# Pensions Q

P135 CFAI Q11 they ask: ‘In 2009, the actual return on Passaic’s plan assets is closest to: A,B,C’ In the answers they use the following formula: Actual return on plan assets = expected return on plan assets plus actuarial gain. How does this work? I’ve never seen that formula before and it doesn’t seem to tie in to any of the other formulas. Is this something I should just learn?

The expected return on assets is determined based on the actuarial assumptions set. If the company sets a 7% expected return on assets and assets at the beginning of the year was \$1000, then the expected nominal return for that year would be \$70. However, if the actual performance of the assets leads to an actual return of 10%, the actual return on assets will be \$100. The actuarial gain on assets is due to the difference in expected/ projected rate (7%) vs actual (10%) leads to an actuarial gain of \$30. actual rate of return = expected rate of return +actuarial gain /loss on assets The expected return on assets will come from the pension expense ( net benefit cost under US GAAP) and the actuarial gain figure will come from the balance sheet reconciliation of the fv of assets.

Just rephrasing what Jeff said: Actuarial gain/loss = Actual return on assets - Expected Return If Actual Return > Expected then Actuarial gain else loss. You’ll have to remember this.

I just memorized the formula