Question

The table below represents the breakdown of the actual returns for a pension fund during a given quarter. The table also contains the benchmark weights and returns against which the pension fund is measured.

	Fund	Fund	Benchmark	Benchmark
	Weight	Return	Weight	Return
Equity	0.65	3.4%	0.60	3.3%
Bonds	0.30	1.5%	0.35	1.6%
Cash	0.05	0.75%	0.05	0.75%

Calculate the contribution of asset allocation to the Fund's outperformance (or underperformance) relative to the Benchmark. The contribution from asset allocation may be positive or negative.

Answer 1

Let the weight of equity in fund = w1 = 0.65

weight of bonds in fund = w2 = 0.30

weight of cash in fund = w3 = 0.05

Let the weight of equity in benchmark = b1 = 0.60

weight of bonds in benchmark = b2 = 0.35

weight of cash in benchmark = b3 = 0.05

Let the return of equity in benchmark = R1 = 3.3%

return of bonds in benchmark = R2 = 1.6%

return of cash in benchmark = R3 = 0.75%

contribution of security selection = [ (w1-b1)*R1] +[ (w2-b2)*R2] + [ (w3-b3)*R3] = [ (0.65-0.60)*3.3] +[ (0.30-0.35)*1.6] + [ (0.05-0.05)*R3] = 0.165 -0.08 + 0 = 0.085%

Since this contribution is positive, the fund outperformed relative to benchmark