Investors in alternative asset classes such

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1 ADREW COER i an analyt in the Alternative Invetment Group at SEI Invetment, Oak, PA. aconner@eic.com Aet Allocation Effect of Adjuting Alternative Aet for Stale Pricing ADREW COER Invetor in alternative aet clae uch a private equity and hedge fund have long had difficulty applying traditional model for making aet allocation deciion. The optimization technique of modern portfolio theory rely heavily on a trio of decriptive tatitic: mean, variance, and covariance. For mot traditional aet clae, the abundance of hitorical data provide a guide for etimating thee parameter. Hoever, for ome alternative aet clae etimating thee characteritic i not alay traightforard. Although time erie of return for both private equity and hedge fund are available from reputable ource, reported return can be mileading. Alternative aet return can exhibit lo volatility and lo correlation ith publicly traded aet clae. Thi ugget that they are potentially diverifying aet and incremental allocation to alternative invetment may decreae overall portfolio rik. The tandard deviation and correlation of reported alternative aet indice, hoever, cannot be taken at face value. Partnerhip holding illiquid ecuritie are valued infrequently and are baed on appraied value, o poition are not marked-to-market. Thi tale pricing dampen actual volatility. The recent literature ha confirmed that tale pricing exit in both hedge fund and private equity. Ane, Krail, and Lie [001] explore the ability of hedge fund manager to mooth return tream, concluding that hedge fund appear to price their ecuritie ith a lag. Anon [00] tudie the ame topic in private equity, and conclude that there i empirical evidence uggeting managed pricing doe occur. He find that general partner implement the rule of conervatim, and mark don valuation more aggreively than they mark them up. It i poible to empirically etimate the true volatility of alternative aet. We hypotheize that there exit an underlying proce of return that could be meaured if poition ere continually marked-to-market a in the public market. We call thi the economic proce of return. The reported index return, baed on tale price, repreent a moothed proce of return. The volatility and correlation of the economic proce repreent actual economic event and are relevant to invetor. Other have ued a imilar theoretical underpinning to adjut alternative aet return for the effect of tale pricing. Ane, Krail, and Lie [001] etimate the true correlation beteen hedge fund tyle and the public market in the preence of tale price due to illiquidity or managed pricing uing a multi-period regreion approach. Gomper and Lerner [1997] employ an interperiod valuation approach to etimate the pricing activity of tale private equity poition, uing public market activity a a proxy for unobervable private market pricing. To circumvent the iue of tale pricing, Long [1999] etimate the volatility of private equity portfolio uing outcome rather than time erie. IT IS ILLEGAL TO REPRODUCE THIS ARTICLE I AY FORMAT 4 ASSET ALLOCATIO EFFECTS OF ADJUSTIG ALTERATIVE ASSETS FOR STALE PRICIG WITER 003 Copyright 003 Intitutional Invetor, Inc. All Right Reerved

2 In thi tudy e apply a method from the real etate finance literature to etimate the characteritic of the economic proce from the moothed proce for everal alternative aet clae. Wherea in traditional market the economic proce i obervable (and reported), in alternative market tale pricing can prevent obervation of the economic proce and the moothed proce i reported. Conequently, e ue the tandard deviation and correlation of the reported moothed proce data to etimate the tandard deviation and correlation of the unobervable economic proce of return. The reult i a et of rik and correlation that have been adjuted for the effect of tale pricing. For alternative aet clae, e refer to the rik and correlation of the reported moothed proce a the reported rik and correlation. We refer to the etimated rik and correlation of the unobervable economic proce a the adjuted rik and correlation. Thi methodology ha to ditinct advantage over exiting method for etimating rik and correlation in the preence of tale pricing. Firt, it i computationally imple. Adjuted parameter are calculated directly from hitorical time erie of index return. Thi technique i appropriate for individual invetment and compoite alike, and for liquidated or ongoing poition. Second, thi methodology provide a conitent frameork for etimating both rik and correlation. Thi include correlation beteen traditional and alternative aet clae, a ell a correlation beteen multiple alternative aet clae. Thi article i divided into four ection. In the firt ection, e dicu the methodology for adjuting rik and correlation for tale pricing. We apply the method to hitorical private equity and hedge fund return in the econd ection. In ection three, e dicu the implication of uing adjuted parameter for optimal portfolio contruction and aet cla diverification along the efficient frontier. Finally, e revie our concluion. METHODOLOGY FOR DE-LAGGIG RETURS Academic and practitioner have developed technique to deal ith tale and appraial-baed pricing in real etate index data. In particular, Geltner [1991] ha developed a method for etimating actual volatility by de-lagging appraial-baed time erie of return. 1 Like real etate, other alternative aet clae are ell uited for thi de-lagging proce. One characteritic of private equity and hedge fund index return that indicate the preence of tale pricing i poitive autocorrelation. Autocorrelation can imply that economic valuation event that occur in one time period are priced-in over ubequent period. Certainly thi i true of private equity portfolio companie, hich mot general partner ill revalue only after a ignificant financing event. It i alo true of hedge fund that invet in illiquid or non-exchange-traded ecuritie. For aet clae ubject to tale pricing, ome proportion of the current period actual economic return i realized, ome proportion of lat period actual economic return i realized, and ome proportion of all previou relevant period actual economic return i realized in the current period. Conequently, uing Geltner model, e define the moothed return proce of aet cla hich e denote SR i, a a eighted average of the economic return proce, denoted ER i. The economic proce i continually priced and i independent and identically ditributed. The eight in the eighted average that contitute the moothed proce decribe the proportion of each previou period economic return that i realized in the current period. A an example, conider ecurity i ith a continually priced economic return tream (ER i ) ith a mean, µ ERi, of 10% and a tandard deviation, ERi, of 0%. If the ecurity in quetion ere ubject to tale pricing uch that only half of thi period economic price change ere realized thi period and the other half ere realized in the next period, there ould exit a correponding moothed return proce (SR i ), uch that: SRit, =. 50 ERit, ERit, -1 Over a full invetment cycle, the mean of the moothed return tream, µ SRi, ould till equal 10%, but the tandard deviation, SRi, ould be muted to 14.1%. Exhibit 1 i a graphical repreentation of thi example. For alternative aet, e oberve the moothed return proce in reported hitorical return tream. Our goal i to etimate the characteritic of the underlying economic proce, pecifically tandard deviation and correlation, by adjuting thoe of the moothed proce. The general form of the moothed proce example decribed above i expreed for aet cla ith relevant lag, here t-n refer to eight applied to the nth order lag of the economic proce, a follo: SR = ER it, (1) WITER 003 THE JOURAL OF ALTERATIVE IVESTMETS 43 It i illegal to reproduce thi article in any format. Reprint@iijournal.com for Reprint or Permiion.

3 E XHIBIT 1 Comparion of Economic Proce and Smoothed Proce ith To Period Lag 50% 40% 30% Smoothed Mean = 10% Standard Deviation = 14.1% 0% Annual Return 10% 0% -10% -0% -30% -40% Economic Mean = 10% Standard Deviatio% Year Economic Proce Smoothed Proce Within thi frameork, Equation ho that the adjutment to the tandard deviation of alternative aet cla denoted by ERi, can be implified to multiplication by a calar. The adjutment factor i a function of the eight in the eighted average moothed proce of aet cla i. ERi = SRi We can ue thi model to etimate the true economic correlation ith other aet clae, hich i alo dampened by tale pricing. A hon in Equation 3, the correlation beteen the economic proce of alternative aet cla i and the traditional aet cla j, denoted r ERERj, can be expreed a the correlation beteen the moothed proce of aet cla i and aet cla j, denoted r SRERj, multiplied by a calar. The adjutment factor for correlation i alo a function of the eight in the eighted average of the moothed proce of aet cla i. 3 1 () Equation 4 provide a formula for the correlation beteen to economic procee of alternative aet clae i and j, r ER. Similar to Equation and 3, the adjutment factor for the correlation beteen alternative aet ERj clae i expreed a the product of the correlation beteen the moothed procee of aet clae i and j, r ERERj and a calar. 4 Equation, 3, and 4 contitute a computationally imple method for etimating true underlying rik and correlation of aet clae in the preence of tale pricing from the rik and correlation of the reported moothed proce of return. Full derivation of the adjutment facr r = r ER ER j SR ER j = r ER ER j SR SR j it, -n jt, -n jt, -n 0 (3) (4) 44 ASSET ALLOCATIO EFFECTS OF ADJUSTIG ALTERATIVE ASSETS FOR STALE PRICIG WITER 003 Copyright 003 Intitutional Invetor, Inc. All Right Reerved

4 E XHIBIT Source for Hitorical Aet Cla Index Data umber of Aet Cla Data Source Data Frequency Obervation (n) Obervation Period Cah T-Bill Monthly 11 January 1985 to Augut 00 U.S. Equity Wilhire 5000 Monthly 11 January 1985 to Augut 00 U.S. Bond Lehman Aggregate Monthly 11 January 1985 to Augut 00 International Equity MSCI EAFE Monthly 11 January 1985 to Augut 00 International Bond SB WGBI Monthly 11 January 1985 to Augut 00 High Yield Bond Lehman CCC Monthly 11 January 1985 to Augut 00 Convertible Arbitrage CSFB Tremont Index Monthly 104 January 1994 to Augut 00 Dedicated Short Bia CSFB Tremont Index Monthly 104 January 1994 to Augut 00 Emerging Market CSFB Tremont Index Monthly 104 January 1994 to Augut 00 Equity Market eutral CSFB Tremont Index Monthly 104 January 1994 to Augut 00 Event Driven CSFB Tremont Index Monthly 104 January 1994 to Augut 00 Fixed Income Arbitrage CSFB Tremont Index Monthly 104 January 1994 to Augut 00 Global Macro CSFB Tremont Index Monthly 104 January 1994 to Augut 00 Equity Long/Short CSFB Tremont Index Monthly 104 January 1994 to Augut 00 Managed Future CSFB Tremont Index Monthly 104 January 1994 to Augut 00 Venture Capital Cambridge Venture Capital Index Quarterly 70 January 1985 to June 00 Buyout & Other Cambridge Private Equity Index Quarterly 65 April 1986 to June 00 tor are found in Geltner, or may be calculated directly by olving for the variance and covariance of Equation 1. USMOOTHIG RISK AD CORRELATIO I PRIVATE EQUITY AD HEDGE FUD RETURS We applied the de-lagging method decribed above to hitorical private equity and hedge fund return. Firt e determined the number of relevant period acro hich de-lagging i neceary. ext e calculated the eight in the eighted average that make up the moothed proce. From the eight e then computed the adjutment factor uing Equation, 3, and 4 and applied them to the moothed proce moment to etimate the moment of the economic proce. The Cambridge Aociate LLC U.S. Venture Capital Index track quarterly time eighted venture capital return back to the firt quarter of The Cambridge Aociate LLC U.S. Private Equity Index track quarterly time eighted buyout, ubordinated debt, and pecial ituation return from the firt quarter of The CSFB/Tremont Hedge Fund Index ha monthly hitorical return for everal hedge fund tyle beginning in January of Some of thee indice exhibit the characteritic of tale-pricing induced moothing: loer than expected abolute rik and correlation ith other aet clae, and ignificant poitive autocorrelation. Our ource for hitorical index data, including traditional aet clae (hich are ued in the optimization in ection three of thi article), are lited in Exhibit. To determine the number of previou period relevant to the current period return, e teted each index for autocorrelation by looking at ucceive lag. We continued to accept the nth lagged period a relevant a long a the nth order autocorrelation a tatitically ignificant ith 90% confidence. Statitical ignificance of the autocorrelation a determined uing a imple t-tet. 5 For hedge fund, hich hold motly public ecuritie, price and return are reported monthly and e therefore ued monthly return. For private equity, reporting i done quarterly, o e ued quarterly return. For venture capital fund, autocorrelation up to the third order ere ignificant, indicating that it take up to three quarter to pa valuation activity through into price. Buyout and other private equity had tatitically ignificant autocorrelation of the firt and econd order. Thi difference ugget that, on average, venture capital portfolio are marked-to-market le frequently than buyout portfolio. Thi reult reflect the fact that buyout portfolio companie tend to be more etablihed and priceable than venture capital portfolio companie. WITER 003 THE JOURAL OF ALTERATIVE IVESTMETS 45 It i illegal to reproduce thi article in any format. Reprint@iijournal.com for Reprint or Permiion.

5 E XHIBIT 3 Reult of Autocorrelation Significance Tet n t, t-0 Hitorical Autocorrelation t, t-1 t, t- t, t-3 t, t-4 t, t-1 t Statitic t, t- t, t-3 t, t-4 Convertible Arbitrage *** 4.94*** 1.69** 1.5* Dedicated Short Bia Emerging Market *** Equity Market eutral ***.01** Event Driven *** 1.4* Fixed Income Arbitrage *** 1.4* Global Macro Equity Long/Short * Managed Future Venture Capital *** 3.98***.56*** Buyout & Other *** 1.34* * Denote tatitical ignificance at a 90% confidence level. ** Denote tatitical ignificance at a 95% confidence level. *** Denote tatitical ignificance at a 99% confidence level. Convertible arbitrage hedge fund had ignificant autocorrelation up to the fourth lag, uggeting that price are lagged up to four month. Equity market neutral, event-driven, and fixed income arbitrage all had tatitically ignificant autocorrelation of the firt and econd order. Emerging market and equity long/hort hedge fund tyle had ignificant firt order autocorrelation only. Dedicated hort bia, global macro, and managed future did not have tatitically ignificant firt order autocorrelation, uggeting that thee three hedge fund tyle do not have a moothed proce aociated ith them. In general, thoe hedge fund tyle that are ubject to tale pricing becaue of illiquidity in the underlying ecuritie (convertible arbitrage and fixed income arbitrage) had a greater number of ignificant lag. Thoe that invet primarily in liquid or public market ecuritie (equity long/hort, dedicated hort bia, global macro, and managed future) had feer relevant lag. While the ignificant autocorrelation cannot necearily be explained entirely by tale pricing, the de-lagging methodology provide a better etimate of rik than uing annualized reported tandard deviation in the preence of autocorrelation, regardle of it ource. Alo, it a the hedge fund tyle ith loer oberved volatility that have the mot ignificant lag and, therefore, had the larget adjutment factor. The three hedge fund tyle ith the loet reported hitorical volatilitie (convertible arbitrage, tandard deviation of 5.4%; fixed income arbitrage, tandard deviation of 4.3%; and equity market neutral, tandard deviation of 3.6%) alo had the three highet adjutment factor. Exhibit 3 contain the reult of the autocorrelation ignificance tet. After finding the appropriate autocorrelation for each alternative aet cla, the next tep i to olve for the eight in the eighted average that i the moothed proce. The eight in the eighted average are ued to adjut the tandard deviation and correlation. The eight themelve are found from the olution to a ytem of equation for the autocorrelation. Appendix A detail the proce for olving for the eight. Once the eight are etimated, Equation, 3, and 4 are then ued to calculate the unmoothing adjutment factor for tandard deviation and correlation. Exhibit 4 ho the eight and the adjutment factor for each of the alternative aet clae. The adjutment factor are applied to the reported hitorical tandard deviation and correlation to compute the adjuted rik and correlation for the alternative aet clae. Exhibit 5 ho the hitorical reported and adjuted rik and correlation for each alternative aet cla. The venture capital tandard deviation increaed the mot dramatically, from 31% to 59%. The convertible arbitrage and emerging market tandard deviation each increaed 5%. ote that the adjutment factor for dedicated hort bia, global macro, and managed future are 1.0, confirming that there i no adjutment for thee three. Meaningful change to correlation included a 0.15 increae to the correlation beteen venture capital and U.S. public equity, implying that private and public equitie are ultimately more imilar invetment than a curory examination of the data ould ugget. Alo, the 0.13 increae to the correlation beteen convertible arbitrage hedge fund and high yield bond upport the intuition that convertible arbitrage trategie hould exhibit expoure to credit pread. 46 ASSET ALLOCATIO EFFECTS OF ADJUSTIG ALTERATIVE ASSETS FOR STALE PRICIG WITER 003 Copyright 003 Intitutional Invetor, Inc. All Right Reerved

6 E XHIBIT 4 Weight and Adjutment Factor for Alternative Aet Clae Etimated Weight For Standard Deviation Adjutment Factor For Correlation ith Traditional Aet Convertible Arbitrage % 18% Dedicated Short Bia % 100% Emerging Market % 105% Equity Market eutral % 106% Event Driven % 107% Fixed Income Arbitrage % 109% Global Macro % 100% Equity Long/Short % 101% Managed Future % 100% Venture Capital % 134% Buyout & Other % 106% E XHIBIT 5 Ra and Adjuted Rik and Correlation for Alternative Aet Clae Equity Market eutral Fixed Income Arbitrage Convertible Arbitrage Dedicated Short Bia Emerging Market Event Driven Global Macro Equity Long/Short Managed Future Venture Capital Buyout & Other Reported Hitorical Rik (Standard Deviation) 5% 19% 0% 4% 7% 4% 15% 13% 13% 31% 9% Adjuted Rik (Standard Deviation) 10% 19% 6% 5% 10% 6% 15% 15% 13% 59% 13% Reported Hitorical Correlation ith Cah ith U.S. Equity ith U.S. Bond ith International Equity ith International Bond ith High Yield Bond ith Convertible Arbitrage 1.00 ith Dedicated Short Bia ith Emerging Market ith Equity Market eutral ith Event Driven ith Fixed Income Arbitrage ith Global Macro ith Equity Long/Short ith Managed Future ith Venture Capital ith Buyout & Other Adjuted Correlation ith Cah ith U.S. Equity ith U.S. Bond ith International Equity ith International Bond ith High Yield Bond ith Convertible Arbitrage 1.00 ith Dedicated Short Bia ith Emerging Market ith Equity Market eutral ith Event Driven ith Fixed Income Arbitrage ith Global Macro ith Equity Long/Short ith Managed Future ith Venture Capital ith Buyout & Other WITER 003 THE JOURAL OF ALTERATIVE IVESTMETS 47 It i illegal to reproduce thi article in any format. Reprint@iijournal.com for Reprint or Permiion.

7 E XHIBIT 6 Efficient Baed on Reported Rik and Correlation 0.0% 18.0% 16.0% 14.0% Expected Return 1.0% 10.0% 8.0% 6.0% 4.0%.0% 0.0% 0.0% 5.0% 10.0% 15.0% 0.0% 5.0% 30.0% 35.0% 40.0% Rik (Standard Deviation) Efficient --Traditional Invetment Efficient --Including Alternative Invetment IMPLICATIOS FOR EFFICIET PORTFOLIOS A hon above, for alternative aet clae ubject to tale pricing, reported hitorical data ill undertate volatility and the abolute value of correlation ith other aet clae. Intuitively one ould expect moothed return to reflect dampened volatility. Appendix B ho mathematically that, given poitive autocorrelation, both the adjuted tandard deviation and correlation ill be greater in abolute value than or equal to the reported verion. Thi ho that reported rik and correlation might overtate the diverification benefit of alternative aet. To tet the aet allocation impact of adjuting the moment of alternative aet return for the effect of tale pricing, e compared to efficient frontier. The firt a optimized baed on reported hitorical rik and correlation and the econd a optimized baed on adjuted hitorical rik and correlation. In both cae e conidered a hypothetical invetor ho ha a budget for alternative aet of no more than 50% of total aet. We applied contraint to reflect the alternative aet budget a ell a to prevent leverage and hort elling at the aetcla level (no allocation to cah and allocation limited to no le than 0% and no greater than 100% for each aet cla). Portfolio on the efficient frontier ere derived uing a mean/variance optimization algorithm. Our goal i to compare the ex-pot efficient portfolio over the hitorical period, o the mean, variance, and correlation input to all optimization ere computed directly from the hitorical return of the indice ummarized in Exhibit. We decribe the efficient frontier optimized uing reported hitorical rik and correlation a the reported-rik frontier and the efficient frontier optimized baed on hitorical rik and correlation adjuted for tale pricing a the adjuted-rik frontier. Exhibit 6 i a graph of the reported-rik frontier and Exhibit 7 i a graph of the adjuted-rik frontier. For reference, each exhibit alo ho an efficient frontier optimized for traditional aet clae only. The relative poition of the to frontier confirm that uing reported hitorical moment undertate portfolio rik. Compared to the reported frontier, each point along the adjuted frontier ha higher rik for each given level of return. That the adjuted frontier appear hifted to the right of the reported frontier. On both frontier the hypothetical invetor conume the entire budget (50% total allocation) for alternative aet at all level of rik. Although the higher adjuted rik of alternative aet clae i built into the adjuted frontier, the overall appetite for alternative aet clae i not reduced relative to traditional aet clae. Rather, the compoition of the traditional portfolio change to compenate for the higher adjuted rik in alternative invetment. To ee ho the compoition of portfolio change 48 ASSET ALLOCATIO EFFECTS OF ADJUSTIG ALTERATIVE ASSETS FOR STALE PRICIG WITER 003 Copyright 003 Intitutional Invetor, Inc. All Right Reerved

8 E XHIBIT 7 Efficient Baed on Rik and Correlation Adjuted for Stale Pricing 0.0% 18.0% 16.0% 14.0% Expected Return 1.0% 10.0% 8.0% 6.0% 4.0%.0% 0.0% 0.0% 5.0% 10.0% 15.0% 0.0% 5.0% 30.0% 35.0% 40.0% Rik (Standard Deviation) Efficient --Traditional Invetment Efficient --Including Alternative Invetment hen the effect of tale pricing are removed, e compared three portfolio from each frontier. The three portfolio are: the minimum variance portfolio, the highet return portfolio, and the maximum Sharpe ratio portfolio. 6 Exhibit 8 ummarize the aet allocation of the three portfolio from each frontier. The lo-rik portfolio from the reported-rik frontier ha a higher return than the lo-rik portfolio from the adjuted-rik frontier by 30 bai point, ith 10 bai point le rik. The optimizer i fooled by tale pricing into allocating to more aggreive aet clae that appear le riky than they actually are. The high-return portfolio from each frontier are identically allocated and have the ame return, 17.5%. Hoever, the volatility of thi allocation i revealed to be much higher than reported hen corrected for the dampening effect of tale pricing. The maximum Sharperatio portfolio are both allocated entirely to bond in the traditional portfolio. Hoever, the adjuted-rik portfolio i allocated more heavily to hedge fund in the alternative portfolio (80% veru 71.5% on the reported-rik frontier) in order to mitigate rik. The adjuted-rik portfolio ha a loer return ith lightly more rik. Incremental allocation to alternative aet are often made ith to goal in mind: potential return enhancement and diverification ith traditional aet clae. Hitorically alternative have certainly provided the former; venture capital, global macro, buyout and other private equity, and equity long/hort ere the top four performing aet clae in our data et. The latter i le traightforard to ae. One method to meaure ho ell diverified a portfolio i relative to other portfolio i uing a tatitic called Diverification Benefit (DB). The DB tatitic meaure the amount that aet clae in a portfolio have reduced each other rik. We define DB a the difference beteen the eighted um of aet cla tandard deviation and the actual portfolio tandard deviation. For a portfolio containing I aet clae ith i of the portfolio allocated to aet cla i and the covariance beteen aet cla i and aet cla j equal to j : I DB = - I i i i i j i = 1 i = 1 j = 1 Intuitively, DB i the difference beteen hat portfolio rik ould be if all aet clae ere perfectly correlated and hat portfolio rik given actual correlation. For the 50 portfolio on the traditional-only efficient frontier, the average DB i.0%, indicating that intra-aet correlation ha reduced portfolio volatility by that amount each year. If indeed alternative aet are uperior diverifier, e expect a higher average DB on the I WITER 003 THE JOURAL OF ALTERATIVE IVESTMETS 49 It i illegal to reproduce thi article in any format. Reprint@iijournal.com for Reprint or Permiion.

9 E XHIBIT 8 Comparion of Three Portfolio from Each LOW RISK PORTFOLIO MAX SHARPE RATIO PORTFOLIO HIGH RETUR PORTFOLIO Reported-Rik Adjuted-Rik Reported-Rik Adjuted-Rik Reported-Rik Adjuted-Rik Portfolio Return 9.3% 9.0% 10.8% 10.% 17.5% 17.5% Portfolio Rik (Standard Deviation).7%.8% 3.0% 3.1% 0.9% 35.3% Aet Allocation Cah 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% U.S. Equity.9%.7% 0.0% 0.0% 50.0% 50.0% U.S. Bond 3.% 31.8% 41.0% 38.7% 0.0% 0.0% International Equity 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% International Bond 11.% 1.8% 9.0% 11.3% 0.0% 0.0% High Yield Bond 3.8%.7% 0.0% 0.0% 0.0% 0.0% Convertible Arbitrage 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% Dedicated Short Bia 9.% 13.8% 3.0% 6.5% 0.0% 0.0% Emerging Market.% 0.7% 0.0% 0.0% 0.0% 0.0% Equity Market eutral 0.3% 15.3% 3.7% 9.5% 0.0% 0.0% Event Driven 0.0% 7.5% 0.0% 4.0% 0.0% 0.0% Fixed Income Arbitrage 11.% 7.4% 0.0% 0.0% 0.0% 0.0% Global Macro 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% Equity Long/Short 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% Managed Future 0.0% 1.8% 0.0% 0.0% 0.0% 0.0% Venture Capital 1.0%.3%.3% 1.0% 50.0% 50.0% Buyout & Other 6.0% 1.4% 1.0% 9.0% 0.0% 0.0% frontier that include allocation to alternative. Thi i the cae; the average DB along the reported-rik frontier i 10.9%, uggeting a ignificant increae in the diverification ithin the portfolio ith the introduction of alternative aet clae. Hoever, the average DB along the adjuted-rik frontier i 5.1%, uggeting that over half of the benefit from diverification aociated ith alternative aet may in fact be illuory derived from the effect of tale pricing. 7 COCLUSIO Reported hitorical data erie do not necearily reflect the true rik and correlation of alternative aet. In the cae of private equity and hedge fund it i often neceary to adjut the reported rik and correlation for the effect of tale pricing. Once thi i accomplihed, invetor are better able to apply traditional mean/variance optimization tool to aid in the aet allocation proce. Uing hitorical data a an example, e have found that adjuting rik and correlation for tale pricing ill ubtantially increae the perceived rik of alternative aet clae and decreae the diverification benefit of alternative aet ith mot traditional aet clae, in our example eliminating half of the diverification benefit aociated ith allocating to alternative aet. Depite th e find that optimal portfolio baed on adjuted rik and correlation do not have a loer overall allocation to alternative aet. Although the overall allocation deciion till include alternative, the compoition of the traditional and alterative portfolio i adjuted to better manage rik. In other ord, adjuting for the effect of tale pricing ha a meaningful effect on the perception of rik and the aet allocation deciion. APPEDIX A Proce for Solving for Weight For + 1 relevant autocorrelation (including the contemporaneou return/or zero lag autocorrelation), there i a ytem of equation that define each autocorrelation of order greater than zero order. For aet cla ubject to tale pricing, the moothed return at time t, denoted SR t, i a function of previou economic return, denoted ER t-n for the nth previou period, and the eight aociated ith each economic return ( t-n ): SR = ER it, The variance of the moothed return ( SRi ) i a function of the variance of the economic return ( ERi ): 50 ASSET ALLOCATIO EFFECTS OF ADJUSTIG ALTERATIVE ASSETS FOR STALE PRICIG WITER 003 Copyright 003 Intitutional Invetor, Inc. All Right Reerved

10 and the kth order erial covariance ( SR ) of the t,srt k moothed return i: SR i t -n = t, = t - k i, - it, - n - k SR SR ER i t n So, the ytem of equation for each autocorrelation decribed by: -k -k r SR t, SR = t - k it, -n for k = 1 to. And the final equation to make the ytem ell pecified i the ealth contraint on the eight that enure that the mean of the economic proce ill equal the mean of the moothed proce. -k ERi APPEDIX B Demontration That the Standard Deviation and Abolute Value of Correlation of the Economic Proce Are Greater Than Thoe of the Smoothed Proce For aet cla ubject to tale pricing, from Equation 1: Since the eight mut um to unity, and it follo that and therefore and ERi SRi = 0 Œn 1 Œn it, - n 0 1 it, - n = The ytem of equation i olved imultaneouly to find the vector of eight ( t-n ), hich can be ued in Equation 1,, and 3 to find the adjutment factor for tandard deviation and correlation. 1 o it, - n it, - n For correlation, from Equation : r r ERi SRi = it, -n 0 = 1 + n = 1 0 A hon above, it, - n n = WITER 003 THE JOURAL OF ALTERATIVE IVESTMETS 51 It i illegal to reproduce thi article in any format. Reprint@iijournal.com for Reprint or Permiion.

11 and o it follo that and therefore n = n = cation benefit aociated ith alternative aet hen adjuting for the effect of tale pricing, are all baed upon the pecific hitorical time period examined in the analyi. Reult may differ hen other time period are ued. REFERECES Anon, Mark J.P. Managed Pricing and the Rule of Conervatim in Private Equity Portfolio. The Journal of Private Equity, Vol. 5, o. (Spring 00), pp Ane, Clifford, Robert Krail, and John Lie. Do Hedge Fund Hedge? The Journal of Portfolio Management, Vol. 7, o. 1 (Fall 001), pp Geltner, David Michael. Smoothing in Appraial-Baed Return. Journal of Real Etate Finance and Economic, 4 (1991), pp EDOTES 1 For thi tudy e are uing Geltner noiele model, ith univariate eight etimation, auming that the number of contituent in our private equity and hedge fund indice i large enough to make random appraial error inignificant. Thi equation i a verion of Geltner Equation Thi equation i derived from a pecial cae of Geltner Equation 1, here aet j i not a real etate aet, but continually priced ithout lag. 4 Thi equation i derived directly from Geltner Equation 1. 5 Where r i the ample correlation coefficient and n i the number of obervation in the ample, the t-tatitic for a correlation coefficient i computed a follo: Gomper, Paul A., and Joh Lerner. Rik and Reard in Private Equity Invetment: The Challenge of Performance Aement. The Journal of Private Equity, Vol. 1, o. 1 (Winter 1997), pp Long, Autin M. Inferring Periodic Variability of Private Market Return a Meaured by from the Range of Value (Wealth) Outcome over Time. The Journal of Private Equity, Vol. 3, o. 3 (Summer, 1999), pp To order reprint of thi article, pleae contact Ajani Malik at amalik@iijournal.com or r n t = r 6 The Sharpe ratio i defined a the ratio of exce return over the rik-free rate to tandard deviation. For thi tudy e ued the hitorical average one-year contant maturity Treaury bond return a a proxy for the rik-free rate. Where R P i the expected return of the portfolio and R rf i the rik-free rate of return and P i the tandard deviation of portfolio return, Sharpe ratio i expreed a follo: RP - R SharpeRatio = P rf 7 The reult of thi tudy, including the abolute level of rik aociated ith each aet cla, the degree of correlation beteen aet clae, and the uggeted reduction in diverifi- 5 ASSET ALLOCATIO EFFECTS OF ADJUSTIG ALTERATIVE ASSETS FOR STALE PRICIG WITER 003 Copyright 003 Intitutional Invetor, Inc. All Right Reerved