On page 417 in the Derivatives book they give the following formula:
RA=(ΔwstocksRB,stocks+ΔwbondsRB,bonds)+(wP,stocksRA,stocks+wP,bondsRA,bonds)
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The first (parenthetical) term above is the value added from the asset allocation decision.
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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.
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- 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%?
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- 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%.