Value Added in Portfolio Management simply explained

In portfolio management, understanding how a portfolio outperforms or underperforms its benchmark is key. This outperformance, known as "value added" or "active return," can be broken down into two main components: asset allocation and security selection.

Let's dive into an example to see how this works in practice.

PORTFOLIO (P):

• Stocks: 60%
• Bonds: 40%

• Stock Performance: 10%
• Bond Performance: 5%

BENCHMARK (B):

• Stocks: 50%
• Bonds: 50%
• Stock Performance: 8%
• Bond Performance: 3%

Calculation of the Total Value Added:
This is the difference between the total return of the portfolio and the total return of the benchmark. It involves calculating the average return attributable to each asset class, weighted by their respective weights in the portfolio and in the benchmark, and then finding the difference.

• Total Return of the PORTFOLIO = 0.6 * 10 + 0.4 * 5 = 6 + 2 = 8% (1)
• Total Return of the BENCHMARK = 0.5 * 8 + 0.5 * 3 = 4 + 1.5 = 5.5% (2)

• TOTAL VALUE ADDED = (1) - (2) = 8 - 5.5 = 2.5%

The term “value added” is often used interchangeably with “active return,” but it can also be broken down to show the source of the performance added relative to the benchmark.

Performance Difference Due to Asset Allocation
(Weight in Asset Class P - Weight in Asset Class B) * Benchmark Performance =

(0.6 - 0.5) * 8 + (0.4 - 0.5) * 3 = 0.8 - 0.3 = 0.5%

We want to know the contribution of the difference in weights assigned by the manager to each asset class relative to the benchmark to the total performance difference between the two.

So, we multiply the BENCHMARK PERFORMANCE by the difference in weights between P and B. This gives us the contribution of each asset class to the over- or under-performance RELATIVE to the BENCHMARK.

Performance Difference Due to Security Selection:

Two methods:

1. By Deduction:
Value Added = Return due to Asset Allocation + Return due to Security Selection

Return due to Security Selection = Value Added - Return due to Asset Allocation

Return due to Security Selection = 2.5 - 0.5 = 2%

2. By Formula:
Weight of Asset Class in the BENCHMARK * (Performance of the Asset Class in the Portfolio - Performance of the Asset Class in the Benchmark)

0.5 * (10 - 8) + 0.5 * (5 - 3) = 2%

We want to isolate the contribution of the asset class to the performance difference between the portfolio and the benchmark, so we weight the difference in performance of the asset class in the portfolio and the benchmark by the weight given to the asset class in the benchmark. We assume the same weighting of assets in P and B. So, if the weight is the same, we effectively exclude the contribution of asset allocation to the overall performance.

Note that for asset and security selection, we factor by the benchmark's performance and the weight of the asset class in the benchmark, respectively, which is always the reference index.
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