Risk and return

Risk is a complex topic. There are many types of risk, and many ways to evaluate and measure risk. However, when it comes to investing, risk can be summarized simply as follows:

Even though this definition of risk sounds simple, questions arise:
 * “Risk is the uncertainty that an investment will earn its expected rate of return.”


 * How is uncertainty of returns (risk) evaluated and measured for different types of investments?
 * What is "expected rate of return", and how is it evaluated?
 * What can be done to manage risk?
 * How does an investor factor risk into investment decisions?
 * Are there differences between short-term risk and long-term risk?
 * The definition above does not distinguish between positive and negative outcomes. Isn't risk just the possibility that the investor will lose money on the investment?

To make wise investment decisions, an investor must spend some time studying the answers to these questions.

Uncertainty of returns as risk
There is very high certainty in the return that will be earned on an investment in a 30-day Treasury bill (T-Bill) or short-term Certificate of Deposit (CD). Similarly, there is fairly high certainty in the return that will be earned over a short period in a money market fund.

Even over longer time periods, the returns earned by money market securities fall into a relatively narrow range.

As seen in the top chart in Figure 1 (covering the years 1928 through 2011), the tallest bar shows that annual returns (horizontal axis) on 3-month T-Bills have fallen in the range of 0% to 5% in 59 years (vertical axis). Returns have been between 0% and 10% in most years (tallest two bars), and between 0% and 15% in all years (all three bars).

T-Bills and CDs are among the investments referred to collectively as money market securities. For an individual investor, a federally-insured bank account also provides a high degree of certainty in the short-term return. The term cash often is used to refer to money market securities and money in bank accounts. Vanguard refers to these types of assets as short-term reserves.

The return on bonds is less certain, and the return on stocks is even more uncertain. Thus, bonds are considered riskier than money market securities (cash), and stocks are considered riskier than bonds.

The middle chart in Figure 1 shows the range of annual returns on 10-Year Treasury Bonds from 1928 through 2011. Note the larger range (dispersion) of returns--from about -11% to +33%.

The bottom chart in Figure 1 shows the range of annual returns on stocks in the S&P 500 from 1928 through 2011. Note the much larger dispersion of returns--from about -44% to +53%.

Relationship between risk and return
Investors are risk averse; i.e., given the same expected return, they will choose the investment for which that return is more certain. Therefore, investors demand a higher expected return for riskier assets. Note that a higher expected return does not guarantee a higher realized return. Because by definition returns on risky assets are uncertain, an investment may not earn its expected return.

Although the charts in Figure 1 show historical (realized) returns rather than expected (future) returns, they are useful to demonstrate the relationship between risk and return. Note that the mean (average) annual return increases as the dispersion of returns increases.

This demonstrates one of the most fundamental axioms of investing: ''Risk and return are inextricably related. Higher returns can only be achieved by taking more risk, but because the risk exists, the higher expected returns may not be achieved.''

"Risk free" return


Money market securities are often referred to as risk-free assets, especially the shorter-maturity securities such as 30-day T-Bills. However, if inflation is considered, even money market securities have some risk. T-Bills and other very short-term money market securities usually earn a positive real (inflation-adjusted) return, and usually respond fairly quickly to changes in inflation. Therefore, these securities usually do not have significant inflation risk. However, as seen in Figure 2, there are times when even 30-day T-Bills have negative real returns. T-bill data source comes from Annual Returns on Stock, T.Bonds and T.Bills: 1928 - Current, Damodaran Online; inflation data comes from Consumer Price Index 1913 -, Minnesota Federal Reserve]. Retrieved 1 April 2012

Uncertainty in real returns can be eliminated by investing in inflation-indexed securities, such as Treasury Inflation Protected Securities (TIPS) and Series I Savings Bonds (I Bonds). Of course in return for this reduction in uncertainty, investors must accept lower expected returns. Marketable inflation-indexed securities also have other risks, such as interest rate risk (i.e., prices decline when interest rates rise) and liquidity risk, as was made evident in late 2008 (September 12 - October 31) when the Vanguard Inflation-Protected Securities fund declined in value by almost 14%. During this same time period other U.S. treasury securities increased in value.

Expected return
(Done working on first pass of this section for tonight)

Risk has been defined as the uncertainty that an investment will earn its expected return, but expected return has not yet been defined (expected return is short for expected rate of return). In finance theory this term has a precise definition.

To estimate the expected return, E(r), for an investment, an analysis of various scenarios is performed. In a simple scenario analysis, three scenarios might be that the future state of the economy can be either booming, experiencing normal growth, or in recession.

Estimates are developed for the probability, p(s), of each scenario occurring and the return, r(s), for that scenario. The probability and return for each scenario are multiplied and the results for all scenarios are summed. Thus, expected return is the weighted average of returns in all possible scenarios.

For three scenarios, s1, s2 and s3, this is expressed mathematically as:


 * E(r) = p(s1) x r(s1) + p(s2) x r(s2) + p(s3) x r(s3)

Assume the estimated probabilities of recession, normal growth and strong growth are 20%, 60% and 20% respectively, and the associated estimated investment returns are -10%, 5%, and 10%. So p(s1) = 20%, r(s1) = -10%, p(s2) = 60%, r(s2) = 5%, p(s3) = 20%, and r(s3) = 10%. For these assumptions, the expected return would be:


 * E(r) = 0.20 x -0.10 + 0.60 x 0.05 + 0.20 x 0.10 = 0.03 = 3%

Extensive research has demonstrated that there are no good forecasters. It follows that scenario analysis itself is fraught with uncertainty. To put it bluntly, expected returns are not observable. (I don't have a copy of this book, but pretty sure he stated this multiple times in the book; will get from library within 2 days and verify). Nevertheless, financial academics and practitioners develop and publish their estimates of expected returns.

Next: OK, so if expected returns are so unreliable, why are we even discussing them? Then, touch on relationship of mean historical returns to expected returns; e.g., how are the calculations similar and how are they different. Caution on using average historical returns to predict expected returns. I think that's about it.

External Links to add:

Various links to GMO's latest 7-year forecast can be found by searching "GMO 7-Year Asset Class Forecasts (February 2012)". Not sure we want to publicize one of these sites though.

Latest GMO 7-Year Asset Class Return Forecasts is available directly on GMO website (https://www.gmo.com/America/Research/), but registration (free) is required.

(Wiki article Historical and Expected Returns includes the 2011 Ferri estimates, but updated estimates for 2012 are available via link; the Bernstein estimates are way dated (2002).)