### VaR and Risk Budgeting in Investment Management

This chapter focuses on risk budgeting in the investment management industry, a practice that is somewhat new. The learner will be asked to identify the investment process and understand policy mix risk and active management risk. Funding risk and sponsor risk, risks that were covered in earlier books for banking institutions, will now be covered with respect to investment management.

Then, we will look at the application of VaR for managing risk and designing guidelines in the investment process, and also the role of the global custodian and the money manager.

Finally, the merits of risk budgeting across asset classes and active managers will be covered.

## VaR Applications to Investment Management

### The Sell Side versus the Buy side

The investment management industry is normally called the “buy side” of Wall Street. Banks, the “sell side,” developed the VaR, which quickly spread among the banking industry. However, it has spread at a slower rate in the investment management industry.

VaR is suitable for an environment where there are short horizons, rapid turnovers, and high leverage. In this respect, historical risk measures are of no use because yesterday’s portfolio profile may be totally unrelated and independent to that of today.

It is particularly important that banks control their risks as banks trading portfolios are highly leveraged. The institution could be easily bankrupted through a sequence of adverse events. As opposed to banks, mutual funds and pension funds usually don’t use leverage. This ensures that there is a reduced necessity to control the downside risk.

Generally, the application of VaR measures is a necessity for bank trading portfolios due to the short horizons, rapid turnover, and high leverage. To control risks, VaR limits, position limits, and stop-loss rules are very applicable.

### The Investment Process

The investment process consists of two steps, namely:

1. Step 1: A consultant provides a long-term asset allocation strategic study. This study is usually based on the mean-variance portfolio optimization. At this point, the expected return is balanced off against risk. Furthermore, the amounts to be invested in various asset classes will be determined by the study.
2. Step 2: The actual fund management is possibly assigned by the fund to a stable of active managers. The managers are frequently examined for performance with their benchmark used as the basis. This evaluation is based on the tracking error (TE). Typically, the risk is regulated via various investment guidelines where the universe of assets to be invested in is defined with some additional regulations.

VaR risk management systems are beneficial to institutions that are exposed to a variety of risks. These criteria are applicable to the investment management industry due to the following reasons:

1. Investments are naturally becoming worldwide;
2. The complexity of financial instruments as time elapses; and
3. The dynamism of most investment portfolios.

### Hedge Funds

Leverage is popular among most hedge funds. Illiquid assets are another type of investment that some funds invest in, but these can be infrequently traded. Therefore, two types of biases can arise in this regard:

1. Artificially lowered correlation with other asset classes: which will give the impression of low systemic risk; and
2. Artificially lowered volatility: which will give the impression of low total risk.

Due to their lack of transparency, hedge funds can pose special problems. A big number of hedge funds do not make public statistics on their positions fearing rivals will use the information against them. It becomes difficult for clients to measure risks accompanying their investments at the hedge fund level and for their portfolio in general.

## What are the Risks?

A risk in investment management can be defined as the risk of loss on the marked-to-market position. However, the perception of risk varies among investment asset managers.

### Absolute and Relative Risks

Risk can be recognized into two definitions:

1. Absolute risk: is the risk of a base currency loss over the time horizon. It can also be termed as asset risk and the appropriate return rate is $${ R }_{ asset }$$.
2. Relative risk: is the risk of a base currency loss in a fund relative to its benchmark. The dollar difference between the fund amount and that of a similar amount invested in the benchmark is a measure of this shortfall.

The tracking error, $$E={ R }_{ asset }-{ R }^{ b }$$, happens to be the relevant return and defines the excess return of the asset over the benchmark. Supposing this is a normal distribution, then the VaR is evaluated from the standard deviation of the tracking error $${ \sigma }_{ E }$$ as:

$$VaR=\alpha { W }_{ o }{ \sigma }_{ E }$$

### Policy Mix and Active Management Risk

Suppose a fund’s investment is allocated to a pool of active managers in various asset classes, then there are two sources of total asset risk:

• Policy mix risk: This is a base currency (dollar) loss due to the fund-selected policy mix.
• Active management risk: This is a risk of a base currency (dollar) loss due to the total deviations from the policy mix. It is an expression of the total profits or losses across all managers in relation to their benchmark.

The absolute risk can be evaluated from fund returns and can be defined as:

$${ R }_{ assets }={ \Sigma }_{ i }{ w }_{ i }{ R }_{ i }$$

Where the weight on fund $$i$$ with return $$R$$ is denoted as $${ w }_{ i }$$. We can decompose this return as follows:

$${ R }_{ asset }={ R }_{ policy\quad mix }+{ R }_{ active\quad mgt }=\sum _{ i }^{ }{ { w }_{ i }^{ b }{ R }_{ i }^{ b } } +\sum _{ i }^{ }{ \left( { w }_{ i }{ R }_{ i }-{ w }_{ i }^{ b }{ R }_{ i }^{ b } \right) }$$

Where $${ R }_{ i }^{ b }$$ represents the return of the benchmark for fund $$i$$ with $${ w }_{ i }^{ b }$$ representing its policy weight. If the pension plan drifts from its policy mix $$\left( { w }_{ j }\neq { w }_{ i }^{ b } \right)$$, the active management portion can be broken down into a term representing the policy decisions and the manager’s performance.

### Funding Risk

In case the assets are supposed to cover fixed liabilities, we may be biased if we are to solely focus on the asset’s volatility. A stream of fixed payments to retirees can be guaranteed by a pension fund whose benefits are defined. Insufficiency to cover these liabilities the deficiency, by the assets, then this will make the owner of the fund to make up the shortfall. Risk should be considered in an asset/liability management (ALM) framework. Funding risk can be described as the risk of the asset value’s insufficiency to cover the fund’s liabilities.

The relevant variable in the surplus $$S$$, defined as the difference between the utility of assets $$A$$ and liabilities $$L$$.

The change becomes

$$\Delta S=\Delta A-\Delta L.$$

Therefore:

$${ R }_{ S }=\frac { \Delta S }{ A } =\frac { \Delta A }{ A } -\frac { \Delta L }{ L } \frac { L }{ A } ={ R }_{ asset }-{ R }_{ liabilities }\frac { L }{ A }$$

Where $${ R }_{ liabilities }$$ is the rate of return of liabilities.

Evaluation of liabilities can be a tall order despite the fact that the asset’s value can be determined by marking-to-market.

This acts as a substitute for an accumulation of benefit obligations – for pension funds, which determines the present value of pension benefits owed to employees whose interest rates are appropriately discounted. In case liabilities are mainly made up of nominal payments, then their values generally act like a short position in a long-term bond that. As a result, interest rates decreases have a likelihood of raising the value of liabilities, hence making the surplus to be negatively affected.

In this regard, the minimum risk position corresponds to an immunized portfolio where the asset duration is in line with that of liabilities. The fund owner’s true long-term risk is represented by the said funding risk. It is necessary for additional contribution to the fund be provided in the event that the surplus turns negative. This is also known as surplus at risk (SAR).

The surplus risk idea can be extended to the risk to the fund’s owner, the sponsor of the plan, who will finally be in charge of the pension fund.

The surplus risk conception can be extending to whoever owns the fund, the sponsor of the plan, who will finally be in charge of the pension fund.

We can differentiate the following risks:

1. Cash flow risk: This is a risk of annual fluctuations in contribution to the pension fund.
2. Economic risk: This occurs when the plan sponsor’s total economic earnings vary. Chances are that the surplus risk will not be a major concern.

## Applying VaR in Risk Monitoring and Control

VaR systems enable those willing to invest to confirm whether the regulations are adhered to by their managers. They are also applicable when market risks are being monitored. Limits on exposures based on name-by-name are an effective way of managing credit risk. Furthermore, some protection against economic risk is guaranteed by VaR systems. Policies and procedures are also a good way to protect against operational risk.

### The Application of VaR in Risk Monitoring

Those investing can oversee their market risk better when a VaR system, and this is applicable in both active and passive management. Due to the substantial changes in the composition of indices, a constant risk is impossible in passive asset allocation (benchmarking).

The inactive allocation, also known as the standard reference, terminates risks due to the substantial change in the indicator. The fund’s risk profile thus can be changed by active portfolio management.

Assuming a sudden jump increase in the fund’s reported VaR is witnessed by the investor, then identifying what caused the jump will become the main concern. The following are some explanations:

1. The manager takes on more risk: Dynamic risk monitoring of the manager is allowed by VaR. A VaR limit or risk budget is of the utmost importance to the manager. If in any manner the VAR limit is exceeded, then there should be a close monitoring of the exceedance which should be flagged immediately.
2. The bets taken by different managers are similar: If the portfolio risk is to be kept at a minimum, then appropriate directions should, therefore, be given to the managers.
3. Markets that are highly volatile: In the event of increased volatility in the current environment, chances are that VaR will increase. The assumption, in this case, is the explicitly modeled time variation. The GARCH models are good examples.

In general, reverse engineering of VaR can be a good way of monitoring the risk source by applying VaR tools. Locating the position changes which have strong impacts on total portfolio risk is possible with component measurement and marginal VaR.

### The Role of the Global Custodian

Central risk management is the principle behind VaR. The use of a single global custodian is the simplest path to centralization and is the cause of the current aggregation of portfolio holding with a single custodian for most investors. With a single global custodian, a consolidated image of the fund’s total exposure is directly provided by position reports.

Some larger plans that do not agree that the function of evaluating risk can be entrusted to a caretaker have developed their own internal system that manages risk – the reason being that their risk control measures are stricter. Moreover, they argue that VaR systems can be incorporated into operations.

Risk management systems are satisfactory to most investors. However, the development of such systems can be an expensive affair. Therefore, the trend will drift towards fewer custodians offering more services.

### The Role of the Money Manager

Currently, as far as money management is concerned, consumers are pushing their managers to ensure that they have an active and appropriate risk management system. This is as a result of their dissatisfaction with only quarterly performance reports.

Managers who lack an all-inclusive risk management system will be disadvantaged in competition. “Risk Standards” advocate the evaluation of risk on both the entire portfolio and each instrument.

### Using VaR to Manage Risks

VaR system is an active practice used to manage risk. Active managers can apply VaR systems for investment guidelines improvement, thus helping the entire process of investment. Theoretically, it is applicable in the calculation of investment managers’ risk-adjusted performance.

### Using VaR to Design Guidelines

Better investment guidelines can be easily developed with appropriate VaR systems. The collection of assets invested in by managers is generally restricted by guidelines of managers set up in an ad hoc fashion. Guidelines usually include limits on notional amounts and/or limits on sensitivities.

Banks know that the belief that limits on notionals and sensitivities are not enough. For simple portfolios that do not use derivatives or leverage, then limits and notionals perform the highest. However, neither risk variations nor correlations will be accounted for. Limits on sensitivities may be better but still can pose problems.

Another challenge is that with the latest financial instruments, tricking these limits is possible. The application of traditional guidelines may be inappropriate for the newer instruments or leverage. Moreover, correlations are not taken into consideration by the traditional guidelines.

### Application of VaR in the Investment Process

The investment process can be improved by a good risk management system, beginning with the asset allocation process at the management level and down to the trading decisions for single stocks. In pension funds’ investment process, the first step, and the most crucial process is the strategic asset-allocation decision. The mean-variance optimization – the identification of the portfolio whose risk-return trade-off is the best – is its core. The process involves applying a set of long-term forecasts for various asset classes.

Practically, the optimization is often constrained in order to have more reasonable solutions. This adjustment may partially defeat the purpose of portfolio optimization and fail to realize the impacts of marginal adjustments from the selected portfolio.

Due to the fact that VaR has a constant mean-variance framework, its tools can be used to allocate funds across asset classes.

Another application of risk management systems is at the trading level. Portfolio managers get paid to take bets, and they are supposed to identify expected returns on various ventures.

To ensure that each asset adds up value to the portfolio, analysts got to be given a measure of its marginal VaR. When two assets have the same predicted returns, then the analyst is entitled to select the one with the less marginal VaR as this will lead to a lower overall portfolio.

## Risk Budgeting

VaR has advanced leading to risk budgeting which is spreading at a great speed in investment management. This idea is the same as a to a top-down allocation of economic risk capital that begins from the asset classes all the way to the preference of the active manager and to the level of individual securities.

### Budgeting across Asset Classes

A merit of budgeting across various asset classes is that it prevents micromanaging the venturing process. Provided the managers are bound to their risk guidelines, they will carry out new transactions without the need for approval from senior management.

### Budgeting across Active Managers

This perspective can be clarified even more if we are to make assumptions on the expected performance of active managers. Active managers are normally assessed based on their tracking error (TE). This is described as the difference between active return and the benchmark.

Let $$\mu$$ be defined as the expected $$TE$$, and $$\omega$$ as the volatility ($$TEV$$). The information ratio is then computed as follows:

$$IR={ \mu }/{ \omega }$$

Managers are frequently assessed with respect to their $$IR$$. For an active manager, the allocation problem strives to maximize the total portfolio’s $$IR$$ with respect to a $$TEV$$ constraint.

Assuming $${ x }_{ i }$$ is the portion invested in manager $$i$$, whose $$TE$$ is $${ \omega }_{ i }$$ with an excess return denoted as $${ \mu }_{ i }$$, then the total portfolio $$p$$ has the following value added:

$${ \mu }_{ P }=\sum _{ i }^{ }{ { x }_{ i }{ \mu }_{ i } } =\sum _{ i }^{ }{ { x }_{ i }\left( { { IR }_{ i }\times \omega }_{ i } \right) }$$

With an assumption that the deviations for each department manager are independent of one another, then the portfolio $$TEV$$ is fixed at:

$${ \omega }_{ P }=\sqrt { \sum _{ i }^{ }{ { x }_{ i }^{ 2 }{ \omega }_{ i }^{ 2 } } }$$

The following is the result of the portfolio $$IR$$ maximization based on a fixed $$TEV$$:

$${ X }_{ i }{ \omega }_{ i }={ IR }_{ i }\left( \frac { 1 }{ { IR }_{ P } } { \omega }_{ p } \right)$$