The road to financial security is a bumpy one -- stocks can and will lose money at times.

These road bumps represent risk. Foolish investors recognize there is risk in our investments and know that risk can be minimized by taking a long-term view. But how many of us really have a good idea of the actual risk we are taking when we invest in stocks? For instance, what are our chances of losing money?

To help us understand more about the risks of investing, let's turn to a tool called Portfolio Forecaster, offered by Financial Engines. This tool was developed based on work by William Sharpe, the Nobel Prize-winning economist who knows a thing or two about risk quantification. His Sharpe Ratio has been used quite a bit around these parts to measure the risk-adjusted performance of many of our mechanical screens. Dr. Sharpe is Professor Emeritus of Stanford University's Business School and Chairman of Financial Engines.

The Portfolio Forecaster will examine your portfolio, chop it up into broad asset categories, and examine the risk profile of individual stocks. The Forecaster will then display a profile of the potential future value of your portfolio. According to the website:

Your Forecast comes from simulating thousands of economic scenarios that show the different paths your portfolio might take in the future. At the end of each simulation, the Forecaster estimates the value of your portfolio. Your Forecast percentage represents how many times your portfolio was able to achieve your goal.

What I found unique about the Portfolio Forecaster is that it breaks down your estimated portfolio value based on probabilities, rather than giving you a single number. For instance, the Forecaster might predict that a hypothetical $10,000 portfolio of four large company stocks has a 6% probability of losing half its value in 15 years, or a 52% chance of more than doubling. The probability is based on different economic scenarios and the risk profile of the stocks or mutual funds you own. Some of the methodology behind the calculations can be found on the website, although most of the details are proprietary information and are not available for review.

To get specific numeric predictions about the risks of investing in different asset classes, I decided to take the Forecaster out for a test drive. To simplify the demonstration, I chose three mutual funds offered by Vanguard, to evaluate the effect of risk on different asset classes. The Vanguard Admiral Short Term Treasury Fund, The Total Bond Market Index Fund, and the Index Trust 500 Fund were used as surrogates for investing in cash equivalents, bonds, and stocks, respectively.

I asked this question: What are the chances of losing any money whatsoever, or of sustaining losses equal to or greater than 15% or 30% of one's initial portfolio over various time periods?

It's important to keep in mind that the Forecaster quotes its returns in inflation-adjusted dollars. Remember that a loss in inflation-adjusted dollars won't necessarily mean an actual loss in real dollars. For instance, if a portfolio of stocks gains a total of 10% over five years, but inflation over that same time period is 15%, Forecaster will report that as a 5% loss even though the total value of your portfolio increased by 10%. The 5% loss reflects a decrease in the purchasing power of your portfolio due to inflation.

Here are the numbers for 5, 10, and 20 year holding periods:

Chance of Loss

5 Years    Any     15%    30%
Cash       13%      3%     3%
Bonds      19%      5%     4%
Stocks     22%     11%     5%

10 Years   Any     15%    30%
Cash        7%      3%     2%
Bonds      10%      5%     4%
Stocks     11%      7%     4%

20 Years   Any     15%    30%
Cash        5%      3%     2%
Bonds       8%      5%     3%
Stocks      8%      6%     3%

(Note that for some of the calculations,
I did some minor extrapolations in order
to get the numbers, since the results
weren't always presented uniformly.)

Let's consider the five-year scenario. Over any five-year span, a portfolio of large cap stocks (as measured by a surrogate for the S&P 500 index) would be expected to lose money relative to inflation in 22% of all the possible economic scenarios -- about one-fifth of the time. A 15% or greater loss would occur in 11% of the possible scenarios, while a loss of 30% or more would occur in 5% of the possible scenarios.

Investing for the long-term mitigates the chances of a loss, but not completely. The percentage of scenarios where our stock portfolio loses money (again, relative to inflation) drops as the time factor increases.

Because the numbers used are inflation-adjusted, you can see that even a portfolio that's invested in short-term U.S. Treasury Bills (our cash-equivalent portfolio used in the demonstration) can lose money relative to inflation.

A surprising finding is that the long-term risk of losing money in bonds is not that different from stocks -- at least for those bonds characteristic of those in the Vanguard Fund we chose as our surrogate. As you can see from the tables above, for the 10-and 20-year investment periods, there's relatively little difference in the chance of losing money when invested in bonds compared the S&P 500 stock index.

The most important thing to realize here is that even a highly diversified stock portfolio like the S&P 500 is expected to lose money relative to inflation about one-fifth of the time over a five year investment period. Foolish Four and Beating the S&P investors hope to beat that, but it would be unrealistic to expect that any strategy should be immune to the risk of loss.

To get a better feel of your individual risk, I'd suggest you run some numbers on your own portfolio. (AOL users can directly import their AOL portfolios into the Forecaster by clicking on the brown Forecast button in the lower left corner.) Change your asset mix around to see how it affects the likelihood of a portfolio loss. Can you handle the risk of loss both financially and psychologically? Knowing the approximate chances of sustaining such losses is an important step in coming to grips with investment risk.

If you're interested in a different perspective for the odds of a loss in your portfolio, I'd suggest taking a look at Jeremy Siegel's Stocks for the Long Run. Some of Professor Siegel's conclusions are summed up here.

Next week we'll look at the other side of the equation. Instead of looking at the chances of losing money in your portfolio, we'll concentrate on the chances of making money. That part of the equation is a lot more fun, isn't it?

Beating the S&P year-to-date returns
(as of 09-05-00):

Bank One (NYSE: ONE) +9.7% PepsiCo (NYSE: PEP) +22.1% Ford Motor Co. (NYSE: F) -3.3%* Bank of America (NYSE: BAC) +8.6% Fannie Mae (NYSE: FNM) -13.9% Beating the S&P +4.6% Standard & Poor's 500 Index +2.6% *Includes Visteon (NYSE: VC) spin-off

Compound Annual Growth Rate from 1-2-87: Beating the S&P +23.3% S&P 500 +17.2%

$10,000 invested on 1-2-87 now equals: Beating the S&P $175,600 S&P 500 $87,700

Read More Foolish Four Reports

Top Dow Stocks
( RP Order )


1. Philip Morris
2. * Caterpillar
3. * Int'l Paper
4. * AT&T
5. * DuPont
6. SBC Comm.
7. Eastman Kodak
8. General Motors
9. Honeywell
10. Procter & Gamble

NOTE: Today's Foolish Four stock selections are marked with an asterisk.

Foolish Four Portfolio

9/6/2000 as of ~5:30:00 PM EDT
Ticker Company Day Chg % Chg Price
EKEASTMAN KODAK-5/8-0.99%$62.63
GMGENERAL MOTORS9/162.14%$74.50
JPMMORGAN (JP)5/163.95%$166.25

  Day Week Month Year
To Date
Foolish Four 1.92% 2.43% 1.69% 3.76% 27.68% 15.40%
S&P 500(DA) -.82% -1.71% -1.51% 1.73% 22.25% 12.50%
NASDAQ -2.88% -4.97% -4.34% -1.12% 85.21% 43.53%
DJIA (DA) .57% .77% .98% -1.50% 24.89% 13.92%

Trade Date # Shares Ticker Cost/Share Price LT % Val Chg

Trade Date # Shares Ticker Cost Value LT $ Val Ch
  Cash: $79.92  
  Total: $5,107.17  

• S&P 500 (DA) = dividend adjusted. Dividends have been added to the total return of the index.
• DJIA (DA) = dividend adjusted. Dividends have been added to the total return of the DJIA.

The Foolish Four Portfolio was launched on December 24, 1998, with $4,000. Additional cash is never added, all transactions are discussed and explained publicly before being made, and returns are compared daily to the S&P 500 and the Dow. (Dividends are included in the yearly, historic and annualized returns.) Stocks are chosen once per year using a formula based on dividend yield and price. See The Foolish Four Explained for details.