Risk and Return in Mutual Fund Selection

How to interpret statistical measures of risk.

  • INVESTORS—AND THE CPAs WHO ADVISE them—need objective criteria so they can understand the risks inherent in mutual fund investing. Understanding the fundamental relationship between risk and return will make it easier for CPAs to provide their clients with responsible and informed investment recommendations.
  • RISK ANALYSIS IS CENTRAL TO MUTUAL fund research. CPAs need to be able to establish realistic expectations for their clients about the expected performance of a fund under various market conditions. The CPAs role is not to eliminate risk but, rather, to control it and make sure clients are adequately compensated for the risks they take.
  • MODERN PORTFOLIO THEORY has developed a number of statistics that make it possible to accurately quantify the relationship between risk and return. These include a mutual funds volatility (standard deviation), how closely it mirrors a particular market index ( R2), its volatility compared with that market index (Beta) and how much the funds risk-adjusted return is attributable to its manager (Alpha).
  • MUTUAL FUND RESEARCH GOES BEYOND comparing a funds lagging returns with relevant market indices. CPAs also should make fund comparisons on a year-by-year basis, with particular attention to how a fund performed in bad markets. Its also important to make sure the current manager of a fund is the one responsible for past successes.
ROBERT A. CLARFELD, CPA/PFS, CFP, is president of Clarfeld & Company, P.C., a New York City CPA financial planning firm. He is chairman of the American Institute of CPAs personal financial planning executive committee investment services task force.
PHYLLIS BERNSTEIN, CPA, is director of the AICPA PFP division. The authors gratefully acknowledge the assistance of Lawrence Busch of Clarfeld & Company in writing this article. Ms. Bernstein is an employee of the American Institute of CPAs and her views, as expressed in this article, do not necessarily represent the views of the AICPA. Official positions are determined through certain specific committee procedures, due process and deliberation.
The mutual funds mentioned in this article are for illustration purposes only and in no way imply a recommendation or endorsement by the authors, the AICPA or the Journal of Accountancy .

M utual fund investors still get only half the story. The focus—in both the financial press and in advertisements—is on investment return, often precisely quantified by historical returns over several time intervals, with any mention of the funds relative risk relegated to imprecise generalities.

Investors—and the CPAs who advise them—need objective criteria concisely communicated to enable them to understand the risks that accompany these returns so they can make rational mutual fund selections. Unfortunately, the financial press often treats mutual fund investors as though they are incapable of understanding basic risk statistics and the fundamental relationship between risk and return that should drive all investment decisions.

The mutual fund universe often is divided into two distinct camps—winners and losers—based solely on performance. The same publication that praises a fund manager for outperforming a bull market will criticize the manager for exceeding market losses in a downturn, even though this is a logical expectation based on the funds aggressive investment style and high-risk profile. Furthermore, the aggressive manager may be investing toward a very different benchmark, say, the Russell growth index rather than the Standard & Poors 500. (See the sidebar ) This type of reporting often comes at an inappropriate point in the investment cycle—promoting high-risk funds at the peak of a bull market, when it is too late for investors to benefit, and defensive funds after the market already has declined.

Mutual fund lists featuring "funds to consider for the next millennium" or "the 17 greatest funds in the history of the universe" appear frequently in the media and make interesting reading. But, over time, such lists have not proven to be particularly insightful. Funds with records of steady gains and favorable risk—reward characteristics usually are better choices for long-term investors. This may be apparent following a deep market correction but difficult to fathom during rising markets, a time when many of these same funds are labeled "laggards." Reducing mutual fund selection to simplistic levels presumes an ignorant investing public, which does little to promote successful investing.

This article is designed to help CPAs interpret the various statistical measures of risk as they apply to mutual funds so they will be in a better position to advise their clients on this often complex aspect of stock and bond investing. Knowing how to interpret this information correctly will make it easier for CPAs to make responsible and informed investment recommendations to their clients.

Many investors believe the United States is in a period of great uncertainty in its investment markets. This is a conclusion that applies during all market conditions—except in hindsight. The risk an investor takes is what provides the opportunity for higher returns. Recognizing this makes it clear that more emphasis should be placed on risk analysis when CPAs and their clients make investment decisions. Risk analysis is central to mutual fund research. Focusing on the long-term relationship between risk and return will enable CPAs to establish realistic expectations as to expected performance under various market conditions.

Net Assets in Mutual Funds
(billions of dollars)
Type Amount
Stock funds $1,865.62
Bond/income funds 907.34
Taxable money market funds 809.11
Tax-free money market funds 149.30
Total $3,731.37
As of February 1997, the combined assets of the nations mutual funds was $3.731 trillion, an increase of more than 24% from the previous year.

Source: Investment Company Institute, Washington, D.C.

Risk exists when there is uncertainty about whether future returns will differ from the expected returns. Risk is an attribute that without context is neither good nor bad. Accordingly, the CPAs role is not to eliminate risk (few clients would be successful in funding their long-term goals with predictable Treasury bill returns) but, rather, to control risk and to make sure that clients are adequately compensated for the risks they take. The difference between the required rate of return on a mutual fund—given its risk—and the risk-free rate is the risk premium .

There are many sources of uncertainty that determine the appropriate risk premium, including market risk, business risk, liquidity risk, financial risk (leverage), duration and credit risk for bonds and political and currency risk for international assets. Investment portfolio risk generally is classified as either systematic or unsystematic . Simply stated, systematic risk is the portion of a portfolios risk that is market related or influenced. Unsystematic risk is the part that is unrelated to the market and is, instead, attributable to unique factors within the particular mutual funds portfolio. For example, a portfolio that is heavily weighted toward auto stocks would be subject to the risks associated with negotiating a new union contract (unsystematic risk) as well as those from the overall market (systematic risk).

Since assuming risk is inherent to the investment process, mutual fund investors must be adequately and consistently rewarded for the risks they assume. Prudent research means searching for fund managers who consistently produce returns justifying the risks they have taken.

Modern portfolio theory research developed a number of statistics that make it possible to more precisely quantify the relationship between risk and return. These measurements help determine

  • A funds volatility (standard deviation).
  • How closely a fund mirrors a particular market index (R²).
  • How volatile a fund is compared with that market index (Beta).
  • How much of a funds risk-adjusted return is created by a talented manager (Alpha).

Standard deviation. Standard deviation is a measure of dispersion. As it relates to investing, it is a measure of how much individual returns vary from the average expected return over a certain period of time. Since the performance history of mutual funds often is reported on the basis of 1-, 3-, 5- or 10-year average annual returns, it is important for CPAs to understand how consistent those returns have been. A high 10-year average annual return may have been achieved by a few outstanding years combined with several mediocre ones. While the average may seem acceptable, the year-to-year swings in performance may not be acceptable to a clients risk tolerance.

Two funds may have arrived at the same place by following very different paths. As shown in exhibit 1, below, American 20th Century Vista, a mid-cap growth fund, has been far more volatile than Mutual Shares, a large-cap value fund that has been a model of consistency, even though their 3- and 10-year total returns are similar. Although these dissimilar funds are being compared here with hindsight, historical standard deviations certainly should contribute to future expectations. The lower a clients risk tolerance, the less likely it is he or she will continue to hold the riskier fund long enough to achieve its ultimate returns.

Exhibit 1: Return vs. Volatility
3-Year 10-Year
Annualized return Standard deviation Annualized return Standard deviation
American 20th
Century Vista
18.06% 24.79% 15.18% 31.45%
Mutual Shares 17.68% 9.81% 15.35% 12.33%
Annual returns
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
American 20th
Century Vista
6.02% 2.44% 52.20% -15.73% 73.69% -2.13% 5.45% 4.68% 46.14% 7.56%
Mutual Shares 6.22% 30.92% 14.93% -9.82% 20.99% 21.33% 21.01% 4.53% 29.11% 20.76%
Source: Morningstar Principia, December 31, 1996.

R². The coefficient of determination (known as R-squared) measures the percentage of a mutual funds movement that corresponds to its benchmark index. That is, the R² shows how much of a funds performance—expressed as a percentage—is explained by the market (systematic risk). Conversely, the difference between a funds R² and 100% indicates how much of that performance is unique to the fund (unsystematic risk) rather than to the market. R² often is referred to as the "goodness of fit" between a fund and the market index it is benchmarked against.

An index fund, such as the Vanguard Index 500 Fund, that tracks the S&P 500 well has an R² approaching 100% and will look like—and perform like—the S&P 500. The lower a funds R², the weaker the market fit and the more nonsystematic or unique attributes contribute to its performance.

Exhibit 2: Goodness of Fit
3 years

S&P 500

Russell 2000
T. Rowe Price
Growth & Income
92% 46%
Acorn 50% 88%

Like risk itself, R² is neither good nor bad. Rather, it is a measure that enables CPAs to better understand the risk characteristics of a given fund. An investor who follows a passive management strategy should screen for index funds with an R² approaching 100% so he or she can attain market performance. An active manager must give up some market fit to concentrate on specific securities or an industry sector that he or she believes is undervalued.

Knowing a funds R² also enables CPAs to determine the relevance of other statistical measures of risk such as Beta and Alpha and the extent to which the definition of the "market" needs to be refined. For example, the T. Rowe Price Growth & Income Fund has an R² of 92% with the S&P 500 vs. 46% with the Russell 2000; the opposite is true for the Acorn fund ( see exhibit 2 ) Knowing the goodness of fit between a fund and its appropriate benchmark is crucial to avoiding meaningless and perhaps misleading analyses.

To evaluate a fund properly, a CPA needs to compare it with an appropriate benchmark. Morningstar, for example, includes in its reports statistics that are based on closely related markets, which it refers to as the "best fit" index. The stocks included in a particular fund also are important. A small cap fund, for example, would be compared with the Russell 2000, which is a small cap benchmark.

Beta. The Beta coefficient compares the variability of a funds historical returns to the market as a whole. That is, Beta measures a funds expected change for every percentage change in the benchmark index. The most common Beta is the S&P 500, which has a Beta of 1.00. Beta is a relative rather than an absolute number (as differentiated from standard deviation, which is an absolute measure of volatility). A mutual fund can be as volatile, more volatile or less volatile than the overall market, which by convention has a Beta of 1.00. If a fund has a below-market Beta of .86, it can be said that the fund has 86% of the volatility of the market. Relative to the market index, it will capture only 86% of the gain in up markets and decline by 86% of the drop in the index in down markets. Correspondingly, a Beta of more than 1.00 indicates a fund is more volatile than the index. Knowing a funds Beta enables CPAs to establish realistic expectations as to a funds volatility compared with the market—a valuable tool in creating a portfolio suited to a clients risk profile.

Exhibit 3: Benchmarking Beta
3 years
S&P 500

S&P 500
Russell 2000

Russell 2000
Emerging Growth
.98 21% 1.45 73%
Source: Morningstar Principia, December 31, 1996.

There is one major caveat to drawing any conclusions from Beta. A fund must significantly correspond to the market being benchmarked for the statistic to be meaningful. It is easy to be fooled into believing a fund has below-market volatility when it is being compared with the wrong index. Specifically, a small company stock fund could have an acceptable Beta calculated against the S&P 500 when in fact the Russell 2000 would be a better fit.

For example, the high-risk PBHG Emerging Growth Fund has a Beta of .98 when compared with the S&P 500 but a more revealing Beta of 1.45 when compared with the Russell 2000. Again, R² becomes important when interpreting these statistics. Exhibit 3 , shows that when viewed alongside its R² for both indices, PBHG Emerging Growths volatility becomes apparent when it is appropriately benchmarked.

Alpha. Alpha represents the difference between a mutual funds actual performance and the performance that would be expected based on the level of risk taken by the manager. It provides CPAs with a means of segregating the performance component attributable to the market from that which reflects the managers contribution. As with Beta, Alpha is a relative rather than an absolute indicator of risk-adjusted performance. If a fund produced the expected return for the level of risk assumed, the fund would have an Alpha of zero. A positive Alpha indicates the manager produced a return greater than expected for the risk taken.

Exhibit 4: Benchmarking Alpha
3 years
S&P 500

S&P 500
Russell 2000

Russell 2000
Small Cap
-1.53% 52% 2.35% 90%
Source: Morningstar Principia, December 31, 1996.

To calculate Alpha, compare the funds actual performance with the risk-adjusted expected return (the risk-free return added to the markets actual return in excess of the risk-free return, adjusted by the funds Beta). This difference is a measure of the managers contribution to return. For example, if the return from the S&P 500 in a given year exceeded the return from Treasury bills by 10%, and the fund was 120% as volatile as the market (a Beta of 1.2), then the fund should have outperformed T-bills by 12%. If the fund actually outperformed T-bills by 15%, its Alpha, or risk-adjusted return, would be +3%. The manager added value to the portfolio by producing a return greater than expected for the level of risk taken. A negative Alpha indicates the manager has not adequately rewarded investors for the risks taken.

Investors seek funds run by managers who consistently produce statistically significant positive Alphas. However, many excellent funds may be eliminated from consideration by rigidly adhering to Alpha. Generally, investors need at least three years of data to draw any kind of meaningful conclusion. Even then, a large positive or negative Alpha in any given period may be due to chance. A series of Alpha calculations over time is needed to determine with statistical significance that the Alpha is successfully differentiating the superior (or inferior) manager from the pack. Also, many funds are managed according to eclectic styles that do not conform closely enough to an established index to render Alpha meaningful. Again, as with Beta, a sufficient goodness of fit to an index (as measured by R²) is needed before Alpha becomes a valid analytical tool. The investment battlefield is littered with the slaughtered expectations of investors who relied on erroneously interpreted Alphas and Betas.

Lazard Small Cap Fund, for example, produces a negative Alpha of -1.53% when compared with the S&P 500 (R² of 52%), but a positive Alpha of 2.35% when measured against its more appropriate benchmark, the Russell 2000 (R² of 90%).

Researching mutual funds that are appropriate for clients goes beyond comparing individual funds lagging returns with relevant indices. The broad market indices certainly should be considered, along with growth or value style-specific indices such as the S&P Barra Growth or the Russell Value. CPAs also should make fund comparisons on a year-by-year basis, taking special note of returns achieved during down market periods (1990 and 1994 are good years to look at for domestic stock funds). Many mutual fund managers simply never have experienced an extended bear market.

The Indices

There is no single index that will tell you how the stock market is doing because "the market" means different things to different people. Two popular stock market indices are

Standard & Poors 500. As the name implies, this index tracks 500 widely held domestic common stocks of large, well-established companies. It often is used as a substitute for the stock market as a whole. The 500 stocks include 400 industrial companies, 40 financial companies, 40 public companies and 20 transportation companies and are market capitalization weighted. The S&P 500 is often used as a benchmark index for comparing equity, asset allocation, balanced and income mutual funds.

Russell 2000. This index consists of the smallest 2,000 companies in the Russell 3000 index, which in turn is composed of the 3,000 largest U.S. companies by market capitalization, representing 98% of the U.S. equity market. The Russell 2000 represents approximately 7% of the Russell 3000 total market capitalization and often is used as a gauge for small company stock investing.

Performance history also should be examined qualitatively to determine its validity. CPAs should research the funds portfolio manager to make sure the same talent currently is in place that produced the past management and performance statistics. Management stability is highly desirable. Investment talent truly can be said to "have legs" on Wall Street.

A better understanding of how risk is measured will not enable CPAs to pick next months darling in the mutual fund performance derby. And while no amount of research can guarantee future fund performance, it certainly can reduce the likelihood of unintended risk by carefully analyzing and interpreting risk statistics. Careful research will enable CPAs and their clients to better understand a mutual funds range of likely outcomes over various time horizons. In a declining market, sometimes this understanding just may provide the marginal comfort that separates those who ride out storms from those who do not.

Selected Mutual Fund Resources
Value Line Fund Analyzer 800-833-0046
Morningstar Principia Plus 800-876-5005
Ibbotson Associates Fund Strategist 312-616-1620


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