UP College of Business Administration Discussion Papers DP No. 1007 November 2010 Performance of Accounting Beta as a Risk Measure by
Joseph Emmanuel L. Angeles*
* PhD Student, UP College of Business Administration  cba@up.edu.ph  +63 2 928 4571 to 75  +63 2 920 7990 http://www.upd.edu.ph/~cba
Performance of Accounting Beta as a Risk Measure
Joseph Emmanuel L. Angeles1
Abstract
This article tests the hypothesis that accounting beta can be used in place of market beta
as a risk measure. Data from the Philippine Stock Exchange are used for hypothesis testing. The
results show that, in general, the estimated sector accounting betas are statistically different from
the estimated sector market betas. The results were robust to the addition of variables for
Philippines Treasury Bill rates or inflation.
Introduction
Market beta is defined as the regression of the return of asset i for the period upon the
return on the market portfolio of all assets taken together.2 Because market betas cannot be
computed for unlisted firms, this paper studies whether accounting beta may be used by unlisted
firms in place of market beta for the purpose of calculating a required rate of return.
Literature Review
Overview
Kantor (1987) writes that very little of the work in efficient capital markets has yet been
translated to the valuation of unquoted companies whose ordinary shares neither trade on an
exchange nor over the counter. Indeed, for unlisted share valuation: 'The importance of the
problem... has been exceeded only by its neglect” [Rice (1950)]. This field does not lack
relevance. Kantor noted that only 2500 (0.35%) of the approximately 700000 companies
1
University President, Angeles University Foundation
W. Sharpe, "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk," Journal of Finance
(September 1964), pp. 425- 442; J. Lintner, "The Valuation of Risk Assets and the Selection of Risky Investments in
Stock Portfolios and Capital Budgets," Review of Economics and Statistics (February 1965) , pp. 13-37; J. Lintner,
"Security Prices, Risk and Maximal Gains from Diversification," Journal of Finance (December 1965), pp. 587-616;
J. Mossin, "Equilibrium in a Capital Asset Market," Econometrica (October 1966), pp. 768-782.
2
1
incorporated in the United Kingdom at that time had their ordinary shares listed, while
approximately 98% of companies were unlisted in Canada. In the Philippine context, there are
approximately 700,000 corporations (stock and non-stock) and partnerships of record in the
Securities and Exchange Commission,3 while only 253 (0.03%) are listed as of July 2010.4
According to Kantor, the academic neglect is the consequence of an inadequate methodology and
the absence of a reliable data base. Thus, Lawson (1980) wrote: “There is no escape from the
fact that financial theory is not yet able to boast of a fundamentalist multi-period model that can
generate tolerable valuations for unquoted companies.” In short, it is far easier to concentrate on
the relatively small proportion of companies which have listing status, using well-tested
methodologies and readily available published data sources.
The Capital Asset Pricing Model (CAPM) presents a relatively well established
framework for assessing the required rate of return for a security but requires market data to
determine the market beta. Since market data are not available for unlisted firms, the CAPM
model in its pure form does not provide any relief. To this end, researchers have searched for
accounting data based proxies for market beta. A suitable proxy would eliminate the market data
requirement and would permit application of CAPM to unlisted firms.
Previous Research
The original theoretical justification for beta as a measure of security risk is the capital
asset pricing model as developed by Sharpe (1964), Lintner (1965), and Mossin (1966). Under
this formulation of asset pricing, the beta is the sole security-specific variable determining
differences in risk premiums among securities. This conclusion holds regardless of whether the
assumption of unrestricted borrowing and lending at a riskless rate is dropped [Black (1972)].
Thereafter, research was conducted on the relationship between earnings and security
prices for the reason that firm earnings play a central role in virtually all valuation models.
Empirical evidence indicates that accounting earnings are the major explanatory variable in
3
As per July 28, 2010 interview of Mr. Alan Pasia, System Developer, Securities and Exchange Commission.
As per July 28, 2010 interview of Ms. Vivian Verano, Executive Assistant, Corporation Finance Department,
Securities and Exchange Commission.
4
2
cross-sectional valuation models5 and that unexpected changes in earnings are associated with
unexpected changes in a security's market value.6 Based upon this research, Beaver, Kettler and
Scholes (1970) wrote that earnings volatility would be one factor affecting price volatility.
Moreover, it was argued that the systematic volatility in earnings would be one factor
determining systematic volatility in the market price. The accounting beta was taken to be a
measure of the former and the market beta as a measure of the latter. This argument has been
developed more rigorously by Pettit and Westerfield (1972). On the divisional level, Gordon and
Halpern (1974) estimated the systematic risk of a project using similar accounting data. They
hypothesized that differences in cost of capital and the interest rate were related to the systematic
risk of the division or the whole firm. The systematic risk was measured by the covariance of the
rates of growth of divisional earnings and operating income of a diversified portfolio of firms
divided by the variance of the latter quantity.
In 1980, Hill and Stone developed an accounting measure for intrinsic systematic risk
from the Hamada-Rubenstein formulas. The Hamada-Rubenstein formulas are risk-composition
formulas that relate the market beta to an intrinsic operating beta and a measure of financial
leverage. Hill and Stone show that an equity beta based on return on equity (ROE) and an
operating beta based on return on assets (ROA) are related as follows:
∑
.
Vos (1992) assesses the required rate of return for unlisted firms using the CAPM model.
Models assessing the required rate of return typically use regressions comparing the returns of
the shares of companies with the returns of the market index, and calculate the slope thereof,
which is otherwise popularly known as Beta. However, since publicly available data on unlisted
companies is rare, this formula could not be used without modification. According to Vos
(1992), accounting betas were first used by Ball and Brown in 1962. The authors ran a regression
of the one year change in firm earnings over one year change in the index of economy wide
5
See M. Miller and F. Modigliani, "some Estimates of the Cost of Capital to the Electric Utility Industry, 19541957," American Economic Review (June 1966), pp. 333-391; and R. Litzenberger and C. Rao, "Estimates of the
Marginal Rate of Time Preference and Average Risk Aversion of Investors in Electric Utility Shares, 1960-66," Bell
Journal of Economics and Management Science (Spring 1971) , pp. 265-277.
6
See R. Ball and P. Brown, "An Empirical Evaluation of Accounting Income Numbers," Journal of Accounting
Research (Autumn 1968), pp. 159-178; W. Beaver, and R. Dukes, "Interperiod Tax Allocation, Earnings
Expectations, and the Behavior of Security Prices," Accounting Review (April 1972), pp. 320- 332; W. Beaver and
R. Dukes, "Delta Depreciation Methods: Some Empirical Evidence," Accounting Review (July 1973), pp. 549-559)
3
earnings of firms in the same year. Based on the results, Vos concluded that accounting betas are
significant determinants of risk for New Zealand listed firms, while they may or may not be for
unlisted New Zealand firms.
Aaker and Jacobson (1987) noted that scholars have criticized accounting ROI as an
inadequate indicator of rate of return since it does not properly relate a stream of profits to the
investment that produced it. Its earnings numerator is a consequence of investment decisions
made in the past, but its assets denominator can be expected not only to have influenced past and
current earnings, but also to influence future earnings. This possible invalidity would adversely
influence an empirical investigation of the association between risk and return that used
accounting ROI both as a dependent variable and as the basis for estimating beta. In addition to
the foregoing critique, Cotner (2000) argues that 1) it makes the unfounded assumption that
EBIT/Total Assets is a perfect proxy for return on equity (Net Income/Equity) used in the
regression model to compute market beta, and 2) ignores many of the nonsystematic risk factors
that should be taken into account in estimating the cost of capital for a privately held firm.
However, Aaker and Jacobsen (1987) noted that empirical studies have surprisingly found a
significant association between annual accounting ROI and stock returns, which are a wellaccepted measure of economic return. Also, a number of studies have found a correlation
between stock price beta and accounting beta [i.e. Beaver & Manegold (1975)]. According to
Hill & Stone (1980), the extent of the association depends on the accounting measure used as an
indicator of return and the time period under study.
Barefield and Comiskey (1971), and Litzenberger and Rao (1971) argue that it is the
inability to forecast earnings and not earnings variability which is important to risk
determination. Barefield and Comiskey (1979) presented evidence which indicated that historic
forecast errors were more effective in explaining differences in systematic risk than historic
earnings variability. These results provided the first empirical test of, and support for the view
that it is inability to forecast and not earnings variability per se that constitutes a fundamental
risk factor. Comiskey, Mulford and Porter (1986) improved on the Barefield and Comiskey
(1979) study by replacing mean earnings per share forecast error, which is a total risk measure,
with a measure of systematic market risk. It tested the degree of association of a measure of
4
earnings variability (accounting beta) and a measure of earnings forecast error (forecast-error
beta) with market beta. He pointed out that there were two components to forecast error: a
company-specific and a market component. The forecast-error beta represented the market
component. It was hypothesized and found that that forecast-error beta has a significantly higher
degree of association with market beta than accounting beta.
Another accounting beta based approach was proposed by Rosenberg and McKibbin
(1973) who used both market-based returns and accounting-based information to predict
systematic risk. They first estimate the ex-post beta for a publicly traded firm by using a timeseries regression with the aim of explaining this ex-post beta by using a set of independent
variables termed "descriptors." Some of these descriptors are means from a time-series of
accounting data, variances from a time-series of accounting data, and contemporaneous
accounting data. Other descriptors are derived from market data. One of these market-data
descriptors is the historical beta. However, assuming that the method was more accurate, critics
argue that cannot be used to estimate beta for a division since some of the descriptors depend on
market data for the firm as a whole.
Fuller and Kerr (1981) employ the analogous firm approach to find a beta for a nontraded
firm or for a division, otherwise known as the pure-play method. The method begins by
identifying another firm with publicly traded stock that is engaged solely in the same line of
business as the division. Critics of this approach argue that firms with publicly traded securities
and in identical lines of business are not easily identifiable.
Ehrhardt and Bhagwat (1991) argue for a full-information approach. Their model follows
the theoretical foundation of the goal programming approach of Boquist and Moore (1972). The
premise is that a firm is simply a portfolio of projects. Thus, the systematic risk of a firm is the
weighted average of the betas in the lines of business that constitute the portfolio. The steps in
the process are as follows: 1) estimate the beta of publicly traded firms; 2) measure the weight of
each business segment using a goal programming; and 3) find segment betas that minimize the
sum of absolute deviations from the firm betas.
5
Cotner and Fletcher (2000) prescribe a different method, which they christen the
“Analytical Hierarchy Process (AHP).” The steps of the method are: 1) establishing a range of
equity premiums that is appropriate for the firm, with medium risk corresponding to the risk of
an average project of the firm; 2) identification of factors that affect firm’s risk (i.e. growth rate
in revenues, fixed operating costs, and interest coverage), classified broadly into revenue factors,
operating factors, financial factors, management/ownership factors, and strategic factors.; 3)
assessing the condition of each factor in the model, and selecting the most appropriate descriptor
term for the level of risk premium relative to that criterion; 4) determining the relative
importance of each criterion to the total risk in the organization.; and 5) multiplying the
numerical values corresponding to the descriptor terms selected for each criterion by the weight
computed for that criterion. However, we note that the article limited discussion to an overview
of the approach and not confirmed its validity. Moreover, while the authors criticize the
arbitrariness of previous models, their own model suffers from the same defects.
Data and Methodology
As an initial test of the accounting beta concept, this paper will determine to what extent
accounting based measures are representative of market based measures of the return on the
market portfolio. For data to represent accounting based measures, we refer to the Return on
Assets and Return on Equity ratios for the PSE index (PSEi), Financials Index, Industrial Index,
Holding Firms Index, Property Index, Services Index, and Mining and Oil Index in the PSE
monthly reports. For data to represent market based measures, we refer to the closing value of
the PSEi index, Financials Index, Industrial Index, Holding Firms Index, Property Index,
Services Index, and Mining and Oil Index at the end of the month in the PSE monthly reports.
Our data set is limited to the PSE monthly reports from September 2006 to May 2010 since the
reports only incorporated Return on Assets and Return on Equity ratios for the above indices
starting September 2006. As control variables, we may use T-bill rate (91 day and 364 day),
Inflation Rate (Annualized Growth Rate), and Dividend Yield. These are also obtained from the
aforestated PSE Monthly Reports. According to macroeconomic theory, this information set
6
would be relevant to investors for asset pricing.7 The PSE Corporate Planning and Research
Section describes the methodology for computing the above variables as follows:
PSEi - The PSEi is the main index of the Exchange. It is composed of a fixed basket of
30 companies, whose selection is based on a specific set of criteria. The PSEi measures the
relative changes in the free float-adjusted market capitalization of the 30 largest and most active
common stocks listed at the PSE. By gauging changes in the stock prices of select listed
companies, the PSEi provides a snapshot of the market’s overall condition. The Exchange uses
free float-adjusted market capitalization for computing the index to make it a more accurate
benchmark of market performance. The free float methodology is deemed to provide a more
accurate reflection of market activity than the full market capitalization methodology which the
Exchange used prior to April 2006. This is because only the actual shares available for trading
are being used to track the performance of the market. It removes the distortion that arises when
companies with large market capitalization dominate the index, even if only a minimal
percentage of their shares are actually traded. Likewise, the use of the free float methodology
rewards companies with wider ownership base by increasing their weights in the index. For any
trading day, the index is computed by deriving the change in the index components’ current total
free float-adjusted market capitalization from the base total free float-adjusted market
capitalization, and multiplying this change with the previous day’s closing index level. The base
total free float-adjusted market capitalization is the sum of all the products of the index stocks’
previous day’s last traded price and their current free float shares.
Sector Indices - To track the performance of specific sectors of the market, the PSE also
maintains six sector indices representing each major sector under the revised industry
classification of the Exchange. These indices are the (1) Financials Index; (2) Industrial Index;
(3) Holding Firms Index; (4) Property Index; (5) Services Index; and (6) Mining & Oil Index. To
qualify for the sector indices, a company must satisfy the following requirements: 1) Liquidity or
Average Daily Trading Value – the value of the company’s shares traded in the PSE’s regular
market during the review period, divided by the days eligible for trading, must not be less than
P1 million; and 2) Tradability – the shares of the company must be traded at least 75% of the
7
See O. Blanchard, Macroeconomics, pp. 321-326 (Prentice Hall, 3rd. ed).
7
days when the shares are eligible for trading. The sector indices have no limit on their number of
constituents, and all companies that meet the two criteria mentioned above gain inclusion in their
respective sector indices.
T-bill rate (91 day and 364 day) and Inflation Rate (Annualized Growth Rate) – The data
for these variables were obtained by the PSE from the Bangko Sentral ng Pilipinas (BSP)
Market Capitalization – This variable is computed by multiplying Last Traded Price by
Outstanding Shares
Dividend Yield – This variable is computed by dividing Total Cash Dividends for the last
12 months by Market Capitalization.
Return on Assets (ROA) – This variable is computed by dividing Trailing 4Q Net Income
by Total Assets.
Return on Equity (ROE) – This variable is computed by dividing Trailing 4Q Net Income
by Total Equity.
We apply the following methodology: 1) determine the market beta (
) by regressing
PSEi on a sector index (i.e. financials); 2) use the estimated market beta in a regression of PSEi
) for the sector (i.e. ROA for the Financials Index). The
on an accounting measure of beta (
hypothesis to be tested is:
Since the question is whether
reject
8
if | |
or 0
or 0 , then the two-sided test rejection rule is used. We
, where c is the two-tailed critical value.8
J. Wooldridge, Introductory Econometrics: A Modern Approach, p. 132 (Southwestern Cengage Learning, 4th ed.).
8
To
estimate
the
dlog
market
dlog
beta,
we
shall
use
the
regression
model . The accounting beta is estimated using the
regression model dlog dlog
. Finally, we calculate
t-values to determine whether the estimated market beta is statistically different from the
estimated accounting beta.
Analysis and Result
Financial Sector
The simple regression of dlog(fin) on dlog(psei) resulted in the following estimates:
.0063
.8969
. 0051 .0722
0.7860
44 The estimated coefficient of .8969 for the financial sector indicates that the relative risk
thereof compared to the risk of the market portfolio risk is lower. The variable dlpsei has a tvalue of 12.42, which is statistically significant at any conventional significance level.
On the other hand, the simple regression of dlog(roafin) on dlog(roapsei) resulted in the
following estimates:
.0097
.7535
. 0189 .3085
0.1244
44 When 91 day t-bill rates and inflation rate were introduced as control variables, the
following results were generated.
dlroapsei
ltbill91
linfl
R-squared
.7535
--------------
--------------
0.1244
9
dlroafin
(.3085)
. 6805
-.0570
-.0086
(.3385)
(.1087)
(.0234)
0.1381
The variable dlroapsei remained statistically significant, whether in a simple regression
or in a multiple regression. The remaining variables were statistically insignificant.
Testing the null hypothesis using the results of the simple regression yielded a t-value of 0.4648, which indicates that
significance level. Using
is not statistically different from
at any conventional
from the multiple regression did not change the results.
Industrial Sector
The simple regression of dlog(ind) on dlog(psei) resulted in the following estimates:
.0052
.8951
. 0069 .0973
44 0.6685
The estimated coefficient of .8951 for the industrial sector indicates that the relative risk
thereof compared to the risk of the market portfolio risk is lower. The variable dlpsei has a tvalue of 9.20, which is statistically significant at any conventional significance level.
On the other hand, the simple regression of dlog(roaind) on dlog(roapsei) resulted in the
following estimates:
.0084 2.1281
. 0133 .2181
0.6938
44 When 91 day t-bill rates and inflation rate were introduced as control variables, the
following results were generated.
10
dlroapsei
ltbill91
linfl
R-squared
--------------
--------------
0.6938
2.0752
.0131
-.0099
(.2402)
(.0771)
(.0166)
2.1281
dlroaind
(.2181)
0.6966
The variable dlroapsei remained statistically significant, whether in a simple regression
or in a multiple regression. The remaining variables were statistically insignificant.
Testing the null hypothesis using the results of the simple regression yielded a t-value of
5.6534, which indicates that
significance level. Using
is statistically different from
at any conventional
from the multiple regression did not change the results.
Holding Firms Sector
The simple regression of dlog(hol) on dlog(psei) resulted in the following estimates:
.0046
1.3156
. 0075 .1054
44 0.7875
The estimated coefficient of 1.3156 for the holding firms sector indicates that the relative
risk thereof compared to the risk of the market portfolio risk is higher. The variable dlpsei has a
t-value of 12.48, which is statistically significant at any conventional significance level.
On the other hand, the simple regression of log(roahol) on log(roapsei) resulted in the
following estimates:
.0069
.7914
. 0127 .2083
44 0.2557
11
When 91 day t-bill rates and inflation rate were introduced as control variables, the
following results were generated.
dlroapsei
ltbill91
linfl
R-squared
--------------
--------------
0.2557
.7665
-.0655
.0003
(.2278)
(.0732)
(.0157)
.7914
dlroahol
.2083
0.2723
The variable dlroapsei remained statistically significant, whether in a simple regression
or in a multiple regression. The remaining variables were statistically insignificant.
Testing the null hypothesis using the results of the simple regression yielded a t-value of 2.5166, which indicates that
significance level. Using
is statistically different from
at any conventional
from the multiple regression did not change the results.
Property Sector
The simple regression of dlog(pro) on dlog(psei) resulted in the following estimates:
.0052
1.2357
. 0067 .0949
0.8014
44 The estimated coefficient of 1.2357 for the property sector indicates that the relative risk
thereof compared to the risk of the market portfolio risk is higher. The variable dlpsei has a tvalue of 13.02, which is statistically significant at any conventional significance level.
On the other hand, the simple regression of dlog(roapro) on dlog(roapsei) resulted in the
following estimates:
12
.0023
.2229
. 0082 .1346
44 0.0612
When 91 day t-bill rates and inflation rate were introduced as control variables, the
following results were generated.
dlroapsei
ltbill91
linfl
R-squared
--------------
--------------
0.0999
.2352
.0012
.0020
(.1488)
(.0478)
(.0103)
.2229
dlroapro
(.1346)
0.0624
The variable dlroapsei was statistically insignificant at the standard confidence levels,
whether in a simple regression or in a multiple regression. The remaining variables were
statistically insignificant.
Testing the null hypothesis using the results of the simple regression yielded a t-value of 7.5245, which indicates that
significance level. Using
is statistically different from
at any conventional
from the multiple regression did not change the results.
Services Sector
The simple regression of dlog(ser) on dlog(psei) resulted in the following estimates:
.0018
.7917
. 0054 .0760
44 0.7211
13
The estimated coefficient of .7917 for the services sector indicates that the relative risk
thereof compared to the risk of the market portfolio risk is lower. The variable dlpsei has a tvalue of 10.42, which is statistically significant at any conventional significance level.
On the other hand, the simple regression of dlog(roaser) on dlog(roapsei) resulted in the
following estimates:
.0009
.1071
. 0102 .1664
44 0.0098
When 91 day t-bill rates and inflation rate were introduced as control variables, the
following results were generated.
dlroapsei
ltbill91
linfl
R-squared
--------------
--------------
0.0098
.0650
.0594
-.0113
(.1810)
(.0581)
(.0125)
.1071
dlroaser
(.1664)
0.0425
The variable dlroapsei was statistically insignificant, whether in a simple regression or in
a multiple regression. The remaining variables were also statistically insignificant.
Testing the null hypothesis using the results of the simple regression yielded a t-value of 4.1142, which indicates that
significance level. Using
is statistically different from
at any conventional
from the multiple regression did not change the results.
Mining & Oil Sector
The simple regression of dlog(min) on dlog(psei) resulted in the following estimates:
.0078
14
1.388
. 0138 .1955
44 0.5456
The estimated coefficient of 1.388 for the mining sector indicates that the relative risk
thereof compared to the risk of the market portfolio risk is higher. The variable dlpsei has a tvalue of 7.10, which is statistically significant at any conventional significance level.
On the other hand, the simple regression of dlog(roamin) on dlog(roapsei) resulted in the
following estimates:
.0327
2.5391
. 0352 .7538
0.2617
44 When 91 day t-bill rates and inflation rate were introduced as control variables, the
following results were generated.
dlroapsei
dlroamin
ltbill91
linfl
R-squared
--------------
--------------
0.2617
2.8729
-.1871
.0899
(.7697)
.1794
(.0498)
2.5391
(.7538)
0.3349
The variable dlroapsei remained statistically significant, whether in a simple regression
or in a multiple regression. The remaining variables were statistically insignificant.
Testing the null hypothesis using the results of the simple regression yielded a t-value of
1.5270, which indicates that
Using
is statistically different from
from the multiple regression did not change the results.
Conclusions
15
at the 5% significance level.
The statistical results indicate that the estimated accounting betas as defined in this paper
are generally statistically different from the estimated market betas. These results would suggest
that accounting beta, as defined in this paper, is an ill fitting substitute for market beta.
However, this does not discount the fact that other formulations of accounting beta, using
other indicators such as return on equity, may result in better estimates and act as a better proxy
for market beta.
We also note that PSE regulations only require listed companies to file interim financial
reports on a quarterly basis.9 This regulatory lag may explain the reduced explanatory power of
the accounting beta. A regression of the PSE data on a quarterly basis rather than a monthly basis
may obtain different results. However, this is not possible at this time given the limited data set
of 44 observations which would be reduced to 11 if data is taken on a quarterly basis.
9
Securities Regulation Code, Rule 17.1(2)(A)(i) and Rule 68.1(8)(d).
16
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