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# P2.T8.12. Surplus at Risk (SaR)

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
AIM: Define and describe the following types of risk: Funding Risk (Surplus at Risk, SaR)

Questions:

12.1. Public Employee Retirement Fund (PERF) has $800 million in assets and$720 million in liabilities, for a current surplus (S) of $80 million. The expected annual return on the surplus scaled by assets, ROA, is 5.0%. The volatility of assets 18.0%, with a normal distribution. If liabilities are unchanged over the year, at the end of one year, there is a 1.0% probability that the pension will have a deficit of what amount? (Note: applies Jorion's example from the assignment) a.$117 million deficit
b. $215 million deficit c.$335 million deficit
d. $455 million deficit 12.2. Public Employee Retirement Fund (PERF) has$600 million in assets and $600 million in liabilities, for a current surplus of zero. The annual expected return on assets is 8.0% with 18.0% volatility per annum; the annual expected return on liabilities is 6.0% with 14.0% volatility per annum. Both are normally distributed. The correlation between assets and liabilities is 0.60. What is the 95% absolute surplus at risk (absolute SaR); i.e., the worst expected SHORTFALL, or loss relative to current surplus of zero, with 95% confidence? (Note: this is similar to a previous FRM question. The method to derive SaR is different, but the assumptions given are different) a.$12.0 million
b. $85.6 million c.$133.6 million
d. $194.0 million 12.3. Public Employee Retirement Fund (PERF) reports a projected benefit obligation (PBO) of$70.0 billion. If the discount rate decreases by 10 basis points, the PBO liability will increase by $1.120 billion. These liabilities behave most nearly like which of the following? (source: variation on FRM handbook question) a. A long position in a bond with maturity of 9.0 b. A long position in a bond with (modified) duration of 9.0 years c. A short position in a bond with maturity of 16.0 years d. A short position in a bond with (modified) duration of 16.0 years Answer: #### njiandan ##### New Member in the third question 12.3. Public Employee Retirement Fund (PERF) reports a projected benefit obligation (PBO) of$70.0 billion. If the discount rate decreases by 10 basis points, the PBO liability will increase by \$1.120 billion. These liabilities behave most nearly like which of the following? (source: variation on FRM handbook question)

a. A long position in a bond with maturity of 9.0
b. A long position in a bond with (modified) duration of 9.0 years
c. A short position in a bond with maturity of 16.0 years
d. A short position in a bond with (modified) duration of 16.0 years

#### ShaktiRathore

##### Well-Known Member
Subscriber
Modified duration=%chg in pbo/chg in discount rate=(1.12/7)/.1=16
Its short position in bond because pbo is to ba paid in the future with receiving pays(coupon)
Thanks.do optiin d