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Quantitative Portfolio Management

Dr. B. Swaminathan, PhDPartner & Director, Research

LSV Asset Management

Professor of FinanceCornell University

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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!

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U.S. Markets: Value vs. Growth in the last 2 years

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LSV past performance

MSCI: Morgan Stanley Capital InternationalEAFE: Europe, Australia, and Far East Index

U.S. Active Strategies YTD 1 Year 5 Years 10 YearsSince

Inception $AUM

LSV Large Cap Value (12/1/93) 6.5% 15.3% 20.7% 11.6% 15.8% $28.2 B

Russell 1000 Value 6.0% 14.5% 18.1% 8.8% 12.4% Closed S&P 500 9.1% 16.5% 15.5% 6.6% 11.0%

Non-U.S. Active Strategies YTD 1 Year 5 Years 7 YearsSince

Inception $AUM

LSV International Value (1/1/98) 12.1% 25.1% 28.0% 18.0% 16.0% $27.3 B

MSCI EAFE Index (net) 13.2% 24.9% 23.6% 8.2% 9.1% Closed MSCI EAFE Value Index (net) 9.6% 22.0% 25.7% 10.8% 11.3%

Periods Ended September 30, 2007

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How does LSV construct its portfolios? Using mean-variance portfolio optimization

theory: 2

},,,{:

21p

wwwσMin

N subject to, (1a)

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N

iiw (wealth constraint) (1b)

P

N

iii rErEw

1

)( (expected return constraint) (1c)

p2 is the portfolio variance which is a function of

individual stock variances and covariances E(rp) is the expected return required from the portfolio wi is the fraction of wealth invested in each security E(ri) is the return expected to be earned in each security

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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.

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Our expertise is estimating expected returns

Our investment philosophy is based on behavioral finance: Stock prices can deviate from Stock prices can deviate from intrinsic/fundamental value because of the actions of naïve intrinsic/fundamental value because of the actions of naïve (unsophisticated) investors who trade based on (unsophisticated) investors who trade based on emotion/psychology as opposed to fundamentals: 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 undervaluedundervalued (price less than intrinsic value) and expected to earn above average returns over the next 2 to 3 years.

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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?

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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.

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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).

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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.

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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.

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Evidence on Value and Momentum

Lakonishok, Shleifer, and Vishny (1994) (LSV) testedValue/glamour strategies using 30 years of data.

Stocks with high fundamental-to-price ratios, book-to-market (B/M), earnings-to-price (E/P), cash flow-to-price (C/P), sales-to-price (S/P) are undervalued or value stocks.

Stocks with low ratios are considered overvalued or glamour stocks.

Sort stocks based on these ratios and buy the value stocks and short the glamour stocks.

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Value strategies based on price ratios

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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.

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Price momentum strategies

Momentum results from Lee and Swaminathan (2000)

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.

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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).

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Behavioral finance explanations of momentum and value

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Combining value and momentum

Late-stage winners High growth in

earnings and sales Overreaction

Winners

Glamour Stocks (Low B/M, High Volume, Long-

Term Positive Earnings Surprises)

Early-stage losers Negative Earnings

Surprises Underreaction

Losers

Late-stage losers Low Growth in

Earnings and Sales Overreaction Value Stocks

(High B/M, Low Volume, Long-Term Negative Earnings

Surprises)

Early-stage winners Positive Earnings

Surprises Underreaction

Momentum Life Cycle Hypothesis (MLC)From: Lee and Swaminathan (2000)

Buy value stockswith positive momentum.

Short sell glamour stocks with negative momentum

LSV model combines value and momentum byputting weights on both

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Major Components of the LSV Model

VALUE

ValueMultiplesFactors

(Cheapness)

LongTerm

PerformanceYr -1 to -5

(Contrarian)

MomentumFactors

Yr -1 to 0

ExpectedReturn+ + =

• 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

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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.

Large Cap Portfolio Investment Process

~ 10,000 STOCK

UNIVERSE

COMPANIES LISTED ON NYSE, AMEX & OTC, EXCLUDING ADR’S, REIT’S, FOREIGN COMPANIES & CLOSED-END FUNDS

~ 1,400 STOCKS

~ 200 STOCK

BUY LIST

STOCKS WITH TOP 15%HIGHEST RANKINGS INVESTMENT GUIDELINES

INDUSTRY LIMITATION COMPANY LIMITATION DIVERSIFICATION OBJECTIVELIQUIDITY OBJECTIVE

90 - 100 STOCKPORTFOLIO PORTFOLIO

CHARACTERISTICS: - LOW M/B, P/E; HIGH DIVIDEND YIELD; BROADLY DIVERSIFIED

Model-basedranking of stocks

Screen for Capitalization,

Liquidity

FUNDAMENTAL VALUE MEASURES AND INDICATORS OF NEAR-TERM APPRECIATION POTENTIAL

Risk Control (Optimizer)

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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.

Sell Discipline

Portfolio Characteristics

RussellLSV Portfolio 1000 Value S&P 500

Price / Earnings 12.2x 14.2x 16.7x

Price / Cash Flow 8.2x 9.2x 11.9x

Price / Book 2.0x 2.1x 2.9x

Dividend Yield 2.5% 2.4% 1.8%

Weighted Average Market Cap $86.5 billion $124.4 billion $110.9 billion

Weighted Median Market Cap $33.2 billion $55.9 billion $59.6 billion

As of 9/ 30/07 Large Cap Value

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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 3Portfolio 20% -3% 20%Benchmark 25% -8% 15%Alpha -5% 5% 5%

We are evaluated on alpha not on raw return!

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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.

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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 8/31/073 and 4: from inception (12/1/93) to 8/31/07

1. The standard deviation of the LSV portfolio is low:LSV R1000V S&P 500

Standard deviation (annualized) 12.3% 12.3% 12.4%

2. The beta of the LSV portfolio is low: R1000V S&P 500

Beta 0.93 0.87

3. The LSV portfolio has offered superior protection in down markets:

Average monthly returns LSV R1000V S&P 500 Down market months -2.3% -2.8% -3.6% Up market months 3.2% 3.1% 3.4%

4. The LSV portfolio exhibits a good risk/ reward trade-off: R1000V

Tracking error (annualized) 4.2%

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Final thoughts.. Keys to successful quantitative

portfolio management: Cutting edge research into new

strategies Careful risk controls Controlling transaction costs Trusting your model