84 Optimizing Optimization
equal to 1. However, when the Utility of tomorrow becomes of lesser concern
than that of today, delta will be less than 1 (and vice versa). For example, a
delta greater than 1 would imply that the trustees prefer to delay gratification.
Each trustee is described by his theta and delta. As expected Utility is criti-
cally dependent on both theta and delta, the different values represent a differ-
ent view of optimal Utility and optimal ECR. Thus, the appropriate values for
each individual endowment have to be carefully chosen to reflect the judgment
of the trustees and their wishes.
Finally , as we are interested in the optimal ECR that maximizes not just
today’s Utility, nor the Utility that we expect throughout the lifetime of the
endowment, but in fact the overall mix of them, we are naturally concerned
with the performance of our investments in the future. For example, if we hold
the view that the future will yield poor total returns, and hence sustain lower
potential consumption, then our expected Utility is designed to reflect this and
would adjust the optimal ECR.
Our discussion has not considered donations. However, we can extend it quite
naturally to include donations. Conceptually, one may think of this as an addi-
tional return to current wealth; this return could be either certain or uncertain.
3.7.7 Practical implications of risk aversion
Using the BITA Endowment model outlined above, we have computed the opti-
mal ECR for an infinitely lived endowment as a function of risk averseness for
three views of what future returns will be: pessimistic, neutral, and optimistic.
Figure 3.5 illustrates the results of our calculations.
There are two clear regimes present, dependent on whether theta is less
than one, or greater than one. These two cases are examined below. In both
instances, delta is assumed constant:
Theta less than 1 — less risk averse
The optimal ECR is less for an optimistic view of the future than for a pes-
simistic view, as greater future returns will yield greater potential consumption
in the future (when they are realized), and hence greater expected Utility. This
is referred to as the Substitution Effect. This is related to the Trustees having
relatively high risk tolerance. In this instance, the risk-tolerant investor lowers
the ECR when he makes an optimistic forecast, as he will be preserving wealth
to invest and consume in the future (the substitution effect).
Theta more than 1 — more risk averse
The optimal ECR is less for a pessimistic view of the future than for an opti-
mistic view, as the high risk aversion of the trustees (measured through the
magnitude of theta) leads to lower spending when poor returns are forecasted.
However, in this instance, the risk-averse investor, susceptible to the uncer-
tainty of future returns, does not wait and increases his or her ECR in the