## University Endowment Return Inequality Revisited

**Do The Rich Know Better? – University Endowment Return Inequality Revisited**

__Tuo Chen __

Columbia University, Graduate School of Arts and Sciences, Department of Economics, Students

March 1, 2016

*American Economic Journal: Economic Policy, March 2016*

**Abstract: **

This paper revisits capital return inequality across university endowments. It combines university-level data on endowment size, investment returns, and portfolio allocations into a unified dataset. Using panel data regression, we replicate Piketty (2014)â€™s finding of a strong impact of size on investment return. Everything else the same, the biggest endowment has a capital return 8% higher than the smallest endowment. How- ever, after adjusting for risk using Sharpe Ratios, the strong positive correlation turns negligible or even negative. This result suggests that the higher return of bigger endowments can be attributed to risk compensation rather than to an informational premium.

### Do The Rich Know Better? – University Endowment Return Inequality Revisited – Introduction

Inequality problems are being heatedly discussed since the publication of Thomas Piketty's Capital in the Twenty-First Century (2014). This book employed long-term historical data from multiple countries to argue that inequality is severe and can be explained by the divergence force summarized in one single equation: r > g, where r stands for the rate of capital return, and g for the growth rate of GDP. He argues that the rate of capital accumulation is bigger than the growth rate of the economy throughout the history of more than 100 years. Therefore, according to this argument, inherited wealth will become more and more concentrated and thus the inequality problem is inevitable without government intervention.

One source of progressive inequality highlighted by Piketty (2014) is capital return heterogeneity, which I refer to in this paper as capital return inequality. To illustrate this phenomenon, consider this simple example: a rich person has wealth of $10000, and a poor person $1000. If both individuals have the same capital return rate equal to 5%, the former earns $450 more than the latter. The capital income inequality will be exacerbated if there is a positive correlation between the size of wealth and the capital return rate. If instead of having the same 5%, the rich person now enjoys a higher rate of return { 10%, then the capital income difference is now amplified to $950.

Piketty documents this type of inequality dynamics by examining the return to university endowments. Specifically, he compares the return to 3 large university endowments (Harvard, Yale, and Princeton) to those of the average university endowment in North America. Based on this information, he argues that capital return inequality is severe. Moreover, he hypothesizes that the endowments of those elite universities have a higher capital return rate just because they have money to hire the best management teams and thus know better about the market. In other words, he argues that large-endowment universities possess an informational advantage relative to small-endowment universities, which allows them to consistently achieve higher rates of return, thereby exacerbating endowment inequalities.

The goal of this paper is to scrutinize Piketty's hypothesis. Toward this objective, we first construct a unique dataset to quantify the magnitude of university-endowment return inequality. The dataset contains between 500 to 1000 universities depending on the year. Second, we identify and quantify the channels through which university-endowment return inequality arises.

The primary source of the data is NACUBO. This is a panel dataset of university-level endowments. It consists of three pieces of information from 2000 to 2013: the size1, the capital returns2, and the portfolio allocations. By combining the size information and the capital return information, I quantify the capital return inequality by panel regression. The panel data structure helps to introduce the university fixed effect, which can be considered as a control for unobserved parameters, such as reputation effect or network effect of universities. The panel regression result shows that if we keep the same fixed effect and only vary the size, then the biggest endowment is predicted to have a capital return rate 8% higher than the smallest endowment. This result is consistent with Piketty's observation. Saez and Zucman (2014) claims that the realized return within an asset class is similar across groups of different sizes, which seems contradictory to my result at first glance. However, there are two important differences: 1. The return rate in this paper is a weighted return of different asset classes; 2. It is the total return including realized and unrealized returns.

In the literature, there exist mainly two explanations of the capital return inequality. One is that larger investors tend to invest bigger portions of their wealth in riskier assets. Since riskier assets have higher expected returns, on average the larger investors outperform the smaller ones. The different asset allocation strategies may stem from several sources. One possible source is that the investment in risky assets requires a fixed cost(Gomes and Michaelides (2005)). This cost seems small for large capital but large for a small one. Thus larger investors are more willing to invest in riskier assets. Another source may be that larger investors have a lower relative risk aversion, thus they are willing to invest proportionately more wealth in riskier assets(Yitzhaki (1987)).

The second explanation focuses on the informational advantage of larger investors(Arrow (1987), Piketty (2014), Kacperczyk, Nosal and Stevens (2014)). Every investor faces the tradeoff: the information is costly but it increases the knowledge of the asset thus reducing the risk, which gives rise to the optimal level of information acquisition. In the equilibrium, the bigger investors choose to invest more in information and thus form a better understanding of the market. Therefore, the bigger investors have a higher return which is not necessarily associated with higher risk.

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