# LO 68.5: Distinguish among the following types of risk: absolute risk, relative risk,

LO 68.5: Distinguish among the following types of risk: absolute risk, relative risk, policy-mix risk, active management risk, funding risk, and sponsor risk.
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.
Professors Note: The authors definition o f tracking error differs from the definition of tracking error in other assigned readings. Jorion defines tracking error as active return minus the benchmark return. In other readings, this value is simply the excess return and tracking error is the volatility (i.e., standard deviation) of the excess return. Throughout this topic, we have expressed excess return as portfolio return minus benchmark return and tracking error as the volatility of the excess return. This methodology follows the definition of tracking error on previous FRM exams.
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. VaR analysis is especially useful here because it can show the risk exposure associated with the two types of risk and how they affect the overall risk of the entire portfolio. 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.
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Topic 68 Cross Reference to GARP Assigned Reading – Jorion, Chapter 17
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.
Fu n d in g Ris k
Funding risk refers to being able to meet the obligations of an investment company (e.g., a pensions 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.
The focus of this analysis is the surplus, which is the difference between the value of the assets and the liabilities, and the change in the surplus, which is the difference between the change in the assets and liabilities:
Surplus = Assets Liabilities
ASurplus = AAssets – ALiabilities
Typically, in managing funding risk, an analyst will transform the nominal return on the surplus into a return on the assets, and break down the return as indicated:
R surplus
ASurplus Assets
AAssets Assets
f ALiabilities) Liabilities ^ _ D , Liabilities , , Assets
,
asset
D . .
liabilities
Liabilities , Assets
,
Evaluating this expression requires assumptions about the liabilities, which are in the future and uncertain. For pension funds, liabilities represent accumulated benefit obligations, which are the present value of pension benefits owed to the employees and other beneficiaries. Determining the present value requires a discount rate, which is usually tied to some current level of interest rates in the market. An ironic aspect of funding risk is that assets for meeting the obligations like equities and bonds usually increase in value when interest rates decline, but the present value of future obligations may increase even more. 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.
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Topic 68 Cross Reference to GARP Assigned Reading – Jorion, Chapter 17
Example: Determining a funds risk profile
The XYZ Retirement Fund has $200 million in assets and$180 million in liabilities. Assume that the expected return on the surplus, scaled by assets, is 4%. This means the surplus is expected to grow by $8 million over the first year. The volatility of the surplus is 10%. Using a Z-score of 1.65, compute VaR and the associated deficit that would occur with the loss associated with the VaR. Answer: First, we calculate the expected value of the surplus. The current surplus is$20 million (= $200 million –$180 million). It is expected to grow another $8 million to a value of$28 million. As for the VaR:
VaR= (1.65)(10%)($200 million) =$33 million
If this decline in value occurs, the deficit would be the difference between the VaR and the expected surplus value: $33 million –$28 million = $5 million. Professors Note: According to the assigned reading, the surplus at risk (SaR) is the VaR amount calculated previously. Note that SaR on previous exams has been approached differently, as illustrated in the following example. Be prepared for either approach on the actual exam. In the example to follow, we will illustrate how to calculate the volatility o f surplus growth. On previous FRM exams, this value has not been provided. Example: Surplus at risk (via computing volatility of surplus) The XYZ Retirement Fund has$200 million in assets and $180 million in liabilities. Assume that the expected annual return on the assets is 4% and the expected annual growth of the liabilities is 3%. Also assume that the volatility of the asset return is 10% and the volatility of the liability growth is 7%. Compute 95% surplus at risk assuming the correlation between asset return and liability growth is 0.4. Answer: First, compute the expected surplus growth: 200 x (0.04) – 180 x (0.03) =$2.6 million
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Topic 68 Cross Reference to GARP Assigned Reading – Jorion, Chapter 17
Next, compute the volatility of the surplus growth. To compute the volatility you need to recall one of the properties of covariance discussed in the FRM Part I curriculum. The variance of assets minus liabilities [i.e., Var(A-L)] = Var(A) + Var(L) – 2 x Cov(A,L). Where covariance is equal to the standard deviation of assets times the standard deviation of liabilities times the correlation between the two. The asset and liability amounts will also need to be applied to this formula.
Variance(A-L) = 2002 x 0.102 + 1802 x 0.072- 2 x 200 x 180 x 0.10 x 0.07 x 0.4
= 400+ 158.76-201.6 = $357.16 million Standard deviation = V357.16 =$18.89
Thus, SaR can be calculated by incorporating the expected surplus growth and standard deviation of the growth.
95% SaR = 2.6 – 1.65 x 18.89 = \$28.57 million
Professors Note: Like VaR, SaR is a negative value since it is the surplus amount that is at risk. As a result, the negative sign is usually not presented since a negative amount is implied.
Pl a n Sp o n s o r Ris k
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. The management should integrate the various risks associated with the movement of the assets and surplus with the overall financial goals of the sponsor. This is aligned with the current emphasis on enterprise-wide risk management.
M o n it o r in g Ris k W it h VaR