Advances in Active Portfolio Management*

Ronald N. KahnGlobal Head of Systematic Investment Research, BlackRock

Q Group Presentation

December 7, 2020

*A new book by Richard Grinold and Ronald Kahn

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Overview

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Active Portfolio Management, 2nd Edition appeared 20 years ago.

• Material is not particularly timebound.

• At the same time, much has changed since then: markets, data, regulations, technology, …

• The authors have advanced the theory and applied it to new problems.

Seems an appropriate time to put together a sequel: Advances in Active Portfolio Management

• Collection of previously published articles—updated, assessed, put into context—along with some new and unpublished material.

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Content

Recap of Active Portfolio Management

Advances in Active Portfolio Management:

• Dynamic Portfolio Management

• Portfolio Analysis and Attribution

Applications of Active Portfolio Management:

• Expected Return

• Risk

• Portfolio Construction

Extras

This Talk: Some Highlights

Investing is fundamentally a dynamic problem. It is not a one-period problem.

At any given time, we have old information decaying in value while we are receiving new information. We can approximate this lumpy dynamic process with a smooth equation:

We also have utility:

Dynamic Portfolio Management:Perspective*

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𝛼! 𝑡 = 𝑒"#$% ⋅ 𝛼! 𝑡 − Δ𝑡 + )𝑆! 𝑡 ⋅ Δ𝑡

utility = 𝐩! ⋅ 𝛼 − "#𝐩! ⋅ 𝐕 ⋅ 𝐩 − 𝑐 𝐩 𝑡 − Δ𝑡 → 𝐩 𝑡

*Garleanu and Pedersen, “Dynamic Trading with Predictable Returns and Trading Costs,” Journal of Finance, December2013 covers similar ground and extends the analysis somewhat.

Dynamic Portfolio Management

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If we make the strong assumption that trading costs are proportional to the variance of the trade basket (and we ignore any constraints), we can derive some analytical results.*

𝑐 𝒑 → 𝒎 =𝒙𝟐⋅ 𝒎 − 𝒑 ! ⋅ 𝐕 ⋅ 𝒎 − 𝒑

First, introduce two important portfolios (one of which we already know):

where d is our rate of trading, which at optimality depends on other model parameters, and

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* “All models are wrong, but some are useful.”𝜓 =𝑑

𝑑 + 𝑔≤ 1

𝒒 𝑡 =𝐕!" ⋅ 𝛼 𝑡

𝜆

𝒎 𝑡 = 𝜓 ⋅ 𝐪 𝑡

optimalpositionsinabsenceofcosts

targetportfolio,takingcostsintoaccount.𝜓 dependson𝑔, 𝑑

Trading Rule (in our analytical model)

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The goal of portfolio management is to track the target portfolio

The term d provides the optimal trading rate and is a function of the model parameters in the analytical model. Note that is the backlog.

The model provides many useful results (also functions of input parameters):

• Breadth, after-cost information ratio, transfer coefficient, average leverage and turnover, average age of information in the portfolio

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𝐦 𝑡 − 𝐩 𝑡 − Δ𝑡

𝐩 𝑡 = 1 − 𝛿 ⋅ 𝐦 𝑡 + 𝛿 ⋅ 𝐩 𝑡 − Δ𝑡

Δ𝐩 𝑡 = 𝑑Δ𝑡 ⋅ 𝐦 𝑡 − 𝐩 𝑡 − Δ𝑡 where𝛿 = ℯ!𝒹#$ ≈ 1 − 𝒹Δ𝑡 for small Δ𝑡

Dynamic Model: Applications and Extensions

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Application: Signal WeightingIn the absence of costs, signal weighting is a topic effectively covered in Active Portfolio Management. We can turn J signals into J characteristic portfolios and then use mean-variance optimization to optimize the weight (or equivalently the risk) we want on each signal in optimal Portfolio Q. The dynamic model provides optimal weights in target Portfolio M:

Extension: Linear and Non-linear Trading RulesInspired by the analytical model but wanting to use a more realistic cost model, we can assume optimal policies of trading as a function of the backlog and determine asset by asset optimal trading rates. This will lead to signal weights at the asset level.

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𝜔>,@ =𝑑

𝑑 + 𝑔@⋅ 𝜔A,@

Dynamic Portfolio Management: Final Comments

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This requires some unnatural

elements like the cost amortization

parameter.

We can capture a dynamic trading

policy with a single period optimization.

One contribution of the dynamic

model is to anchor us to the fundamentally

dynamic nature of the effort.

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Portfolio Analysis and Attribution

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Turn disparate asset attributes into portfolios. The attributes are the potential explanatory variables (e.g. alpha sources and risk factors).

– This is different from the traditional regression-based approach where we regress asset returns on explanatory variables. Here we start by turning every variable into a portfolio.

Assembling the explanatory variables is the creative step, as in regression analysis.

Examine the correlation and risks of those portfolios. The analysis is centered on a covariance matrix (which may have nothing to do with the attributes or portfolio construction).

First the structure, then the questions. We risk biasing our analysis if we build an ad hoc structure for every question we want to analyze.

Same framework for ex ante and ex post. Ex ante we can explain portfolio alpha, variance, opportunity loss, and transfer coefficient. Ex post, we can explain portfolio return, the opportunity set, and assess risk controls.

One key advantage of this approach is to decouple attribution and risk analysis from risk model details. We require a covariance matrix but do not necessarily use factors that may underlie it.

– If we use the same factors as in the traditional regression approach, we will find the same results. If we struggled with large residuals before, this will not reduce them.

We use the attributes to explain these correlationsThis can facilitate interesting analyses, e.g. how is my portfolio exposed to old ideas like the alphas from three months ago?

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Portfolio Analysis and Attribution

Mid-Horizon fund with varying

exposure to old alpha ideas.

Portfolio Analysis and Attribution

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The book also describes how to use optimizer constraints and costs in the attribution.

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Expected Return: Are Benchmark Portfolios Efficient?

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Fundamental question for investors: can active managers add value?Approach:• Build ex post efficient frontier from a set of N building block assets over T

periods. The assets include:

–The benchmark portfolio

–N-1 active strategies easily described before inspecting the data. The paper (and the chapter) use four factor portfolios: value, size, momentum, volatility.

Apply the Gibbons, Ross, Shanken (GRS) test to determine if the maximum Sharpe Ratio portfolio on the efficient frontier is statistically distinct from the benchmark. Test assumes normal distributions.

Expected Return: Are Benchmark Portfolios Efficient?

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Power of the test is proportional to T – N so choose the building block assets judiciously. GRS chose sector portfolios, capitalization deciles, and beta deciles.

The book describes a less elegant but more straightforward simulation approach that can take into account non-normal returns. We can then ask where the ex post result appears in the distribution of possible outcomes.

The original paper appeared in 1992 and showed that 4 of 5 benchmarks (US, UK, Japan, Australia) looked inefficient through the lens of this particular test. Only Germany looked efficient.

Expected Return: Smart Beta

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Active products with some of the benefits of index products.• Active in that the goal is to outperform the market.

• Transparent and rules-based, like indexing, with fees between those of active and index products.

Smart beta products attempt to provide exposures to key elements of active management. For equities, these include:

This idea goes right back to Stephen Ross in 1976• And Black, Jensen & Scholes mentioned the Low Volatility effect in 1972.

To first order, today’s smart beta products are the quant equity strategies of the late 1980s.

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QualityLow

VolatilityValue MomentumSmall Size

Disruptive Innovation

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This is more than a new product. This is a disruptive "innovation" for active management.

Funny to call this an innovation when the ideas have been around for decades. But this isn’t an investment innovation, it is a product innovation.

Suddenly, important components of successful active management have been carved out and offered to investors for below active fees.

Smart Beta Factors: Already Part of Investment Management

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Investment Return

Cap-weighted Index Benchmark

ReturnActive Return

Return from Average (Static)

Exposures to Smart Betas

“Pure Alpha” Return

Stephen A. Ross, Daniel Kahneman, Amos Tversky, Sanford Grossman, and Joseph Stiglitz (from left to right) are academics responsible for theories connected to the above return streams.Source: BlackRock, as of September 30, 2019. For illustrative purposes only.

• Thisdecompositionofactivereturnroughlydividesupthedriversofsuccessfulactivemanagementwithriskpremiaononesideandinformationalinefficienciesontheother.

• Thisleadstoverydifferentapproachestoactivemanagement.

• Thisdecompositioncanalsohelpusbuildoptimalportfoliosofproducts.

Risk premia,

Behavioral anomalies

Informational Advantages

Data Source: eVestment. Analysis by BlackRock. As of 12/31/2017

What Fraction of Active Returns Are Smart Beta?

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0%

5%

10%

15%

20%

25%

5% 10% 20% 30% 40% 50% 60% 70% More

FractionofM

anagersineachBucket

PercentofActiveRiskBudgetExplainedbyFactors

138 International Equity ManagersMean = 35%

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Portfolio Construction: Dangers of Diversification

Challenges of managing multiple manager portfolios: a central task for investors.

Standard approach: mean-variance applied to investment products.

Three issues:

• Concentration of generic risk and exposure to tail risk

• Temptation to leverage

• Tendency to forget the big picture (problem for multi-strategy funds in particular)

One solution: seek out orthogonal strategies as much as possible.

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Portfolio Construction:

Mean-Varianceand Scenario-based Approaches

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Investors tend to use mean-variance approaches to portfolio construction while expected utility maximization (using scenario-based approaches) is more popular in academia.• One criticism of mean-variance is that

it is blind to higher moments of the return distribution.

At a high level, the paper shows that mean-variance is hard to beat for problems involving many assets and a benchmark, and with the asset universe changing over time. Scenario-based approaches can make sense for problems involved a steady universe of a few assets and a focus on total returns (e.g. strategic asset allocation).

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Portfolio Construction:

Mean-Varianceand Scenario-based Approaches

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One key contribution of this chapter is its detailed focus on avoiding pitfalls of scenario-based approaches. In particular, it’s important to control the analysis so that in the absence of any non-consensus information it leads to a consensus solution.

This is built into mean-variance optimization relative to a benchmark. If your forecast alphas are all zero, the benchmark is the optimal choice.

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Summary

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The book covers advances to the theory covered in Active Portfolio Management, as well as new applications of that theory.

The focus remains on how to best build active portfolios based on non-consensus information.

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Appendix: Table of Contents

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The following notes should be read in conjunction with the attached document:

• This material is provided for information purposes only and is not intended to be an offer or invitation to anyone to invest in any BlackRock products or services. The information and opinions contained herein are not guaranteed as to accuracy or completeness and are subject to change without notice.

• Past performance is not a guide to future performance.

• All financial investments involve an element of risk. Therefore, the value of your investment and the income from it will vary and your initial investment amount cannot be guaranteed.

• No part of this material may be reproduced, stored in any retrieval system or transmitted in any form or by any means, electronic, mechanical, recording or otherwise, without the prior written consent of BlackRock.

• UNLESS OTHERWISE SPECIFIED, ALL INFORMATION CONTAINED IN THIS DOCUMENT IS CURRENT AS OF {December 7, 2020}.

BlackRock® is a registered trademark of BlackRock, Inc. All other trademarks are the property of their respective owners.

© 2020 BlackRock, Inc. All rights reserved.

Important notes

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