• Illiquidity risk causes the investor to behave in a more risk-averse fashion toward both liquid and illiquid assets. Illiquidity risk induces time-varying, endogenous risk aversion. Harvard discovered in 2008 that although it is wealthy, it cannot “eat” illiquid assets. Illiquid wealth and liquid wealth are not the same; agents can only consume liquid wealth. Thus, the solvency ratio of illiquid to liquid wealth affects investors’ portfolio decisions and payout rules – it becomes a state variable that drives investors’ effective risk aversion.
• The following are the major impacts of infrequent trading on asset allocation:
  
  • Illiquidity Reduces Optimal Holdings – The optimal holding of an asset largely depends upon liquidity associated with it. If liquidity is higher, the optimal allocation is greater. This table shows the optimal rebalancing value of an asset as a percentage of the portfolio with respect to its average turnover.
    
  • Rebalance Illiquid Assets to Positions below the Long-Run Average Holding – In the presence of infrequent trading, illiquid asset wealth can vary substantially and is right-skewed. Suppose the optimal holding of illiquid assets is 0.2 when the liquidity event arrives. The investor could easily expect illiquid holdings to vary from 0.1 to 0.35, say, during non-rebalancing periods. Because of the right-skew, average holding of illiquid asset is 0.25, say, and is greater than optimal rebalanced holding. The optimal trading point of illiquid assets is lower than the long-run average holding.
  • Consume Less with Illiquid Assets – Payouts, or consumption rates, are lower in the presence of illiquid assets than when only comparable liquid assets are held by the investor. The investor cannot offset the risk of illiquid assets declining when these assets cannot be traded. This is an unhedgeable source of risk. The investor offsets that risk by eating less.
  • There Are No Illiquidity “Arbitrages” – In a mean-variance model, two assets with different Sharpe ratios and perfect correlations produce positions of plus or minus infinity. This is a well- known bane of mean-variance models, and professionals employ lots of ad hoc fixes, and arbitrary constraints, to prevent this from happening. This does not happen when one asset is illiquid—there is no arbitrage. Investors do not load up on illiquid assets because these assets have illiquidity risk and cannot be continuously traded to construct an “arbitrage.”
  • Investors Must Demand High Illiquidity Hurdle Rates – This table gives the premiums on an illiquid asset required by an investor to bear illiquidity risk. The more frequently the asset is traded, the lower the premium. For example, one study indicates that private equity investments generate returns 6% higher than public markets to compensate investors for illiquidity. Let’s define the illiquidity premium, or hurdle rate, as a certainty equivalent. Suppose an investor holds two liquid assets and replaces one asset with another that is identical except for being illiquid. The illiquidity premium is the increase in the expected return of the illiquid asset so that the investor has the same utility as the case when all assets are liquid. When liquidity events arrive every six months, on average, an investor should demand an extra 70 basis points. (Some hedge funds have lockups around this horizon.) When the illiquid asset can be traded once a year, on average, the illiquidity premium is approximately 1%. When you need to wait ten years, on average, to exit an investment, you should demand a 6% illiquidity premium. That is, investors should insist that private equity funds generate returns 6% greater than public markets to compensate for illiquidity. Most illiquid assets are not generating excess returns above these hurdle rates.
    

Liquidating Harvard

• In 2008, the Harvard University’s endowment, which was the world’s largest at that time – fell victim to the worldwide plunge in asset prices triggered by the financial crisis. In contrast to its 15% average annual returns since 1980, Harvard’s endowment suffered its worst decline in history, falling 22% between July 1 and October 31, 2008. More than $8 billion in value had been wiped out in three months.
• Harvard Management Company (HMC), the fund’s manager of Harvard’s endowment, was one of the early adopters of the endowment model, which recommends that long-term investors hold lots of illiquid, alternative assets, especially private equity and hedge funds. Advocated by David Swensen in his influential book, Pioneering Portfolio Management, the endowment model was based on the economic concept of diversification originally attributable to Harry Markowitz (1952). Through diversification, a portfolio of many low-correlated assets has a risk-return trade-off superior to that of conventional portfolios consisting of only stocks and bonds. Swensen went further and advocated holding large proportions of illiquid private equity and hedge funds. Not only were these assets supposed to have low correlations to stocks and bonds, but they potentially carried an illiquidity risk premium.
• Swensen argued that in liquid markets, the potential for making excess returns (or “alpha”) was limited. In these markets, crowded with thousands of active managers vying for an edge, information is freely available and almost everyone has access to it. Illiquid asset markets, like venture capital and private equity, had large potential payoffs for investors who had superior research and management skills. Swensen argued that alpha was not competed away in illiquid assets because most managers have short horizons. University endowments, with their longer horizons, would seem to have an advantage in illiquid assets. Swensen recommended that long- term institutions with sufficient resources who can carefully select expert managers in the alternative, illiquid assets could achieve superior risk-adjusted returns.
• Following Swensen’s advice, many endowments, including Harvard, loaded up with illiquid assets during the 1990s. In 2008, HMC held 55% of its portfolio in hedge funds, private equity, and real assets. Only 30% was in developed-world equities and fixed income, with the remainder of its portfolio in emerging-market equities and high-yield bonds.
• In its desperate need for cash, HMC tried to sell some of its $1.5 billion private equity portfolios. But buyers in secondary markets demanded huge discounts. Harvard was desperate to sell. All the short-term decisions for Harvard leaders were painful: slashing budgets, hiring freezes, and the postponement of the university’s planned Allston science complex. Asset- liability management for Harvard University had failed.
• On 10th September 2009, Harvard Management Company (HMC) reported today that the University’s endowment was valued at $26.0 billion as of June 30 – 29.5 percent less than the record $36.9 billion reported for the prior fiscal year. That result reflects a negative 27.3 percent investment return on endowment assets
• Source:http://harvardmagazine.com/2009/09/sharp-endowment-decline-reported
• So, the question is whether the endowment model with illiquid, alternative assets is appropriate in the longer term.

Sources Of Illiquidity

• Clientele effects and participation costs – Entering markets can be costly; investors often must spend money, time, or energy to learn their way around and gain the necessary skills. In many large, illiquid asset markets, only certain types of investors with sufficient capital, expertise, and experience can transact.
• Transaction costs – These include commissions, taxes, and, for certain illiquid assets, the costs of due diligence, title transfers, and the like, as well as the bread-and-butter costs incurred for trading. It also includes fees paid to lawyers, accountants, and investment bankers.
• Search frictions – For many assets, you need to search to find an appropriate buyer or seller. For example –
  • Only certain investors have the skills to value a complicated structured credit product.
  • Few investors have sufficient capital to invest in skyscrapers in major metropolitan areas.
  • You might have to wait a long time to transact.
• Asymmetric information – Markets can be illiquid because one investor has superior knowledge compared with other investors. Fearing they’ll be fleeced, investors become reluctant to trade. When asymmetric information is extreme – all the products are lemons, and no one wants to buy a lemon – markets break down. Many liquidity freezes are caused by these situations. The presence of asymmetric information also causes investors to look for nonpredatory counterparties, so information is a form of search friction.
• Price impact – Large trades will move markets.
• Funding constraints – Many of the investment vehicles used to invest in illiquid assets are highly leveraged. Even investing in a house requires substantial leverage for most consumers. If access to credit is impaired, investors cannot transact in illiquid asset markets.

Characteristics Of Illiquid Markets

• Most Asset Classes Are Illiquid – Except for “plain-vanilla” public equities and fixed income, most asset markets are characterized by long periods, sometimes decades, between trades, and they have very low turnover. Even among stocks and bonds, some sub-asset classes are highly illiquid. Equities trading in pink-sheet over-the-counter markets may go for a week or more without trading. The average municipal bond trades only twice per year, and the entire muni-bond market has an annual turnover of less than 10%. In real estate markets, the typical holding period is four to five years for single-family homes and eight to eleven years for institutional properties. Holding periods for institutional infrastructure can be fifty years or longer and works of art sell every forty to seventy years, on average. Thus, most asset markets are illiquid in the sense that they trade infrequently, and turnover is low.
• Illiquid Asset Markets Are Large – The illiquid asset classes are large and rival the public equity market in size. In 2012, the market capitalization of the NYSE and NASDAQ was approximately $17 trillion. The estimated size of the U.S. residential real estate market is $16 trillion, and the direct institutional real estate market is $9 trillion. In fact, the traditional public, liquid markets of stocks and bonds are smaller than the total wealth held in illiquid assets.
• Investors Hold Lots of Illiquid Assets – Illiquid assets dominate most investors’ portfolios. For individuals, illiquid assets represent 90% of their total wealth, which is mostly tied up in their house – and this is before counting the largest and least liquid component of individuals’ wealth, human capital. There are high proportions of illiquid assets in rich investors’ portfolios, too. High net worth individuals in the United States allocate 10% of their portfolios to “treasure” assets like fine art and jewelry. This rises to 20% for high-net-worth individuals in other countries. The share of illiquid assets in institutional portfolios has increased dramatically over the past twenty years. It was reported that, in 2011, the average endowment held a portfolio weight of more than 25% in alternative assets versus roughly 5% in the early 1990s. In 1995, Pension funds held less than 5% of their portfolios in illiquid alternatives, but this figure was close to 20% after 2010.
• Liquidity Dries Up – Many normally liquid asset markets periodically become illiquid. During the 2008 to 2009 financial crisis, the market for commercial paper (or the money market) – usually very liquid – experienced “buyers’ strikes” by investors unwilling to trade at any price. This was not the first time that the money market had frozen: trading in the commercial paper also ceased when the Penn Central railroad collapsed in 1970. In both cases, the Federal Reserve had to step in to restore liquidity. During the financial crisis, liquidity also dried up in the repo market (which allows investors to short bonds), residential and commercial mortgage-backed securities, structured credit, and the auction rate security market (a market for floating rate municipal bonds). The last example was one of the first markets to become illiquid at the onset of the financial crisis in 2008 and at the time of writing in 2013 is still frozen. This market is dead in its present form. Illiquidity crises occur regularly because liquidity tends to dry up during periods of severe market distress. The Latin American debt crisis in the 1980s, the Asian emerging market crisis in the 1990s, the Russian default crisis in 1998, and of course the financial crisis of 2008 to 2009, were all characterized by sharply reduced or completely evaporated liquidity. Major illiquidity crises have occurred at least once every ten years.

Illiquid Asset Return Biases

• The true illiquid asset losses are usually greater than the reported ones, i.e., illiquid asset returns are not the ‘actual’ returns. Three key biases cause people to overstate expected returns and understate the risk of illiquid assets:
  • Survivorship bias
  • Infrequent sampling
  • Selection bias

    Hence, in illiquid asset markets, investors must be highly skeptical of reported returns.

Illiquid Asset Return Biases – Survivorship Bias

• Survivorship bias results from the tendency of poorly performing funds to stop reporting. Many of these funds ultimately fail – but we only rarely count their failures. This makes true illiquid asset returns worse than the reported data. Surviving funds in illiquid asset management are like people who smoke too much but are lucky enough to survive. We observe the returns of surviving funds precisely because they are still around, and they are generally above average. All of the unlucky illiquid managers disappear and thus stop reporting returns. Of course, these non-survivors have below-average returns, which are not included in the analysis. This produces reported returns of these illiquid assets that are “too good to be true”.
• There are data biases other than survivorship bias: for funds specializing in very illiquid assets, reporting returns to database vendors is almost always voluntary. This introduces reporting biases. Survivorship bias results when your fund is in the database now and you stop reporting returns because you know your returns are going to be low. Reporting bias also occurs when you don’t start reporting your returns in the first place because your fund never achieves a sufficiently attractive track record.
• The only way to completely remove the effect of survivorship bias is to observe the entire population of funds. Unfortunately, in illiquid asset markets, we never observe the full universe.
• We can gauge the impact of survivorship bias with mutual funds – which are quite liquid. Studies show mutual fund returns are 1% to 2% lower than reported and returns may be as much as 4% lower for illiquid asset markets.

Illiquid Asset Return Biases – Infrequent Sampling

• With infrequent trading, estimates of risk – volatilities, correlations, and betas – are too low when computed using reported returns. To illustrate the effect of infrequent trading, consider this figure which plots prices of an asset that starts at $1. Each circle denotes an observation at the end of each quarter. The prices appear to be drawn from a series that does not seem excessively volatile; the standard deviation of quarterly returns computed using the prices is 0.23.
  
  
• The true daily returns for the same asset are plotted in this figure. These are much more volatile than the ones in Panel B. Prices go below 0.7 and above 3.0 in Panel B with daily sampling, whereas the range of returns in Panel A is between 1.0 and 2.5 with quarterly sampling. The volatility of quarterly returns, computed from (overlapping) daily data this figure is 0.28, which is higher than the volatility of quarterly-sampled returns of 0.23 in the previous figure
• For a full comparison, this figure plots both the quarterly and daily sampled returns and just overlays both figures in one picture. Infrequent sampling has caused the volatility estimate using the quarterly sampled returns to be too low. The same effect also happens with betas and correlations – risk estimates are biased downward by infrequent sampling.
  

UNSMOOTHING RETURNS

• The quarterly observed returns are too smooth, and we need to tease out the true, noisier returns. This process is called unsmoothing or de-smoothing. Unsmoothing is a filtering problem. Filtering algorithms are normally used to remove noise from signal. The key difference is that unsmoothing adds noise back to the reported returns to uncover the true returns.
• The unsmoothing process has several important properties:
  • Unsmoothing affects only risk estimates (e.g., volatility) and not expected returns (This is a point I’m totally convinced about, but there is some hint of inconsistency in the GARP book regarding this, and feel that Schweser has interpreted it wrongly and chosen the wrong side of that inconsistency by writing that it affects both risk and return estimates)
  • Unsmoothing has no effect if the observed returns are uncorrelated.
  • Unsmoothing is an art, as it requires good statistical skills along with underlying economic knowledge of the structure of the illiquid market to interpret what is a reasonable lag structure and to judge how much unsmoothing is required.
• Sample selection bias results from the tendency of returns only to be observed when underlying asset values are high. For example – Buildings tend to be sold when their values are high, otherwise, many sellers postpone sales until property values recover. This causes more transactions to be observed when the underlying real estate values are high.
• In private equity, selection bias is acute. In buyout funds, companies are taken public only when stock values are high. Many venture capital investments are structured over multiple rounds. Better-performing companies tend to raise more money in more rounds. The venture capitalist tends to sell a small company, and the transaction is recorded, when the company’s value is high. Distressed companies are usually not formally liquidated, and these “zombie” companies are often left as shell companies. When observing old companies without recent transactions, it is not clear whether these companies are alive and well or whether they are zombies.

Illiquid Asset Return Biases – Selection Bias

• To illustrate the selection bias problem, consider this figure which shows the full universe of returns of an illiquid asset marked by dots. These returns (on they-axis) are plotted contemporaneous with market returns (on the x-axis). In the full universe, there is no alpha, and the intercept of the line summarizing the relationship between the illiquid asset and the market goes through the origin. This line is called the security market line (SML) whose slope is the beta of the illiquid asset and is a measure of risk.
  
• This figure illustrates the sample selection problem. Bad returns, which are below the X- Axis, are not observed in the databases i.e., we record transactions only when prices are high. An estimated SML fitted to these observed returns yields a positive alpha when the true alpha is zero. The slope of the fitted SML is flatter than the slope of the true SML in the previous figure, and hence we underestimate beta. When we compute the volatility of the observed returns, we only count those returns that are high, and so the volatility estimate is biased downward. Thus, we overestimate expected return, and we underestimate risk as measured by beta and volatility.
  
• The effect of selection bias can be enormous. According to an estimation, expected returns for the same asset class are reduced downwards by 2% to 5% per month (arithmetic returns) when selection bias is taken into account. Another study estimates an alpha of more than 90% for venture capital log returns. However, alpha falls to —7% after correcting for sample selection bias.
• The effect of selection bias in real estate is smaller, perhaps because the underlying volatility of real estate returns is lower than private equity.
• Overall, sample selection bias results in overestimated expected returns and underestimated risk as measured by beta and the standard deviation of returns (i.e., volatility).

Illiquidity Risk Premiums

• Illiquidity risk premiums compensate investors for the inability to access capital immediately. They also compensate investors for the withdrawal of liquidity during illiquidity crises.
• There are four ways an asset owner can capture illiquidity premiums:
  • By setting a passive allocation to illiquid asset classes, like real estate
  • By choosing securities within an asset class that are more illiquid, that is by engaging in liquidity security selection
  • By acting as a market maker at the individual security level (described next)
  • By engaging in dynamic strategies at the aggregate portfolio level (described later)
• Economic theory states that there should be a premium for bearing illiquidity risk, although it can be small. In models where illiquidity risk has small or no effect on prices, illiquidity washes out across individuals. A particular individual may be affected by illiquidity – illiquidity can crimp his consumption or affect his asset holdings (as in the asset allocation model with illiquidity risk that I present below) – but other agents will not be constrained, or they trade at different times. Different agents share risk among themselves, which mutes the impact of illiquidity. Thus, in equilibrium, the effects of illiquidity can be negligible

Harvesting Illiquidity Premiums – Market Making

• A market maker supplies liquidity by acting as an intermediary between buyers and sellers. Liquidity provision is costly. Market makers need capital to withstand a potential onslaught of buy or sell orders. In compensation for these costs, market makers buy at low prices and sell at prices around “fair value.” Investors transacting with the market maker pay the bid-ask spread.
• In liquid stock and bond markets, market making is now synonymous with high-frequency trading by investors who build massive computer infrastructure to submit buy and sell orders within fractions of a second. More than 70% of dollar trading volume on U.S. equity exchanges is believed due to high- frequency traders. Many successful hedge funds specialize in high-frequency trading.
• Large asset owners, like sovereign wealth funds and large pension funds, are in a position to act as liquidity providers, especially in more illiquid markets. They can accept large blocks of bonds, shares, or even portfolios of property at discount and sell these large blocks at premiums. Buyers and sellers will come to them as they develop reputations for providing liquidity.
• A market maker faces a risk that a buyer has nonpublic information, and the stock is selling at a price that is too high or too low relative to true, fundamental value. A buyer knowing that the stock will increase in value will continue to buy and increase the price. In this case, the market maker has sold too early and too low. This is adverse selection.

Illiquidity Risk Premiums Across Asset Classes

• This figure is from Antti IImanen’s (2011) book, Expected Returns, and plots average returns on illiquidity estimates. The average returns are computed from (reported) data over 1990 to 2009. The illiquidity estimates represent IImanen’s opinions. Some private equity investments are more liquid than certain hedge funds, and some infrastructure investments are much less liquid than private equity, so it is hard to pigeonhole these asset classes in terms of illiquidity. Nevertheless, this figure seems to suggest a positive relation between how illiquid an asset class is and its expected return.
  
• The previous figure represents “conventional” views among most market participants that there is a reward to bearing illiquidity across asset classes. This view is flawed for the following reasons:
  • Illiquidity biases – As discussed, reported data on illiquid assets cannot be trusted. The various illiquidity biases result in the expected returns of illiquid asset classes being overstated using raw data.
  • Ignores risk – Illiquid asset classes contain far more than just illiquidity risk. Adjusting for these risks makes illiquid asset classes far less compelling. Chapter 3 showed that the NCREIF real estate index (despite the artificial rosiness of its raw returns) is beaten by a standard 60% equity and 40% bond portfolio. The average hedge fund and private equity fund, respectively, provide zero expected excess returns. In particular, after adjusting for risk, most investors are better off investing in the S&P 500 than in a portfolio of private equity funds.
  • There is no “market index” for illiquid asset classes – No investor receives the returns on illiquid indexes. An asset owner never receives the NCREIF return on a real estate portfolio, for example. The same is true for most hedge fund indexes and private equity indexes. In liquid public markets, large investors can receive index market returns and pay close to zero in fees. In contrast, NCREIF is not investable as it is impossible to buy all the underlying properties in that index. Since all asset owners own considerably fewer properties than the thousands included in NCREIF, they face far more idiosyncratic risk. While this large amount of idiosyncratic risk can boost returns in some cases, it can also lead to the opposite result. Returns to illiquid asset investing can be far below a reported index.
  • You cannot separate factor risk from manager skill – Tradeable and cheap index funds in bond and stock markets allow investors to separate systematic returns from management prowess. In illiquid markets, no such separation is possible: investing in illiquid markets is always a bet on management talent. The agency issues in illiquid asset markets are first- order problems. Agency problems can, and often do, overwhelm any advantages that an illiquidity risk premium may bring.

Illiquidity Risk Premiums Within Asset Classes

• While there do not seem to be significant illiquidity risk premiums across classes, there are large illiquidity risk premiums within asset classes.
• Within all the major asset classes, securities that are more illiquid have higher returns, on average, than their more liquid counterparts. These illiquidity premiums can be accessed by dynamic factor strategies which take long positions in illiquid assets and short positions in liquid ones. As illiquid assets become more liquid, or vice versa, the investor rebalances.

Illiquidity Risk Premiums Within Asset Classes – US Treasures

• A well-known liquidity phenomenon in the U.S. Treasury market is the on-the-run/off-the-run bond spread. Newly auctioned Treasuries (which are “on the run”) are more liquid and have higher prices, and hence lower yields, than seasoned Treasuries (which are “off the run”). The spread between these two types of bonds varies over time reflecting liquidity conditions in Treasury markets.
• There were pronounced illiquidity effects in Treasuries during the 2008 to 2009 financial crisis. Treasury bonds and notes are identical, except that the U.S. Treasury issues bonds with original maturities of twenty to thirty years, and notes originally carry maturities of one to ten years. But after ten years, a Treasury bond originally carrying a twenty-year maturity is the same as a Treasury note. If the maturities are the same, whether this particular security is a bond, or a note should make no difference. During the financial crisis, Treasury bond prices with the same maturity as Treasury notes had prices that were more than 5% lower – these are large illiquidity effects in one of the world’s most important and liquid markets.

Illiquidity Risk Premiums Within Asset Classes – Corporate Bonds

• Corporate bonds that trade less frequently or have larger bid-ask spreads have higher returns. In 2007, researchers observed that illiquidity risk explains 7% of the variation across yields of investment-grade bonds. Illiquidity accounts for 22% of the variation in junk bond yields; for these bonds, a one basis point rise in bid-ask spreads increases yield spreads by more than two basis points.

Illiquidity Risk Premiums Within Asset Classes – Equities

• There are several variables related to illiquidity that are shown to impact equity returns. Studies indicate that less liquid stocks earn higher returns than more liquid stocks.
• Illiquidity factors that impact equity returns are:
  • Bid-ask spreads.
  • Volume.
  • Turnover.
  • Volume measured by whether the trade was initiated by buyers or sellers.
  • Ratio of absolute returns to dollar volume, called the “Amihud measure.”
  • Price impact of large trades.
  • Informed trading measures (i.e., adverse selection).
  • Quote size.
  • Quote depth.
  • Frequency of trades.
  • Number of “zero” returns (in liquid markets returns are usually not zero).
  • Return autocorrelations (which are a measure of stale prices).
• These are all illiquidity characteristics, which are properties unique to an individual stock. There are also illiquidity risk betas. These are covariances of stock returns with illiquidity measures, like market illiquidity or signed volume. Researchers estimate illiquidity risk premiums at 1% to 8% depending on the illiquidity measure used. Some reports suggest that these equity illiquidity premiums have diminished considerably – for some illiquidity measures the risk premiums are now zero! In pink sheet stock markets, which are over-the-counter equity markets, illiquidity risk premium is almost 20% compared to about 1% for comparable listed equities.

Illiquidity Risk Premiums Within Asset Classes – Illiquid Assets

• There are higher returns to hedge funds that are more illiquid, in the sense that they place more restrictions on the withdrawal of capital (called lockups) or for hedge funds whose returns fall when liquidity dries up. Franzoni, Nowak, and Phalippou (2012) report that there are significant illiquidity premiums in private equity funds – typically 3%. In real estate, Liu and Qian (2012) construct illiquidity measures of price impact and search costs for U.S. office buildings. They find a 10% increase in these illiquidity measures leads to a 4% increase in expected returns.

Illiquidity Risk Premiums Within Versus Across Asset Classes

• We are yet to develop formal equilibrium models explaining the large illiquidity risk premiums within asset classes but not across asset classes because of limited integration across asset classes. There are significant impediments to switching capital and investment strategies seamlessly even across liquid stock and bond markets. Investors put asset classes into different silos and rarely treat them consistently as a whole. This happens on both the sell-side, where fixed income, equity desks, and other divisions rarely talk with each other, and on the buy-side, where each asset class is managed by separate divisions. (Canada Pension Plan’s factor investing strategy is a notable exception to this.) The potential mispricing of illiquidity across asset classes could reflect institutional constraints, slow-moving capital, and limits to arbitrage.
• On the other hand, perhaps asset class illiquidity risk premiums might be small because investors overpay for illiquid asset classes; they chase the illusion of higher returns and bid up the prices of these illiquid assets until the illiquidity premiums go away. Lack of integrated asset class markets cause investors to make ill-informed decisions for illiquid asset classes. In contrast, within asset classes – especially the more liquid stock and bond markets – illiquidity- shy investors are willing to pay for the privilege to trade as soon as they desire. As investors compete within an asset class, they covet and pay up for liquidity.
• Exchanges for secondary transactions in hedge funds and private equity have sprung up, but these markets are still very thin. Many transactions do not take place on organized secondary market platforms.
• There are two forms of secondary markets in private equity.
  • First, in secondary (and tertiary) market buyout markets, private equity firms trade private companies with each other. These markets have blossomed: in 2005, secondary buyouts represented around 15% of all private equity buy-out deals. From the perspective of asset owners (limited partners [LPs]), this market provides very limited exit opportunities from the underlying private equity funds.
  • Secondary markets for LPs, which allow them to exit from private equity funds, are much smaller, more opaque, and still remain relatively immature. Bid-ask spreads in these transactions are enormous. The secondary market for LPs was dominated in the 1990s by distressed sellers. Specialized firms on the other side of these deals got discounts of 30% to 50%; there was a reason these firms were called “vultures.” In the 2000s, discounts fell to below 20% but shot up during the financial crisis. Harvard University found this out when it tried to disinvest in private equity funds during 2008 and faced discounts of 50%.

Stationary Markets For Hedge Funds And Private Equity

• Discounts for hedge funds are much smaller than private equity. This reflects the fact that hedge fund investors can, in most cases, access capital at predetermined dates after lockups have expired and notice requirements have been satisfied (unless the hedge fund imposes gates). Reflecting this greater underlying liquidity, hedge fund discounts in secondary markets in 2007 and 2008 were around 6% to 8%. (A few hedge funds that are closed to new investors actually trade at premiums.)
• The nascent secondary markets for private equity and hedge funds are tremendous opportunities for large asset owners to supply liquidity. Secondary private equity is like second- hand cars that are still brand new. When you drive a new car off the lot, it immediately depreciates by a quarter, even though it is exactly the same as a car sitting in the dealer’s inventory. Secondary private equity is still private equity, and you can get it a lot cheaper than direct from the dealer.

Portfolio Choice With Illiquid Assets

• In deciding on how much of their portfolios to devote to illiquid assets, investors face many considerations specific to their own circumstances. Investors have different horizons. Illiquid markets don’t have tradeable indices, so investors have to find talented active portfolio managers. Then they face agency issues and evaluating, and monitoring portfolio managers requires skill. Thus, the premium for bearing illiquidity risk might be individual-specific. Computing these illiquidity premiums requires asset allocation models with liquid and illiquid assets. These models also prescribe an optimal amount of illiquid assets to hold.
• The fact that you cannot trade an illiquid asset now but will do so in the future makes illiquid asset investing a dynamic, long-horizon problem. There are two important aspects of illiquidity
  • large transaction costs
  • long times between trading (infrequent trading)

Asset Allocation With Transaction Costs

• George Constantinides (1986) was the first to develop an asset allocation model where the investor had to pay transaction costs. Selling $100 of equities, for example, results in a final position of $90 with 10% transactions costs. The investor trades infrequently to save on transactions costs.
  • Constantinides proved that the optimal strategy is to trade whenever risky asset positions hit upper or lower bounds. Within these bounds is an interval of no trading. The no- trading band straddles the optimal asset allocation from a model that assumes you can continuously trade without frictions. The no-trade interval is a function of the size of the transaction’s costs and the volatility of the risky asset.
  • Constantinides estimates that for transactions costs of 10%, there are no-trade intervals greater than 25% around an optimal holding of 25% for a risky asset with a volatility of 35%. That is, the asset owner would not trade between (0%, 50%) – indeed, very large fluctuations in the illiquid asset position. Illiquid asset investors should expect to rebalance very infrequently.
  • Constantinides’ model can be used to compute an illiquidity risk premium, defined as the expected return of an illiquid asset required to bring the investor to the same level of utility as in a frictionless setting. This is the risk premium the investor demands to bear the transactions costs and is a certainty equivalent calculation. For transaction costs of 15% or more, the required risk premium exceeds 5%. Compare this value with (the close to) zero additional excess returns, on average, of the illiquid asset classes in data.
• A major shortcoming of the transaction costs models is that they assume trade is always possible by paying a cost. This is not true for private equity, real estate, timber, or infrastructure. Over a short horizon, there may be no opportunity to find a buyer. Even if a counterparty can be found, one needs to wait for due diligence and legal transfer to be completed and then the counterparty can get cold feet. Many liquid assets also experienced liquidity freezes during the financial crisis where no trading (at any price) was possible because no buyers could be found.

Asset Allocation With Infrequent Trading

• Illiquidity risk causes the investor to behave in a more risk-averse fashion toward both liquid and illiquid assets. Illiquidity risk induces time-varying, endogenous risk aversion. Harvard discovered in 2008 that although it is wealthy, it cannot “eat” illiquid assets. Illiquid wealth and liquid wealth are not the same; agents can only consume liquid wealth. Thus, the solvency ratio of illiquid to liquid wealth affects investors’ portfolio decisions and payout rules – it becomes a state variable that drives investors’ effective risk aversion.
• The following are the major impacts of infrequent trading on asset allocation:
  
  • Illiquidity Reduces Optimal Holdings – The optimal holding of an asset largely depends upon liquidity associated with it. If liquidity is higher, the optimal allocation is greater. This table shows the optimal rebalancing value of an asset as a percentage of the portfolio with respect to its average turnover.
    
  • Rebalance Illiquid Assets to Positions below the Long-Run Average Holding – In the presence of infrequent trading, illiquid asset wealth can vary substantially and is right-skewed. Suppose the optimal holding of illiquid assets is 0.2 when the liquidity event arrives. The investor could easily expect illiquid holdings to vary from 0.1 to 0.35, say, during non-rebalancing periods. Because of the right-skew, average holding of illiquid asset is 0.25, say, and is greater than optimal rebalanced holding. The optimal trading point of illiquid assets is lower than the long-run average holding.
  • Consume Less with Illiquid Assets – Payouts, or consumption rates, are lower in the presence of illiquid assets than when only comparable liquid assets are held by the investor. The investor cannot offset the risk of illiquid assets declining when these assets cannot be traded. This is an unhedgeable source of risk. The investor offsets that risk by eating less.
  • There Are No Illiquidity “Arbitrages” – In a mean-variance model, two assets with different Sharpe ratios and perfect correlations produce positions of plus or minus infinity. This is a well- known bane of mean-variance models, and professionals employ lots of ad hoc fixes, and arbitrary constraints, to prevent this from happening. This does not happen when one asset is illiquid—there is no arbitrage. Investors do not load up on illiquid assets because these assets have illiquidity risk and cannot be continuously traded to construct an “arbitrage.”
  • Investors Must Demand High Illiquidity Hurdle Rates – This table gives the premiums on an illiquid asset required by an investor to bear illiquidity risk. The more frequently the asset is traded, the lower the premium. For example, one study indicates that private equity investments generate returns 6% higher than public markets to compensate investors for illiquidity. Let’s define the illiquidity premium, or hurdle rate, as a certainty equivalent. Suppose an investor holds two liquid assets and replaces one asset with another that is identical except for being illiquid. The illiquidity premium is the increase in the expected return of the illiquid asset so that the investor has the same utility as the case when all assets are liquid. When liquidity events arrive every six months, on average, an investor should demand an extra 70 basis points. (Some hedge funds have lockups around this horizon.) When the illiquid asset can be traded once a year, on average, the illiquidity premium is approximately 1%. When you need to wait ten years, on average, to exit an investment, you should demand a 6% illiquidity premium. That is, investors should insist that private equity funds generate returns 6% greater than public markets to compensate for illiquidity. Most illiquid assets are not generating excess returns above these hurdle rates.