Optimal solutions for optimization in practice 83
endowment levels to fall; too little current spending benefits future students at
the expense of today’s scholars. Selecting a distribution rate appropriate to the
endowment portfolio increases the likelihood of achieving a successful balance
between demands of today and responsibilities of tomorrow. (pp. 33 and 34)It is our contention that for infinitely lived endowments, future returns
are more significant than volatility, yet this is often not the focus of invest-
ment professionals advising trustees on the strategy to pursue. In developing
our concept of theta as a measure of investor attitude to risk, we will seek to
encapsulate the unusual characteristics of infinitely lived endowments.
By contrast, investors with a finite investment horizon will be greatly con-
cerned with volatility, as the requirement to meet liabilities at an inopportune
time in market cycles can have devastating consequences.
3.7.6 Decision making under uncertainty
We proceed to quantify the above discussions and suggest a model for deter-
mining the optimal sustainable Endowment Consumption Rate (ECR) of
Foundations, subject to their needs and constraints (we defer discussion of
ECR optimality until later, but for clarity at this point, it is measured as a per-
centage of the real value of the endowment). In this context, the expendable
endowment is defined as the real value of the endowment multiplied by the
ECR; a monetary value that will vary with the real value of the endowment.
Central to our approach has been the idea of Utility, which may be thought
of as a formal way of representing the “ well-being ” of an endowment through
time, as a function of its expendable endowment. For example, if a charitable
organization is capable of donating £ 2 million to worthy causes this year, as
opposed to £ 1 million, its Utility will be greater. Within this context, the optimal
ECR maximizes the expected Utility throughout the entire lifetime of the endow-
ment. It should be noted that perpetual endowments gain no Utility from main-
taining capital per se, except in so much as it will support future expenditure.
To determine the optimal ECR requires the trustees to have a view on both
present and expected future Utility, taking account of the inflationary impact
on goods and services and the future investment returns.
We consider the nature of an endowment’s Utility to be dependent on the
risk averseness of the trustees, an attribute we label theta. We define a value of
theta that is equal to zero as representing risk neutrality, with risk averseness
increasing proportionally with larger values. We only allow positive values of
theta, as trustees are not expected to be indifferent to risk. Generally, the more
risk averse we are, the more we will prefer certain consumption now, to uncer-
tain consumption later.
In addition to theta, an endowment’s long-term expected Utility will also be
dependent on the subjective discount rate (referred to here as delta). When cir-
cumstances are such that there is no time preference (when today’s Utility is
as important to the trustees as tomorrow’s Utility), then we define delta to be