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### Quantitative Portfolio Management

Dr. B. Swaminathan, PhD

Partner & Director, Research

LSV Asset Management

Professor of Finance

Cornell University

LSV Asset Management

- LSV in business for 12 years
- More than $75 billion under management
- Academic foundation
- Deep value equity orientation; stock selection based on proprietary quantitative models
- Domestic / International
- Well diversified / risk controlled
- Active money manager, not a hedge fund!
- Objective: to beat the market!

LSV past performance

MSCI: Morgan Stanley Capital International

EAFE: Europe, Australia, and Far East Index

How does LSV construct its portfolios?

- Using mean-variance portfolio optimization theory:

Inputs to the problem

- Start with a list of stocks (say the most “attractive” 100 stocks in the U.S. stock market).
- Input the return each stock is expected to earn over the next year. You will have a column of 100 expected returns.
- Estimate each stock’s variance and covariances with every other stock. You will have a 100100 variance-covariance matrix.
- Add additional constraints as necessary (industry constraints, short-selling constraints, socially responsible investing constraints).
- Construct a portfolio with the highest expected return for a given level of risk.

Our expertise is estimating expected returns

- Our investment philosophy is based on behavioral finance: Stock prices can deviate from intrinsic/fundamental value because of the actions of naïve (unsophisticated) investors who trade based on emotion/psychology as opposed to fundamentals:
- Extrapolation bias
- Overconfidence bias
- We believe such mispricing/inefficiencies can be identified through careful empirical research involving historical stock market data and exploited to earn above average returns.
- Our quantitative model is built to identify securities that are undervalued (price less than intrinsic value) and expected to earn above average returns over the next 2 to 3 years.

Market efficiency and behavioral finance: A digression

- Market efficiency Price = Intrinsic Value
- Questions:
- Are the markets efficient? (Are the prices right?)
- Can we beat the market? (Is there free lunch?)
- If the prices are right can we earn free lunch?
- Does “no free lunch” imply prices are right?

Apparent violations of market efficiency

- Reversals at short horizons (day, week, month): buy loser, sell winner.
- Momentum at intermediate horizons ( 3 to 12 months): buy winner, sell loser.
- Reversals again (value/glamour) at long horizons (3 to 5 years): buy loser, sell winner.

Rational paradigm

- Rational beliefs:
- Update beliefs using Bayes theorem.
- Rational preferences: Maximize expected utility where:
- people prefer more to less
- diminishing marginal utility of wealth (as you get wealthier an extra $1 of wealth brings a smaller increase in utility).

What is behavioral finance?

- Behavioral finance attempts to understand the evolution of security prices and explain the observed stock return predictability using models in which agents are not fully rational.
- According to Barberis and Thaler (2003), behavioral finance contends “that some financial phenomena can be better understood using models in which some agents are not fully rational.”
- Thus, behavioral finance considers models in which (a) investors’ beliefs are not updated in a rational manner and (b) investors’ utility functions are different from those suggested by the expected utility theory.

Value and Momentum: Two major ingredients of the LSV model

- Value Value stocks (price below intrinsic value) outperform Glamour stocks (price above intrinsic value) over the next five years.
- Strategies based on fundamentals-to-price ratios.
- Strategies based on long-term (3 to 5 year) returns.
- Momentum Past winners outperform Past losers over the next year.
- Price momentum.
- Earnings momentum.
- LSV model combines value and momentum.

Evidence on Value and Momentum

Lakonishok, Shleifer, and Vishny (1994) (LSV) tested

Value/glamour strategies using 30 years of data.

Contrarian strategies based on past returns

- Originally studied by De Bondt and Thaler (1985). The results above from Fama and French (1996).
- “1” is the portfolio of longer-term losers and “10” is the portfolio of longer-term winners. The idea is that longer-term losers recover while longer-term winners experience a price decline.

Price momentum strategies

Jegadeesh and Titman (1993) showed that winners outperform losers.

Lee and Swaminathan (2000) confirm these findings and show that trading volume can be used to enhance momentum.

Earnings Momentum Strategies

- Quarterly earnings surprises are defined as the scaled difference between this quarter’s earnings and earnings the same quarter last year (3rd quarter 2007 vs. 3rd quarter 2006).
- Low represents portfolios with negative earnings surprises and High represents portfolios with positive earnings surprises.
- Chan, Jegadeesh, and Lakonishok (1996).

Combining value and momentum

Buy value stocks

with positive momentum.

Short sell glamour stocks with negative momentum

LSV model combines value and momentum by

putting weights on both

Momentum Life Cycle Hypothesis (MLC)

From: Lee and Swaminathan (2000)

Value

Multiples

Factors

(Cheapness)

Momentum

Factors

Yr -1 to 0

Long

Term

Performance

Yr -1 to -5

(Contrarian)

Expected

Return

+

+

=

- Cash flow
- Earnings
- Book
- Sales

- Poor long-run stock returns
- Slow long-run earnings growth
- Slow long-run sales growth

- Share price momentum
- Earnings Momentum
- Analysts Revisions
- Earnings Changes
- Earnings Surprises

Major Components of the LSVModel

Variance-Covariance Matrix

- We estimate variance-covariance matrix based on historical data over the last five years.
- Most value added in long-term portfolio management comes from having better estimates of expected returns or alphas.
- Different approaches to estimating variance-covariance matrix do about the same in forecasting risk in the long-run.

UNIVERSE

COMPANIES LISTED ON NYSE, AMEX & OTC,

EXCLUDING ADR’S, REIT’S, FOREIGN

COMPANIES & CLOSED-END FUNDS

Screen for

Capitalization,

Liquidity

~ 1,400

STOCKS

FUNDAMENTAL VALUE MEASURES

AND INDICATORS OF NEAR-TERM

APPRECIATION POTENTIAL

Model-based

ranking of stocks

~ 200

STOCK

BUY LIST

STOCKS WITH TOP 15%

HIGHEST RANKINGS

INVESTMENT GUIDELINES

INDUSTRY LIMITATION

COMPANY LIMITATION DIVERSIFICATION OBJECTIVE

LIQUIDITY OBJECTIVE

Risk Control (Optimizer)

90 - 100 STOCK

PORTFOLIO

PORTFOLIO CHARACTERISTICS:

- LOW M/B, P/E; HIGH DIVIDEND

YIELD; BROADLY DIVERSIFIED

Large Cap Portfolio Investment Process

A STOCK IS SOLD WHEN:

- MODEL RANKING FALLS BELOW THE TOP 40%.
- PORTFOLIO WEIGHT EXCEEDS 2.5% RELATIVE TO THE BENCHMARK.

TURNOVER

- APPROXIMATELY 30% PER YEAR.

Alpha and tracking error

- Since our portfolios are compared to benchmarks such as Russell 1000, S&P 500 etc., what is relevant to us is not the total return, but the level of outperformance, abnormal return, or alpha:
- Case 1 Case 2 Case 3

Portfolio 20% -3% 20%

Benchmark 25% -8% 15%

Alpha -5% 5% 5%

We are evaluated on alpha not on raw return!

Alpha and tracking error

- Abnormal return = rp – rBM where rp is the portfolio return and rBM is the benchmark return.
- Alpha = E(rp – rBM)) (average abnormal return).
- Tracking error = StdDev(rp – rBM); It is a measure of additional (idiosyncratic) risk a portfolio manager takes by deviating from the benchmark.
- The objective is to earn high alpha at a low tracking error or achieve a high information ratio.
- Information Ratio = Alpha/Tracking Error.
- In the mean-variance problem, we use abnormal return instead of raw return and the variance-covariance matrix is also based on abnormal returns.
- Construct a portfolio that maximizes alpha given a target tracking error.

Various risk controls

- Low to moderate target tracking error (around 4% to 5% for our US large cap strategy).
- Industry and sector constraints (not deviating too much from the benchmark weights).
- Beta is a measure of comovement of a portfolio with the market index (we do not have explicit targets).
- 80 to 120 stocks in a portfolio to achieve broad diversification.

Risk of the LSV Large Cap Portfolio

1 and 2: 5 years as of 8/31/07

3 and 4: from inception (12/1/93) to 8/31/07

Final thoughts..

- Keys to successful quantitative portfolio management:
- Cutting edge research into new strategies
- Careful risk controls
- Controlling transaction costs
- Trusting your model

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