Some Consequences of the Valuation Model When Expectations are Taken to be Optimum Forecasts

THE MAJORITY of theoretical work on the valuation of assets under
uncertainty begin with an equa-tion of the form
where, taking the assets to be shares, Vn(T) is the value of a share at time
n,D*,, is the expected dividend to be paid per share at time n + j, the
expectation being made at time n,P*,,,. is the expected price of the share
at time n + j, where again the expectation is formed at time n, r is a
discount rate, and T is the investor's horizon. The equation thus involves
both the expected flow of dividends and the price at which one expects to
sell the share at the end of the horizon period. If one further expects
future prices to be equal to the expected future value of the share, it is
sensible to put
by the same argument as before. Substituting, one has the indefinite
horizon valuation formula
which is the form that will be considered henceforth. A detailed account
of this model and some of its uses can be found in Van Horne (1971).
Some studies have considered a world with no uncertainty, in which
D*n+j may be replaced by D,+,, the actual dividend paid at time n + j.
However, as the world of the stock market is very clearly one of considerable
uncertainty, such models seem to be of extremely limited use.