One of the central ideas of investing is that a rational investor weighs the risk associated with each investment alternative against the expected returns. If markets work properly, riskier investments will have a higher expected return.

This does not mean that if you hold onto a risky investment long enough that you will eventually make money. What the balance of risk and return implies is that if you are willing to bear the higher risks associated with businesses with large uncertainty in future earnings — good and bad — you will have a greater potential for high returns. To exploit this effectively, an investor needs to have a range of investments in his/her portfolio that are not too highly correlated to one another. This is the essence of portfolio theory.

Before you can even consider the portfolio effects, however, note that the ‘rational investor’ needs three critical pieces of information:

1) Estimate of expected future return

2) Estimate of future volatility (range of future returns)

3) Estimate of correlation of an asset to other assets

People spend an awful lot of time thinking about the first of these three (analyzing how well a stock or fund will do) and very little time on the other two of the three. When you are analyzing a set of decisions with uncertain outcomes (i.e. like investing), all of modern finance and statistics (and their cousin game theory) teaches us that items two and three are as important as item one.

Investing is about risk and return, but the majority of investors do not understand the rudiments of risk and this means that **many investors are ultimately likely to have less than ideal portfolios, no matter how good they are at stock picking**. Let me say this in a different way. If you were to have the magical ability to know the expected future return on every stock but ignored items two and three above, your outcomes are unlikely to be very good.

Now, perhaps you are in the minority of investors who actually have a pretty good handle on how risky your investments are and how they are coupled to the broader market. Further down in this paper, I have a table that shows the total volatility and Beta for a range of stocks and ETF’s (don’t look yet!). These risk measures are from the last three years (through January 31, 2006). Let’s see how good we really are at estimating the risk of some well-known investments. I bet that many of the results will surprise most people. Remember—don’t look at the results until you have taken a shot at the answers.

In case you are not familiar with the strict definition of Beta, it is a measure of the correlation of an investment to the broader market and serves as a measure of correlation across a portfolio.

The standard variable used to estimate volatility is the standard deviation in return and we look at the annual returns.

If you know Beta and standard deviation in annual return, you have a pretty good grasp of the risk associated with an investment, whether it’s a stock, mutual fund, or ETF.

Okay here goes….

**Question 1:** Volatility for SPY over the past three years is:

a) 120% of the long-term average for the S&P500 history

b) Equal to the long-term average for the S&P500

c) 90% of the long-term average for the S&P500

d) 60% of the long-term value for the S&P500

**Question 2:** QQQQ has been more volatile than SPY by how much?

a) More than 1.5 times as volatile but less than 2 times as volatile

b) More than 2 times as volatile but less than 2.5 times as volatile

c) More than 2.5 times as volatile

**Question 3:** HHH (the Internet-focused ETF) has been more volatile than SPY by how much?

a) More than 1.5 times as volatile but less than 2 times as volatile

b) More than 2 times as volatile but less than 2.5 times as volatile

c) More than 2.5 times as volatile

**Question 4:** Over the past three years, which has been more volatile, Ford (NYSE:F) or Yahoo! (YHOO)?

a) YHOO more volatile than F

b) F more volatile than YHOO

**Question 5:** Which has had a higher Beta over the last three years, YHOO or F?

a) YHOO has a Beta than is equal to F

b) YHOO has a Beta that is more than twice as high as F

c) F has a Beta that is more than twice as high as YHOO

**Question 6:** Which has been more volatile over the past three years, Toyota (NYSE:TM) or Microsoft (NASDAQ:MSFT)?

a) MSFT has been more than 2 times as volatile as TM

b) MSFT has been more than 1.5 times as volatile as TM but less than 2 times as volatile as TM

c) MSFT has been more volatile than TM but less than 1.5 times as volatile as TM

d) MSFT has been less volatile than TM

**Question 7:** AMD has been more volatile than INTC over the past three years by how much?

a) AMD has been 1.2 times as volatile as INTC

b) AMD has been 1.5 times as volatile as INTC

c) AMD has been twice as volatile as INTC

**Question 8:** How does the total volatility of Apple Computer (NASDAQ:AAPL) compare to HHH (Internet focused ETF)?

a) HHH is 1.5 times as volatile as AAPL

b) HHH and AAPL show essentially equal volatility

c) AAPL is 1.5 times as volatile as HHH

**Question 9:** What is Yahoo!’s Beta (using the past three years of market activity)?

a) Beta < 100%

b) Beta = 100%

c) Beta >130%

That’s all the questions, but don’t look at the answers just yet.

Whether or not you actually invest in any of these stocks or ETF’s, is it clear why knowing these kinds of statistics matter? If Yahoo! has Beta substantially greater than 100% then a position in Yahoo increases your portfolio sensitivity to the U.S. market, and vice versa. If you believe that the internet companies as a whole have greater growth potential than Apple computer (AAPL), you may want to invest in HHH and skip AAPL, but that decision must be a function of the total risk associated with AAPL vs. HHH. To what extent is MSFT’s business model sufficiently ‘understood’ by the market that its volatility declines?

In terms of looking at the most recent three years relative to the expected future of the market, it is also important to have a sense as to whether the fairly recent volatility in your portfolio is a function of total market volatility and also whether you should expect total market volatility to increase or decrease in the future. If you have your own analysis or projections about how well any company or sector will do relative to the market as a whole (and even if these estimates for expected future returns are really good), you still need to know the Beta and total volatility in order to be able to make rational allocation decisions.

Okay—now look at the answers (below this paragraph). Were you surprised? When I first saw some of these results, they surprised me. The point of this little exercise is to show that our expectations of the risk of investments may not be consistent with reality—and this is not surprising if you have seen some of the work in recent years on behavioral finance. The way to manage these issues is to get acquainted with risk measures and factor these into your investing strategy using portfolio considerations. There is no question that considering investment risk via Beta and standard deviation will improve most investor’s portfolio performance.

** Answers:**

Question 1: d (source)

The long-term average standard deviation in annual return for the S&P500 is around 15%

Question 2: a (1.7 times as volatile -- source)

Question 3: c (HHH has shown annual standard deviation in return 2.9 times SPY)

Question 4: b (Ford has been more volatile than YHOO over the past three years)

Question 5: c (Ford has had a Beta that is more than three times that of Yahoo!)

Question 6: (MSFT has been less volatile than TM over the past three years)

Question 7: c (see table below)

Question 8: c (see table below)

Question 9: a (Beta = 95%)

**Summary Data**

Historical values for Beta and Standard Deviation in annual return (i.e. volatility) over the past three years, during which the Standard Deviation in return for the S&P500 has been 8.9%. These results calculated using Quantext Portfolio Planner

For more information, please visit Quantext's portfolio planning page.