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Andrea Reed, Cristian Tiu and Uzi Yoeli

The process of risk management for institutional investors faces two challenges. First,
since most institutions are decentralized as opposed to being direct investors in assets, it is
diffcult to separate the risks of the assets in the portfolio from the risks generated by the
investment decisions by the fund management to construct the portfolio. To address this
issue, we propose a risk measurement methodology which calculates the risk contributions
of individual securities and investment decisions simultaneously. This decomposition is ap-
plicable to any decentralized investor as long as its relevant risk measurement statistic can
be additively decomposed. Second, statistics used to measure risk may not coincide with
institution-specific investment risks, in the sense that the utility employed in asset allocation
may be unrelated to the risk measure utilized. For example, an institution may do mean-
variance asset allocation, but inconsistently measure the risk of the portfolio using Value at
Risk. We apply this methodology to a particular type of decentralized investor, specifically,
endowment funds where the relevant risk statistic is the downside risk of returns relative
to actual payout levels, plus inflation. We show how downside risk can be decomposed and
apply our simultaneous downside risk decomposition empirically on a sample of U.S. endow-
ment funds. We find that an endowment's asset allocation to U.S. Equity, consistent with
having the largest weight in the average endowment portfolio, generates about 50% of total
endowment returns but almost 100% of total portfolio downside risk. We further find that
tactical allocations (or timing) have economically small contributions to both returns and
risk. Finally, we find that the allocations to U.S. Fixed Income and to Hedge Funds as well
as active investment decisions (except for tactical) contribute positively to returns, while
reducing portfolio downside risk. The risk contributions are sensitive to changes in payout
levels and an increase in the latter may offset the risk reducing power of active investing.

Keywords: Risk Management, Asset Allocation, Downside Risk, Endowment Funds