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Risk is never easy to define. Although financial publications spend inordinate amounts of time discussing the concept of risk in investments, there is always room for more debate. The difficultly in defining risk lies in the fact that it means something different to each investor. For one investor, it may mean there is a chance that they will lose money in the next year. For another investor, it might mean there is a chance that their portfolio’s returns will be very different from market returns. One commonly used definition states that risk is the probability of an investment to achieve lower returns than expected. This article provides a bit of clarity for our investors by taking a closer look at some of the more common measures of risk.

The most common risk measure is **standard deviation**. Standard deviation is an absolute form of risk measure; it is not measured in relation to other assets or market returns. Standard deviation measures the spread of returns around the average return. For example, the average annual return for the S&P 500 from 1970-2012 was 11.5% with a standard deviation of 17.6. Assuming the distribution of the returns is “normal,” this means that 95% of annual returns were within two standard deviations of the average annual return—between -23.7% and 46.7%. A higher standard deviation indicates that the investor holding the asset will experience greater uncertainty in annual returns. In exchange for this uncertainty, investors expect higher returns. Equity securities (stocks) are typically associated with higher risk and higher annual returns. Fixed income securities (bonds) typically exhibit smaller standard deviations than equity securities and usually earn lower average annual returns.

*Here is a table of annualized standard deviations of some of Wespath's funds as of December 31, 2013. The standard deviation is based on 36 months of historical returns.*

US Equity Fund | 12.26% |

International Equity Fund | 16.14% |

Fixed Income Fund | 3.97% |

Inflation Protection Fund | 5.05% |

Multiple Asset Fund | 9.23% |

Another absolute risk measure that is commonly used in fixed income security analysis is **duration**. Rising interest rates have a negative impact on the investment returns of fixed income securities because their coupon or annual payment is fixed by definition. When interest rates rise, new bonds are issued at a higher coupon. This makes older bonds that were issued at lower coupon, less desirable. An investor in the market to purchase bonds will prefer the new bond with a higher coupon over the older one. Due to this higher demand of newer bonds, older bonds with fixed and lower coupons will be trading at a lower price or at a discount. Duration is a measure of this effect—a bond’s change in price due to changes in interest rates. The price of a bond with five-year duration will decrease by five percentage points when the interest rates increase by 1 percentage point, and vice versa. Bonds with longer maturity will have a higher duration than bonds with shorter maturities, and are therefore riskier. Typically, investors require higher returns to hold bonds with long maturities and higher durations.

Risk is not always seen as an absolute value. Often it is important to know the risk of a security or how a portfolio performs in relation to the general market. One relative form of risk measure is the **beta**, which measures how sensitive an asset’s return is to an index. A deeper dive into the concepts of correlation and standard deviation will help explain this concept.

Correlation measures the strength of the relationship between the investment returns of two assets. A positive correlation indicates that the returns of both assets move in the same direction. Conversely, a negative correlation indicates that the returns of the two assets move in opposite directions. The correlation coefficient also provides information on how closely each asset’s returns follow movements in the other asset’s returns.

Beta is the correlation between an asset’s returns multiplied by the ratio of the asset’s standard deviation. As noted above, standard deviation measures the spread of annual returns around the average annual return. Simply, beta measures the amount of asset volatility (asset standard deviation) that is correlated to the market’s volatility (market standard deviation).

In contrast to standard deviation, beta measures the relationship of an asset’s returns to an index or market of similar assets. A beta of one indicates that the asset’s return will move in tandem with the market. A higher beta represents a more volatile asset (as compared to the market) and a lower beta represents a less volatile asset. Beta is the inherent risk (also known as the market risk) of the asset; it is calculated using regression analysis of historical returns.

*This table shows the one-year beta of six companies in the S&P 500 Index as of September 30, 2013 (Source: Bloomberg).*

Morgan Stanley | 1.56 |

General Moters Co. | 1.29 |

Apple Inc. | 1.01 |

Google Inc. | 0.95 |

McDonald's Corp. | 0.73 |

Wal-Mart Stores Inc. | 0.68 |

*For example, absent specific news for the company, one would expect the stock of Morgan Stanley to increase 1.56% if the market as a whole increases by 1%.*

One of the advantages of measuring an asset’s risk using beta is that it is easily quantifiable. Ascribing a number to an abstract concept, such as market risk, allows investors to compare assets. Another advantage is that, unlike standard deviation, beta is a relative measure. Since risk is an inherent characteristic of all securities, and therefore an unavoidable fact of investing, it makes sense to look at an asset’s risk in relation to the market risk.

Using beta as a risk measure also has some drawbacks. Beta is calculated using historical data. Experienced investors know that historical performance is not an indicator of future returns. Similarly, historical standard deviations and correlations are not an indicator of future standard deviations and correlations. Another disadvantage is that correlations of all assets tend to increase during periods where the market performs extremely well or extremely poorly. This phenomenon obfuscates asset behavior. A closer look at the most recent recessionary period illustrates this phenomenon.

During the financial crisis of 2008, all asset prices were severely depressed. The historical correlations between different assets failed to hold as market and economic conditions put downward pressure on all prices. Therefore, all assets experienced similar trends in investment returns. This caused correlations between asset returns to increase and risk measures, such as beta, to become useless.

Since 2008, many investors began using alternative correlation calculations when developing portfolios instead of using beta. For instance, some investors are calculating the correlation between assets and various economic factors, such as inflation or gross domestic product growth. Studies have shown that correlations between asset returns and these economic factors do not increase in times of extreme market movements as significantly as correlations between asset and market returns. Using these alternative correlation calculations helps investors construct portfolios that diversify and mitigate the impact of economic events.

Risk remains an abstract concept that is hard to quantify and to define. There are many who question investors’ ability to distill this complex concept to a mere statistical calculation. Thus, many continuously try to redefine risk in terms that make sense for their portfolios. Staying at the forefront of this ongoing effort in understanding risk is a necessity for all investors.

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