JEAN-PAUL PAQUIN, ANNICK LAMBERT AND ALAIN CHARBONNEAU 279probabilistic approaches to risky investment decisions were swept away
by the Sharpe–Lintner–Mossin CAPM revolution as it became the creed of
modern financial theory. Such a result was unavoidable given that, under the
capital asset pricing theory, the dispersion (as well as the higher moments)
in the probability distribution of future cash flows became an irrelevant
statistic. Systematic risk, as calculated by the beta, became the only relevant
measure of risk.
However, probabilistic information has crept back into the process of
risky investment evaluation when various authors have drawn a close par-
allelbetweenriskycapitalinvestmentsandfinancialoptions, thusgivingrise
to real option theory (Brennan and Schwartz, 1985; Copeland andAntikarov,
2001; Cox, Ross and Rubinstein, 1979; Dixit and Pindyck, 1994; Ingersoll, Jr.
and Ross, 1992; Trigeorgis, 1993). However, notwithstanding the CAPM
orthodoxy, how can one justify the reintroduction of total risk considera-
tions in the investment decision when systematic risk should be the only
relevant datum?
In pursuance of the Hillier probabilistic approach, this chapter deals with
capital investment decisions for which total risk is relevant to the firm. In the
first part we revisit and summarize some of the main research results that
have lead some authors to come to the conclusion that under financial dis-
tress total risk matters to the firm. Such a conclusion is reached after drawing
a clear distinction between the concept of systematic risk as proposed by aca-
demics under the Modigliani–Miller capital budgeting normative paradigm
and the concept of total effective risk as implicitly used by managers under a
positive probabilistic paradigm. Such a distinction will entail the use of two
totally different measures of risk: (a) risk measured by the mean volatility
of rates of return around a market index of central tendency, and (b) risk
measured by the lower-tail of a NPV probability distribution. Section 15.2
discusses the systematic risk and the perfect economy, while section 15.3
deals with the total risk and the real economy.
Section 15.4 will address the question of the project NPV probability
distribution; for one cannot estimate the lower-tail of a NPV probability dis-
tribution without specific knowledge as to its total probability distribution.
In the second part, we derive important results concerning the investment
project NPV distribution when the operating cash flows probability distribu-
tions are unknown and not independent in probability (for example, are not
independent identically distributed (independent identically distributed)
random variables, or are not normal independently distributed random
variables). Specifically, we will deal with serially correlated discounted net
cash flows. We will also demonstrate that, although first-order autocorre-
lated cash flows do not invalidate the Central Limit Theorem’s asymptotic
convergence properties to a Normal distribution, the introduction of any
discount rate in the NPV equation does so, except for the very special case
where net cash flows are normally distributed. Does this result imply that