The overall message of this section is that, while one can certainly argue
in favor of a FAR-based approach to capital budgeting, the argument is
somewhat more delicate than it might have appeared in section 2, and it
does not apply in all circumstances. In order for a FAR-based approach to
make sense, not only must managers have long horizons, but they must be
relatively unconstrained by their current capital structures.
4.Implementing a FAR-Based Approach: Measuring β*Part of the appeal of a FAR-based approach to capital budgeting is that it
appears to be very close to the textbook CAPM method. However, as noted
in section 2 above, the one hitch is that, in order to implement a FAR-based
approach, one needs to know β, which is the value of βthat would prevail
in a rational expectations world; that is, the fundamental risk of the assets
in question. And given the underlying premise of the article—that the stock
market is inefficient—one cannot simply assume that a βcalculated using
observed stock returns will yield a good estimate of β. Thus the following
question arises: as a practical matter, how close to β* can one expect to get
using the standard regression methodology for calculating β?
A. Theoretical ConsiderationsIn order to clarify the issues, it is useful to begin with a more detailed ana-
lytical comparison of the value of a βcomputed from actual stock return
data—which I will continue to denote by βr—versus that of β*. To do so, I
will generalize somewhat from the setting of the previous sections by enter-
taining the possibility that there is mispricing of the market as a whole as
well as mispricing of individual stocks. In addition, and somewhat trivially,
I will allow for more than one period’s worth of stock returns.
Note that in any period t, for any stock i, we can always make the fol-
lowing decomposition:
Rit≡R*it+Nit, (16)where Ritis the observedreturn on the stock, R* is the return that wouldit
prevail in a rational expectations world—that is, the portion of the observed
return due to “fundamentals”—and Nitis the portion of the observed return
due to “noise.” We can also make a similar decomposition for the observed
return on the market as a whole, RMt:
RMt≡R*Mt+NMt. (17)Clearly, as a general matter, the βcalculated from observed stock returns,
βri=cov(Rit, RMt)/var(RMt) will not coincide with βi=cov(R, it RMt)/var(RMt).
To get a better intuitive handle on the sources of the difference between βri
RATIONAL CAPITAL BUDGETING 621