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Introduction Conventional capital asset pricing model (CAPM) specified
independently by Sharpe (1964), Lintner (1965), Mossin (1966), and extended by Black
(1972) relates the firm's expected rate of return to the term premium of the riskless
interest rate and the risk premium of the market. Since its inception, this ex ante model
is criticized by many empirical researchers, most notably Fama and French, who attempted
to test its predictive power and found that CAPM was not as robust as it is alleged to be.
Ross (1975) derives a more generalized version of the CAPM called the arbitrage pricing
theory (APT) which allows multiple factors to explain the variability of the firm's
expected return, but does not specify any explanatory variable to model it. Relying on the
logic behind the APT and the results of their widely quoted test of market efficiency,
Fama and French (1992, 1995, 1996) build on the CAPM by specifying two other variables in
addition to the market risk premium namely, size premium (market equity value) and
distress premium (book-to-price ratio). Based upon this three factor model (TFM), they
conclude that securities markets maintain their informational efficiency and that the TFM
has a higher explanatory power than the CAPM. However, the inclusion of these two
accounting-based variables into the CAPM does not provide the theoretical construct behind
the vanished return anomalies and enough reasons as to why size and relative distress can
cause the realized abnormal stock returns. Since size and distress are measured from the
firm's reported book and market equity values, their linkage to the firm's assets value
can also be established in order to see how the firm's investment and operating activities
might have some impacts on them. The changes in book and market equity values could signal
the investors about the firm's future earnings prospect as a result of its internal
strategic investment and operating decisions. Therefore, the search for this type of
private information contained in size and relative distress will enable the investors to
form a more accurate probability belief and rational expectations about the future stock
price and returns, thereby increasing the predictive power of the CAPM.
This paper is divided into four sections. Section one
deals with the literary review on TFM and its rationale. The appropriate paradigm to
analyze the value of the firm's investment and operating flexibility, or real options, in
relation to its size and relative distress is discussed in Section
two along with my research hypotheses. Section three
characterizes the data set appropriate for the test and proposes the research methodology
for testing the hypotheses. Finally, conclusion and recommendation for the
operationalization of this study are given in the Section four.
Review of the Three Factor Model Back to
Top
Fama and French (1992, 1995, 1996) developed the TFM to
explain and capture the cross-sectional excess stock returns. Their studies suggest that
size and book-to-price ratio (B/P) add more explanatory power to the standard CAPM in
deriving the stock returns after finding out that their combined effects seems to
overshadow the effects of leverage, earning-to-price ratio (E/P), and cash-flow-to-price
ratio (C/P). Size contributes to the excess returns in the following manner. Small stocks
tend to have lower earnings on book equity than do big stocks, controlling for B/P ratios.
However, Banz (1981) finds a contradiction that average returns on small stocks are too
high given their market b estimates, and average returns on big stocks are too low.
Huberman and Kandel (1987) find evidence that there is covariation in the returns on small
stocks that is not captured by the market risk premium and is compensated in average
returns. Size premium which turns out to have a negative relationship with the stock
returns should offer an additional explanation on the cross-sectional behavior of average
returns. B/P ratio, on the other hand, is suggested by Chan and Chen (1991) to serve as a
proxy in indicating the relative level of distress of the firm. Stattman (1980),
Rosenberg, Reid, and Lanstein (1985), and Chan, Hamao, and Lakonishok (1991) conclude that
distress premium and average stock returns are strongly positively correlated and are not
captured by the market return. Thus, Fama and French model and test these two factors
along with the market risk premium and find them able to capture most of the market
anomalies in average stock returns which are not explained by the standard CAPM.
The TFM's ex ante cross-sectional expected excess returns is
given by:
E[ri] - rf = bi(E[rm]-rf)
+ si(SMB) + hi(HML)
- where
E[ri] - rf = expected excess return on portfolio i
E[rm] - rf = expected excess return on a market portfolio m
SMB = return difference between small-stock and big-stock portfolios
HML = return difference between distressed and strong stock portfolios
bi, si, hi = coefficients of market risk, size, and
distress premium factors
Expressing the above equation in terms of ex post
time-serial excess returns gives:
rit - rf = ait + bit(rmt-rf)
+ sit(SMB) + hit(HML) + eit
- where
rit - rf = realized excess return on portfolio i at time t
rmt - rf = realized excess return on market portfolio m at time t
ait = intercept term of the regression line
eit = random residual return on portfolio i at time t
The rationale for TFM is provided by Fama (1994) based
on a generalized mean-variance efficient (MVE) portfolio concept of Merton's (1973)
intertemporal capital asset pricing model (ICAPM). ICAPM investors not only are concerned
with the risk-returns tradeoff but also interested in hedging more specific state-variable
risks as a result of consumption-investment tradeoff. The optimal portfolios are,
therefore, multifactor mean-variance (MMV) efficient. The MMV portfolios are spanned by
the risk-free security and any three linearly independent MVE portfolios including two
risky state-contingent market portfolios and a zero-covariance market portfolio. In terms
of expected excess returns, the intercepts in the regressions are zeros. In terms of
realized excess returns, the R 2 of
the regressions are equal to one.
The candidate MMV portfolios' risk premia identified for TFM are 1) the
market premium, 2) the size premium, and 3) the distress premium. The size and distress
factors are able to describe the returns based on E/P, C/P, and sales-rank index
identified by Lakonishok, Shleifer, and Vishny (1994) as well. One advantage of TFM over
the other models is that market, size, and distress premia are less correlated with one
another. This makes the TFM regression coefficients easier to interpret. Other proxies for
the MMV portfolios are not as robust as those included in the TFM. Sales rank, for
example, suffers errors-in-variable problem because this proxy is not adequately
diversified thereby confounding the model.
Theoretical Basis on Real Options and Research
Hypotheses Back to Top
Black (1986) links the market price of security to the
fundamental value of the firm. Changes in the fundamentals have a direct impact on the
expected return and the risk characteristic of the security price. Since the value of the
firm is a function of the expected future cash flows discounted by the appropriate cost of
capital, the market price of stock is therefore the function of the underlying cash flows
of the firm. In the literature on investment under uncertainty, the net present value of
the project is not only determined by the expected future cash flows stream and the
discount rate, but also the value of the options to commit or delay committing the firm's
resource in such investment. Conditioned on uncertain investment costs and future incomes,
the net present value of the project has to be adjusted to account for the flexibility in
waiting for more information to reduce the uncertainties before making any investment
outlay. Therefore, the firm's project value which determines the future prospect of its
earnings depends also on the options to invest, delay investment, or abandon an investment
altogether. This investment flexibility is referred to as real options or options on real
assets as opposed to financial options.
Two main features of investment
flexibility are irreversibility and deferrability. According to Pindyck (1988),
irreversibility means that once the investment decision is made, the capital expenditures
incurred in the project are partially or totally sunk costs. In other words, if the firm
decides to abandon the project, it has to forego such investment partially or completely.
This has an important implication to and impact on the firm's asset allocation decision
since irreversibility imposes high exit penalty for ineffectual investment. The degree of
irreversibility varies depending on how marketable or liquid the abandoned assets are from
which the firm can retrieve some residual value. If it were relatively high, the project
is perceived to have low flexibility and thus low real options. If the exit costs were low
for the firm to abandon the project, its real options value increases.
McDonald and Siegel (1986) treat deferrability as analogous to the time
value of financial options in which the firm can opt to delay the investment until
favorable market conditions materialize or new information improves the probability of
project's success. This source of real options depends on how sustainable the investment
opportunity is over a certain period. If the opportunity is either now or never, then
deferrability has zero real options value. In contrast, the project can be delayed
indefinitely, the real options value approaches infinity and the project may never be
implemented. To be consistent with the option pricing paradigm, it is assumed that there
exists a certain date that the project must be implemented, or exercise date. However, the
investment costs on that exercise date cannot be determined at present the same way as the
strike prices on financial options are. Therefore, the value of deferrability depends on
exercise date and the information prevailing on that date.
Beside investment flexibility, there are separate
treatments of real options which involve operating flexibility. Operating
flexibility refers to the latitude in the firm's decision to utilize its assets
strategically to enhance earnings potential for the upside opportunities while hedging
them for the downside risks. Majd and Pindyck (1987), Carr (1988), and Trigeorgis (1993)
identify the staged investment option for the firms engaging in the long-term
capital-intensive projects in which each stage in the development can be viewed as an
option on the value of subsequent stages. Brennan and Schwartz (1985), McDonald and Siegel
(1985), Trigeorgis and Mason (1987), and Pindyck (1988) study the scale alteration option
for natural resource and cyclical industries in which the firms can expand or contract
their operating scales based upon the expected market conditions. The abandonment option
is extended from the scale alteration option by Myers and Majd (1990) that in case of
prolonged decline in market conditions, the firms can abandon their current operations
permanently and realize the resale value of their assets in secondary market. Margarbe
(1978), Kensinger (1987), Kulatilaka (1988), and Kulatilaka and Trigeorgis (1993) classify
the switch use option into two types: product flexibility and process flexibility. If
prices of or demand for products change, the firms can alter the output mix of the
facility. Alternatively, the same products can be produced using different mixes of
inputs. The early or preemptive investments in R&D, undeveloped land, strategic
acquisition, and infrastructure represent the growth option. Myers (1977), Trigeorgis
(1988), Pindyck (1988), Brealey and Myers (1991), and Chung and Charoenwong (1991) find
that these types of investment are prerequisite to a chain of interrelated projects which
open up future growth opportunities. Finally, different kinds of operating flexibility can
be combined as being the collective real options, both upside-potential enhancing calls
and downside-protection puts. Their combined options interact and yield different value
from the sum of separate option values.
However, these real options cannot be easily detected or merely
observed from the market-based data which impose even more difficulty on their proxies
identification. Nonetheless, we may resort to certain accounting-based measures which are
publicly available and objectively enough to proxy for investment and operating
flexibility such as the ratio of fixed assets to total assets (FTA) and the degree of
operating leverage (DOL). By definition, DOL means the potential use of fixed operating
costs including depreciation of fixed assets to magnify the effect of changes in sales on
the firm's earnings before interest and taxes (EBIT). It can be derived as follows:
DOL = CM/(CM-FC) = % DEBIT/%DS
- where
CM = contribution margin = sales - total variable costs
FC = fixed operating costs
S = dollar sales level
Changes in fixed costs can affect operating leverage
significantly. The firm can incur fixed costs rather than variable costs, or substituting
one types of cost for the other. Increase in fixed costs would increase operating leverage
and vice versa.
FTA measures the level of the firm's commitment in fixed assets which
can be proxied for relative size and degree of irreversibility. High FTA means larger
fixed-assets base which could incur high exit costs to the firm. Firms with low FTA have a
relatively smaller fixed-assets base which provides them with less exit burden and higher
investment flexibility. DOL, on the other hand, measures how well the firm utilizes its
fixed assets to generate higher earnings before interest and taxes which, in effect,
reduce its level of distress and thereby offering high real options. Small firms tend to
have lower intensity of fixed capital investment than large firms which provide them with
higher investment flexibility and high average stock returns. Distressed firms which have
employed more fixed capital investment experience higher operating flexibility and possess
high real options which result in their high average stock returns. Both are not captured
by market risk premium because they are firm-specific characteristics.
This rationale helps shape my conjecture about the relationship between
size premium and investment flexibility and between distress premium and operating
flexibility. The following hypotheses are proposed:
- H1
: Size is positively correlated with FTA and DOL. Small firms tend to
have high investment flexibility due to low FTA but low operating flexibility because of
low DOL. The net effect on real options is positive since investment flexibility outweighs
operating flexibility.
H2: Distress is negatively correlated with FTA and DOL. Distressed firms
tend to have low investment flexibility due to high FTA but high operating flexibility as
a result of high DOL. The net real options is positive because operating flexibility
outweighs investment flexibility.
These two hypotheses shall be modified for the
regression models in terms of size and distress premia to coincide the transformation of
average returns to excess returns.
Proposed Data Source and Research Methodology Back to
Top
To be consistent with Fama and French's (1996) study,
the monthly excess returns on four portfolios from NYSE, AMEX, and NASDAQ between 1963 and
1993 based on size and distress proxies are used. The size proxy is derived as follows. At
the end of June of each year t, stocks from the three exchanges are allocated to two
groups (Small or Big) based on whether their June market equity is below or above the
median value. The distress proxy is derived in the same manner as in the size proxy by
allocating stocks to two groups (Low or High) based on the breakpoints for the bottom 50%
and top 50% of the values of B/P for NYSE stocks. Four size-distress portfolios are
defined as the intersections of the two market equity values and the two B/P groups. SMB
is the difference between the average returns on the two small-stock portfolios (S/L and
S/H) and the average returns on the two big-stock portfolios (B/L and B/H). HML is the
difference between the average returns on the two high-distress-stock portfolios (S/H and
B/H) and the average returns on the two low-distress-stock portfolios (S/L and B/L).
For the two real options independent variables, the method of deriving
the proxies are similar to the one employed on size and distress dependent variables. The
investment flexibility proxy using the firms' FTA ratios are grouped into two: high
investment flexibility (HIF) and low investment flexibility (LIF), based on the
breakpoints for the bottom 50% and top 50% of the value of FTA. Notice that low FTA
signifies HIF and high FTA means LIF. The operating flexibility proxy based on DOL is
calculated from the percentage change in earnings before interest and taxes (EBIT) divided
by the percentage change in sales. High DOL means high operating flexibility (HOF) while
low DOL refers to low operating flexibility (LOF). DIF is the difference between HIF and
LIF. DOF is the difference between HOF and LOF.
The ordinary least squares (OLS) estimation model is
proposed to be a statistical tool to find the relationships between TFM factors and the
real options variables. The assumptions for the model are:
- The time-series patterns of variance are constant.
The time-series patterns of random errors are uncorrelated.
The explanatory variables, i.e., FTA and DOL, are deterministic.
The regression model for testing H1 is given
by:
SMBt = at + b(DIFt)
+ g(DOFt) + et
The regression model for testing H2 is given by:
HMLt = at
+ b(DIFt) + g(DOFt) + et
- where
SMBt = return difference between small- and big-stock portfolios at time t
HMLt = return difference between distress and glamour portfolios at time t
DIFt = difference between high and low investment flexibility at time t
DOFt = difference between high and low operating flexibility at time t
Conclusion and Recommendation Back to
Top
The contribution of this paper is for investment
theorists, empiricists, and practitioners to gain more understanding about Fama and
French's TFM as to why the two additional risk factors, i.e., size and distress, are more
parsimonious than other factors identified by previously such as E/P and C/P. Undeniably,
there should be an explanation behind these two factors' ability to capture abnormal
returns in excess of market risk premium. One of the more distinct explanations is based
on the analysis of real options possessed by small and/or distressed firms. Small firms
benefit from not committing capital intensive investment which is translated into high
investment flexibility, but lose from not having enough fixed expenditures to lever their
earnings. The net effect on real options is positive since their investment flexibility
has more value than operating flexibility. Distressed firms tend to make high capital
investment in fixed assets thereby losing investment flexibility, but gain operating
flexibility from potential earnings growth when their fixed assets contribute to the
higher DOL. Their net real options value is also positive because operating flexibility in
the future outweighs the current investment flexibility.
If the hypotheses were true, they would imply that value
stocks (i.e., small and/or distressed stocks) should not be undervalued based on their
poor earnings and prospects. Their real options values will reveal their firm-specific
risk premia to be captured by the market return. This should resolve the market anomaly or
behavioral puzzle as to why value stocks earn higher average returns than growth stocks.
The same reasons can be used to explain why growth stocks earn lower average returns. It
is simply that large and/or glamour stocks do not have the embedded real options or that
their real options have been used up or depleted already. These implications should lead
to more extensive research about the intra-actions among different kinds of real options
and inter-actions between real options and stock returns.
The empirical test of my hypotheses will prove that the above
implications are true, based on the ordinary least squares (OLS) statistical technique.
However, the assumptions on constant variance and uncorrelated errors can be relaxed by
using the generalized least squares (GLS) model. The results from both techniques may
improve our understanding about the relationships between real options and size and
distress premia. After this preliminary study is done, it is recommended that further
investigation on the patterns of variance and errors be conducted using the generalized
autoregressive conditional heteroskedastic (GARCH) model which will support the use of GLS
model suggested previously.
I believe the links between market-based and firm-based risk premia can
be established through the real options analytical framework. The only problem is how we
can identify the proper proxies for real options. My suggestion here is to use the
accounting-based measures of fixed assets employment (FTA) and utilization (DOL). Other
non-accounting measures may serve as the better proxies but may lack desirable properties
of observability and objectivity which are very important for market-based asset valuation
and risk-premium evaluation.
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Back to Top
* Worapot Ongkrutaraksa is a lecturer in Finance
and Strategic Management at Maejo University's Faculty of Agricultural Business, Chiang
Mai, Thailand. He used to conduct his post-graduate research in financial economics at
Kent State University and international political economy at Harvard University through
the Fulbright sponsorship between 1995 and 1998.
E-mail: worapot@iname.com
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