Funding Risk

AIM 75.8: Explain how VAR can be applied to measuring funding risk, and compute the negative surplus associated with a VAR level of loss.

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:

^ ASurplus AAssets surplus Assets Assets

' ALiabilities

, Liabilities ,

Liabilities "

Assets

' LiabilitiesN 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.

Example: Determining a fund's 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

(= $200M - $180M). It is expected to grow another $8 million to a value of $28 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.

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