### Illiquid Assets

The aim of this chapter is to undertake an evaluation of the features of illiquid markets. The relationship between illiquidity and market imperfections will be examined. The chapter further goes ahead to conduct an assessment of the effect of biases on illiquid assets’ reported returns.

Furthermore, the unsmoothing of returns and its properties will be described. There will also be a comparison of illiquidity risk premiums across and within all categories of assets. Finally, we will look at the choice of portfolio decisions concerning the inclusion of illiquid assets.

# Liquidating Harvard

The plunge of asset prices in the Harvard University’s endowment, due to the financial meltdown of 2008, came to a surprise to many. This was the worst ever recorded decline suffered by Harvard’s endowment, contrary to its 15% average annual returns since 1980. Within three months, a whopping over $8 billion in value had been wiped out. An alarm was raised to the Council of Deans by the President and Executive Vice President due to the impending budget shortfall as a result of the collapse of the endowment. Each school had to cut expenses and compensations and their ambitions scaled back in the midst of reduced revenues. A large share (over a third) of the university’s expenses was covered by earnings from the endowment. One of the early adopters of the endowment model was the Harvard Management Company (HMC). The model recommends that lots of illiquid, alternative assets should be held by long-term investors. The basis of this model was the concept of diversification that was originally attributed to Harry Markowitz. The risk-return trade-off of a portfolio with many assets that have a low correlation, with diversification, is superior as compared to that of conventional portfolios made up of only bonds and stocks. According to the theory, there was a limited potential for making excess returns in liquid markets. Similar to venture capital and private equity, there were large potential payoffs in illiquid asset markets for investors whose management and research skills were superior. It would appear that university endowments had an advantage in illiquid assets due to their longer-term horizons as compared to short-term fund managers. For long-term institutions whose resources are sufficient and has the ability to select expert asset managers, superior risk-adjusted returns could be achieved by illiquid assets. 55% of HMC’s portfolio was held in hedge funds, private equity, and real assets in 2008. A further 30% was in developed-world equities and fixed income and the remaining 15% in equities of emerging-markets and high-yield bonds. Desperation for cash led HMC to attempt selling its$1.5 billion private equity portfolio. However, huge discounts were demanded by buyers in secondary markets.

# Illiquid Asset Markets

## Sources of Illiquidity

The following taxonomy was provided by Vayanos and Wang on how illiquidity arises as a result of market imperfections:

1. Effects of clientele and costs of participation: Only certain types of investors are able to transact in most large illiquid markets since they have sufficient capital, expertise, and experience.
2. Costs of transaction: They are made up of commissions, taxes, the expense of due diligence (for some illiquid assets), and the bread-and-butter costs incurred for trading. Other fees are paid to lawyers, accountants, and investment bankers.
3. Search frictions: Most assets may require you to search to find an appropriate buyer or seller, and this is possible only for some investors with the expertise to value complicated structured credit products.
4. Asymmetric information: Illiquidity in the market may arise due to an investor having superior knowledge in comparison to others. The other investors, therefore, become reluctant to trade due to the fear of being fleeced.
5. Price impact: Markets are usually moved by large trades.
6. Funding constraints: There is high leverage on most of the investment vehicles applied when investing in illiquid assets. Transaction in illiquid asset markets becomes hard for investors when access to credit is impaired.

## Characteristics of Illiquid Markets

Some level of illiquidity has often been witnessed in all markets although the level of illiquidity varies across assets. The manifestation of illiquidity is usually as infrequent trading, small amounts being traded, and low turnover.

1. Most asset classes are illiquidLong periods between trades, sometimes extending to decades with very low turnover, is a common characteristic of most asset markets. The only exception is plain-vanilla equities and fixed income. For institutional infrastructures, the average holding period can be fifty years or longer. This infrequent trading and low turnover is the cause of illiquidity for most asset markets.
2. Illiquid asset markets are largeThe large size of illiquid asset classes rivals the size of the public equity market. As compared to the total wealth held in illiquid assets, the traditional public, liquid markets of stocks and bonds are smaller.
3. Investors hold lots of illiquid assetsThe portfolios of most investors are dominated by illiquid assets. 90% of the total wealth, for most individuals, is illiquid assets and mostly tied up in their house – and this does not include the largest and least liquid component of their wealth, human capital.
4. Liquidity dries upPeriodically, many apparent liquid asset markets drift to illiquidity. At least once in every decade, major illiquidity crises have been witnessed, most in tandem with large downturns in asset markets.

## Illiquid Asset Reported Returns are not Returns

Investors should be highly skeptical of reported returns in illiquid asset markets, because of the following biases:

1. Survivorship bias
2. Infrequent sampling
3. Selection bias

## Survivorship Bias

The tendency of poorly performing funds to stop reporting leads to the survivorship bias. Ultimately, most of these funds will fail, although their failures are rarely counted. Therefore, as compared to the reported data, the true illiquid asset returns are worse due to this fact.

In illiquid asset management, the returns of surviving funds are observed because they are still around and generally, they are above average, while all the unlucky illiquid managers disappear and hence stop reporting returns.

Observing the entire population of funds is the only way to completely eradicate the impact of the survivorship bias. However, it is impossible to observe the full universe of funds in the illiquid asset markets.

Mutual funds are used to gauge the effect of survivorship bias. Since they fall under the 1940 Investment Act, these funds are required to report their returns to the Securities and Exchange Commissions. This way, we can see the whole universe of mutual funds, at least when the funds are registered, and to calculate the impact of survivorship.

Furthermore, when one fails to start reporting their returns in the first place since their funds never achieve a sufficiently attractive track record, the reporting bias occurs.

When calculated using reported returns, risk estimates (volatilities, correlations, and betas) are too low, with infrequent trading.

If prices of an asset starting at one dollar are plotted in a panel with each circle denoting an observation at the end of each quarter, one sample path where prices have gone up and then down can be chosen to reflect the happenings in equity during the 2000s’ Lost Decade.

It can be observed that infrequent sampling causes the volatility estimates to be too low, using the quarterly sampled returns. A similar effect is observed with betas and correlations, where infrequent sampling causes a downward bias in risk estimates.

# Unsmoothing Returns

We need to go from a panel that samples quarterly to one that samples daily returns in order to account for the infrequent trading bias. This is because quarterly observed returns are too smooth, hence the need to tease out the true, noisier returns. This is the unsmoothing or de-smoothing process.

Unsmoothing can be termed as a filtering problem. Normally, the filtering algorithm is used to separate signals from noise. To uncover the true returns, unsmoothing will add the noise back to the reported returns.

Let’s denote the true return at the end of the period $$t$$ as $${ r }_{ t }^{ \ast }$$, which is unobservable. Let the observable returns follow:

$${ r }_{ t }^{ \ast }=c+\emptyset { r }_{ t-1 }^{ \ast }+{ \varepsilon }_{ t },\quad \quad \quad \quad \quad \left( I \right)$$

Where the autocorrelation parameter is given as $$\emptyset$$, and in absolute value is less than one. This equation is an autoregressive (AR) process and the “1” implies that the autocorrelation effects are captured in one lag.

The equation can be used to invert out the true returns in the event that the observed returns are functions of current and lagged true returns – transfer function or observation equation.

If only the averaging returns for this period and the past period are involved in the smoothing process, the observe returns can be filtered to estimate the true returns, $${ r }_{ t }$$, from observed returns, $${ r }_{ t }^{ \ast }$$, via the following relation:

$${ r }_{ t }=\frac { 1 }{ 1-\emptyset } { r }_{ t }^{ \ast }-\frac { \emptyset }{ 1-\emptyset } { r }_{ t-1 }^{ \ast }\quad \quad \quad \quad \left( II \right)$$

The observed returns are unsmoothed by equation $$\left( II \right)$$. The equation should have a zero correlation in case the assumption on the transfer function is right. As compared to the observed returns, the variance of the true returns is higher:

$$var\left( { r }_{ t } \right) =\frac { 1+\emptyset ^{ 2 } }{ 1-\emptyset ^{ 2 } } var\left( { r }_{ t }^{ \ast } \right) ,$$

Therefore, the unsmoothed return at time $$t$$, $${ r }_{ t }^{ \ast }$$, is a weighted average of the unsmoothed, or return at $$t$$, $${ r }_{ t }^{ \ast }$$ and $${ r }_{ t-1 }^{ \ast }$$ (the lagged unsmoothed return in the previous period).

The following are crucial features of the unsmoothing process:

1. Only risk estimates are affected by unsmoothing and not expected returns.The first and last price observations are only necessary for mean estimation. The shock is spread over several periods, through smoothing, but all the shocks are still counted.
2. In case the observed returns are uncorrelated, unsmoothing has an effect.Since illiquid asset values are appraised in most cases, reported illiquid asset returns are auto-correlated. Smoothing is induced by the appraisal process as appraisers apply both the most recent and comparable sales. Furthermore, more shady aspects of subjective valuation procedures are as a result of autocorrelation. In most cases, it is expected that there is autocorrelation in true illiquid asset returns. Persistent return is a characteristic of informationally inefficient markets whose capital is slow-moving.
3. Unsmoothing is an artTo describe reported returns, the unsmoothing in equations $$\left( I \right)$$ and $$\left( II \right)$$ applies the simple possible auto-correlated process, an AR(I). More than first-order lag effects are observed in many illiquid assets. A time-series model that properly fits the reported return data with a general transfer function assumption is normally applied in an unsmoothing procedure that is considered good.

## Selection Bias

The tendency of returns to be observed only when there are high underlying asset values leads to the sampling selection bias. There is an acute selection bias in private equity. Companies are only taken out when stock values are high in private equity. The structure of most venture capital investments is over multiple rounds.

Many rounds are involved by better-performing firms to raise money. There is a tendency, by many venture capitalists, to sell a small company and record the transaction when the value of the company is high.

James Heckman developed the statistical methodology for addressing the selection bias. The threshold above which returns are observed is allowed to vary over time depending on the company or property-level characteristics.

Sometimes, the model of risk is extended to multifactor models as opposed to just applying the market portfolio as the sole risk factor. There can be enormous selection bias effects. Due to the low underlying volatility of real estate returns as compared to private equity, in real estate, the impact of selection bias can be lower.

Investors are compensated by illiquidity risk premiums for the inability to immediately access capital. Investors are also compensated for the withdrawal of liquidity during illiquidity crises.

The following are the ways through which illiquidity premiums can be captured by asset owners.

1. A passive allocation should be set to illiquid asset classes, e.g., real estate;
2. Securities should be chosen within asset classes that are more illiquid by engaging in liquidity security selection;
3. The asset owner can be a market maker at the individual security level; and
4. At the aggregate portfolio level, the asset owner should engage in dynamic strategies.

According to economic theory, there should be a premium for bearing illiquidity risk, although it can be small. Illiquidity washes across individuals in models where illiquidity risk has small or no effect on prices. There can be negligible effects of illiquidity at equilibrium.

## Illiquidity Risk Premiums across Asset Classes

Conventional views among market participants may be flawed due to the following reasons:

1. Illiquidity biases: It is almost impossible to trust reported data on illiquid assets;
2. Ignoring risks: Since illiquid asset classes contain more than just liquidity risk, adjusting for all of the risks makes illiquid asset classes far less compelling.
3. Lack of market index for illiquid asset classes: There are no real illiquid indexes investors can track.
4. Factor risk cannot be separated from a manager skill: Investors are allowed to separate systematic returns from the management process through tradable and cheap index funds in bond and stock markets. However, in illiquid asset markets, it is impossible to have such a separation, since investing in illiquid markets is always a bet on management talent.

## Illiquidity Risk Premiums within Asset Classes

More illiquid securities within all the major asset classes have higher returns as compared to their liquid counterparts. The dynamic factor strategies that can be applied in the accessing of these illiquidity premiums should take long positions in illiquid assets and short positions in liquid ones.

## U.S. Treasuries

The on-the-run/off-the-run bond spread is a well-known illiquidity phenomenon in the U.S. Treasury market. As compared to the seasoned Treasuries, there is more liquidity and higher prices in newly auctioned Treasuries, and therefore lower yields. Between these two bond types, the spread changes with time reflecting liquidity conditions in Treasury markets.

During the 2008-2009 financial crisis, there were pronounced illiquidity effects in Treasuries. Apart from the fact that the U.S. Treasury issues bonds whose original maturities are twenty to thirty years and the maturity originally carried by loans ranges between one to ten years, Treasury bonds and notes are identical. However, Treasury bond prices with similar maturities as Treasury notes were not priced identically during the financial crisis.

## Corporate Bonds

The returns of corporate bonds that trade less frequently are higher and their bid-ask spreads larger. 7% of the variation across yields of investment-grade bonds is explained by the illiquidity risk.

22% of the variation across junk bond yields is accounted for by illiquidity. For these bonds, a rise of one basis point in the bid-ask spreads leads to a more than two basis points increase in yield spreads.

## Equities

Returns in equity markets are predicted by most illiquidity variables, with less liquid stocks whose returns are higher. These variables are made up of: volume, turnover, bid-ask spreads, the absolute returns to dollar volume ratio, large trades’ price effects, trading measures that are informed, depth and quote size, trade frequency, and many more.

These properties are unique to an individual stock and are all illiquidity characteristics. Illiquidity betas are also a factor, and so are covariances of stock returns with illiquidity measures such as signed volume or market illiquidity.

## Illiquid Assets

Hedge funds that are more illiquid have higher returns as they place more restrictions on the withdrawal of capital or for hedge funds with returns that fall when illiquidity dries up. In private equity funds, the illiquidity is significant – typically 3%. In real estate, a 10% rise in illiquidity risk measures causes an increase in expected returns by 4%.

## Market Making

Illiquidity is supplied by market makers when they act as intermediaries between buyers and sellers. To withstand a potential onslaught of buy or sell orders, market makers need capital. They can be transacting with investors having superior information at any time.

The market makers will purchase at low prices and sell at fair value prices in compensation for these costs. The bid ask-spread is paid by investors who transact with market makers.

By building high-frequency trading systems, illiquidity risk premium cannot be collected by many asset owners. They also won’t wish to join this business. However, large asset owners have a way to do a low-frequency version of market making.

They can act as liquidity providers, particularly in markets that are more liquid. Large blocks of bonds, shares, or portfolios or property can be accepted at discount and sold at premiums. This can be done by computing limits within their constraints on how much they are willing to transact.

## Secondary Markets for Private Equity and Hedge Funds

In private equity, secondary markets are of two forms. First, private equity companies trade private companies in secondary markets. No exit opportunities are provided by this market for the private equity funds, and at worst is a merry-go-round of private equity companies swapping companies in a circular fashion.

At best, asset owners are allowed to better value their illiquid investments by more transactions at market prices. For hedge funds, discounts are much smaller as compared to private equity. In most cases, hedge fund investors can access capital at predetermined dates after the expiry of lockouts.

For large asset owners, the secondary markets are tremendous opportunities to supply liquidity.

Aware that the value of a stock will continue increasing, a buyer will continue to buy and increase the price. This makes the market maker sell too early and too low. This is known as adverse selection.

## Rebalancing

Dynamic portfolio strategies are the last way through which an asset owner can supply illiquidity. The impact of this on the asset owner’s total portfolio can be far larger as compared to liquidity security selection or market making since it happens to be a top-down asset allocation decision.

The simplest way to provide illiquidity is through rebalancing, which includes the foundation of all long-horizon strategies. Asset owners are forced by rebalancing to purchase at low prices when others want to sell. Illiquid asset holdings should also be rebalanced when the chance is given.

For rebalancing to occur, the context must be illiquid markets. However, large declines are often exhibited by prices due to blowouts in asymmetric information, or funding costs rapidly increasing to force investors to offload securities.

Illiquidity premiums are given up by large asset owners when they sheepishly track standard indexes. Liquidity will be demanded by asset owners in the event that indexes change their constituents because they are forced to follow these changes.

# Portfolio Choice with Illiquid Assets

Many considerations faced by investors are specific to their own circumstances in deciding on how much of their portfolios should be devoted to illiquid assets. Investors will have to look for talented active portfolio managers due to the fact that illiquid markets lack tradable indices.

There might be an individual-specific premium for bearing illiquidity risk. Asset allocation models, with liquid and illiquid assets, are requirements in calculating these illiquidity premiums. An optimal portfolio of illiquid assets to be held is also prescribed by these models. The two crucial aspects of illiquidity are large transaction costs and long waiting periods between trades.

## Asset Allocation with Transactions Costs

An asset allocation model where the investor had to pay transaction costs was first developed by George Constantinides. Trading whenever risky asset conditions hit the upper or lower bounds is the optimal strategy. There is an interval of no trading within these bounds.

The optimal asset allocation from a model which assumes that one can continuously trade without frictions is straddled by the no-trading band. Very infrequently, illiquid asset investors should expect to rebalance.

An illiquidity risk premium can be calculated using the Constantinides’ model. Defined as the expected return of an illiquid asset necessitated the investor be brought to a similar level with utility as in a setting that is frictionless.

The assumption that trade is always possible by paying a cost is a major shortcoming of the transaction costs model. During the financial crisis, liquidity freezes were also experienced by most illiquid assets as no trading was possible since buyers could not be found.

## Asset Allocation with Infrequent Trading

Despite the fact that illiquid assets cannot be traded, it is possible for investors to trade in case of an illiquidity event arrives. This arrival is modeled by a Poisson arrival process with intensity $$\lambda$$. $${ 1 }/{ \lambda }$$ is the interval between liquidity events.

Search-based frictions have been modeled using Poisson arrival events. Due to illiquidity risk, the investor behaves in a fashion that is more risk-averse towards both liquid and illiquid assets. Time-varying, endogenous risk aversion is introduced by illiquidity risk.

## Illiquidity Markedly Reduces Optimal Holdings

Supposing a weight is close to the standard 60% equity allocation held by most institutions, the asset becomes more illiquid as we go up in rows.

If an average of six months is the period by which risky assets can be traded, the optimal holding of illiquid asset contingent on the arrival of illiquidity event is 44%. The optimal allocation is 11% when the average intervals between trades are 5 years. This reduces to 5% for ten years.

## Rebalance Illiquid Assets to Positions Below the Long-Run Average Holding

There can substantial variation in the right-skewed illiquid asset wealth in the presence of infrequent trading. As compared to the long-run average holding, there is a lower optimal trading point for illiquid assets.

## Consume Less with Illiquid Assets

In the presence of illiquid assets, consumption rates or payouts are lower when compared to a case whereby the investor only holds comparable liquid assets. The risk of decline in illiquid assets can’t be offset by the investor when these assets cannot be traded. To offset that risk, the investor consumes less.

## There Are no Illiquidity Arbitrages

Positions of plus or minus infinity are often produced by two assets with different Sharpe ratios and perfect correlations, in a mean-variance model.

This well-known bane of mean-variance models is employed by professionals of ad hoc fixes, and arbitrary constraints, to stop this from happening. In case one asset is illiquid, then there is no arbitrage.

## High Illiquidity Hurdle Rates Must be demanded by Investors

Assuming that two liquid assets are held by an investor and one asset is replaced with another identical one apart from illiquid. The increase in the expected return of the liquid asset is the illiquidity premium and is meant for investors to have a similar utility as the case of liquid assets.

An investor should demand an extra 70 basis points in the event liquidity events arrive every six months. The illiquidity premium is approximately 1% in the event that the illiquid asset can be traded once a year. For ten years, an illiquidity premium of 6% should be demanded.

# Practice Questions

1) The process of unsmoothing has some properties that are very crucial. Which of the following is NOT one of the important properties of the unsmoothing process?

1. Unsmoothing is an art
2. If the observed returns are uncorrelated, unsmoothing has no effect
3. Unsmoothing poses illiquidity risk across asset classes
4. Only risk estimates, rather than expected returns, are affected by unsmoothing