The Benefits and Costs of Illiquidity

January 2004

Hilary TillResearch Associate, EDHEC-Risk Institute

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A version of this article was published in Risk Magazine in November of 2003; and in the edited book, Intelligent Hedge Fund Investing (Edited by Barry Schachter), Risk Books, 2004, http://www.RiskBooks.com.

Hilary Till co-founded Premia Capital Management, LLC with Joseph Eagleeye. She is a portfolio manager at this Chicago-based firm. Premia Capital specialises in detecting pockets of predictability in derivatives markets using statistical techniques. The firm solely trades principal-only capital.

Ms. Till is also a principal of Premia Risk Consultancy, Inc., which advises investment firms on derivatives strategies and risk management policy.

The author is also a Research Associate at the EDHEC-Risk Institute.

Prior to Premia, Ms. Till was Chief of Derivatives Strategies at Boston-based Putnam Investments. She has B.A. in Statistics with general honors from the University of Chicago and an M.Sc. in Statistics from the London School of Economics (LSE.) She studied at LSE under a private fellowship administered by the Fulbright Commission.

EDHEC is one of the top five business schools in France. Its reputation is built on the high quality of its faculty and the privileged relationship with professionals that the school has cultivated since its establishment in 1906. EDHEC Business School has decided to draw on its extensive knowledge of the professional environment and has therefore focused its research on themes that satisfy the needs of professionals.

EDHEC pursues an active research policy in the field of finance. EDHEC-Risk Institute carries out numerous research programmes in the areas of asset allocation and risk management in both the traditional and alternative investment universes.

Copyright © 2013 EDHEC

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I. IntroductionIlliquidity is a common feature of alternative investments, whether one chooses venture capital, private equity, or hedge funds. For hedge funds, the illiquidity can arise from the contracts an investor enters into, which may have one year or longer lock-ups or can arise from the type of investments that a hedge fund specialises in. A hedge fund’s investments may include over-the-counter derivatives instruments, which may be difficult to value, or small-capitalisation stocks, which may trade infrequently, for example.

In an era of subdued return expectations, investors may be motivated to look upon alternative strategies, including hedge funds, more favourably than in the past. Despite the fanfare surrounding hedge funds, they remain a niche investment. According to indicative estimates by Morgan Stanley [2001], investments in hedge funds amount to about 1% of the size of the global capital markets. Figure 1 shows the breakdown of the global capital markets by investment category.

One difficulty in evaluating hedge funds is coming up with a framework in which their benefits and risks are compared to traditional investments in an appropriate fashion. In the last couple of years there has been a lot of progress in coming up with new risk assessment techniques to evaluate those hedge fund strategies that have highly asymmetric outcomes; see, for example, a summary of these advancements in Till [2004]. This article will discuss progress in another area: how to explicitly take into consideration the illiquid nature of alternative investments, particularly including hedge funds. This article will specifically discuss the benefits and costs of illiquidity along with proposed quantitative adjustments that enable one to compare illiquid investments on a level playing field with liquid investments.

Figure 1

“Does not include cash equivalents and short-duration fixed income. Estimates for year-end 2000, based on ICI, MSCI, MAR, FRM, [and] Morgan Stanley estimates.”Source: Morgan Stanley Quantitative Strategies, “Hedge Funds Strategy and Portfolio Insights,” December 2001, Exhibit 1.

I. The Costs of Liquidity (or the Benefits of Illiquidity)

A. Liquidity is OverratedThere is nothing inherently bad about an illiquid investment. As a matter of fact, David Swensen of Yale University’s endowment, has noted that “American investors, particularly those with long time horizons, pay far too much for liquidity,” according to an Economist article. With liquidity overpriced, Swensen advocates investments where an institution gets paid for illiquidity. One then uses diversification for risk control rather than paying for liquidity. Yale’s asset allocation is shown in Figure 2. Note that 61% of the endowment is in alternative investments.

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Figure 2

Source: “Climbing Ivy,” Barron’s, June 23, 2003, p. F3.

B. Tick-by-Tick Evaluation of a Good Investment is PainfulOne seemingly positive feature of a liquid investment is the ability to receive continuous pricing on that investment. But is that really a positive? Nassim Taleb provides an example in Fooled By Randomness that makes one reconsider that benefit.

Taleb notes that a 15% return with a 10% volatility per year provides a 93% probability of making money in any given year. But this also translates into a 50% of chance of making money in any given second. Figure 3 reproduces his chart of the probability of making money over different time scales, given this investment’s return and risk parameters.

Figure 3

Source: Taleb, Nassim, Fooled By Randomness, Texere (New York), 2001, Table 3.1.

The significance of losing money about half the time that one makes money over the very short-term is that the joy of making money is not equivalent to the larger degree of pain one feels in losing money. If an investor is watching their investments tick-by-tick in an eight-hour day, Taleb points out that he or she will have 241 pleasurable minutes versus 239 unpleasurable minutes in this example. If the trader feels the negative effect say 2.5 times more than the magnitude of the positive one, then that trader could easily become emotionally burned out. This would adversely affect the trader’s ability to stay with a good investment.

In coming up with this example, Taleb was not advocating illiquid investments. But this example does show one potential disadvantage of a deeply liquid investment if an investor is unable to stand back from its daily movements.

A New Yorker cartoonist once made light of the inability of investors to stand back from the daily fluctuations in their portfolio. The cartoonist created a scenario that one would not expect will ever occur; a news anchor is shown stating, “There was no trading today on the New York Stock Exchange. Everybody was happy with what they owned.”

C. Predictability is at Long Time framesProfessor John Cochrane of the University of Chicago notes that stock and bond returns have a substantial predictable component at long time horizons. In a Federal Reserve Board article, Cochrane provides an example of an equity-forecasting model in which month-to-month returns are quite unpredictable. But at a five-year time horizon, the returns seem very predictable. Figure 4 shows the “results at different horizons [which] are reflections of a single underlying phenomenon.”

Figure 4

Source: Cochrane, John, “New Facts in Finance,” Economic Perspectives, Federal Reserve Board of Chicago, Third Quarter, 1999, Table 1.

Cochrane notes that “if daily returns are very slightly predictable by a slow-moving variable, that predictability adds over long horizons.”

Given Taleb’s observations on an investor’s emotional reactions to random fluctuations in the profitability of a good investment strategy, one might wonder how many investors could take advantage of such return predictability if one needs a five-year time horizon to benefit from it. Perhaps it would be easier to do so if the investment were illiquid.

D. Buy-and-Hold Strategies Have Provided Superior ReturnsA recent study by Dalbar, the fund consultancy, found that investors in mutual funds had unexpectedly low returns over the period, 1984 to 2002, according to a Financial Times article. The average U.S. equity fund investor earned only 2.6% per year over this period while the S&P 500 returned 12.2% over the same period. The average U.S. fixed income investor earned 4.2% annually whereas the long-term government bond index returned 11.7% over the period.

Over the nineteen-year period under examination, the Dalbar study found that investors had attempted to time their entry and exit into and out of mutual funds. “They typically put their money into a [mutual] fund after the S&P rose, and pulled it out when the S&P fell.” Unfortunately this strategy has left investors with equity returns that are lower than the inflation rate. The average holding period for an equity mutual fund was found to be about two years.

A natural response to this study is to advocate buy-and-hold strategies. But one wonders how realistic that advice is for investments that are packaged in vehicles that offer daily liquidity like mutual funds.

The Dalbar study illustrates the normal, but suboptimal, investor reaction to the highs and lows of a volatile, deeply liquid investment. Gary Knapp provided a similar example concerning the track record of a futures trading fund whose results were exceptionally volatile in a 2002 5

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presentation. The trader reported impressive, compounded annualised returns. These reported returns were technically accurate. But they did not reflect the actual experience of the fund’s investors, who like, mutual fund investors, fled the fund after it had large draw-downs and flew into the fund after it posted large gains. When Knapp calculated the internal rate of return of the fund based on the fund’s average money under management, he came up with sub-Treasury returns. He concluded that an investor would need to be “contra-human” in order to be able to actually experience the fund’s impressive annualized returns.

E. Intentional Return Smoothing: Education versus ObfuscationClifford Asness, Robert Krail, and John Liew of AQR Capital Management report that anecdotally a number of hedge fund managers may take advantage of the illiquid nature of their investments to smooth their reported returns:

“One anonymous hedge fund investor told us an anecdote about a manager selling this as a positive feature, since if he smoothes his returns (lowering his perceived volatility and market exposure) the hedge fund investor will also get to report smoothed returns to his constituents.”

The authors note that while it is plausible that this return smoothing could lead to better long-term investor behaviour, they would instead advocate investor education over obfuscation.

Later in this article, we will discuss several researchers’ approaches to ferreting out and correcting for any intentional or unintentional return smoothing on the part of managers of illiquid investments. As noted in the introduction, this is necessary if one wants to compare illiquid investments on a level playing field with liquid investments.

II. The Costs of (and Caveats Due to) Illiquidity

A. An Investor Cannot Rebalance His or Her PortfolioIn evaluating illiquid alternative investments, an investor should understand that one loses the ability to rebalance a portfolio should other superior investment opportunities arise. Kevin Terhaar, Renato Staub, and Brian Singer of UBS Global Asset Management also point out that when one establishes a policy portfolio, which includes allocations to illiquid investments, the actual weightings can deviate from the policy’s weightings because of liquidity constraints in entering and exiting investments.

When one chooses to invest in illiquid investments such as venture capital, real estate, and hedge funds, an investor needs to ensure that the range of allocations that may occur over time is acceptable. As an example, the UBS researchers simulate the 10-year investment experience of allocating to both traditional and alternative investments where the policy mix is 80% in diversified, global securities and 20% in alternative investments. A further breakdown among alternative investments is shown in Figure 5.

The UBS researchers provide a summary of the results of simulating 1,000 10-year investment experiences, which include allocations to alternative investments:

“While the target policy risk is 10.1%, the expected or forecast risk is above 11.5% in 5% of the periods. This increase in expected risk occurs because the actual allocation to riskier alternative investments varies over time, due to the constrained ability to rebalance. The actual alternatives weight is greater than 28%, compared to the target of 20%, in 5% of the periods. This considerable difference is driven in large part by the huge swings in private equity allocation; whereas the target allocation is 5%, the actual weight exceeds 14% of the portfolio in 5% of the simulation periods.”

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The researchers conclude that an investor must have a sufficiently high tolerance for risk to accept the “periodically elevated risk levels.” That investor must also have a long enough time horizon to ensure that they are able to benefit from the expected higher returns of the illiquid investments.

Figure 5

Source: Terhaar, Kevin, Renato Staub, and Brian Singer, “Determining the Appropriate Allocation to Alternative Investments,” Journal of Portfolio Management, Spring 2003, Exhibit 8.

B. An Investor is Short a Put Option That an investor lacks rebalancing flexibility when owning illiquid investments can also be thought of in option terms. A holder of illiquid investments is short put options while a holder of liquid assets is long put options. Presumably a holder of liquid assets would be successful in implementing a dynamic stop-loss policy. This dynamic stop-loss policy can be modelled as a put option, according to Myron Scholes of Oak Hill Capital Management. Scholes explains:

“A put option provides the equivalent of a dynamic liquidity cushion. A put-protected position self-liquidates as money is lost and markets become more illiquid. The cost of this protection is the value of liquidity.”

One can think of certain hedge fund strategies as earning their returns for taking on liquidity risk. For example, one could argue that a relative-value bond fund earns its returns by taking on the illiquid assets that international banks desire to lay off when in need of reducing risk. The fund hedges this risk by shorting liquid assets. A relative-value bond fund thereby provides a reinsurance function for financial institutions, but it also exposures the fund to liquidity crises. As a result, an examination of empirical data shows that relative-value bond funds have short-option-like returns. An investor in such funds assumes the risk of systemic financial distress and provides other investors with the flexibility of being able to readily liquidate their investments. A relative-value bond fund is in essence providing real options to other investors.

C. Default and Liquidation RiskThe previous section emphasised the illiquidity of the underlying investments of a certain type of hedge fund. Another source of illiquidity in hedge fund investments arises from the nature of the contract that investors enter into with hedge fund managers. Hari Krishnan of Morgan Stanley and Izzy Nelken of Super Computer Consulting note that:

“If a hedge fund has a one-year lockup, funds can typically only be taken out at the end of a calendar year following the year of investment. Thus, an investor who allocates money in

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January 2002 can only take the money out in December of 2003, and the effective lockup period is two years.”

During the lockup period, the hedge fund manager may alter the hedge fund’s leverage level according to the manager’s interests, which may not coincide with what is optimal for the investor. Krishnan and Nelken note that anecdotally a manager will alter their leverage policy according to how the hedge fund is performing with respect to its previous high watermark. Typically a hedge fund needs to outperform a previous high watermark before receiving an incentive fee.

The manager’s leverage policy (or behaviour) can have a meaningful impact on an investment’s performance. Say an investor believes in the underlying investment process that a hedge fund is pursuing. Say those returns have a certain mean return and standard deviation. The returns that the investor will actually receive will be very path-dependent since the hedge fund manager will likely alter their leverage level according to how performance compares to the previous equity high.

Krishnan and Nelken note that if a hedge fund reaches a certain loss threshold, the manager may substantially decrease leverage in order to prevent redemptions and therefore lose an ongoing management fee stream. They note that once redemptions occur, there may be a further sharp decline in the value of the hedge fund’s investments due to concentrated liquidation pressure.1

On the other end of the performance spectrum, once a hedge fund earns a certain amount in a year, the hedge fund manager may also decrease leverage in order to “coast.” Perhaps earning greater than expected returns would alarm clients about the risks being taken so that there would be limited benefit in posting extraordinary returns. Finally, if a hedge fund’s returns are in the neighbourhood of the previous high watermark then the manager may use maximum leverage to increase their future expected incentive compensation.

An interesting consequence of the path-dependent nature of hedge fund returns, under this model of hedge fund manager behaviour, is that if one had another investment that had the same underlying return process but did not have lock-ups (and incentive fees), then one would expect a different return stream to accrue to the end-investor. This is because the dynamic leverage scheme outlined in the previous paragraph would likely not occur.

Based on Krishnan and Nelken’s framework, one can figure out the cost of the illiquid nature of hedge fund contracts as follows. Create a well-specified underlying return generating process; come up with a model of a hedge fund manager’s leverage policy; and figure out the threshold level of losses at which investors will attempt en masse to liquidate their investments. Calculate the risk-adjusted returns of the underlying return generating process absent dynamic leverage and forced liquidation pressure. Next calculate the risk-adjusted returns of the hedge fund investment, complete with the manager’s and investors’ behaviours factored in. The difference in these two risk-adjusted returns provides one with a measure of the cost of this form of illiquidity.

D. Stale Pricing1. Inaccurate Relationship Between InvestmentsAnother signature aspect of investing in illiquid investments is that these investments may be marked based on old (or “stale”) prices. If one uses unadjusted historical data to compare liquid and illiquid investments, one may not be getting a true picture of the underlying economic relationship between these investments.

1 - Clifford De Souza of Citigroup’s Fund of Hedge Fund’s unit has formally modelled the probability of a fund being at risk to concentrated liquidation pressure. Given a fund’s expected return, volatility, and latest high watermark, there is some threshold negative performance level at which a cycle of redemptions starts to occur, which leads to more redemptions, which then puts the fund’s survival at risk. The market extracts a premium from a fund in distress. One can calculate the probability of a fund entering into a “critical liquidation cycle” based on how far away the current NAV is from the threshold negative performance or “barrier” level, normalised by the fund’s return and volatility. De Souza uses the mathematics of barrier option pricing to come up with this probability.

The principals of AQR Capital Management have built a convincing argument that the lack of relationship of hedge fund indices to the S&P 500 is largely due to the reporting of stale prices for hedge fund positions. The authors use the CSFB/Tremont hedge fund indices in their research.When the authors regress the CSFB/Tremont Aggregate Hedge Fund Index’s returns versus lagged returns of the equity market, they find a strong relationship between the hedge fund index and the S&P using data from January 1994 to September 2000. Because there is such a strong relationship once they compare the hedge fund index’s returns to dated returns in the stock market, they infer that hedge funds making up the index may have been using stale pricing in evaluating their holdings.

Investors might consider hedge funds for their portfolios because they would like to diversify away some of their equity market exposure. Given that investment rationale, the AQR researchers recalculate the Sharpe ratio of a number of hedge fund styles if one hedged out their true equity market exposure taking into consideration the stale-pricing effect.

Figure 6 shows the authors’ results. “Monthly Unhedged Sharpe Ratio” is the unadjusted Sharpe ratio of the hedge fund style. “Monthly Beta Hedged Sharpe Ratio” is the Sharpe ratio of the hedge fund style if it were hedged according to its relationship with the stock market based on regressing contemporaneous returns. “Summed Beta Hedged Sharpe Ratio” is the Sharpe ratio of the hedge fund style if it were hedged according to its relationship with the stock market, which includes the stale-pricing effect.

Figure 6

Source: Asness, Clifford, Liew, John, and Robert Krail, “Do Hedge Funds Hedge?,” Journal of Portfolio Management, Fall 2001, Table 6.

With several noteworthy exceptions, the figure above illustrates that once market exposure is taken into consideration, the attractiveness of a number of hedge fund strategies declines fairly dramatically. Further, the adjusted Sharpe ratios shown in the last column of Figure 6 (Summed Beta Hedged Sharpe Ratios) are mostly negative, indicating that at least over the period, January 1994 to September 2000, there is no evidence that most categories of hedge funds were able to add value after taking into consideration their actual equity market exposure.

2. Real Economic ImpactMila Getmansky, Andrew Lo, and Igor Makarov of the MIT Laboratory for Financial Engineering note that the economic impact of stale pricing “can be quite real.” In a very timely analogy, the authors note that the “spurious serial correlation [induced by illiquidity] can lead to wealth transfers between new, existing, and departing investors, in much the same way that using stale prices for individual securities to compute mutual-fund net-asset-values can lead to wealth transfers between buy-and-hold investors and day-traders.”

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E. Valuation RiskIf a fund manager elects to imperfectly value a portfolio of illiquid securities, that manager risks the dire consequences of violating investor trust. Specifically, if a manager mismarks their portfolio beyond some threshold level above its true liquidation value, then that manager risks investors losing faith in that manager. The result can be that a massive liquidation occurs, causing the terminal value of the portfolio to plummet to a level beyond a more reasonable liquidation value. The market extracts a penalty for the fund’s breach of trust.

Andrew Weisman of Strativarius Capital has proposed a mathematical framework for modelling this scenario. An investor in a fund of illiquid instruments is short a barrier option that will be exercised against that investor if the fund’s manager smoothes valuation too much. For this risk to be acceptable, the investor should be earning a premium that is at least equal to the value of the barrier option.

Stated another way, an investor in illiquid securities earns a premium for taking on the risk of managed pricing, which may not accurately reflect realistic liquidation values. If there is enough of a gap between stated and reasonable pricing, the market imposes a penalty by forcing liquidation at levels that are far below normal liquidation values.

The scenario outlined by Weisman is not only an issue for hedge funds but also for mutual funds that contain large concentrations of illiquid securities. In December of 2003, the U.S. Securities and Exchange Commission (SEC) leveled fraud charges against a mutual fund for mispricing two high yield municipal bond funds during the year 2000. According to the SEC, “the vast majority of bonds held by the Funds were unrated and illiquid.” The mutual fund advisor “failed to set prices for the bonds which reflected their fair value in a current sale.” Instead, the advisor sold, redeemed, and repurchased Fund shares at NAV’s calculated with “smoothed” bond prices. This action temporarily decreased “the negative impact that a precipitous drop in the bonds’ values would have on the Funds’ NAV’s.” When the Funds attempted to meet redemption requests, the managers experienced difficulty in trying to sell holdings at values near their priced levels. As the Funds’ distress became widely known, it became difficult to liquidate securities even at sharply devalued prices. Figure 7 shows the NAV history for one of the Funds.

Figure 7

Source: Bloomberg

This recent case provides a good example of the valuation risk assumed with a portfolio that has a concentration of illiquid securities and yet provides ample redemption opportunities for its investors.

III. Quantitative Approaches to Adjusting for Illiquidity

A. Stale PricingThere have basically been two suggested approaches for adjusting stale pricing so that one can compare illiquid investments with liquid investments. One approach is to infer the underlying economic returns of an investment from the original price series. The other approach is to alter one’s performance evaluation metric so that it accurately reflects the statistical properties of the illiquid investment.

1. Un-smoothing Pricesa. “De-lagging” the Return SeriesProfessor Chris Brooks of the University of Reading (UK) and Professor Harry Kat of City University (London) report that the monthly returns of hedge fund indices show significant serial correlation. The researchers examine hedge fund index data from January 1995 through April 2001. Specifically, these researchers find that:

“All of the Convertible Arbitrage [hedge fund] indices have a first order serial correlation of at least 0.4, which are also statistically significant at the 1% level. A similar feature is observed for Distressed Securities and some of the Risk Arbitrage, Emerging Markets and Equity Market Neutral [hedge fund] series. It is also reflected in the Fund of Funds results ….”

The authors note that this level of autocorrelation is not consistent with idea of efficient markets:

“One possible explanation is that the nature of hedge funds’ strategies leads their returns to be inherently related to those of preceding months. As this implies lags in the major systematic risk factors, however, this is not the most plausible explanation. An alternative explanation lies in the difficulty for hedge fund managers to obtain up-to-date valuations of their positions in illiquid and complex over-the-counter securities. When confronted with this problem, hedge funds either use the last reported transaction price or an estimate of the current market price, which may easily create lags in the evolution of their net asset value. This would explain why the Convertible Arbitrage and Distressed Securities indices exhibit the most significant autocorrelation.” If we assume that the autocorrelation in prices of an investment is an artifact of lagged pricing then one may attempt to infer the underlying economic process by “de-lagging” the observed series. This approach has been advocated by at least three different groups of researchers: Brooks and Kat, SEI Investments, and by John Okunev of Principal Global Investors (USA) and Derek White of the University of New South Wales (Australia). This methodology was originally created for adjusting real estate data.

The researchers at SEI Investments find that when they apply this approach to private equity and hedge fund data, the diversification benefit of allocating to alternative assets is reduced by half. That said, the optimal portfolios “do not have a lower allocation to alternative assets.” One additional change is that “the composition of the traditional and alternative portfolios is adjusted to better manage risk.”

Okunev and White find that the primary effect of “unsmoothing” returns of fixed-income hedge funds is obtaining a better indication of underlying risk:

“… the true risk for many fixed income hedge fund strategies is at least 60 to 100% greater than that observed through reported returns.”

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b. Generic Model DecompositionAnother approach is to attempt to infer what the underlying factors are that drive a hedge fund portfolio’s return. Andrew Weisman of Strativarius Capital and Jerome Abernathy of Stonebrook Structured Products LLC advocate this approach in a chapter of the book, Risk Budgeting.

Based on a qualitative review of an individual hedge fund, the authors decide which assets and option types that a hedge fund investment likely has an exposure to. They then use an optimisation technique that fits the hedge fund’s returns to these exposures. The particular non-parametric, non-linear optimisation technique they choose is based on their experience of which characteristics are most important in evaluating a manager. They try to capture the manager’s large winning and losing months, the manager’s use of leverage, and the inflection points of the manager’s returns.

Weisman and Abernathy take the investment performance produced by the likely factors driving a portfolio’s return and compare it with the manager’s reported performance. They notice a tendency for manager performance to be less volatile than the performance produced by their optimisation. They hypothesise that given that certain over-the-counter securities are difficult to value since they are illiquid, their owners may underestimate the periodic changes in the value of these holdings. With their derived performance figures, the authors are in a position to evaluate the real underlying volatility of a portfolio and thereby adjust the risk measure used in evaluating a manager.

2. Adjust Evaluation Statistics (Not the Return Data)Professor Andrew Lo of the Massachusetts Institute of Technology proposes directly taking into consideration the serial correlation of hedge fund return data in coming up with a “robust Sharpe ratio.” In the presence of positive serial correlation, it not appropriate to take a monthly Sharpe ratio and multiply it by square root of 12 to annualise this statistic. This annualisation technique is only appropriate for monthly returns that are independent of each other.

When Lo examined twelve hedge funds of varying styles, he found that most of the funds exhibited meaningful serial correlation. The importance of this finding is that:

“the annual Sharpe ratio [was] … overstated by as much as 65% due to the presence of serial correlation in monthly returns, and once this serial correlation … [was] properly taken into account, the rankings of hedge funds based on Sharpe ratios change[d] dramatically.”

B. Simulations, not OptimisationsAnother proposed quantitative adjustment for handling illiquid investments is to rely on simulations, not optimisations. Referring back to the UBS Global Asset Management work, the UBS researchers point out that in coming up with recommended policy mixes, it is not appropriate to use multi-period optimisation techniques. This is because an implicit assumption with such techniques is that one can rebalance the portfolio during each period. And as noted before, a distinguishing feature of alternative investments is their lock-up periods and illiquidity. Therefore, the UBS researchers use simulations to take into consideration the lack of rebalancing opportunities that occur when using alternative investments:

“Simulations permit the inclusion of both the cost of illiquidity (allowing rebalancing only to the extent possible in practice) and the benefit of illiquidity (the liquidity premium).”

C. Replace Point-Estimate Prices with Probabilistic ValuationsAdil Abdulali, Leslie Rahl, and Eric Weinstein note that there are types of investments in which there may be an absence of consensus pricing. The authors refer to these investments as “translucent” as opposed to ones that can be “transparently” priced or whose pricing is “opaque.” Transparently

priced investments include large capitalisation stocks and on-the-run U.S. Treasuries. Opaque investments include real estate and fine art. Translucent investments, which in the valuation-risk spectrum lie between transparent and opaque investments, can include high-yield bonds, convertible bonds, and mortgage-backed securities (MBS). One would regard these investments as illiquid.

The authors provide an example of a mortgage-backed security derivative in which broker-dealers provided markedly divergent indicative valuations. This is an example of a translucent investment. The absence of consensus pricing should be regarded as a source of risk for which the investor should be compensated.

The authors also note that strictly speaking, it is inappropriate to value an entire investment with one price; one would expect that pricing should depend on the volumes that need to be bought or sold. One would also expect that the time frame over which buying and selling activity needs to occur should impact price. Therefore, the authors advocate “replacing point asset values with parameterised ones.” They note, though, that “even for constant size and volume, translucent assets have a range of prices,” as the MBS derivative example showed.

For a translucent investment, one would only have real data on its pricing if the investor chose to liquidate the position. But even in this scenario, the situation is surprisingly ambiguous. In the authors’ example, if an investor were given a range of indicative quotes, one of which was particularly low, a risk-averse investor may decide to liquidate the position whereas a more risk-welcoming investor would not be induced to sell.

Therefore, the liquidation value of a position may depend on an investor’s risk preferences. For our purposes, this means that an additional parameter in valuing a position is the investor’s risk tolerance.

The authors propose coming up with “phantom prices” for translucent assets by:• Choosing a probability distribution from which the sample of indicative prices was generated; and• Creating a function to represent how risk averse the investor is.

They use this information to solve for:

“… the lowest single definite price [that the investor] would accept for … [the] asset in exchange for the ambiguous situation of the multiple indicative prices if … [the investor’s] intention were to immediately liquidate the security.”

This “lowest single definite price” is the authors’ “phantom price.” Using their framework, one could theoretically infer what the hedge fund manager’s risk tolerance was in pricing their portfolio. One could also create a series of phantom prices using the manager’s average level of risk tolerance and compare this series with the manager’s marks. The goal would be to recalculate the portfolio’s risk-adjusted return measures with the phantom prices. This framework was originally developed in the June 2002 Risk magazine article, “Hedge Fund Transparency: Quantifying Valuation Bias for Illiquid Assets,” by Eric Weinstein and Adil Abdulali.

The authors provide an example of a manager who claimed a Sharpe ratio of 2.34. When the authors use a phantom-price evaluation framework with a constant level of risk aversion that matches up with the manager’s inferred average level, the recalculated Sharpe ratio changes to 0.45. They conclude that the manager is engaging in “volatility smoothing.”

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In summary, the authors advocate replacing point-estimate valuations of illiquid investments with a probabilistic approach to pricing. Based on an investor’s risk tolerance, one would map the probabilistic range of prices into a “phantom price.” One would then recalculate risk-adjusted return measures with the phantom prices and compare this new measure with what the manager reports. This would provide an insight into the amount of managed pricing the manager might be engaging in.

IV. ConclusionAs investors consider larger allocations to alternative investments, researchers are attempting to come up with proper ways of comparing their performance characteristics with traditional, deeply liquid investments. This article summarised the current literature on evaluating the costs and benefits resulting from the illiquid nature of most alternative investments.

There may be behavioural benefits to enforcing a long-term investment horizon on investors in illiquid investments. But assuming that an investor already has a long-term investment focus, that investor must decide whether the return premium one receives from holding illiquid investments is sufficient compensation for the added default, liquidation, and valuation risks one assumes.

References• Abdulali, Adil, Leslie Rahl, and Eric Weinstein, “Phantom Prices, Valuation, and Liquidity: The Nuisance of Translucence,” Chapter 8, A Guide to Fund of Hedge Funds Management and Investment, (Leslie Rahl, Editor), Alternative Investment Management Association (London), 2002.

• Asness, Clifford, Liew, John, and Robert Krail, “Do Hedge Funds Hedge?,” Journal of Portfolio Management, Fall 2001, pp. 6–19.

• Brewster, Deborah, “Investor Timing Decisions ‘Key to Return From Fund,’” Financial Times, December 1, 2003, p. 27.

• Brooks, Chris and Harry Kat, “The Statistical Properties of Hedge Fund Index Returns and Their Implications for Investors,” Journal of Alternative Investments, Fall 2002, pp. 26-44.

• “Climbing Ivy,” Barron’s, June 23, 2003, p. F3.

• Cochrane, John, “New Facts in Finance,” Economic Perspectives, Federal Reserve Board of Chicago, Third Quarter, 1999.

• Conner, Andrew and the SEI Investment Team, “The Asset Allocation Effects of Adjusting Alternative Assets for Stale Pricing,” Research from SEI Investments, January 2003.

• “Contrary-wise,” The Economist, May 13, 2000, pp. 77-78.

• De Souza, Clifford, “Leverage and Hedge Funds,” Riskinvest USA 2003 conference, Boston, 11/4/03.

• Getmansky, Mila, Andew Lo, and Igor Makarov, “An Econometric Model of Serial Correlation and Illiquidity in Hedge Fund Returns,” MIT Laboratory for Financial Engineering, 4/28/03.

• Knapp, Gary, “A Volatility Balanced Approach to Constructing a Diversified Hedge Fund Portfolio,” Presentation to Chicago QWAFAFEW, 10/24/02.

• Krishnan, Hari and Izzy Nelken, “A Liquidity Haircut for Hedge Funds,” Risk magazine, April 2003, pp. S18-S21.

• Lo, Andrew, “The Statistics of the Sharpe Ratio,” Financial Analysts Journal, July/August 2002, pp. 36-52.

• Morgan Stanley Quantitative Strategies, “Hedge Funds Strategy and Portfolio Insights,” December 2001.

• Okunev, John and Derek White, “Hedge Fund Risk Factors and Value at Risk of Credit Trading Strategies,” Principal Global Investors (USA) and University of New South Wales (Australia) Working Paper, August 2003.

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• “SEC Levels Fraud Charges Against Heartland Advisors, Inc., 12 Company Officials and Others for Misrepresentations, Mispricing and Insider Trading in Two High Yields Bond Funds,” SEC website, 12/11/03, http://www.sec.gov/litigation/admin/2003-171.htm, http://www.sec.gov/litigation/admin/ia-2201.htm, andhttp://www.sec.gov/litigation/admin/33-8346.htm.

• Taleb, Nassim, Fooled By Randomness, Texere (New York), 2001.

• Terhaar, Kevin, Renato Staub, and Brian Singer, “Determining the Appropriate Allocation to Alternative Investments,” Journal of Portfolio Management, Spring 2003, pp. 101-110.

• Till, Hilary, “Risk Measurement of Investments in the Satellite Ring of a Core-Satellite Portfolio: Traditional versus Alternative Approaches,” Singapore Economic Review, April 2004, pp. 105-130.

• Weinstein, Eric and Adil Abdulali, “Hedge Fund Transparency: Quantifying Valuation Bias for Illiquid Assets,” Risk magazine, June 2002, pp. S25-S28.

• Weisman, Andrew, “An Option-Based Methodology for Relative Evaluation of Manager Performance Across Strategies With Varying Liquidity Characteristics,” Risk Magazine’s 5th Annual Quantitative Trading and Investment Strategies for Global Derivatives, Quant 2003 Congress, New York, 11/19/03.

• Weisman, Andrew and Jerome Abernathy , “The Dangers of Historical Hedge Fund Data,” In L. Rahl, ed. Risk Budgeting, Risk Books (London) 2000, pp. 65-81.

15

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