Resource /Energy Economics and Policy, Risk and Uncertainty,

Hotvedt, James E.

Tedder, Philip L.

English

Research Papers in Economics

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-  it = a +  bmt + et
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  it = 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.
135a =  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  (et)
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  (r2)  is  a
measure of the percentage  of total risk (varia-
Dt =  cash dividend for time period t t  cash dividend for time period t  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 t and
=periodmo  t  o  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
~~time  period  t.  ^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  = 0.0527  + 1.549  .356  14.4 Crown  Z.  it =  0.0527  + 1.549  m t .356
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  11.8
an independent factor unique to the particular  Int.  Pap.  it =  0.0631  + 1.0292  m t .242  8.3
asset (et) [3].  Westvaco  it = 0.0523  + 1.2406  m t .279  10.1
The  y-intercept  (a)  is  the  asset's  rate  of  Weyco  i 
=
0.0732  + 0.9071  m  .123  3.6
return when the market is stationary (Mt =  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.
136Table  1 shows the results of the characteris-  companies  listed on the  NYSE, the  values  for
tic line analysis for each of the five companies.  Crown Zellerbach and Potlatch are apparently
The  time  series  used  included  seven  years  higher  and  that  for  Weyerhaeuser  lower,
(1970-1976),  each  observation  being  one  whereas the values for International Paper and
quarter. Thus 28 observations were used.  Westvaco  conform  fairly  well to  those tested.
The  portion  of  total  risk accounted  for  by  Blume [3] found an average coefficient  of deter-
systematic,  nondiversifiable  risk  ranges  from  mination  (r 2)  to  be  .25  which  indicates  that
12.3 to 35.6 percent. The former figure is some-  about  25  percent  of  total  risk  is  systematic
what suspect because the value for each of the  risk.  Independent  studies  do  not  appear  to
other  four companies  is  greater  than  24  per-  complement  each  other,  however,  because
cent.  The  beta coefficients  range  from  0.9071  King  [7]  found  average  systematic  risk to  be
to 1.549,  indicating that the rates  of return  of  about 50 percent of the total.  Brealey [4]  found
the  companies  are  relatively  stable,  except  the  proportion  of  earnings  movements  asso-
that of Crown  Zellerbach.  Indeed,  the  returns  ciated  with market  movements  to  be  27  per-
of the four companies  closely follow changes in  cent (about equal to the conclusion  by Blume).
the overall market.  In  addition,  Brealey's  results  indicated  that
The  high  beta  value  for  Crown  Zellerbach  approximately  27  percent  of total risk  in the
indicates volatility in its rate of return  in rela-  paper  industry  was  related  to movements  in
tion  to  market  changes.  For  example,  if  the  the  market.  This  value  conforms  to  those  of
market  index  (as  measured  by  SP)  were  in-  International  Paper  and  Westvaco,  both  of
creasing,  the  rate  of  return  of  Crown  Zeller-  which  are multiproduct  companies  but which
bach's common stock would increase  154.9 per-  derive  most of their income from pulp,  paper,
cent  of the  increase  in the  market  index.  Con-  and paper product sales.
versely,  a decrease  in the  market  index would
result in a decrease equivalent to 154.9 percent
of the decrease in the market rate.  Although a  DISCUSSION
substantial  return is possible in  an advancing
market,  the prospects for heavy losses in a de-  The time  span used  may  have had  an influ-
clining market are equally probable.  ence  on the statistical results of the character-
TABLE2.  TOTAL,  UNSYSTEMATIC,  istic  line  analysis.  For  example,  one  might
AND  SYSTEMATIC  RISK  AS-  expect  the  beta  coefficient  to  stabilize  or
SOCIATED  WITH  EACH  OF  become  stationary as the time series increases
THE  FIVE  FOREST  PRO-  [2,  5].  However,  too  long a period  allows  dilu-
DUCTS COMPANIES  tion of the influence or effect that changes in a
company  might have on changes in its rate of
Cmpay  TRa  SRb  Uc  return. For example, management may become
more or less conservative,  management  might
Crown  Z.  .0657  .0234  .0423  introduce  modern  technological  developments
Potlatch  .0270  .0084  .0186  into its manufacturing or administrative  func-
Int.  Pap.  .0428  .0104  .0324  tions, the company  may increase the diversifi-
Westvaco  .0538  .0150  .0388  cation of its products or mergers, and so on.
The  validity  of results  in risk analysis  has
Weyco  .0652  .0080  .0572  been  questioned  when  single assets  are anal-
yzed rather than a portfolio.  Indeed,  it may be
aTotal risk = Variance (i t) t =  1,28.  difficult to determine changes in the rate of re-
turn  of  one  stock  on  the  basis  of  market
hSystematic risk = [b
2 (Variance (ml))l  = [r
2 (Variance (i,))l.  changes  because  other  factors  may  have  an
Unsvstematic risk = total risk - systematic risk,  effect  [4].  Brealey  [4]  states that if individual
stocks  are  aggregated  into  a  portfolio  these
Table 2  shows total risk and its components,  other  factors  may  be  diversified  away.  If  so,
systematic  and unsystematic risk,  for the five  then market changes can be assumed to be the
companies.  Although  Crown  Zellerbach  has  major determinant  of changes  in the  value of
the greatest  volatility  in its rates of return  in  group stocks, and market changes  can be used
comparison  with  changes  in  the  market,  its  with greater  assurance  in predicting  changes
total risk  (.0657 or  6.57  percent)  is not out of  in the rate of return  from a  portfolio  than  in
line with that of the other companies.  Indeed,  predicting changes  in the price  of any individ-
the total risk values  for Crown  Zellerbach and  ual stock.
Weyerhaeuser are nearly equal.  Thus, it  may have been more appropriate  to
In comparison with the systematic risk asso-  compare  risks  of  alternative  well-diversified
ciated  with  stocks  of  hundreds  of  other  portfolios  by  comparing  their  beta  values.
137With 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," Journal  of Fi-
nance, Volume 29, No. 5, 1974, pp. 1491-1494.
[3]  Blume, MarshallE. "On the Assessment of Risk," Journal  of 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," Journal  of 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," Journal  of Finance,  Volume 30, No. 1, 1975, pp. 193-200.
138

A Note on Justifying Beta as a Measure Risk,&quot;

An Analysis of Alternative Measures of Investment Risk,&quot;

An Introduction to Risk and Return from Common Stocks,

Investment Analysis and Portfolio Management,

Investments: Analysis and Management,

Market and Industry Factors in Stock Price Behavior,&quot;

On the Assessment of Risk,&quot;

On the Assessment of Risk: Some Further Considerations,&quot;

SYSTEMATIC AND UNSYSTEMATIC RISK OF RATES OF RETURN ASSOCIATED WITH SELECTED FOREST PRODUCTS COMPANIES

SYSTEMATIC AND UNSYSTEMATIC RISK OF RATES OF RETURN ASSOCIATED WITH SELECTED FOREST PRODUCTS COMPANIES

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Research Papers in Economics