Topics 65-68

Question 1

Evaluate the characteristics of illiquid markets

Answer 1

There are several 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.

Question 2

Examine the relationship between market imperfections and illiquidity

Answer 2

Imperfections that encourage illiquidity include:

• Market participation costs. In many illiquid markets, only certain types of investors have the expertise, capital, and experience to participate. This is called a clientele effect. There will be less liquidity in markets that are suited to a limited number of investors and/or where there are barriers to entry in terms of required experience, capital, or expertise.
• Transaction costs.

When acknowledging the existence of transaction costs (i.e., acknowledging that markets are imperfect), some academic studies assume that as long as an investor can pay the transaction costs (and sometimes these costs are large), then any investor can transact (i.e., any asset can be liquid if one can pay the transaction cost). However, this is not always true. For example, there are:

• Difficulties finding a counterparty (i.e., search frictions).
• Asymmetric information. Some investors have more information than others. If an investor fears that the counterparty knows more than he does, he will be less willing to trade, which increasing illiquidity. When asymmetric information is extreme, people assume all products are lemons. Because no one wants to buy a lemon, markets break down. Often liquidity freezes are the result of asymmetric information.
• Price impacts.
• Funding constraints.

Question 3

Assess the impact of biases on reported returns for illiquid assets.
Describe the unsmoothing of returns and its properties.

Answer 3

Three main biases that impact returns of illiquid assets are:

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 performing 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 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.

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).

Impacts of sample selection bias include:

• Higher reported alphas relative to true alphas because only high prices are recorded.
• Lower reported betas than true betas because there are fewer (only high) prices recorded, flattening the security market line (SML).
• 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.

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.

Question 4

Illiquidity Risk Premiums Across Asset Classes

Answer 4

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.
• 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.
• 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.

Question 5

Illiquidity Risk Premiums Within Asset Classes

Answer 5

• Less liquid assets generally have higher returns than more liquid assets, within asset classes.
• Larger bid-ask spreads and infrequent trading led to higher yields in corporate bond markets.
• Studies indicate that less liquid stocks earn higher returns than more liquid stocks.

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.
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. O f the four ways investors can harvest the illiquidity premium, this is the easiest to implement and can have the greatest effect on portfolio returns.

Question 6

Evaluate portfolio choice decisions on the inclusion of illiquid assets

Answer 6

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

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.
• 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 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 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.

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.

Question 7

Distinguish among the inputs to the portfolio construction process

Answer 7

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.

Question 8

Evaluate the methods and motivation for refining alphas in the implementation process

Answer 8

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 manager’s estimated alphas (an input into a meanvariance optimization analysis) in ways that effectively impose the various constraints.

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 manager’s 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.

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.

Question 9

Describe neutralization and methods for refining alphas to be neutral

Answer 9

• Neutralization is the process of removing biases and undesirable bets from alpha. There are several types of neutralization: benchmark, cash, and risk-factor.
• 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.
• 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.
• 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.
• An active portfolio can also be made cash neutral, by adjusting the alphas so that the portfolio has no active cash position. It’s possible to make the alpha values both cash- and benchmark-neutral.

Question 10

Describe the implications of transaction costs on portfolio construction

Answer 10

Transaction costs occur at points in time, while the benefits (i.e., additional return) are realized over time.

Question 11

Assess the impact of practical issues in portfolio construction, such as determination of risk aversion, incorporation of specific risk aversion, and proper alpha coverage

Answer 11

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:

risk aversion = information ratio / (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/ (2x10) = 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.

Active risk is just another name for tracking error. Also note that in the risk aversion equation, the desired level of 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.
• 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.

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 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

average alpha for the stocks with forecasts = (weighted average of the alphas 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.

Question 12

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

Determine the optimal no-trade region for rebalancing with transaction costs.

Answer 12

If transaction costs are zero, a manager should revise a portfolio every time new information arrives. 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) x (marginal contribution to active risk of asset)]

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.

Question 13

Evaluate the strengths and weaknesses of the following portfolio construction techniques: screens, stratification, linear programming, and quadratic programming

Answer 13

The following four procedures comprise most of the institutional portfolio construction techniques: screens, stratification, linear programming, and quadratic programming. In each case the goal is the same: high alpha, low active risk, and low transaction costs.

An active manager’s value depends on her ability to increase returns relative to the benchmark portfolio that are greater than the penalty for active risk and the additional transaction costs of active management.

(portfolio alpha) — (risk aversion) x (active risk)² — (transaction costs)

Screens

• Screens are just what you would expect; they allow some stocks “through” but not the rest.

Stratification

• Stratification refers to dividing stocks into multiple mutually exclusive categories prior to screening the stocks for inclusion in the portfolio. For example, we could divide the portfolio into large-cap, medium-cap, and small-cap stocks and further divide these categories into six different industry categories; giving us 18 different size-sector categories.
• Stratification is a method of risk control. If the size and sector categories are chosen in such a way that they capture the risk dimensions of the benchmark well, portfolio risk control will be significant. If they are not, risk control will not be achieved.
• Stratification will reduce the effects of bias in estimated alphas across the categories of firm size and sector. However, it takes away the possibility of adding value by deviating from benchmark size-sector weights. Using stratification, any value from information about actual alphas (beyond their category) and about possible sector alphas is lost.

Linear Programming

• Linear programming is an improvement on stratification, in that it uses several risk characteristics, for example, firm size, returns volatility, sector, and beta. Unlike stratification, it does not require mutually exclusive categories of portfolio stocks. The linear programming methodology will choose assets for the optimal portfolio so that category weights in the active portfolio closely resemble those of the benchmark portfolio. This technique can also include the effects of transaction costs (which reduces turnover) and limits on position sizes.
• Linear programming’s strength is creating a portfolio that closely resembles the benchmark. However, the result can be a portfolio that is very different from the benchmark with respect to the number of assets included and any unincluded dimensions of risk.

Quadratic Programming

• Quadratic programming can be designed to include alphas, risks, and transaction costs.
• Additionally, any number of constraints can be imposed. Theoretically, this is the best method of optimization, as it efficiently uses the information in alphas to produce the optimal (constrained) portfolio.

Question 14

Describe dispersion, explain its causes, and describe methods for controlling forms of dispersion

Answer 14

• For portfolio managers, dispersion refers to the variability of returns across client portfolios. One dispersion measure is the difference between the maximum return and minimum return over a period for separately managed client accounts.
• Managers can reduce dispersion by reducing differences in asset holdings between portfolios and differences in portfolio betas though better supervision and control. Other causes of dispersion are outside the manager’s control. Different portfolio constraints for different accounts will unavoidably increase dispersion (e.g., not being able to invest in derivatives or other asset classes).
• Of course, if all client accounts were identical there would be no dispersion. All accounts will not be identical in the presence of transaction costs, however. The existence of transaction costs implies that there is some optimal level of dispersion.
• A greater number of portfolios and higher active risk will both increase optimal dispersion, and for a given number of portfolios, dispersion is proportional to active risk. As long as alphas and risk are not constant (an unlikely occurrence) dispersion will decrease over time and eventually convergence (of account returns) will occur. However, there is no certainty as to the rate at which it will occur.

Question 15

Portfolio variance and Individual VaR

Answer 15

Question 16

VaR for uncorrelated positions and Undiversified VaR

Answer 16

Question 17

Simplified formula for standard deviation of a portfolio

Answer 17

Question 18

Marginal VaR

Answer 18

Question 19

Describe the challenges associated with VaR measurement as portfolio size increases

Answer 19

Incremental VaR is the change in VaR from the addition of a new position in a portfolio. Since it applies to an entire position, it is generally larger than marginal VaR and may include nonlinear relationships, which marginal VaR generally assumes away.

The incremental VaR is the difference between the new VaR from the revaluation minus the VaR before the addition. The revaluation requires not only measuring the risk of the position itself, but it also requires measuring the change in the risk of the other positions that are already in the portfolio.

For small additions to a portfolio, we can approximate the incremental VaR with the following steps:

• Step 1: Estimate the risk factors of the new position and include them in a vector [r|].
• Step 2: For the portfolio, estimate the vector of marginal VaRs for the risk factors [MVaR].
• Step 3: Take the cross product.

Question 20

Component VaR

Answer 20

If the returns do not follow an elliptical distribution, we can employ other procedures to compute component VaR. If the distribution is homogeneous of degree one, for example, then we can use Eulers theorem to estimate the component VaRs. The return of a portfolio of assets is homogeneous of degree one because, for some constant, k, we can write:

k x R_p = Σ_i^N k x w_i x R_i

The following steps can help us find component VaRs for a non-elliptical distribution using historical returns:

• Step 1: Sort the historical returns of the portfolio.
• Step 2: Find the return of the portfolio, which we will designate R_P(VaR), that corresponds to a return that would be associated with the chosen VaR.
• Step 3: Find the returns of the individual positions that occurred when R_P(VaR) occurred.
• Step 4: Use each of the position returns associated with R_P(VaR) for component VaR for that position.

To improve the estimates of the component VaRs, an analyst should probably obtain returns for each individual position for returns of the portfolio slightly above and below R_P(VaR). For each set of returns for each position, the analyst would compute an average to better approximate the component VaR of the position.

Component VaR = Portfolio VaR * position weight * beta(B,P)
Component VaR = Position VaR * correlation(B,P)
Component VaR = marginal VaR (B, P) * Position

where B is the position

Question 21

Apply the concept of marginal VaR to guide decisions about portfolio VaR

Answer 21

A manager can lower a portfolio VaR by lowering allocations to the positions with the highest marginal VaR. If the manager keeps the total invested capital constant, this would mean increasing allocations to positions with lower marginal VaR.

Question 22

Explain the difference between risk management and portfolio management, and describe how to use marginal VaR in portfolio management

Answer 22

Efficient frontier is the plot of portfolios that have the lowest standard deviation for each expected return (or highest return for each standard deviation) when plotted on a plane with the vertical axis measuring return and the horizontal axis measuring the standard deviation. The optimal portfolio is represented by the point where a ray from the risk-free rate is just tangent to the efficient frontier. That optimal portfolio has the highest Sharpe ratio:

Sharpe ratio = (portfolio return — risk-free rate) / (standard deviation of portfolio return)

Question 23

Define risk budgeting

Answer 23

Risk budgeting is a top-down process that involves choosing and managing exposures to risk. The main idea is that the risk manager establishes a risk budget for the entire portfolio and then allocates risk to individual positions based on a predetermined fund risk level. The risk budgeting process differs from market value allocation since it involves the allocation of risk.

Question 24

Describe the impact of horizon, turnover, and leverage on the risk management process in the investment management industry

Answer 24

Question 25

Describe the investment process of large investors such as pension funds

Answer 25

• The first step in the investment process is to determine the long-term, strategic asset allocations.
• The second step in the investment process is to choose the managers who may either passively manage the fund (i.e., simply track the benchmarks) or actively manage the fund in an effort to outperform the benchmarks. The investors should review the managers’ activities and performance periodically.
• Because of increased globalization, complexity, and the dynamic nature of the investment industry, simply measuring risk using historical measures is no longer adequate, which has increased the need for VaR.

Question 26

Describe the risk management challenges associated with investments in hedge funds

Answer 26

Hedge funds are a very heterogeneous class of assets that include a variety of trading strategies. Since they often use leverage and trade a great deal, their risk characteristics may be more similar to the “sell side” of the industry. Hedge funds have some other risks like liquidity and low transparency. Liquidity risk has many facets. First, there is the obvious potential loss from having to liquidate too quickly. Second, there is the difficulty of measuring the exact value of the fund to be able to ascertain its risk. Furthermore, the low liquidity tends to lower the volatility of historical prices as well as the correlations of the positions. These properties will lead to an underestimation of traditional measures of risk. In addition to these risks, there is the low level of transparency. This makes the risk measurement difficult with respect to both the size and type. Not knowing the type of risk increases the difficulty of risk management for the entire portfolio in which an investor might include hedge funds.

Question 27

Distinguish among the following types of risk: absolute risk, relative risk, policy-mix risk, active management risk

Answer 27

Absolute or asset risk refers to the total possible losses over a horizon. It is simply measured by the return over the horizon. Relative risk is measured by excess return, which is the dollar loss relative to a benchmark. The shortfall is measured as the difference between the fund return and that of a benchmark in dollar terms. VaR techniques can apply to tracking error (i.e., standard deviation of excess return) if the excess return is normally distributed.

Distinguishing policy mix from active risk is important when an investment firm allocates funds to different managers in various asset classes. This breaks down the risk of the total portfolio into that associated with the target policy (i.e., the weights assigned to the various funds in the policy) and the risk from the fact that managers may make decisions which lead to deviations from the designated weights.

Often, active management risk is not much of a problem for several reasons:

• For well-managed funds, it is usually fairly small for each of the individual funds.
• There will be diversification effects across the deviations.
• There can be diversification effects with the policy mix VaR to actually lower the total portfolio VaR.

Question 28

Funding Risk

Answer 28

Funding risk refers to being able to meet the obligations of an investment company (e.g., a pension’s payout to retirees). Put another way, funding risk is the risk that the value of assets will not be sufficient to cover the liabilities of the fund. The level of funding risk varies dramatically across different types of investment companies. Some have zero, while defined benefit pension plans have the highest.

When assets and liabilities change by different amounts, this affects the surplus, and the resulting volatility of the surplus is a source of risk. If the surplus turns negative, additional contributions will be required. This is called surplus at risk (SaR).

One answer to this problem is to immunize the portfolio by making the duration of the assets equal that of the liabilities. This may not be possible since the necessary investments may not be available, and it may not be desirable because it may mean choosing assets with a lower return.

Question 29

Plan Sponsor Risk

Answer 29

The plan sponsor risk is an extension of surplus risk and how it relates to those who ultimately bear responsibility for the pension fund. We can distinguish between the following risk measures:

• Economic risk is the variation in the total economic earnings of the plan sponsor. This takes into account how the risks of the various components relate to each other (e.g., the correlation between the surplus and operating profits).
• Cash-flow risk is the variation of contributions to the fund. Being able to absorb fluctuations in cash flow allows for a more volatile risk profile.

Ultimately, from the viewpoint of the sponsor, the focus should be on the variation of the economic value of the firm.

Question 30

Apply VaR to check compliance, monitor risk budgets, and reverse engineer sources of risk

Answer 30

Risk management is necessary for all types of portfolios— even passively managed portfolios.

Monitoring the risk of actively managed portfolios should help identify the reasons for changes in risk. Three explanations for dramatic changes in risk are (1) a manager taking on more risk, (2 ) different managers taking similar bets, and (3) more volatile markets. Thus, when there is an increase in the overall risk of a portfolio, top management would want to investigate the increase by asking the following questions.

• Has the manager exceeded her risk budget?
• Are managers taking too many of the same style bets? If the managers are acting independently, it is possible that they all start pursuing strategies with the same risk exposures. This could happen, for example, if all managers forecast lower interest rates. Bond managers would probably begin moving into long-term bonds, and equity managers would probably begin moving into stocks that pay a high and stable dividend like utility companies and REITs. This would drastically increase the interest rate risk of the overall portfolio.
• Have markets become more volatile? If the risk characteristics of the entire market have changed, top management will have to decide if it is worth accepting the volatility or make decisions to reduce it by changing the target portfolio weights. VaR can also be reverse engineered by utilizing the VaR tools outlined in the previous topic, such as component VaR and marginal VaR. This method can be used provided that all relevant risks have been identified within the risk management system.

There is a trend in the investment industry toward management choosing a global custodian for the firm. Such a choice means an investor aggregates the portfolios with a single custodian, which more easily allows a consolidated picture of the total exposures of the fund. The custodian can combine reports on changes in positions with market data to produce forward-looking risk measures. Thus, the global custodian is an easy choice in pursuing centralized risk management. Along with the trend toward global custodians, there has been a trend in the “custodian industry” toward fewer custodians that can provide more services. Large custodian banks such as Citibank, Deutsche Bank, and State Street are providing risk management products.

Question 31

Explain how VaR can be used in the investment process and the development of investment guidelines

Answer 31

Investment Guidelines

• VaR can help move away from the ad hoc nature and overemphasis on notionals and sensitivities that characterize the guidelines many managers now use. Clearly, ad hoc procedures will generally be inferior to formal guidelines using established principles. Also, limits on notionals and sensitivities have proven insufficient when leverage and positions in derivatives exist. The limits do not account for variations in risk nor correlations. VaR limits include all of these factors.

Investment Process

• VaR can help in the first step of the investment process, which is the strategic asset-allocation decision. Furthermore, VaR can measure specific changes in risk that can result as managers subjectively adjust the weights from those recommended by pure quantitative analysis.
• VaR is also useful at the trading level. A trader usually focuses on the return and stand-alone risk of a proposed position. The trader may have some idea of how the risk of the position will affect the overall portfolio, but an adequate risk management system that uses VaR can give a specific estimate of the change in risk.

Question 32

Describe the risk budgeting process and calculate risk budgets across asset classes and active managers

Answer 32

• Risk budgeting should be a top down process. The first step is to determine the total amount of risk, as measured by VaR, that the firm is willing to accept. The next step is to choose the optimal allocation of assets for that risk exposure.
• The goal will be to choose assets for the fund that keep VaR less than this value. Unless the asset classes are perfectly correlated, the sum of the VaRs of the individual assets will be greater than the actual VaR of the portfolio. Thus, the budgeting of risk across asset classes should take into account the diversification effects. Such effects can be carried down to the next level when selecting the individual assets for the different classes.
• The traditional method for evaluating active managers is by measuring their excess return and tracking error and using it to derive a measure known as the information ratio. Excess return is the active return minus the benchmark return. The information ratio of manager i is:

IR_i = (expected excess return of the manager) / (the manager’s tracking error)