A blended benchmark is rebalanced at a stated frequency, and computing it at the wrong frequency can turn a manager's outperformance into underperformance.
A blended benchmark return is calculated by weighting the component index returns at each rebalancing date, usually every month, and chain-linking the period results. In an illustrative year, a 60/40 equity and bond benchmark rebalanced monthly returns 8.07 per cent, while multiplying the two annual index returns by 60 and 40 per cent gives 7.83. The 24 basis point gap is enough to turn a fund's 7.95 per cent from a win into a loss.
Worked in full in Asset Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
An investment management agreement defines the benchmark as, say, "60% MSCI World, 40% Bloomberg Global Aggregate, rebalanced monthly". The rebalancing frequency is part of the definition. A monthly rebalanced blend assumes the weights are reset to 60/40 at each month end; a blend computed from annual returns assumes they were set on 1 January and left to drift. Both are legitimate benchmarks; they are different benchmarks, and only one is in the contract.
The index returns below are illustrative, not market data.
| Month | Equity index | Bond index | 60/40 blend | Cumulative blend |
|---|---|---|---|---|
| 1 | 3.0 | -0.5 | 1.60 | 1.60 |
| 2 | -2.5 | 1.2 | -1.02 | 0.56 |
| 3 | 4.1 | -0.8 | 2.14 | 2.72 |
| 4 | -6.2 | 2.1 | -2.88 | -0.24 |
| 5 | 5.0 | -1.0 | 2.60 | 2.35 |
| 6 | 2.2 | 0.3 | 1.44 | 3.83 |
| 7 | -3.8 | 1.6 | -1.64 | 2.12 |
| 8 | 1.5 | -0.2 | 0.82 | 2.96 |
| 9 | 4.4 | -0.9 | 2.28 | 5.31 |
| 10 | -1.9 | 0.8 | -0.82 | 4.44 |
| 11 | 3.6 | -0.4 | 2.00 | 6.53 |
| 12 | 2.0 | 0.6 | 1.44 | 8.07 |
| Year | 11.20 | 2.78 | 8.07 |
Blend in month t = 0.60 × equity return in month t + 0.40 × bond return in month t
Annual blended return = (1 + blend1) × (1 + blend2) × ... × (1 + blend12) − 1
Excel, returns as decimals in B2:C13: =0.6*B2+0.4*C2 in D2, copied down, then =PRODUCT(1+D2:D13)-1
Month 1: 0.60 × 3.0 + 0.40 × (−0.5) = 1.60. Month 4: 0.60 × (−6.2) + 0.40 × 2.1 = −2.88. Compounding all twelve gives 8.07 per cent.
The alternative most people compute is 0.60 × 11.20 + 0.40 × 2.78 = 7.83 per cent. That is exactly the return of a 60/40 portfolio bought on 1 January and never rebalanced: by December its equity weight has drifted to 61.9 per cent and bonds to 38.1.
| Method | Benchmark | Fund | Excess return |
|---|---|---|---|
| Monthly rebalanced, as contracted | 8.07 | 7.95 | -0.12 |
| Weighted annual returns (buy and hold) | 7.83 | 7.95 | 0.12 |
The gap is 24 basis points, or 943,761 on a 400,000,000 mandate. It comes from rebalancing: each month the blend sells some of whichever index has just outperformed and buys the other. In a year where the two indices alternate, as here, that earns a reversal premium. In a year of steady equity gains, buy and hold would win instead, because the drifting weight rides the trend. Neither direction is reliable, which is why the definition has to be applied as written.
Monthly rebalancing is the common default because it matches how performance is usually measured and reported: the manager's return is chain-linked monthly, so the benchmark it is compared with should be built on the same grid. Some published blended indices rebalance daily, and a daily blend is the purer comparison for a manager who trades daily. Annual or drifting blends suit a mandate where the client sets the strategic weights once a year and expects the manager to live with the drift.
Whatever the choice, three things should be written down: the rebalancing frequency, the date convention for month ends when the indices close in different time zones, and what happens when a component index is replaced. A benchmark that is recomputed by the custodian on one convention and by the manager on another will produce two excess returns for the same year, and the dispute will be about arithmetic, not skill.
| Equity/bonds | Monthly rebalanced | Weighted annual | Gap, bp |
|---|---|---|---|
| 50/50 | 7.23 | 6.99 | 24 |
| 60/40 | 8.07 | 7.83 | 24 |
| 70/30 | 8.88 | 8.67 | 21 |
| 80/20 | 9.68 | 9.52 | 16 |
The gap is largest when the weights are balanced and shrinks as one component dominates, since a near single-asset benchmark has little to rebalance. Twenty basis points is a material share of the excess return a low tracking error mandate targets, and it feeds straight into tracking error and the information ratio.
There are two. The first is computing the blend from annual or quarterly index returns when the agreement says monthly, which is the 7.83 against 8.07 above. The second is adding monthly blended returns instead of compounding them: the twelve months here sum to 7.96 per cent, a figure that corresponds to no portfolio at all. Benchmark returns must be linked the same way as the fund's, which for a mandate means the time-weighted method in how to calculate time-weighted return.
Check the index variants too: net or gross dividends, hedged or unhedged currency, and the closing time of each index. A blend of a net-dividend equity index and a hedged bond index is a different benchmark from its gross, unhedged twin, often by more than the rebalancing effect.
How one mandate produces several correct returns is the subject of the book, and the free workbook for this case reproduces the calculations.
Put the monthly equity and bond index returns in two columns, compute =0.6*B2+0.4*C2 for each month, then compound with =PRODUCT(1+D2:D13)-1. In the illustrative year that gives 8.07 per cent. Multiplying the two annual returns by 60 and 40 per cent instead gives 7.83 per cent, which is the return of a portfolio never rebalanced during the year.
Rebalancing sells what has risen and buys what has fallen each month. When the components move in opposite directions and reverse, that adds return; in a persistent trend it subtracts. In the illustration the rebalanced 60/40 earns 8.07 per cent, 24 basis points more than buy and hold, whose equity weight drifts to 61.9 per cent by year end.
No. Summing the monthly blended returns ignores compounding: in the illustration the twelve months add up to 7.96 per cent, while the compounded return is 8.07. The gap grows with volatility and with the level of returns, so annual and multi-year figures must always be chain-linked.
This article is one calculation from Asset Management. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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