# Quiz: Duration Mismatch Scenario

A pension plan has a Duration mismatch such that liability duration is greater than asset duration by 2, then if rates drop by 50 bps, what % return will the plan surplus experience? Assume plan is fully funded all other factors remain same.

surplus will decrease by 1%?

-1%

Duration of surplus -2 * Interest rate change -(-.5%) = -1%.

Fully funded means surplus = 0?

deriv108 Wrote: ------------------------------------------------------- > Fully funded == surplus is 0? Yes, but because the duration is mismatched, you still face interest rate risk.

+1%

Sorry -1%

Negative 1%

“Surplus portfolio” returns are fuzzy in ALM context Directionally you are all correct, BUT ehh! if surplus starts out at zero and if it goes to say \$5million underfunded status (-\$5m), what rate of return did the surplus “segment” experience? (-5 - 0)/0 = undefined. Other scenarios will show that the mismatched duration differential itself doesn’t define the return, the surplus amount does matter too. Agree?

…say plan was underfunded by \$5m (-\$5m) and the duration mismatch further worsens the mistmatch say by \$2m (-\$2m), what is the return? (-7) - (-5)/(-5) = 40% positive return ?!

.5% drop in interest rate. asset will increase by 2*0.005=0.001 i.e 1% where as liabiity will also increase by 1*0.005=0.5% isnt that surplus will increase by 1% - 0.5% = 0.5% anybody can confirm… feelin lost

Infinitely negative. since the plan is fully funded, the original surplus is zero. As we don’t know what the actual durations of the asset or liability but that the duration of the liability is twice that of the asset, a fall in rates results in the plan becoming underfunded by X amount. (X-0)/0 is infinite is it not?

Fully funded doesn’t mean 0 surplus, it can also mean positive surplus.

bpdulog Wrote: ------------------------------------------------------- > Fully funded doesn’t mean 0 surplus, it can also > mean positive surplus. Hmm…dont agree, I always thought it mean assets = liabilities. Positive surplus was overfunded status.

idreesz Wrote: ------------------------------------------------------- > bpdulog Wrote: > -------------------------------------------------- > ----- > > Fully funded doesn’t mean 0 surplus, it can > also > > mean positive surplus. > > Hmm…dont agree, I always thought it mean assets > = liabilities. Positive surplus was overfunded > status. In a fully funded plan, the ratio of plan assets to plan liabilities is 100 per- cent or greater (a funded status of 100 percent or greater) (Level III Volume 2 Behavioral Finance, Individual Investors, and Institutional Investors , 4th Edition. Pearson Learning Solutions 359).

-1%

In industry we have also used loss in surplus or gain in surplus to assets base not just to surplus. Couldn’t find anywhere in the texts how it was done.

Correct me if I’m wrong but since the question doesn’t state the actual duration of of the liability or asset you can’t determine the % change in the surplus even if we assume that fully funded can mean overfunded.

Kwonyboy Wrote: ------------------------------------------------------- > Correct me if I’m wrong but since the question > doesn’t state the actual duration of of the > liability or asset you can’t determine the % > change in the surplus even if we assume that fully > funded can mean overfunded. He’s asking for the % return, not the % change.