© 2000 John Petroff

E- Risk adjusted rate of return

Portfolio theory has shown that all the five first components of interest rates discussed in the previous section can be combined into one single rate of return because all financial assets are affected similarly. That return is the return on a riskless asset, which is identical for all markets and all securities. As a riskless asset, government issues are often used: for instance, U.S. Treasury Bills. (Treasury Bills are indeed backed by the tax collecting authority of the American government and, because they are short term - less than 90 days for a large proportion of them, they have little default risk or interest rate risk.) What needs to be estimated for individual securities is only the last component of risk premium.

The portfolio theory shows that investors hold diversified portfolios of various types of securities, combining purchases of some 15 to 20 higher-return and higher-risk assets with a strategy of placing or borrowing at the riskless asset rate in order to achieve a desired risk-return trade-off that satisfies their personal aversion for risk and eagerness to seek the highest return possible. An arbitrage (described in Chapter 4 Section F-2) takes place between securities, as those with comparable return and risk are sold in exchange for lower risk or higher return.

For each individual security, the market (or average) return for this type of security is incremented by an amount of risk perceived by investors in that security's price volatility compared to the volatility of the market overall. The outcome of this theory is that the required rate of return used in any valuation, is market driven and, therefore, an objective consensus of market participants. Participants observe the performance of a firm in satisfying their expectations of income, growth and stability, and bid the price of the company shares up or down, and by the same token, the required rate of return down or up. (See the last section of this chapter for the inverse relationship that always exists between price and rate of return: when one goes up, the other goes down.)

See review questions Q-2E.1 through Q-2E.12.

1)- Risk measurement

In practice, price volatility of a stock relative to volatility of the market is measured by coefficient BETA. Values of BETA's for all major stocks are calculated by major brokerage firms (and other institutions). The market is represented by an appropriate index such as the NYSE composite index. If R_i if the rate of return of a stock i and R_m is the rate of return of the market m in which stock i is traded, then BETA is given by the formula

BETA = Covariance(R_i,R_m)/ Variance(R_m)

The required rate of return R_i for stock i is

R_i = RFR + BETA_i (R_m - RFR)

where RFR = risk free rate such as that of US treasury bills,

R_m = average return of the market for that type of security.

Note that (R_m -RFR) is the market risk premium. As seen in the previous section, the risk premium for stocks is larger than that for bonds, as one would expect indeed.

BETA values of less than one indicate a stock that is less volatile (i.e. more stable) than the overall stock market, whereas a BETA of more than one indicates a stock that is more volatile than the market. The overall market BETA is naturally one.

See review questions Q-2E1.1 through Q-2E1.6.

See research assignment R-E1.1.

2)- Problems with risk measurement

There are problems with BETA because BETA coefficient estimates are unstable. They tend to vary more when short time periods are used for their estimation, and when the estimation is performed on small companies with relatively little trading, than when estimates are obtained for long periods and widely traded companies. Industry BETA coefficients (i.e. risk premium calculated for a group of firms in the same industry) are more stable and reliable. Some estimation techniques for individual companies use an adjusted BETA obtained by averaging an individual stock price BETA with an industry BETA.

See review questions Q-2E2.1 through Q-2E2.3.

See research assignment R-2E2.1.

3)- BETA estimates

Despite statistical difficulties, BETA estimates are widely used. Financial analysts, brokers, investors and other stock traders have now access to several estimates of BETA values for all major stocks, as mentioned in Chapter 1 Section D-4b. It is up to an analyst to choose between them and stay with one set of estimates in a consistent manner. Table T-2.3 below shows that, for a group of 66 randomly chosen stocks, the estimated adjusted BETA's by two different services using different price series and market indexes, are very similar.

As a basis for comparison of company BETAs, BETA estimates of groups of companies in the same industry are used. Table T-2.4 below presents industry BETAs for a selected group of industries. As can be expected the industry BETAs are closer to one than the values of individual companies shown in the range of BETAs column. The average of all industry BETAs is naturally one. What is of particular interest in Table T-2.4 is that BETA estimates correspond to what one would expect for each particular industry. For instance, utilities and food industries are less than or equal to one, as one would intuitively assume because their sales and profits are known to be stable. At the other end of the spectrum, growth industries (such as computer software and services) and cyclical industries (such as air transport, home building and autos and trucks) are well above one. Basic products and services (such as household products and banking, respectively), are just equal to one.

For Russian companies, one can't expect to find BETA estimates now and for some time to come, because there are not enough statistics available to conduct the regression analysis. In addition, the Russian stock market is thin and sporadic trading tends to destabilize prices. Nevertheless, because of the immediate relevance of these values to market participants, it can be expected that some service will soon publish initial BETA estimates for Russian stocks. In the meantime, it can be helpful in some cases to rely on estimates obtained in the U.S. (or another Western country) for particular industries and use these values as substitutes for Russian values.

Here is an example of required rate of return calculation for Silicon Graphics in Spring of 1995. For instance, the risk free rate in Spring 1995 was 6.58% (which is the yield shown in Table T-2.2 above for 30 year US bonds, and which is the appropriate rate to use because it reflects long term issues). If the small stock arithmetic mean return of 18.4% is used, it gives a market risk premium of 11.82%. The BETA for Silicon Graphics is given as 1.59. Thus, the required rate of return for Silicon Graphics stock is Ri = 6.58 + 1.59 (18.4 - 6.58) = 6.58 + 1.59(11.82) = 25.37 %

A required rate of return such as the one presented in the example above, would be used in the valuation of the common stock of Silicon Graphics with the discounted dividends formula presented in Chapter 3 Section D-1. Or it can be compared, as such, with other rates of return of similar companies and with the actual returns earned over several years.

Another estimate of required rate of return for Silicon Graphics could be based on recent NYSE data instead of the 60 year average. In the Spring of 1995, the NYSE, as well all the other American stock markets, had experienced an unusually strong bull (i.e. upward) trend. Since the beginning of the year, stock prices broke record levels week after week. In July 1995, the composite NYSE index showed an increase of 20.08% for the past 52 weeks, and the NASDAQ composite index (which is an index of smaller company stocks traded over the counter, and which better represents the type of stock Silicon Graphics is), showed an increase of 37.26%. While these rates should be more appropriate for the estimation of a stock value in July 1995, it is not sure that the bull market will continue and not reverse itself soon. This shows that market attitudes are important considerations which cannot be ignored but are difficult to incorporate in an estimation process. More will be said on this subject in subsequent chapters.

See review questions Q-2E3.1 and Q-2E3.2.

See research assignment R-2E3.1.

4)- Limitations and extensions of risk measurements

In addition to instability of BETA estimates, portfolio theory has been criticized by practitioners for its efficient market hypothesis which states that market prices reflect all available information immediately. Practitioners point to wide daily swings in prices on all stock exchanges without any significant new information coming to light. Also, if prices do reflect all information, there wouldn't be any point in conducting any company analysis because stocks would never be mispriced. These issues will be touched upon once again in subsequent chapters as trading strategies (see in particular Chapter 4 Section F-2) and analytical methods (see Chapter 5 Section J) are discussed.

See research assignment R-2E4.2.

This section briefly presented a major contribution of modern portfolio theory to the understanding of rates of return adjustment for risk present in company stock. For a more complete treatment of portfolio theory one should refer to many excellent texts devoted to capital assets pricing model (CAPM) or arbitrage pricing theory (APT). The adjustment for risk presented here for stocks is naturally valid for all other forms of financial assets and financial decisions, as will be apparent in subsequent chapters.

The adjustment of required rate of return by inclusion of risk measured by BETA is the most common method. There are instances, however, when risk cannot be measured objectively because there is no market for a particular financial asset in question. This is the case, for instance, of a bank loan which the bank suddenly determines as potentially non recoverable. As will be seen in Chapter 3 Section C-2, the practice is to set aside a reserve for potential loss. The amount of the reserve is determined from prior experience with similar loans. No theory has yet been formulated for appropriate mark down of a financial asset in the presence of additional risk or uncertainty from various negative new events or circumstances. Yet, there are a few other instances when that is necessary, such as when a stock of a closely-held corporation to be acquired, has no active market, see Chapter 4 Section H.

See review questions Q-2E4.1 through Q-2E4.3.

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