Optimal solutions for optimization in practice 85
face of an optimistic forecast. It is the uncertainty of future consumption that
affects this soul, not any self-doubts about his or her future forecast.
When the view of future returns is neutral, then the optimal ECR decreases
as theta increases, analogous to the canonical relationship between risk and
return.
For the first example, the trustees are advised to consume more when a pes-
simistic view of future returns is held than when an optimistic view of future
returns is held. In the converse situation, this relationship is reversed. The rea-
sons for these choices can be understood in terms of what economists refer to
as Income and Substitution effects. We recognize that these ideas are difficult
and counterintuitive. Readers who might need further assurance should con-
sult Ingersoll (1987).
This section does not consider empirical analysis. This is partly because his-
torical data on charities and endowments is hard to come by. However, empiri-
cal work in financial economics has found values of theta close to 2. Whilst
this analysis has been for household investment, it is still probably relevant for
the charity and endowments sector. We may consider trustees to be less risk
averse than household investors, but it is probably the case that theta should
be greater than 1.
Intuition suggests that if we are optimistic about the future, we should
increase ECR. However, this is not necessarily true, and if it is, it may not be
for the reasons that motivate the intuition.
(^6) ECR
Optimistic
Pessimistic
Neutral
Increasing risk aversion
5
4
3
2
0.6 0.8 1.2 1.4
θα
Figure 3.5 The optimal rate of expendable endowment versus the risk-averseness of
the endowment’s trustees, under three separate future investment scenarios: pessimistic
(squares); neutral (stars); and optimistic (diamonds).