STOCHASTIC

SOME EFFECTS OF TAXES ON RISK-TAKING 299
V s^M, X;aO(i= 1 N).
i " l
Taking the deterministic equivalent of this programme yields
subject to
max
>•>*,+ E /^-f-'W/ X ,v, 2 0, then
expression (3.4) also holds as an equation. Then, substituting (3.4) in (3.5) and (3.6)
and dividing (3.5) and (3.6) gives, after some simplification,
" x-
"1+ E — cov 2;
^2~ f l _ 1 ° 3 x 2 (3 -j\
Of, — + E — cov i»;
x2 ; = 2ij
We get at most (N-2) equations of the form of (3.7) in the (N-2) ratios - J (j = 3,
x2
..., N). These ratios are, if they exist, determined by the means, variances and co-variances
but are independent of the investor's risk preference F~' and of his funds available for
investment M.
It follows from the separation theorem that we need only concern ourselves with
two assets, all risky assets treated as one and the riskless asset.
Assuming that the investor maximizes expected return while imposing a probabilistic
constraint, we can formulate the problem as follows.
maxEkrT
...(3.8)
i For a presentation of the Kuhn-Tucker conditions see e.g. Charnes, Cooper [1].
3. EFFECTS OF TAXES ON RISK TAKING 323