Why 5 percent? An analysis of optimal endowment spending rates

Steven L. Green (Department of Economics, Baylor University, Waco, Texas, USA)

Studies in Economics and Finance

ISSN: 1086-7376

Publication date: 2 October 2009



Some members of Congress in the USA have expressed serious concern that endowment spending rates of major American universities are too low. The purpose of this paper is to derive optimal spending rates and compare them with actual rates to determine if this concern is warranted.


A Cobb‐Douglas utility function is used to represent the trade‐off between current spending and endowment (which allows more future spending). Maximization of this function subject to relevant constraints yields a formula for the optimal endowment spending rate, which takes the form of a difference equation. The steady‐state solution to this difference equation is explored, along with the nature of convergence to the steady‐state. Relevant data are obtained from American universities with endowments over $500 million in 2007 to determine the optimal spending rates implied by the theory. These optimal rates are then compared with actual average spending rates.


Actual average spending rates are just below 5 per cent, which is well below the optimal rates of 7‐8 per cent implied by the theory.

Practical implications

The results provide some support for regulations mandating minimum average spending rates from university endowments over time.


This paper is the first to model this problem using a theoretical framework that closely parallels the actual trade‐off considered by university investment managers, and it is the first to compare actual and theoretically optimal rates of endowment spending.



Green, S. (2009), "Why 5 percent? An analysis of optimal endowment spending rates", Studies in Economics and Finance, Vol. 26 No. 4, pp. 216-231. https://doi.org/10.1108/10867370910995681

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