Risk and return: an introduction
Risk and return is a complex topic. There are many types of risk, and many ways to evaluate and measure risk. In the theory and practice of investing, a widely used definition of risk is:
Note that this definition does not distinguish between loss and gain. Typically, individual investors think of risk as the possibility that their investments could lose money. They are likely to be quite happy with an investment return that is greater than expected - a “positive surprise.” However, since risky assets generate negative surprises as well as positive ones, defining risk as the uncertainty of the rate of return is reasonable. Greater uncertainty results in greater likelihood that the investment will generate larger gains, as well as greater likelihood that the investment will generate larger losses (in the short term) and in higher or lower accumulated value (in the long term.)
In financial planning, the investment goal must be considered in defining risk. If your goal is to provide an acceptable amount of retirement income, you should construct an investment portfolio to generate an expected return that is sufficient to meet your investment goal. But because there is uncertainty that the portfolio will earn its expected long-term return, the long-term realized return may fall short of the expected return. This raises the possibility that available retirement funds fall short of needs - that is, the investor might outlive the investment portfolio. This is an example of "shortfall risk." The magnitude and consequences of the potential shortfall deserve special consideration from investors.  However, since the uncertainty of return could also result in a realized return that is higher than the expected return, the investment portfolio might "outlive" the investor. Therefore, considerations of shortfall risk are subsumed by considering risk as the uncertainty of investment return.
Risk as the uncertainty of returns
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. There is very high certainty in the return that will be earned on an investment in money market securities such as Treasury bills (T-Bills) or short-term certificates of deposit (CDs). Similarly, there is fairly high certainty in the return that will be earned over a short period in a money market fund. Money market fund holdings consist of T-Bills, CDs, and other money market securities.
For an individual investor, a federally-insured bank account also provides a high degree of certainty in the short-term return.
Even over longer time periods, the returns earned by money market securities fall into a relatively narrow range.
Figure 1. Risk vs. Return: 1928 - 2011
The annual returns on 3-month T-Bills (representing "cash") have fallen in the range of 0% to 15% during the 84 year period from 1928 through 2011. This range of returns is represented in Figure 1 by the vertical bar on the far left (above the label "U.S. Treasury Bills). Also note the tick mark showing the average annual return of 4%.
The middle vertical bar in Figure 1 represents the range of annual returns on 10-Year U.S. Treasury Bonds over the same time period. Note the larger range (dispersion) of returns--from about -11% to +33%. Also note the somewhat larger average annual return of 5%.
The far right vertical bar in Figure 1 represents the range of annual returns on U.S. stocks (as represented by stocks in the S&P 500) over the same time period. Note the much larger dispersion of returns--from about -44% to +53%. Also note that the average annual return of 11% is significantly higher.
As the chart indicates, the return on bonds is less certain than the return on cash, and the return on stocks is less certain than the return on bonds. Thus, bonds are considered riskier than cash, and stocks are considered riskier than bonds. [note 2]   
The chart also shows that historically, over the relatively long time period of 84 years from 1928 through 2011, higher risk has been rewarded with higher average annual returns--at least in the United States. This pattern is not unique to the U.S., but it is not the same in all countries.
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 generally can be achieved only by taking more risk, but because the risk exists, the higher expected returns may not result in higher realized returns.
If inflation is considered, even money market securities have some risk. They may not achieve the expected real (inflation-adjusted) return. Unexpected inflation may reduce the real return below the expected return of the money market investment. 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). In return for this reduction of uncertainty, investors must accept lower expected returns. Even inflation-linked securities have risks; e.g., TIPS have interest-rate risk, re-investment risk, and liquidity risk. No investment is truly risk-free.
Managing portfolio risk
Risk can be reduced through diversification.
The risk of investing in a single risky security, such as a stock or corporate bond, is very high due to the company-specific risks. Any number of unfortunate events could impact the rate of return. In the worst possible case, the company could go bankrupt, and the investor could lose the entire value of the investment. Company-specific risk is generally referred to as unsystematic risk or nonsystematic risk. Other names are unique-risk, firm-specific risk, or diversifiable risk.
Unsystematic risk can be eliminated by holding a broad portfolio of risky assets; e.g., many different securities in many different industries. This is easy to accomplish by owning a total market stock or bond index fund. Unsystematic risk is risk that can be "diversified away."
The risk that remains after diversifying away unsystematic risk is systematic risk. Other names are market risk or non-diversifiable risk. A total stock or bond market fund has systematic risk. This is risk impacting an entire asset class, such as when rising real interest rates impact the entire bond market.
In an efficient market, assets with known systematic risks will be priced lower and thereby compensate investors through higher expected returns. This expected relationship only applies to systematic risks. There is no reward for incurring unsystematic risk, and investors may therefore seek broad diversification without reducing the expected return of their portfolio.
After diversification, the next step in managing portfolio risk is asset allocation.
In theory, asset allocation is the process of selecting an appropriate mixture of risk-free assets and risky assets. Optimally, the risky portion of the portfolio includes all risky assets; e.g., stocks, bonds, real estate, etc. A 30-day T-Bill is most commonly used to represent the risk-free asset.
In practice, short-term, high quality bonds are considered to be relatively risk free, and so are typically considered part of the (relatively) risk-free portion of the portfolio. Although a bond fund that includes riskier bonds (e.g., corporate bonds and bonds with longer maturities) is technically a risky asset, the risk is low in comparison to stocks. In the context of investing according to the Bogleheads® investment philosophy, broad-based, short- to intermediate-term bond funds often are used for the low-risk portion of the portfolio, and broad-based stock funds are considered to comprise the risky portion of the portfolio.
Selecting the appropriate asset allocation (ratio of risky assets to low-risk assets) is essential to designing a portfolio that matches the investor's ability, willingness, and need to take risk..
An illustrative example
Specific types of risk
Portfolio theory makes an important distinction between two types of risks:
- Unsystematic risk: the measure of risk associated with a particular security; also known as diversifiable risk. This risk can be mitigated by holding a diversified portfolio of many different stocks in many different industries. 
- Systematic risk: also known as market risk. Systematic risk is faced by all investors due to market volatility. This risk cannot be diversified away. This is the type of risk most people are referring to when they casually use the term "risk" when discussing investments. 
Some additional risks faced by all investments include:
- Liquidity risk--the risk that an asset cannot be sold when desired or in sufficient quantities because opportunities are limited. Treasury securities (with the exception of inflation protected Treasury bonds) have the least liquidity risk.
- Political risk--the risk to an investment due to changes in the law or political regime. Potential changes in tax law or changes in a country's structure of governance are sources of political risk.
- Inflation risk--stocks, bonds and cash are all subject to the risk that one's investment will not keep pace with inflation. This risk can be mitigated by investing in inflation-protected Treasury bonds, such as TIPS or I-bonds.
- Financial risk--the risk due to the capital structure of a firm. Corporate debt magnifies financial risk to a company's stocks and bonds.
- Management risk--investors using actively managed funds are exposed to the risk that fund or portfolio managers will under-perform benchmarks due to their management decisions or style. Investors can avoid this risk by selecting passively-managed index funds.
Bond investors also face the following major risks:
- Interest rate risk--the risk associated with changes in asset price due to changes in interest rates. Bonds and bond funds face this type of risk. As interest rates rise, prices on existing bonds decline and vice versa. Interest rate risk is greater for bonds with longer maturities, and lower for bonds having short maturities.
- Credit risk--the risk of default. Holders of corporate and municipal bonds face this risk.
Other risks applicable to bond investments include:
- Call risk--the risk that a bond issuer, after a decline in interest rates, may redeem a bond early, forcing the bond holder to find a replacement investment that may not pay as well as the original bond.
- Reinvestment risk--the risk that earnings from current investments will not be reinvested at the same rate of return as current investment yields. Coupon payments from a bond may suffer reinvestment risk if they cannot be reinvested at the same rate as the bond's yield.
- Currency risk--investors in international stocks and bonds are also exposed to the risk caused from changes in currency exchange rates. Investments in currencies other than the one in which the investor purchases most goods and services are subject to currency risk.
Individual investors are exposed to two additional risks:
- Longevity risk--the risk an investor will outlive his/her money.
- Shortfall risk--the risk the portfolio will not provide sufficient returns to meet the investor's goal(s). John Bogle states:
Consideration of bonds as an important asset class implicitly requires us to recognize, as I quoted in "Common Sense on Mutual Funds", that “risk is not short-term volatility, for the long term investor can afford to ignore that. Rather, because there is not a predestined rate of return, only an expected one that may not be realized, the risk is the possibility that, in the long-run, stock returns will be terrible."(Footnote 3) Put another way, the risk is that the investment portfolio might not provide its owner—individual or institution—with adequate cash to meet future requirements for essential outlays. In short, that the investor will lose a ton of money, just when it is needed the most.
— Bogle, John. 
- At some time in the future, the actual return will be one of many possible outcomes. The various outcomes have some probability of occurring. The expected return is just the average of these possible returns weighted (multiplied) by the respective probabilities of occurring.
- Standard deviation is a statistical measure that often is used to quantify the dispersion (variation) of investment returns which provides a standardized way to compare risk for different investments. Standard deviation increases as dispersion of annual returns increases. This is illustrated by the standard deviation of the asset classes shown in the returns history shown in Figure 1.
- US Treasury bills standard deviation 3.04%
- US 10-year Treasury bonds standard deviation 7.78%
- US S&P 500 index of stocks standard deviation 20.11%
- For those who have never experienced a significant downturn in the market, please read this forum post by Taylor Larimore (November 15, 2008). Here's an excerpt:
Figures cannot convey the horrifying and debilitating effects of a deep and long bear market. You watch in agony as month after month your life savings evaporate before your eyes. Gloom and doom articles are in the media, radio, (and now TV and internet). Nearly everyone else is selling. You have no idea when, or if, your portfolio will stop losing money.
Your friends and relatives urge you to sell. Nearly all financial experts recommend "sell". You are ridiculed for trying to hold on. You begin to have self-doubt. Dispair sets in. Buying stocks is unthinkable. Suicide's increase.
That's what a bad bear market is like.
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- See Systematic Risk Definition, investopedia. Retrieved 1 April 2012.
- Vanguard’s Investment Philosophy We Believe #7. Retrieved 2 April, 2012.
- "Risk and Risk Control in an Era of Confidence (or is it Greed?)".(Footnote 3) Lawrence Siegel, the treasurer of the Ford Foundation, writing in the Journal of Portfolio Management. Retrieved 4 April 2012.
- Vanguard. The truth about risk. Investing Truths. The Vanguard Group, Inc. Retrieved on 4/1/2012
- The file used to generate the Figures is available as a free download from Google Docs: Risk - Historical Performance of Bonds and Stocks.xlsx.
- Philips,, Christopher B.; Walker, David J. and Kinniry Jr., Francis M (05/04/2012), "Dynamic correlations: Implications for portfolio construction". Vanguard Investment Counseling & Research. Retrieved 17 May 2012.