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SOUTHERN JOURNAL OF AGRICULTURAL ECONOMICS JULY, 1978
SYSTEMATIC AND UNSYSTEMATIC RISK OF
RATES OF RETURN ASSOCIATED WITH SELECTED
FOREST PRODUCTS COMPANIES
James E. Hotvedt and Philip L. Tedder
The objective of most investors in stocks or an investor wishes to invest in assets whose
other assets is to maximize the expected re- rates of return follow those of the market as a
turns in a given risk class; in other words, to whole. A measurement of systematic and un-
minimize risk for a given level of expected re- systematic risk is needed from which the per-
turns [6]. Although "risk" may connote the centage of total risk accounted for by each can
chance of injury or loss, the term is not defined be calculated.
so narrowly in this article. Rather, it is used to The purpose of this article is to measure
reflect volatility in stock or other assets' rates total, systematic, and unsystematic risk of the
of return and should not be confused with risk rates of return of a select group of forest pro-
and uncertainty in the production process. ducts firms.
Risk, as approached herein, equals the var- In measuring risk it is desirable to determine
iance of historical rates of return about the that portion associated with the market and
average rate of return [6]. that portion associated with the company it-
Total risk of an investor's investment port- self. Are rates of return of forest products com-
folio can be reduced through investment panies relatively volatile? Or do they generally
diversification, that is, by the purchase of dif- follow market changes and trends? Unsyste-
ferent kinds of assets (stocks, bonds, securi- matic risk will measure the former and un-
ties, real estate, etc.) and by the purchase of systematic risk the latter.
stocks or bonds from more than one company
or industry. However, risk cannot be reduced
in this way beyond a certain limit because
changes in over-all market conditions affect MODEL
price variations in all stocks and other assets
and this variability cannot be eliminated com- A statistical model is used to separate total
pletely by diversification [4]. risk into its components. The expected rate of
As a result, it is desirable to separate total return on an asset is considered to be a linear
risk, or variation in rates of return, into two function of a risk-free rate and the expected re-
components-one reflecting that portion of an turn on a market factor. Because such a func-
asset's price movements caused by changes in tion cannot be observed in practice, the expect-
the market as a whole and a second reflecting ed rate of return is estimated by considering
that portion of an asset's price movements rate of return as a function of an overall market
caused by factors or variables unique to the rate of return [8]. Thus a means is provided for
company or industry itself. The former is measuring an asset's sensitivity to market
called "systematic risk" (and is nondiversifi- changes.
able) and the latter "unsystematic risk" [51. The statistical model commonly used is [8]:
Unsystematic risk, related to such factors as
labor strikes, inventions, research and develop- i t = a + bm t + e t
ments, (^) and the like is diversifiable.
A stock is said to be more desirable for port- where
folio diversification purposes if only a small
proportion of its volatility can be attributed to i t = rate of return of a particular corn-
the impact of the market [4], unless, of course, pany's assets in time period t
James (^) E. Hotvedt is a Graduate Research Assistant in Forestry (^) Economics, Virginia Polytechnic Institute and State University, (^) and Philip L. Tedder is Assistant Professor (^) of Forest Management, Oregon State University. (^) This article was completed while the authors were (^) Instructor and Assistant Professor, respectively, at the University (^) of Arkansas at Monticello.
a = y-intercept an^ index^ of^ systematic,^ nondiversifiable risk. b = slope of^ the^ regression^ line^ It^ indicates^ how^ the^ return^ for^ a^ given^ asset M (^) t = market rate^ of^ return^ in^ time^ period^ t^ varies^ with the^ market.^ If^ the^ coefficient^ is and greater^ than^ one,^ an^ asset's^ rate^ of^ return^ in- e (^) t = random error about the regression creases^ (decreases)^ at^ a^ faster^ rate than^ the line in time period t.^ market's.^ This^ value^ indicates^ what^ Francis^ 16] calls an "aggressive asset."^ A^ coefficient^ less For the five^ forest^ products^ companies,^ the^ than^ one^ indicates^ that^ an^ asset's^ rate^ of
assets to be evaluated are^ their^ common^ stocks.^ return^ moves^ counter^ to^ that^ of^ the^ market^ as^ a
The rate of^ return^ (it) on^ each^ company's^ com-^ whole^ [3].
mon stocks is calculated as^ follows^ [6]:^ The^ statistic^ representing^ random^ error^ (e^ t) D + P. -P about the^ characteristic^ line^ cannot^ be^ esti- t t+- Pt mated^ in^ practice.^ Theoretically,^ however,^ it it= represents that portion of total risk^ affected^ by t characteristics unique^ to^ the^ company^ or industry itself.
^^^~~~~~where ~The coefficient of^ determination^ (r
(^2) ) is a
measure of the percentage of^ total^ risk^ (varia- Dt (^) t = cash dividendcash dividend forfor^ timetime^ periodperiod^ tt tion in the rate of return of the asset) explained Pt+l = common stock price at end of time by changes in the market index. Thus, the coef- period=periodmo tt^ ando ct b iand ficient of determination is that statistic used to
Pt = common stock price at beginning of measure the^ percentage^ of^ total^ risk^ accounted
~~timet. period ^for by systematic,^ nondiversifiable^ risk^ [61.
The market rate of return (M) is reflected by^ EXAMPLE Standard and Poor's^ (SP)^ market^ index^ [4,^ 6]. The market rate of return is calculated^ as:^ unsystematic^ risk Total, systematic, and^ unsystematic^ risk associated with the^ rates^ of^ return^ of^ five SPt+-SPt forest products^ companies^ are^ calculated^ to Mt- p illustrate how the model is used. The firms SPt analyzed are Crown Zellerbach,^ Potlatch, where International^ Paper,^ Westvaco,^ and Weyerhaeuser. Each^ firm^ is^ large,^ having^ land- SP+ = value of^ the^ SP^ index^ at^ the^ end^ of^ holdings^ and processing^ plants^ in^ more^ than the time period^ t^ and^ one^ region^ of^ the^ country.^ The^ analysis^ allows SP = value of the SP index^ at^ the^ begin-^ total^ risk^ and^ its^ components^ for^ each^ of^ the ning of time period t.^ companies^ to^ be^ compared.^ In^ addition,^ the results of such an analysis aid^ in^ determining
Dividends are^ excluded^ purposely^ from^ the^ whether^ large^ forest^ products^ companies^ are market rate^ of^ return^ calculations and^ thus^ the^ more^ or^ less^ susceptible^ than^ companies^ in resulting index is downward biased.^ Provided^ other^ industries^ to^ factors^ that^ affect^ the that dividends are excluded consistently,^ market^ as^ a^ whole,^ or^ to^ factors^ which^ are^ in- comparisons of statistical results and^ of^ risk^ herent^ or^ unique^ to^ the^ particular^ companies^ or are valid [6]. industries^ themselves. The model^ results^ in^ a^ regression^ line,^ often^ TABLE^ 1.^ RESULTS^ OF^ CHARACTERIS- termed a "characteristic line," and the charac- TIC LINE ANALYSIS teristic line reflects the^ "nature^ of^ systematic and unsystematic risks; it^ shows^ the^ relation- ships of some asset with^ the^ market"^ [6].^ ompany^ Charaeristic^ F-Valuea Indeed, the hypothesis is that the rate of (^) Crown Z. i (^) t == 0.05270.0527^ ++^ 1.5491.549^ mt .356.356^ 14. return of an asset^ (it )^ is^ a^ linear^ function^ of^ a market factor common to^ all^ assets^ (Mt )^ and^ of^ Potlatch^ i^ =^ 0.0131^ +^ 0.929^ m^ .312^ 11. an independent^ factor^ unique^ to^ the particular^ Int.^ Pap.^ i^ t^ =^ 0.0631^ +^ 1.0292^ mt^ .242^ 8.
asset (et) [3]. Westvaco^ i^ t =^ 0.0523^ +^ 1.2406^ mt^ .279^ 10.
The y-intercept (a) is the asset's rate of Weyco i =0.0732^ +^ 0.9071^ m^ .123^ 3. return when the^ market^ is^ stationary^ (M^ t =^ 0). The beta^ coefficient^ (b)^ is^ a^ measure^ of^ the slope of the characteristic line; it measures the aAll equations and beta coefficients^ are^ significant^ at^ the volatility of an asset's rate of return in relation .05^ level^ except^ those^ for^ Weyerhaeuser^ which^ are^ signifi-
to the market rate of return [1]^ and^ therefore^ is^ cant^ at^ the^ .10^ level.
With such an^ approach,^ however,^ the^ compari-^ return^ does^ tend^ to^ persist^ over^ time^ then^ this
sons of risks associated^ with the^ selected^ pattern^ might^ continue^ in^ the^ future.^ If^ so, group of forest products firms would have been^ then^ risk^ analysis^ may^ provide^ an investor
precluded. with^ a^ means^ of^ estimating^ the^ likely^ degree^ of
Future work involves isolating those^ factors^ fluctuation^ or^ variation^ of^ his^ investments^ in which contribute to the unsystematic risk^ relation to^ the market^ and^ the risk^ that^ their portion of the rates of returns to^ forest^ product^ value^ may,^ at^ any^ time,^ be^ below^ his expecta- companies. tions^ [4]. If the relative volatility of^ an^ asset's^ rate^ of
REFERENCES
[1] Babcock, Guilford C.^ "A^ Note^ on^ Justifying^ Beta^ as^ a^ Measure^ Risk,"^ Journal^ of^ Finance,^ Vol-
ume 27, No.^ 3,^ 1972,^ pp.^ 699-702. [2] Baesel, Jerome B. "On the Assessment^ of^ Risk:^ Some^ Further^ Considerations,"^ Journalof^ Fi- nance, Volume 29, No.^ 5,^ 1974,^ pp.^ 1491-1494. [3] Blume, MarshallE. "On^ the^ Assessment^ of^ Risk,"^ Journalof^ Finance,^ Volume^ 26,^ No.^ 1,^ 1971, pp. 1-10. [4] Brealey,^ Richard^ A.^ An^ Introduction^ to^ Risk^ and^ Return^ from^ Common^ Stocks,^ Cambridge: The MIT Press, Massachusetts Institute^ of^ Technology,^ 1969. [5] Cohen, Jerome B.,^ Edward^ D.^ Zinbarg,^ and^ Arthur^ Zeikel.^ Investment^ Analysis^ and^ Portfolio Management, Homewood, Illinois:^ Dow^ Jones-Irwin^ Inc.,^ 1973. [6] Francis,^ Jack^ Clark.^ Investments:^ Analysis and^ Management,^ New York:^ McGraw-Hill Book Company, 1972. [7] King, B. F. "Market and Industry Factors^ in^ Stock^ Price^ Behavior,"^ Journalof^ Business,^ Vol- ume 39, No. 2, 1966, pp. 139-190. [8] Schwendiman, Carl J. and George E.^ Pinches.^ "An^ Analysis^ of^ Alternative^ Measures^ of^ Invest- ment Risk," Journalof^ Finance,^ Volume^ 30,^ No.^ 1,^ 1975,^ pp.^ 193-200.
