<h2>CHAPTER 1</h2><p><b>Asset Allocation for Hedge Fund Strategies: How to Better Manage Tail Risk</p><p>Arjan Berkelaar, Adam Kobor, and Roy Kouwenberg</p><br><p>ABSTRACT</b></p><p>Most approaches to risk budgeting are based on tracking error and value at risk(VaR). In addition, the return streams from any investment process are usuallyassumed to be serially uncorrelated and normally distributed. This assumption,however, does not necessarily hold in reality. In this chapter, we consider tworelatively new risk measures that are better suited to deal with nonnormal andserially correlated return streams and that are superior to tracking error (orvolatility) and value at risk. We show how these measures can be used indetermining an optimal risk allocation, allowing investors to better manage thetail and drawdown risks in their portfolios. By better managing these risks,investors can achieve superior risk-adjusted returns.</p><br><p><b>INTRODUCTION</b></p><p>Many institutional investors are searching for sources of diversification andreturn-enhancing strategies in order to improve the performance of theirportfolios. An area where many of them hope to achieve superior risk-adjustedreturns is hedge funds. Shifting asset allocations toward hedge funds is not aguarantee of success, however. Unlike equity and bond markets that compensateinvestors with a positive risk premium over the long term, returns fromselecting hedge fund managers are conditional on skill. To be successful inpicking hedge funds, a strong risk management process and a disciplinedinvestment approach are required.</p><p>Most approaches to risk and asset allocation, both in practice and in theacademic literature, are based on standard deviation and value at risk. Inaddition, the return streams are usually assumed to be normally distributed.This assumption is quite convenient, allowing investors to use the well-knownmean-variance workhorse to derive optimal allocations. We refer interestedreaders to Berkelaar et al. (2006) for a risk budgeting framework wheninvestment returns are normally distributed. In the case of hedge funds,however, the normal distribution fails to adequately describe the returndistribution. Basing risk allocations on mean-variance optimization may resultin a considerable misallocation of risk that could result in suboptimalportfolios and lower investment returns.</p><p>In this chapter, we consider conditional value at risk (CVaR)—a relativelynew risk measure that is better suited to deal with nonnormal return streams.The advantage of this risk measure is that it is easy to use and allows fornumerical tractability. In this chapter, we derive optimal portfolios for mean-CVaRinvestors and compare results with those of a mean-variance investor.Others have also studied the impact of skewness and fat tails on optimalportfolios. Krokhmal et al. (2003) consider a portfolio of individual hedgefunds and study the performance of various risk constraints, including CVaR andconditional drawdown at risk (CDaR), with in-sample and out-of-sample tests.Amin and Kat (2003) study the optimal allocation among stocks, bonds, and hedgefunds in a mean-variance-skewness optimization framework. Kouwenberg (2003)studies the added value of investment in individual hedge funds for investorswith passive stock and bond portfolios, taking into account the nonnormality ofthe return distribution.</p><p>We use the Hedge Fund Research, Inc. (HFRI) indexes for several hedge fundstrategies to determine optimal allocations. The period for the historical timeseries is January 1990 to December 2007. We show that investors who manage tailrisk by basing their portfolios on mean-CVaR optimization should be able toproduce superior returns on their hedge fund portfolio. Using historical returnsfor several hedge fund strategies, the incremental return could be as much as100 to 200 basis points (bps). We also present results based on a forward-lookingsimulation model for hedge fund returns with more modest assumptionsabout expected returns. In this case, the incremental return is about 40 to 60bps.</p><p>This chapter is organized as follows. The second section of this chapterdiscusses the CVaR measure. We also show to what extent risk could beunderestimated by assuming that returns are serially uncorrelated and normallydistributed. This chapter's third section discusses a framework that can beapplied to develop forward-looking return scenarios for a wide range of...