Building Blocks of Active Equity Portfolio Construction

Active returns are assessed in relation to a benchmark. If a portfolio holds the same securities in the same proportions as the benchmark, no active return exists. However, active return emerges when the portfolio manager starts to allocate more or less to certain securities compared to the benchmark. The equation depicts this:

$$ R_A = \sum \Delta W_i R_i $$

Where:

\(R_A\) = Active return.

\(R_i\) = Return from security i.

\(\Delta W\) = The active weight security i.

Sources of Active Returns

Active returns can be earned through the following categories:

1. Exposure to rewarded factors: These are attributes linked to positive long-term returns, such as beta, size, and value. This aligns with the concept of Smart Beta discussed earlier.
2. Tactical exposures to mispriced securities, sectors, or rewarded risks: Managers with valuation insights can profit from mispricing by making strategic investments.
3. Idiosyncratic risk (Luck): This risk arises from luck and isn’t attributable to the previous two factors.

The breakdown of realized active return (historical return) is illustrated by the following equation:

$$ R_A = \sum (B_{pk} – B_{bk}) \times F_k + (\alpha + e) $$

Where:

\(B_{pk}\) = Portfolio sensitivity to a rewarded factor.

\(B_{bk}\) = Benchmark sensitivity to a rewarded factor.

\(F_k\) = The return of the rewarded factor.

\(\alpha\) = The return attributable to alpha (manager skill).

\(e\) = The return attributable to idiosyncratic risk (noise, chance, etc.).

Integrating the Building Blocks Breadth of Expertise

A manager demonstrates breadth of expertise by effectively merging all sources of active return to generate portfolio alpha. The fundamental law of active management provides a useful formula to dissect the elements contributing to outperforming a benchmark, allowing the calculation of the expected active return:

$$ E(R_A) = IC \ BR^{0.5} \sigma_{RA}\ TC $$

Where:

\(E(R_A)\) = Active return expected.

\(IC\) = Information coefficient.

\(BR^{0.5}\) = Square root of the breadth.

\(\sigma_{RA}\) = Manager's active risk.

\(TC\) = Transfer coefficient.

The information coefficient gauges the correlation between manager forecasts and actual expected returns. This could be thought of as a number between -1 and 1 which indicates how well the manager predicts movements in market prices.

Breadth refers to the number of independent decisions a manager makes annually. More independent decisions tend to result in higher active returns.

The transfer coefficient (TC) measures portfolio construction constraints. It varies between 0 and 1, with 1 signifying complete freedom and 0 indicating total constraints. A TC of 0 means no active returns can be earned, as per the fundamental law of active management.

Question

According to the fundamental law of active management, a portfolio with higher constraints would be expected to experience:

1. Lower TC; lower active returns.
2. Higher TC; lower active returns.
3. Lower TC; higher active returns.

Solution

The correct answer is A.

It suggests that higher constraints would lead to a lower Information Coefficient (IC) and a lower Breadth (BR). If this were true, the Information Ratio (IR) would decrease, leading to lower active returns. This is a reasonable interpretation of the fundamental law of active management, so this choice is correct.

Formula:

$$ E(R_A) = IC \ BR^{0.5} \ \sigma_{RA} \ TC $$

TC with Value of 1:

$$ 1= (1) \times (1) \times (1) \times (1) $$

TC with Value of 0:

$$ 0= (1) \times (1) \times (0) \times (1) $$

B is incorrect. It implies that higher constraints would lead to a higher Information Coefficient (IC) and lower Breadth (BR). If this were the case, the Information Ratio (IR) could go either way. The IR depends on both IC and BR, and it's not clear how they would change in relation to each other when constraints increase. So, this choice is not necessarily correct because it oversimplifies the relationship.

C is incorrect. It suggests that higher constraints would lead to a higher Information Coefficient (IC) and a higher Breadth (BR). While a higher BR may lead to the potential for more independent investment opportunities, this alone doesn't guarantee higher active returns. A higher IC is important for generating more accurate forecasts, but it's not clear how the trade-off between IC and BR would work with increased constraints. This choice oversimplifies the relationship and is not necessarily correct.

Reading 26: Active Equity Investing: Portfolio Construction

Los 26 (a) Describe elements of a manager's investment philosophy that influence the portfolio construction process