# LO 68.8: Describe the risk budgeting process and calculate risk budgets across

LO 68.8: Describe the risk budgeting process and calculate risk budgets across asset classes and active managers.
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. As an example, a firms management might set a return volatility target equal to 20%. If the firm has \$100 million in assets under management and assuming the returns are normally distributed, at a 95% confidence level, this translates to:
VaR = (1.65) x (20%) x (\$100 million) = \$33 million
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.
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Topic 68 Cross Reference to GARP Assigned Reading – Jorion, Chapter 17
Example: Budgeting risk across asset classes (part 1)
A manager has a portfolio with only one position: a \$500 million investment in W. The manager is considering adding a \$500 million position X or Y to the portfolio. The current volatility of W is 10%. The manager wants to limit portfolio VaR to \$200 million at the 99% confidence level. Position X has a return volatility of 9% and a correlation with W equal to 0.7. Position Y has a return volatility of 12% and a correlation with W equal to zero. Determine which of the two proposed additions, X or Y, will keep the manager within his risk budget.
Currently, the VaR of the portfolio with only W is:
VaR^ = (2.33)(10%)(\$500 million) = \$116.5 million
When adding X, the return volatility of the portfolio will be:
8.76% = V (0.52)(10%)2 +(0.52)(9%)2 + (2)(0.5)(0.5)(0.7)(10%)(9%)
VaRW+X = 2.33(8.76%)(\$ 1,000 million) = \$204 million
When adding Y, the return volatility of the portfolio will be:
7.81% = V (0.52 )(10% )2 +(0.52)(12% )2
VaRw+y = (2.33)(7.81 %)(\$ 1,000 million) = \$182 million
Thus, Y keeps the total portfolio within the risk budget.
Example: Budgeting risk across asset classes (part 2)
In the previous example, demonstrate why focusing on the stand-alone VaR of X and Y would have led to the wrong choice. Answer:
Obviously, the VaR of X is less than that of Y.
VaRx = (2.33)(9%)(\$500 million) = \$104.9 million
VaRy = (2.33)(12%)(\$500 million) = \$139.8 million
The individual VaRs would have led the manager to select X over Y; however, the high correlation of X with W gives X a higher incremental VaR, which puts the portfolio of W and X over the limit. The zero correlation of W and Y makes the incremental VaR of Y much lower, and the portfolio of W with Y keeps the risk within the limit.
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Topic 68 Cross Reference to GARP Assigned Reading – Jorion, Chapter 17
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:
(expected excess return of the manager)
(the managers tracking error)
For a portfolio of funds, each managed by a separate manager, the top management of the entire portfolio would be interested in the portfolio information ratio:
(expected excess return of the portfolio)
(the portfolios tracking error)
If the excess returns of the managers are independent of each other, it can be shown that the optimal allocation across managers is found by allocating weights to managers according to the following formula:
IRj x (portfolios tracking error) weight of portfolio managed by manager i = ————————————— – IRP x (managers tracking error)

1

One way to use this measure is to budget portfolio tracking error. Given the IRp, the IRp and the managers tracking error, top management can calculate the respective weights to assign to each manager. The weights of the allocations to the managers do not necessarily have to sum to one. Any difference can be allocated to the benchmark itself because, by definition, IRbenchmark = 0.
Determining the precise weights will be an iterative process in that each selection of weights will give a different portfolio expected excess return and tracking error. Figure 2 illustrates a set of weights derived from the given inputs that satisfy the condition.
Figure 2: Budgeting Risk Across Active Managers
Tracking Error
Information Ratio
Manager A Manager B Benchmark Portfolio
5.0% 5.0% 0.0% 3.0%
0.70 0.50 0.00 0.82
Weights 51% 37% 12% 100%
Although we have skipped the derivation, we can see that the conditions for optimal allocation hold true:
For A: 51% =
For B: 37% =
(3%) (0.70) (5%) (0.82)
(3%) (0.50) (5%)(0.82)
The difference between 100% and the sum of the weights 51% and 37% is the 12% invested in the benchmark.
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Topic 68 Cross Reference to GARP Assigned Reading – Jorion, Chapter 17
Ke y Co n c e pt s
LO 68.1 Risk budgeting is a top-down process that involves choosing and managing exposures to risk.
LO 68.2 Compared to banks on the sell side, investors on the buy side have a longer horizon, slower turnover, and lower leverage. They have tended to use historical risk measures and focus on tracking error, benchmarking, and investment guidelines. Banks use forward- looking VaR risk measures and VaR limits. Investors seem to be using VaR more and more, but they have to adapt it to their needs.
LO 68.3 Investors are relying more on VaR because of increased globalization, complexity, and dynamics of the investment industry. They have found simply measuring risk from historical measures is no longer adequate.
LO 68.4 Hedge funds have risk characteristics that make them more similar to the sell side of the industry like the use of leverage and high turnover. In addition to that, they have other risks such as low liquidity and low transparency. Low liquidity leads to problems in measuring risk because it tends to put a downward bias on volatility and correlation measures.
LO 68.3 Absolute or asset risk refers to the total possible losses over a horizon. Relative risk is measured by excess return, which is the dollar loss relative to a benchmark. VaR measures can apply to both.
The risk from the policy mix is from the chosen portfolio weights, and active risk is from individual managers deviating from the chosen portfolio weights.
Funding risk is the risk that the value of assets will not be sufficient to cover the liabilities of the fund. It is important for pension funds. In applying VaR, a manager will add the expected increase in the surplus to the surplus and subtract the VaR of the assets from it. The difference between the expected surplus and the portfolio VaR is the shortfall associated with the VaR.
Two components of sponsor risk are cash-flow risk, which addresses variations of contributions to the fund, and economic risk, which is the variation of the earnings.
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Topic 68 Cross Reference to GARP Assigned Reading – Jorion, Chapter 17
LO 68.6 Risk monitoring is important in large firms to catch rogue traders whose activities may go undetected with simple periodic statements. It is also needed for passive portfolios because the risk characteristics of the benchmarks can change. Risk monitoring can also determine why changes in risk have occurred (e.g., individual managers exceeding their budget, different managers taking on the same exposures, or the risk characteristics of the whole market changing).
There is a trend toward using a global custodian in the risk management of investment firms. It is an easy means to the goal of centralized risk management. The custodians can combine reports on changes in positions with market data to produce forward-looking risk measures. Those that choose not to use a global custodian have done so because they feel they have tighter control over risk measures and can better incorporate VaR systems into operations.
LO 68.7 There is a trend of investment managers incorporating VaR systems into their investment management process. There is evidence that money managers are differentiating themselves with respect to their risk management systems, and those that do not use such systems are at a competitive disadvantage.
VaR techniques can help move away from the ad hoc nature and overemphasis on notionals and sensitivities that characterize the guidelines many managers now use. Such guidelines are cumbersome and ineffective in that they focus on individual positions and can be easily circumvented.
VaR is useful for the investment process. When a trader has a choice between two new positions for a portfolio, the trader can compare the marginal VaRs to make the selection. When deciding whether to increase one existing position over another, the trader can compare the excess-return-to-MVaR ratios and increase the position in the one with the higher ratio.
LO 68.8 Budgeting risk across asset classes means selecting assets whose combined VaRs are less than the total allowed. The budgeting process would examine the contribution each position makes to the portfolio VaR.
For allocating across active managers, it can be shown that the optimal allocation is achieved with the following formula:
IR: x (portfolios tracking error) weight of portfolio managed by manager i = —————————- ;———– IRp x (managers tracking error)
.
For a given group of active managers, the weights may not sum to one. The remainder of the weight can be allocated to the benchmark, which has no tracking error.
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Topic 68 Cross Reference to GARP Assigned Reading – Jorion, Chapter 17
Co n c e pt Ch e c k e r s
1.
With respect to the buy side and sell side of the investment industry:
the sell side has relied more on VaR measures.
I. the buy side uses more leverage. II. A. I only. B. II only. C. Both I and II. D. Neither I nor II.
2.
3.
Compared to policy risk, which of the following is not a reason that management risk is not much of a problem? A. There will be diversification effects across the deviations. B. Managers tend to make the same style shifts at the same time. C. For well-managed funds, it is usually fairly small for each of the individual
D. There can be diversification with the policy mix VaR to actually lower the total
funds.
portfolio VaR.
Using VaR to monitor risk is important for a large firm with many types of managers because: A. it can help catch rogue traders and it can detect changes in risk from changes in it can help catch rogue traders and it can detect changes in risk from changes in benchmark characteristics.
B. although it cannot help catch rogue traders, it can detect changes in risk from
changes in benchmark characteristics.
C. although it cannot detect changes in risk from changes in benchmark
characteristics, it can help detect rogue traders.
D. of no reason. VaR is not useful for monitoring risk in large firms.
4.
VaR can be used to compose better guidelines for investment companies by:
focusing more on overall risk.
I. relying less on notionals. II. A. I only. B. II only C. Both I and II. D. Neither I nor II.
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Topic 68 Cross Reference to GARP Assigned Reading – Jorion, Chapter 17
In making allocations across active managers, which of the following represents the formula that gives the optimal weight to allocate to a manager denoted z, where IRj and IRp are the information ratios of the manager and the total portfolio respectively?
a A.
IR P x (portfolios tracking error) —————————————- . IRi x (managers tracking error)
IRi x (managers tracking error) IRp x (portfolios tracking error)
IRi x (portfolios tracking error) IRp x (managers tracking error)
IRp x (managers tracking error) IRi x (portfolios tracking error)
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Topic 68 Cross Reference to GARP Assigned Reading – Jorion, Chapter 17
Co n c e pt Ch e c k e r An s w e r s
1. B Compared to banks on the sell side, investors on the buy side have a longer horizon,
slower turnover, and lower leverage. Banks use forward-looking VaR risk measures and VaR limits.
2. B
If managers make the same style shifts, then that would actually increase management risk. All the other reasons are valid.
3. A
4. C
5. C
Both of these are reasons large firms find VaR and risk monitoring useful.
Investment companies have been focusing on limits on notionals, which is cumbersome and has proved to be ineffective.
r
r
. IRs X (portfolios tracking error) weight or portfolio managed by manager i = —————————————- IRP x (managers tracking error) ,
,
, ,
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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:
Ri s k M o n i t o r i n g a n d Pe r f o r m a n c e M e a s u r e m e n t
Topic 69
Ex a m Fo c u s
Most of this topic is qualitative in nature, however, it does contain several testable concepts. Many of the concepts covered here are also covered in other assigned readings, so this topic should serve as reinforcement of those concepts. For the exam, focus on the three pillars of effective risk management: planning, budgeting, and monitoring. Understand the concept of a risk management unit (RMU) and be able to discuss its appropriate role within a company. Always keep in mind while reviewing this topic that it is the amount of risk taken that ultimately drives the level of returnsrisk is the cost of returns.
Ris k M e a s u r e s