 # Active return formula

On page 417 in the Derivatives book they give the following formula:

RA=(ΔwstocksRB,stocks+ΔwbondsRB,bonds)+(wP,stocksRA,stocks+wP,bondsRA,bonds)

1. The first (parenthetical) term above is the value added from the asset allocation decision.

2. The second term is the value added from security selection within the stock and bond portfolios.

Then they provide an example: Fund, Fund return, benchmark return, value added: Fidelity Magellan, 35.3%, 32.3%, 3.0% Pimco Total return: -1.9%, -2.0%, 0.1% Portfolio return: 23.4%, 18.6%, 4.8% Consider an investor who invested in both actively managed funds, with 68% of the total portfolio in Fidelity and 32% in PIMCO. Assume that the investor’s policy portfolio (strategic asset allocation) specifies weights of 60% for equities and 40% for bonds.

1. Regarding the second term (security selection): Using the actual weights of 68% and 32% in the Fidelity and PIMCO funds, the combined value added from security selection was 0.68(3.0%) + 0.32(0.1%) = 2.1%. It seems they use active total weights, whilst it says in the formula they should use the portfolio weights, hence 60 and 40%?
1. The active asset allocation weights in 2013 were 68% – 60% = +8% for equities and –8% for bonds, so the value added by the active asset allocation decision was 0.08(32.3%) – 0.08(–2.0%) = 2.7%. The total value added by the investor’s active asset allocation decision and by the mutual funds through security selection was 2.1% + 2.7% = 4.8%. To confirm this total value added, note that the return on the investor’s portfolio was 0.68(35.3%) + 0.32(–1.9%) = 23.4% and the return on the policy portfolio was 0.60(32.3%) + 0.40(–2.0%) = 18.6%, for a difference of 23.4% – 18.6 = 4.8%.

Is that a question?

1. Regarding the second term (security selection): Using the actual weights of 68% and 32% in the Fidelity and PIMCO funds, the combined value added from security selection was 0.68(3.0%) + 0.32(0.1%) = 2.1%. It seems they use active total weights, whilst it says in the formula they should use the portfolio weights, hence 60 and 40%?