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LO 66.7: Determine the optimal no-trade region for rebalancing with transaction costs.
If transaction costs are zero, a manager should revise a portfolio every time new information arrives. However, as a practical matter, a manager should make trading decisions based on expected active return, active risk, and transaction costs. The manager may wish to be conservative because these measures are uncertain. Underestimating transaction costs, for example, will lead to trading too frequently. In addition, the frequent trading and short time horizons would cause alpha estimates to exhibit a great deal of uncertainty. Therefore, the manager must choose an optimal time horizon where the certainty of the alpha is sufficient to justify a trade given the transaction costs.
The rebalancing decision depends on the tradeoff between transaction costs and the value added from changing the position. Portfolio managers must be aware of the existence of a no-trade region where the benefits of rebalancing are less than the costs. The benefit of adjusting the number of shares of a given portfolio asset is given by the following expression:
marginal contribution to value added = (alpha of asset) [2 x (risk aversion) x (active risk)
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Topic 66 Cross Reference to GARP Assigned Reading – Grinold and Kahn, Chapter 14
If this value is between the negative cost of selling and the cost of purchase, the manager would not trade that particular asset. In other words, the no-trade region is as follows:
(cost of selling) < (marginal contribution to value added) < (cost of purchase)
Rearranging this relationship with respect to alpha gives a no-trade region for alpha:
[2 x (risk aversion) x (active risk) x (marginal contribution to active risk)] (cost of selling) < alpha of asset < [2 x (risk aversion) x (active risk) x (marginal contribution to active risk)] + (cost of purchase)
The size of the no-trade region is determined by transaction costs, risk aversion, alpha, and the riskiness of the assets.
P o r t f o l io C o n s t r u c t io n Te c h n iq u e s

LO 66.6: Describe portfolio revisions and rebalancing, and evaluate the tradeoffs between alpha, risk, transaction costs, and time horizon.

LO 66.3: Assess the impact of practical issues in portfolio construction, such as determination of risk aversion, incorporation of specific risk aversion, and proper alpha coverage.
We need a measure of active risk aversion as an input to determine the optimal portfolio. As a practical matter, a portfolio manager does not likely have an intuitive idea of optimal active risk aversion in mind, but will have good intuition about his information ratio (the ratio of alpha to standard deviation) and the amount of active risk (as opposed to active risk aversion) he is willing to accept in pursuit of active returns. An equation that translates those values into a measure of active risk aversion is:
. . information ratio risk aversion = ———- 7—- ;—–
.
2 x active risk
For example, if the information ratio is 0.8 and the desired level of active risk is 10%, then the implied level of risk aversion is:
0.80 2×10
0.04
The utility function for the optimization is: utility = active return (0.04 x variance). Of course, the accuracy of the estimate of active risk aversion is dependent on the accuracy of the inputs, the information ratio, and the preferred level of active risk.
Professors Note: Remember that active risk is just another name for tracking error. Also note that in the risk aversion equation, the desired level o f active risk is measured in percentage points rather than in decimal form.
In addition to active risk aversion, aversion to specific factor risk is important for two reasons. First, it can help the manager address the risks associated with having a position with the potential for large losses. For example, the risk from a portfolio with sector risks that do not match those of the benchmark portfolio. Second, appropriately high risk aversion values for specific factor risks will reduce dispersion (of holdings and performance) across portfolios when the manager manages more than one portfolio. Setting high risk aversion values for factor specific risks will increase the similarity of client portfolios so that they will tend to hold the same assets. Considering these two effects of specific factor risk aversion values will help a manager determine appropriate values to include in portfolio optimization.
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Topic 66 Cross Reference to GARP Assigned Reading – Grinold and Kahn, Chapter 14
Proper alpha coverage refers to addressing situations where the manager has forecasts of stocks that are not in the benchmark or where the manager does not have alpha forecasts for stocks in the benchmark. When the manager has information on stocks not in the benchmark, a benchmark weight of zero should be assigned for benchmarking, but active weights can be assigned to these stocks to generate active alpha.
When there is not an alpha forecast for stocks in the benchmark, adjusted alphas can be inferred from the alphas of stocks for which there are forecasts. One approach is to first compute the following two measures:
value-weighted fraction of stocks with forecasts = sum of active holdings with forecasts
(weighted average of the alphas with forecasts) average alpha for the stocks with forecasts = ————;————- ;——————;————— (value-weighted fraction of stocks with forecasts)
The second step is to subtract this measure from each alpha for which there is a forecast and set alpha to zero for assets that do not have forecasts. This provides a set of benchmark- neutral forecasts where assets without forecasts have alphas of zero.
Po r t f o l io Re v is io n s a n d Re b a l a n c in g

LO 66.4: Describe the implications of transaction costs on portfolio construction.
Transaction costs are the costs changing portfolio allocations, primarily trading commissions and spreads. Transaction costs reduce active portfolio returns relative to those of the benchmark portfolio and are uncertain, although typically less so than alphas. Because of this, transaction costs are an important input into the portfolio optimization process. Including transaction costs in portfolio optimization increases the importance of both precision in estimating alphas and of the choice of scale.
Transaction costs occur at points in time, while the benefits (i.e., additional return) are realized over time. Consider two stocks, one of which will return 2 % over 6 months, at which time it can be replaced by another stock that returns 2 % over 6 months, and another stock which will return 4% over 1 year. Also, assume transaction costs are 1%. The annual returns on the first stock will be approximately (2 % 1%) x 2 = 2 % and the annual returns
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on the second stock will be approximately 4% 1% = 3%. With uncertain holding periods across portfolio holdings, the question arises over what period transaction costs should be amortized. Precision in scale is important in addressing the tradeoff between alphas and transaction costs. .Annual transaction costs will be the cost of a round-trip trade divided by the holding period in years.
P r a c t ic a l Is s u e s

LO 66.3: Describe neutralization and methods for refining alphas to be neutral.
Neutralization is the process of removing biases and undesirable bets from alpha. There are several types of neutralization: benchmark, cash, and risk-factor. In all cases, the type of neutralization and the strategy for the process should be specified before the process begins.
Benchmark neutralization eliminates any difference between the benchmark beta and the beta of the active portfolio. In this case we say the portfolio alpha of the active portfolio is zero. Consider an active portfolio that has a beta of 1.1 when the benchmark portfolio has a beta of 1. This represents an active bet on market (and benchmark portfolio) returns. When market returns are high, the active portfolio will outperform the benchmark portfolio;
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Topic 66 Cross Reference to GARP Assigned Reading – Grinold and Kahn, Chapter 14
when returns are low (less than the risk-free rate) the active portfolio will underperform the benchmark portfolio. The alphas can be adjusted so that the active portfolio beta is the same as the benchmark portfolio beta, unless the manager intends to make an active bet by increasing or decreasing the active portfolio beta relative to that of the benchmark. Matching the beta of the active portfolio to the beta of the benchmark portfolio is referred to as benchmark neutralization. Note that this neutralization is equivalent to adding a constraint on portfolio beta in a mean-variance optimization.
Computing modified benchmark-neutral alpha involves subtracting (benchmark alpha x active position beta) from the alpha of the active position. For example, assume benchmark alpha is equal to 0.013%. If an active position has an alpha of 0.3% and a beta of 1.2, the modified benchmark-neutral alpha will equal: 0.3% (0.013% x 1.2) = 0.48%.
In the explanation, we used a single risk factor, market risk. There may be other risk factors, such as those from a multi-factor returns generating model, that lead to unintended risk exposures relative to the benchmark. For example, consider the risk factor small cap returns minus large cap returns. The alpha inputs may produce an active portfolio with a greater sensitivity to this risk factor if the portfolios weight on small-cap firms is larger than that of the benchmark portfolio. Again, if this is unintended, alphas can be adjusted so that the beta of the active portfolio with respect to this risk factor matches that of the benchmark portfolio.
The active portfolio may also be neutralized with respect to industry risk factors, by matching the portfolio weights of each industry to those of the benchmark portfolio. In this case, subtracting the average alpha for an industry from the alphas of each firm within that industry will result in an active portfolio that is neutral relative to the benchmark with respect to industry risk factors. In each of our examples, neutralization reduces active risk by matching the factor risks of the active portfolio to those of the benchmark portfolio.
An active portfolio can also be made cash neutral, by adjusting the alphas so that the portfolio has no active cash position. Its possible to make the alpha values both cash- and benchmark-neutral.
Tr a n s a c t io n C o s t s

LO 66.2: Evaluate the methods and motivation for refining alphas in the implementation process.
A portfolio can be optimized, based on the inputs, using mean-variance analysis. In most cases there are significant constraints imposed on the asset weights, either by client or manager requirements. A client (or regulations) may prohibit short sales. A manager may impose an upper limit on active risk or on maximum deviations from benchmark weights. As more constraints are introduced, simple mean-variance analysis, maximizing active return minus a penalty for active risk, can become quite complex.
An alternative approach is to adjust the managers estimated alphas (an input into a mean- variance optimization analysis) in ways that effectively impose the various constraints. Consider an account for which short selling is prohibited. Rather than performing an optimization that constrains asset weights to be non-negative, we can use the optimization
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Topic 66 Cross Reference to GARP Assigned Reading – Grinold and Kahn, Chapter 14
equations (in reverse) to solve for the set of alphas that would produce non-negative weights in an unconstrained mean-variance optimization. The optimal weights are moved toward benchmark weights. This method allows us to focus on the effects of a specific constraint on alphas, the key input for active portfolio construction.
Before we examine refining alphas to satisfy other constraints, such as a constraint on the beta of the active portfolio, we consider two techniques that are often employed after refining alphas for various client or manager imposed constraints: scaling and trimming.
An often used equation for alpha is:
alpha = (volatility) x (information coefficient) x (score)
Where volatility refers to residual risk, the information coefficient (IC) measures the linear relationship between the managers forecasted asset alphas and actual asset returns, and score is expected to be approximately normally distributed with a mean of 0 and a standard deviation of 1. Considering that volatility (residual risk) and information coefficient (IC) are relatively constant, we can see that the standard deviation (scale) of portfolio alphas is proportional to the standard deviation of the score variable. Alphas will have a mean of zero and a scale approximately equal to volatility x information coefficient when score follows a standard normal distribution. With an information coefficient of 0.10 and residual risk of 30%, the scale of the alphas will be 0.10 x 30% = 3%; the alphas will have a mean of zero and a standard deviation of 3%.
If we compare the scale (standard deviation) of the refined alphas from our earlier discussion of a prohibition on short sales to the scale of the original unconstrained alphas, we can calculate the decrease in the information coefficient that results from the decrease in the scale of the alphas due to the imposition of the constraint. If the adjusted alphas do not have the appropriate scale, they can be rescaled.
Another refinement to manager alphas is to reduce large positive or negative alpha values, a process called trimming. The threshold for large values might be three times the scale of the alphas. For large alpha values, the reasons supporting these values are re-examined. Any alphas found to be the result of questionable data are set to zero. Additionally, the remaining large alphas may be reduced to some maximum value, typically some multiple of the scale of the alphas.

LO 66.1: Distinguish among the inputs to the portfolio construction process.
The process of constructing an optimal investment portfolio requires several inputs: Current portfolio: The assets and their weights in the current portfolio. Relative to the
other inputs, the current portfolio input can be measured with the most certainty.
Alphas: The expected excess returns of portfolio stocks (relative to their expected returns).
This input is subject to forecast error and bias.
Covariances’. Estimates of covariances are subject to estimation error.
Transaction costs: Transaction costs are estimated and increase as more frequent portfolio changes are made.
Active risk aversion’. Refers to the strength of the preference for lower volatility of the
difference between actively managed portfolio returns and benchmark portfolio returns.

LO 65.6: Evaluate portfolio choice decisions on the inclusion of illiquid assets. * 1
In determining the portfolio allocation to illiquid asset classes, or any asset class for that matter, investors must consider their personal circumstances. The illiquid asset allocation decision is influenced by different investment horizons, the lack of tradeable indices, the need to hire talented active portfolio managers, and the need to monitor those managers. Portfolio choice models that include illiquid assets must consider two important aspects of illiquidity that impact investors: 1. Long time horizons between trades (i.e., infrequent trading).
2. Large transaction costs.
Asset Allocation to Illiquid Asset Classes with Transaction Costs
The primary issue with asset allocation models that include transaction costs is that they assume an asset will always trade if the counterparty pays the transaction cost. However, this is not true in private equity, infrastructure, real estate, and timber markets. It is not (or may not) be possible to find a buyer in a short period of time. Counterparties, if identified, must perform due diligence, which takes time. In some cases, the counterparty, upon completion of due diligence, chooses not to buy the asset. In periods of stress, even liquid asset classes face liquidity freezes and it becomes impossible to find buyers at any price.
Asset Allocation to Illiquid Asset Classes with Infrequent Trading
As anyone trying to sell in a period of illiquidity knows, one cannot eat illiquid assets. Consider the example of Harvard University, briefly described earlier. The only way the university could generate cash for operations in a period of significant losses and illiquidity across what some would consider some of the most liquid assets (i.e., commercial paper and repurchase agreements), Harvard would have had to sell at huge discounts. Only liquid assets can be consumed. As a result, illiquidity has a major effect on investors portfolio choices. Illiquidity causes the following with respect to portfolio choice: Reduces optimal holdings. The less frequently a liquidity event is expected to occur, the
lower the allocation to the illiquid asset class.
Rebalancing illiquid assets (i.e., when there is infrequent trading in the asset class) causes allocations to vary significantly. The investor must wait until the liquidity event arrives. As such, the allocation prior to a liquidity event (or during nonrebalancing periods) can vary from too high to too low relative to the optimal allocation.
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Topic 65 Cross Reference to GARP Assigned Reading – Ang, Chapter 13

Investors cannot hedge against declining values when an asset cannot be traded. As a result, illiquid asset investors must consume less than liquid asset investors to offset the risk.
There are no illiquidity arbitrages. To construct an arbitrage, an asset must be
continuously traded. Illiquid assets are not continuously traded.
Due to infrequent trading, illiquid asset investors must demand an illiquidity risk
premium. 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.
The inclusion of illiquid assets in a portfolio is not as simple or desirable as it might seem. The following points should be considered: 1. Studies show that illiquid assets do not deliver higher risk-adjusted returns.
2.
Investors are subject to agency problems because one must rely on the talents and skills of the manager. It is difficult to monitor external managers (e.g., private equity managers).
3.
In many firms, illiquid assets are managed separately from the rest of the portfolio.
4.
Illiquid asset markets are less efficient than stock and bond markets. Illiquid asset investors face high idiosyncratic risks. There is no market portfolio of illiquid assets. Recall the example of the NCREIF versus the individual investor. It is not possible for most investors to hold thousands of properties, and small numbers of properties can lead to undiversified, property specific risks (but also returns, making illiquid assets compelling to investors). Illiquid assets are compelling because:
There are large information asymmetries in illiquid asset markets. High transaction costs keep many investors out of the market. Management skill is crucial and alpha opportunities are widely dispersed. All of these factors suggest there are great opportunities for the skilled investor to profit from investments in illiquid assets. Investors must have the skills and resources to find, evaluate, and monitor illiquid asset opportunities. Endowments like Harvard, Yale, and Stanford have the skills and resources. Unskilled investors, even those endowments at less sophisticated, skilled, and connected schools, can lose big in illiquid asset markets.
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Topic 65 Cross Reference to GARP Assigned Reading – Ang, Chapter 13
Ke y Co n c e pt s
LO 65.1 There are four main characteristics that describe illiquid asset markets, including: 1. Most asset classes are illiquid, at least to some degree.
2. Markets for illiquid assets are large.
3.
Illiquid assets comprise the bulk of most investors portfolios.
4. Liquidity dries up even in liquid asset markets.
LO 65.2 Market imperfections encourage illiquidity in asset markets. Specifically, market participation costs (i.e., clientele effects) and transaction costs give rise to illiquidity. Some academic models assume that all assets can be traded if one will pay the required (sometimes very high) transaction cost. However, this is not necessarily true in illiquid asset markets. There are search frictions (i.e., difficulties finding a counterparty and information asymmetries), price impacts, and funding constraints that may prevent trades from occurring, no matter how high the transaction cost.
LO 65.3 In general, investors should be skeptical of reported returns in illiquid asset markets as they are generally overstated. There are reporting biases that result in artificially inflated returns. The three main biases that impact reported illiquid asset returns are: 1. Survivorship bias: Poor performing funds often quit reporting results. Also, many poor
performing funds ultimately fail. Finally, some poor performing funds never begin reporting returns because performance is weak. All of these factors lead to survivorship bias. Survivorship bias leads to an overstatement of stated returns relative to true returns.
2. Selection bias: Asset values and returns tend to be reported when they are high. For example, houses and office buildings typically are sold when values are high. These higher selling prices are used to calculate returns. This results in sample selection bias, which again leads to overstated returns.
3.
Infrequent trading: Illiquid assets, by definition, trade infrequently. Infrequent trading results in underestimated risk. Betas, return volatilities, and correlations are too low when they are computed using the reported returns of infrequently traded assets.
LO 65.4 Unsmoothing adds noise back to reported returns to uncover the true, noisier returns. This process affects risk and return estimates and could have a dramatic effect on returns.
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LO 65.5 There is little evidence that there are large illiquidity risk premiums across asset classes. However, there are large illiquidity risk premiums within asset classes.
There are four primary ways that investors can harvest illiquidity premiums: 1. Allocating a portion of the portfolio to illiquid asset classes like real estate. This is
passive allocation to illiquid asset classes.
2 . Choosing more illiquid assets within an asset class. This means engaging in liquidity
security selection.
3. Acting as a market maker for individual securities.
4. Engaging in dynamic factor strategies at the aggregate portfolio level. This means
taking long positions in illiquid assets and short positions in liquid assets to harvest the illiquidity risk premium. Of the four ways investors can harvest illiquidity premiums, this is the easiest to implement and can have the greatest effect on portfolio returns.
LO 65.6 There are several points to consider when deciding to allocate portfolio resources to illiquid assets: 1. Studies show that illiquid assets do not deliver higher risk-adjusted returns.
2.
Investors are subject to agency problems because one must rely on the talents and skills of portfolio managers. It is difficult to monitor external managers.
3.
In many firms, illiquid assets are managed separately from the rest of the portfolio.
4.
Illiquid asset investors face high idiosyncratic risks. There is no market portfolio of illiquid assets. Illiquid assets are compelling because illiquid asset markets are less efficient than stock and bond markets, there are large information asymmetries in illiquid asset markets, high transaction costs keep many investors out of the market, management skill is crucial, and alpha opportunities are widely dispersed.
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Topic 65 Cross Reference to GARP Assigned Reading – Ang, Chapter 13
Co n c e pt Ch e c k e r s
1.
2.
3.
4.
5.
Global liquidity crises generally occur because: A. governments choose not to engage in monetary policy actions to stimulate
economies. financial distress causes markets to freeze.
B. C. markets for illiquid assets shrink, causing liquidity issues to infect traditional
asset classes.
D. transaction costs increase as developing economies get stronger.
When an investor has difficulty finding a counterparty for a complicated credit product like a structured debt instrument, this is known as: A. market participation costs. B. agency costs. C. search frictions. D. selection bias.
Blue Sky Funds, a private equity fund, has suffered low returns for the last five years. As a result, the find has decided to quit reporting returns. The fund did report returns each year for the last 10 years when performance was strong. This problem of reporting leads to: A. survivorship bias. B. sample selection bias. C. D. attrition bias.
infrequent trading bias.
Which of the following variables is not an illiquidity factor that affects equity returns? A. Measures of adverse selection. B. The number of recorded positive returns. C. Turnover. D. Volume.
Rick Faircloth, a general partner and portfolio manager with Faircloth Funds, is considering ways in which his company can profit from illiquidity risk premiums. Fie has studied several alternative methods for harvesting illiquidity risk premiums. Which of the following strategies might Faircloth implement that will likely have the greatest effect on portfolio returns? A. Acting as a market maker for individual securities. B. Choosing the most illiquid assets within an asset class, even if the asset class is
generally considered to be liquid.
C. Allocating a portion of a portfolio to illiquid asset classes. D. Using dynamic factor strategies at the aggregate portfolio level.
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Topic 65 Cross Reference to GARP Assigned Reading – Ang, Chapter 13
Co n c e pt Ch e c k e r An s w e r s
1. B
In stressed economic periods, such as during the 2007-2009 financial crisis, liquidity can dry up. Major liquidity crises have occurred at least once every ten years across the globe, in conjunction with downturns and financial distress.
2. C Difficulties finding a counterparty are called search frictions. For example, it may be difficult to find someone to understand/purchase a complicated structured credit product. It may also be difficult to find buyers with sufficient capital to purchase multimillion dollar office towers in major metropolitan areas. No matter how high the transaction costs, it may take weeks, months, or years to transact in some situations. Asymmetric information can also be a type of search friction as investors search for non-predatory counterparties with which to transact.
3. A There are no requirements for certain types of funds, like private equity funds, to report
returns. As such, poorly performing funds have a tendency to stop reporting. Additionally, many poorly performing funds ultimately fail. Performance studies generally include only those funds that were successful enough to survive over the entire period of analysis, leaving out the returns of funds that no longer exist. Both of these factors result in reported returns that are too high. This is called survivorship bias.
4. B There are several variables related to illiquidity that are shown to impact equity returns. They are bid-ask spreads, volume, turnover, volume measured by whether the trade was initiated by buyers or sellers, the ratio of absolute returns to dollar volume, the price impact of large trades, informed trading measures (i.e., adverse selection), quote size and depth, the frequency of trades, the number of zero returns, and return autocorrelations. It is not the number of recorded positive returns, but the number of recorded zero returns, that are relevant.
5. D There are four primary ways that investors can harvest illiquidity premiums:
1. Allocating a portion of the portfolio to illiquid asset classes like real estate (i.e., passive
allocation to illiquid asset classes).
2. Choosing more illiquid assets within an asset class (i.e., liquidity security selection).
3. Acting as a market maker for individual securities.
4. Engaging in dynamic factor strategies at the aggregate portfolio level. This means
taking long positions in illiquid assets and short positions in liquid assets to harvest the illiquidity risk premium. Of the four ways investors can harvest illiquidity risk premiums, this is the easiest to implement and can have the greatest effect on portfolio returns.
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The following is a review of the Risk Management and Investment Management principles designed to address the learning objectives set forth by GARP. This topic is also covered in:
Po r t f o l i o C o n s t r u c t i o n
Topic 66
Ex a m Fo c u s
This topic addresses techniques for optimal portfolio construction. We will discuss important inputs into the portfolio construction process as well as ways to refine the alpha inputs as an alternative to imposing constraints directly into the portfolio optimization calculations. The role of transaction costs in determining optimal rebalancing is also explained. For the exam, pay attention to the discussions of refining alphas and the implications of transaction costs for both rebalancing and dispersion of returns across separately managed portfolios. Also, be prepared to compare and contrast the various methods of portfolio construction: screening, stratification, linear programming, and quadratic programming.
Th e Po r t f o l io C o n s t r u c t io n Pr o c e s s

LO 65.5: Compare illiquidity risk premiums across and within asset categories.
Illiquidity Risk Premiums Across Asset Classes
As part of the analysis in Antti Ilmanens 2011 book Expected Returns, we can relate liquidity to expected returns as shown in Figure 1. Note, however, that we cannot completely pigeonhole asset classes based on illiquidity (e.g., some private equity funds are more liquid than some hedge funds or infrastructure investments). Also note that, in this analysis, returns are computed over the period 1990 to 2009 and the illiquidity estimates are just estimates (i.e., they represent Ilmanens opinions). Ilmanens work does imply a positive relationship between the illiquidity of an asset class and its expected return. Venture capital is considered the least liquid and has the highest expected return, between 16% and 17%. Buyout funds and timber are also illiquid but command lower expected returns, approximately 13% and close to 12%, respectively. Hedge funds are more liquid and are expected to earn a little more than 12%. Real estate is on par with hedge funds in terms of liquidity but commands a lower return of nearly 8%. Equities are much more liquid and earned a bit more than 4% over the period. Cash is the most liquid and it too earned a little over 4% during the period. 1
1.
Ilmanen, A. (2011). Expected Returns: An Investors Guide to Harvesting Market Rewards. Chichester, West Sussex, U.K.: Wiley.
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Venture Capital
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et Equity

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.
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t
j U.S. Real Estate
Global Sovereigns^ U.S. Fixed Income Infrastructure
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Cash Deposits
Most Liquid
Increasing Illiquidity
Most Illiquid
18
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Ua&*t
uO<U < < 3
&
It is the conventional view that there is a premium for illiquidity However, this may not be true. First, there are illiquidity biases. As discussed previously reported returns of illiquid assets are too high (i.e., overstated if using raw, unsmoothed data) and risk and correlation estimates are too low.
Second, illiquid asset classes such as private equity buyout funds, and physical assets like timber contain significant risks beyond liquidity risk. After adjusting for these risks, illiquid asset classes are much less attractive. According to one study after adjusting for risk, most investors are better off investing in the S&P 500 than in a portfolio of private equity.
Third, there is no market index for illiquid assets. Private equity hedge fund, and real estate indices are not investable, so no investor is actually earning the index return. For example, the NCREIF includes thousands of properties. Because individuals do not typically own thousands of properties, they are much more subject to idiosyncratic risks and are less diversified within the asset class.
Fourth, you must rely on manager skill in illiquid asset classes. There is no way as there is with tradeable, cheap bond and equity index funds, to separate factor risk (i.e., systematic risk) from the talents of fund managers. As noted, there is no way to earn index returns. If an investor cannot earn index returns in illiquid asset class markets, he has no way of separating passive returns from alpha generated by active managers.
These factors imply that it may not be possible to generate substantial illiquidity risk premiums across illiquid asset classes. However, there is evidence of large illiquidity risk premiums within asset classes.
Illiquidity Risk Premiums Within Asset Classes
Less liquid assets generally have higher returns than more liquid assets, within asset classes. Currently there is no formal theory about why illiquidity risk premiums exist within asset
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Topic 65 Cross Reference to GARP Assigned Reading – Ang, Chapter 13
Figure 1: Liquidity vs. Expected Returns
Topic 65 Cross Reference to GARP Assigned Reading – Ang, Chapter 13
classes but not between. It might be that investors simply overpay for illiquid asset classes, chasing the illusion of higher returns. It may also be that firms do not manage portfolios as a cohesive whole, but instead put asset classes in different silos. Mispricing (i.e., the lack of a premium across classes) may be due to slow-moving capital across classes, limits to arbitrage, and institutional constraints (e.g., the fixed-income desk doesnt talk to the equity traders, and so on).
Illiquidity Effects in U.S. Treasury Markets
On-the-run (i.e., newly issued) Treasury bills (T-bills) are more liquid and have lower yields than ofiF-the-run (seasoned) T-bills. The difference is called the on-the-run/off-the-run bond spread. During the 20072009 financial crisis, same maturity T-bonds andT-notes traded with different yields. While prices should have been the same, T-bond prices were more than 5% lower than T-note prices. Given that the U.S. Treasury market is one of the largest and most liquid in the world, it is surprising to observe large illiquidity effects.
Illiquidity Effects in Corporate Bond Markets
Larger bid-ask spreads and infrequent trading led to higher yields in corporate bond markets. Studies indicate that illiquidity risk explains 7% of the variation in investment grade bond yields and 22% of the variation in junk bond yields. Also, as bid-ask spreads increase, yield spreads increase by more than double the amount (e.g., a one-basis point increase in the bid-ask spread results in a more than two-basis point increase in the yield spread).
Illiquidity Effects in Equity Markets
Price impact of large trades. Informed trading measures (i.e., adverse selection). 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.
Quote size. Quote depth.
Number of zero returns (in liquid markets returns are usually not zero). Return autocorrelations (which are a measure of stale prices). All of these factors are characteristics of illiquidity that are unique to each stock. There are also illiquidity risk betas that are covariances of stock returns with illiquidity factors. Researchers estimate illiquidity risk premiums at 1% to 8% depending on the illiquidity measure used. Research also indicates that risk premiums have declined, although studies find a 1% risk premium for listed equities compared to a 20% risk premium for OTC stocks.
Frequency of trades.
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Topic 65 Cross Reference to GARP Assigned Reading – Ang, Chapter 13
Secondary Markets for Private Equity and Hedge Funds
Private equity funds trade companies with each other, providing needed liquidity. In 2005, these secondary buyouts represented about 15% of all private-equity buyout deals. This does allow funds to get out of specific deals, may give limited partners (LPs) some cash in the process, and may allow LPs to better understand the values of portfolio companies. However, secondary buyouts do not allow limited partners to get out of the private equity fund itself.
LPs can exit private equity funds in secondary markets. However, these markets are immature, small, and more opaque. Firms participating in these markets on the buy side were called vultures in the 1990s. Buyers took advantage of distressed sellers, getting discounts of 30% to 50%. Discounts fell below 20% in the early 2000s, but shot up again during the 2007-2009 financial crisis.
Harvard University saw its endowment fall by more than $8 billion, or 22%, between July 1, 2008, and October 31, 2008. Harvard relies on the endowment for some of its operating funds. Endowment fund managers attempted to sell stakes in private equity to free up cash for operations and faced discounts of 50%.
Because hedge fund investors can typically redeem their investments at predetermined dates, discounts on secondary market transactions are much smaller than in private equity investments. During the recent financial crisis, hedge fund discounts were 6% to 8% on average. Some funds traded at a premium, even during the crisis, due to strong demand (i.e., the funds were closed to new investors). Large asset owners like sovereign funds and pension funds can supply liquidity in hedge fund and private equity markets, buying stakes at reduced prices and harvesting illiquidity risk premiums.
In sum, there are four ways that investors can harvest illiquidity premiums: 1. Allocating a portion of the portfolio to illiquid asset classes like real estate. This is
passive allocation to illiquid asset classes.
2 . Choosing more illiquid assets within an asset class. This means engaging in liquidity
security selection.
3. Acting as a market maker for individual securities. For example, Dimensional Funds
Advisors (DFA) is a liquidity provider that buys stock at a discount from those wanting to sell quickly and sells small-cap stocks at a premium to investors demanding shares. The firm avoids adverse selection problems by choosing counterparties who fully disclose information about stocks. The firm is trustworthy in its dealings and does not manipulate prices or engage in front running. Sovereign wealth funds, large pension funds, and other large asset owners can also act as market makers, providing liquidity while buying at discounts and selling at premiums.
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Topic 65 Cross Reference to GARP Assigned Reading – Ang, Chapter 13
4. Engaging in dynamic factor strategies at the aggregate portfolio level. This means taking long positions in illiquid assets and short positions in liquid assets to harvest the illiquidity risk premium. Investors rebalance to take advantage of the liquidity differences as less liquid assets become more liquid. Rebalancing the portfolio is the simplest way to provide liquidity. As long as buyers buy when others want to sell and sell when others want to buy, rebalancing is countercyclical. Of the four ways investors can harvest the illiquidity premium, this is the easiest to implement and can have the greatest effect on portfolio returns.
Po r t f o l io Al l o c a t io n t o Il l iq u id As s e t s

LO 65.4: Describe the unsmoothing of returns and its properties.
In general, investors should be skeptical of reported returns in illiquid asset markets. The reason is that reported returns are generally overstated. There are reporting biases that result in inflated returns. Three main biases that impact returns of illiquid assets are:

Survivorship bias. Selection bias. Infrequent trading.
Survivorship Bias
There are no requirements for certain types of funds (e.g., private equity, hedge funds, buyout funds, and so on) to report returns to database providers. As such, poorly perform- ing funds have a tendency to stop reporting. Additionally, funds may never begin reporting because returns are not high enough to appeal to investors. This results in reporting biases. In addition, many poorly performing funds ultimately fail. Performance studies generally include only those funds that were successful enough to survive over the entire period of
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Topic 65 Cross Reference to GARP Assigned Reading – Ang, Chapter 13
analysis, leaving out the returns of funds that no longer exist. Both of these factors result in reported returns that are too high. This is called survivorship bias. Non-surviving funds have below average returns and surviving funds have above average returns, but it is the sur- viving fund returns that are reported. Studies show mutual fund returns are 1% to 2% low- er than reported and returns may be as much as 4% lower for illiquid asset markets. While the solution to survivorship bias seems obvious (to observe the entire universe of funds), it is impossible to do in illiquid asset markets.
Sample Selection Bias
Asset values and returns tend to be reported when they are high. For example, houses and office buildings typically are sold when values are high. Often, a seller will wait until property values recover before selling. These higher selling prices are then used to calculate returns. This results in sample selection bias.
The problem with selection bias is especially prevalent in private equity markets. Buyout funds take companies public when stock prices are high. Venture capitalists sell companies when values are high. Distressed companies are often not liquidated and left as shell companies (these are sometimes called zombie companies). It is difficult to tell, based on old data without any recent transactions, if a company is alive or whether it is a zombie.
Impacts of sample selection bias include:

Higher reported alphas relative to true alphas because only high prices are recorded. For example, one study estimates an alpha of more than 90% for venture capital log returns. However, alpha falls to 7% after correcting for sample selection bias. .Another study estimates returns are decreased 2% to 5% per m onth if you correct for the bias. Lower reported betas than true betas because there are fewer (only high) prices recorded, flattening the security market line (SML). The effect is smaller for real estate returns because volatility is lower than in private equity and studies often include downturns such as what happened in real estate in the early 1990s and the early 2000s.
Lower reported variance of returns than the true variance of returns because only high
returns are counted (i.e., underestimated risk).
In sum, sample selection bias results in overestimated expected returns and underestimated risk as measured by beta and the standard deviation of returns (i.e., volatility).
Infrequent Trading
Illiquid assets, by definition, trade infrequently. Infrequent trading results in underestimated risk. Betas, return volatilities, and correlations are too low when they are computed using the reported returns of infrequently traded assets. Returns for these infrequently traded assets are smoothed. For example, if one compares quarterly returns to the daily returns of the same asset, quarterly returns will appear (and actually be) less volatile. Prices will often be higher or lower in a given investment horizon, than it appears when examining quarterly returns. The computed standard deviation of returns often will be lower when examining quarterly returns compared to daily returns. Also, correlations with other asset classes (e.g., liquid assets such as large-cap stocks) will be artificially low because return volatility is muted by infrequent trades.
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It is possible to unsmooth or de-smooth returns using filtering algorithms. Filtering algorithms generally remove noise from signals. However, unsmoothing adds noise back to reported returns to uncover the true, noisier returns. Unsmoothing returns affects risk and return estimates, and could have a dramatic effect on returns. For example, reported real estate returns during the 1990s downturn were 5.3%. The corresponding unsmoothed returns were 22.6%. The National Council of Real Estate Investment Fiduciaries (NCREIF) returns reached -8.3% in December 2008. Unsmoothed returns during the same quarter were 36.3%. The standard deviation of the raw returns was 2.25% during the same quarter compared to 6.26% for unsmoothed returns. For comparison, stock return volatility was approximately 7.5% per quarter. Correlations between the S&P 500 Index and NCREIF returns increased from 9.2% to 15.8% when returns were unsmoothed.
Il l iq u id it y Ris k P r e m iu m s