280 NPV PROBABILITY DISTRIBUTION OF RISKY INVESTMENTSthe probabilistic approach, as a general approach to capital investment, is
at a dead-end? This is the question which will be addressed in part three of
the article.
Section 15.5 will explore the extent to which positive discount rates can
invalidate the applicability of the CLT to the derivation of the NPV prob-
ability distribution. Such an exploration is carried out in two steps. The
first step involves computer simulations to generate NPV probability distri-
butions with first-order and second-order autoregressive cash flows under
three probability distributions (normal, uniform, and double-exponential).
Section 15.6 consists in testing the statistical difference between the simu-
lated NPV probability distributions and a normal probability distribution.
The statistical test will involve a chi-square test and will aim at deter-
mining at the 1% level of significance the threshold discount rate over
which the CLT is invalidated when applied to the NPV model. Section 15.7
concludes.
15.2 SYSTEMATIC RISK AND THE PERFECT ECONOMY
When the CAPM was introduced in the mid-1960s, it was rapidly adopted by
the academic community because of its theoretical elegance, its conceptual
contribution, and also because of its mathematical and statistical simplic-
ity. However, many of the model’s assumptions did not hold in reality.
According to Milton Friedman (1953), this should not be considered as a
fundamental flaw for any theory has to be judged, not by the realism of its
assumptions, but by extent to which it provides meaningful explanations
and valid predictions. An examination of the CAPM’s logical consequences
against observed reality becomes unavoidable.
A plethoric number of empirical studies have therefore attempted to val-
idate the CAPM as an explanatory and predictive theory. “However, in
general, the results offer only limited support of the CAPM” (Levy and
Sarnat, 1994: 337). In complete contradiction with the CAPM’s most fun-
damental precept, studies by Miller and Scholes (1972) and Levy (1978)
showed that unsystematic risk (measured by the residual variance) turned
out to be statistically significant in the determination of securities’ required
rates of return. Such a result could be attributed to the violation of one of
the CAPM’s most basicsine qua nonassumption which states that investors
hold diversified portfolios. However, as was shown by Blume, Crocket and
Friend (1974), the typical investor holds but a very limited number of secu-
rities in his portfolio, less than four stocks on average. This might very well
explain the greatest challenge to the CAPM when Fama and French (1992)
found no systematic relation between return and risk as measured by beta.
Given that investors do not hold diversified market portfolios, it was no
surprise for Levy and Sarnat (1994: 339) also to conclude that systematic