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Corporate Finance

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Corporate Finance ...

    Econometrics of Financial Markets, NES 2006/7

    Lecture notes for the course

    ECONOMETRICS OF FINANCIAL MARKETS

    Lecture 1. Introduction

Structure of the course:

    ? Objective:

    o Understand the dynamics of financial asset prices / returns

    o Master tools of the empirical analysis of financial data

    ? Specifics of the analysis:

    o Econometric methods

    ? Statistics theory, distributions, time series and panel data analysis

    o Theory of asset pricing

    ? Efficient markets, CAPM, APT

    o Practice of financial markets

    ? Returns vs. profits, organization of trade, strategies of market participants

Major events in the Russian stock market in 2006

    ? Growth of RTS by 70%

    o From 1100 to 1800

    ? High volatility

    o Falling to 1300 in May from 1600 in March

    ? Large difference between different stocks

    o Oil: Lukoil vs. Rosneft vs. TNK-BP

    o Mobile: Vimpelcom vs. MTS

    ? Main factors

    o High oil prices

    o Strengthening of ruble

    o Gradual increase in interest rates

    Lectures 2-4. Tests of return predictability

Plan

    ? Specifics of financial data ? The efficient market hypothesis

    ? Tests for return predictability:

    o WFE: autocorrelations, variance ratios, and regression analysis

    o SSFE: informational and operational efficiency

    Specifics of financial data

    How to explain asset prices/returns? ? Prices are not stationary!

    ? Returns

    o Simple: R = (P-P)/P ttt-1t-1

    ? Easy to compute portfolio return

    o Log: R = ln(P/P) ttt-1

    ? Easy to aggregate over time

    ? Doesn't violate limited liability

    o Arythmetic vs geometric average

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    Econometrics of Financial Markets, NES 2006/7

Market microstructure effects

    ? Which prices to use to measure returns?

    o Average vs. close

    o Bid vs. ask

    ? Can you make real profit out of paper returns?

    o Transaction costs, including bid-ask spread

    o Liquidity

    o Price impact

Stylized facts about the financial markets

    ? Non-normality

    o Thick tails

    o Asymmetry

    ? Returns

    o Negative autocorrelation at ultra-short horizon

    o Positive autocorrelation at short horizon

    o Negative autocorrelation at long horizon

    o Cross-correlation

    ? Volatility

    o Clustering in time

    o Inverse relation with prices

    o Smaller when the market are closed

    o Higher in times of forecastable releases of info

    o Inverse relation with auto-correlation

    o Common factors for different assets

    o Too high relative to fundamentals: often explosive growth or crashes

    The efficient market hypothesis ? First by Bachelier (1900)

    ? The classical formulation by Fama (1970)

The efficient market hypothesis (EMH): stock prices fully and correctly reflect all relevant info

    P = E[P |I] + ε, t+1t+1tt+1

    where the forecast error has zero expectation and orthogonal to I t

    In terms of returns: R = E[R |I] + ε, t+1t+1tt+1

    where E[R |I] is normal return or opportunity cost implied by some model t+1t

Different forms of ME wrt the information set:

    ? Weak: I includes past prices

    ? Semi-strong: I includes all public info

    ? Strong: I includes all info, including private info

Different types of models:

    ? Constant expected return: E[R] = μ tt+1

    o Tests for return predictability

    ? CAPM: E[R] R = β(E[R] R) ti,t+1FitM,t+1F

    o Tests for mean-variance efficiency Is market efficiency testable? ? Multi-factor models

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    Econometrics of Financial Markets, NES 2006/7 What if the EMH is rejected?

    ? The joint hypothesis problem: we simultaneously test market efficiency and the model

    o Either the investors behave irrationally,

    o or the model is wrong

    ? One cannot earn money on this

    o Ex-ante expected profit within information and transaction costs

    If the EMH is not rejected, then… ? the underlying model is a good description of the market,

    o the fluctuations around the expected price are unforecastible, due to randomly arriving

    news

    ? there is no place for active ptf management…

    o technical analysis (WFE), fundamental analysis (SSFE), or insider trading (SFE) are

    useless

    o the role of analysts limited to diversification, minimizing taxes and transaction costs

    ? or corporate policy:

    o the choice of capital structure or dividend policy has no impact on the firm‟s value (under

    MM assumptions)

    o still need to correct market imperfections (agency problem, taxes, etc.)

Is perfect ME attainable?

    ? The Grossman-Stiglitz paradox:

    o there must be some strong-form inefficiency left to provide incentives for information

    acquisition

    ? Operational efficiency:

    o one cannot make profit on the basis of info, accounting for transaction costs

Testing the EMH:

    ? Tests of informational efficiency:

    o Finding variables predicting future returns

    o Statistical significance

    ? Tests of operational efficiency:

    o Finding trading rules earning positive profit taking into account transaction costs and risks

    o Economic significance

    ? Tests of fundamental efficiency:

    o Whether market prices equal the fundamental value implied by DCF

    o Whether variability in market prices is consistent with variability in fundamentals

    Tests of return predictability

Different properties of the stochastic processes:

    ? Martingale: E[X] = X tt+1t

    o First applied to stock prices (but they must be detrended)

    ? Fair game: E[Y] = 0 tt+1

    o Under EMH, applies to the unexpected stock returns: E[R - k] = 0 tt+1t+1

    Simplest model: constant expected return, E[R] = μ tt+1

    Sufficient conditions:

    ? Common and constant time preference rate

    ? Homogeneous expectations

    ? Risk-neutrality

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    Econometrics of Financial Markets, NES 2006/7

    Random walk with drift: P = μ + P + ε tt-1tTo ensure limited liability: lnP = μ + lnP + u tt-1t

The random walk hypotheses:

    2? RW1: IID increments, ε ~ IID(0, ζ) t

    o Any functions of the increments are uncorrelated 2o E.g, arithmetic (geometric) Brownian motion: ε (u) ~ N(0, ζ) tt

    ? RW2: independent increments How are random walk o Allows for unconditional heteroskedasticity

    hypotheses related to ? RW3: uncorrelated increments, cov(ε, ε) = 0, k>0 tt-kunit root tests?

    Tests for RW1:

    ? Sequences and reversals

    o Examine the frequency of sequences and reversals in historical prices

    o Cowles-Jones (1937): compared returns to zero and assumed symmetric distribution

    ? The Cowles-Jones ratio of the number of sequences and reversals:

    CJ=N22/N=[p+(1-p)]/[2p(1-p)], where p is the probability of positive return sr

    ? H: CJ=1, rejected 0

    o Later: account for the trend and asymmetry, H not rejected 0

    ? Runs

    o Examine # of sequences of consecutive positive and negative returns

    2? Mood (1940): E[N] = Np (1-p)+p,… runs,iiii

    ? ME not rejected

Tests for RW2:

    ? Technical analysis

    o Axioms of the technical analysis: What is the link between ? The market responds to signals, which is reflected

    technical analysis and in ΔP, ΔVol

    ? Prices exhibit (bullish, bearish, or side) trend market microstructure? ? History repeats

    o Examine profit from a dynamic trading strategy based on past return history (e.g., filter rule:

    buy if past return exceeds x%)

    ? Alexander (1961): filter rules give higher profit than the buy-and-hold strategy

    ? Fama (1965): no superior profits after adjusting for trading costs

    ? Pesaran-Timmerman (1995): significant abnormal profits from multivariate

    strategies (esp in the volatile 1970s)

Tests for RW3:

    ? Autocorrelations

    o For a given lag

    ? Fuller (1976): asy distribution with correction for the small-sample negative bias in

    autocorrelation coef (due to the need to estimate mean return)

    o For all lags: Portmanteau statistics

    ? Box-Pierce (1970): Q ? T Σ

    2ρ(k) k

    ? Ljung-Box (1978): finite-sample correction

    o Results from CLM, Table 2.4: US, 1962-1994

    ? CRSP stock index has positive first autocorrelation at D, W, and M frequency

    ? Economic significance: 12% of the variation in daily VW-CRSP predictable from

    the last-day return

    What is the relation between 4 VR and autocorrelations?

    Econometrics of Financial Markets, NES 2006/7

    ? The equal-wtd index has higher autocorrelation

    ? Predictability declines over time

    ? Variance ratios: VR(q)?Var[r(q)]/(q Var[r]) tt

    o H: VR=1, the variance of returns is a linear function of the time interval 0

    o In general, VR is a function of autocorrelation coefficients

    ? E.g., VR(2)=1+2ρ 1o Results from CLM, Tables 2.5, 2.6, 2.8: US, 1962-1994, weekly

    ? Indices: VR(q) rises with time interval, predictability declines over time, is larger

    for small-caps

    How to reconcile positive ? Individual stocks: weak negative autocorrelation

    ? Size-sorted portfolios: sizeable positive cross-autocorrelations of autocorrelations, large-cap stocks lead small-caps indices with negative ? Time series analysis: ARMA models autocorrelations of o Testing for long-horizon predictability: regressions with

    individual stocks? overlapping horizons, R(h)=a+bR(h)+u, t=1,…,T t+htt+h

    ? Serial correlation: ρ(k) = h-k => use HAC s.e.

    o Results from Fama-French (1988): US, 1926-1985

    ? Negative autocorrelation (mean reversion) for horizons from 2 to 7 years, peak of

    b=-0.5 for 5y

    ? Poterba and Summers (1988): similar results based on VR

    o Critique:

    ? Small-sample and bias adjustments lower the

    significance

    Why use 3 approaches ? Results are sensitive to the sample period, largely due

    to 1926-1936 (the Great Depression) (autocorrelation, VR, and regression Interpretation: analysis) to test ME? ? Behavioral: investor overreaction o Assume RW with drift, E

    [R] = μ tt+1o There is a positive shock at time η

    o The positive feedback (irrational) traders

    buying for t=[η+1:η+h] after observing

    R η

    o SR (up to η+h): positive autocorrelation,

    prices overreact

    o LR (after η+h): negative autocorrelation,

    prices get back to normal level

    o Volatility increases

    ? Market microstructure: non-synchronous

    trading

    o Low liquidity of some stocks (assuming

    zero returns for days with no trades)

    induces negative autocorrelation (and

    higher volatility) for them, positive

    autocorrelation (and lower volatility) for

    indices, lead-lag cross-autocorrelations

    o Consistent with the observed picture

    (small stocks are less liquid), but cannot

    fully explain the magnitude of the

    autocorrelations

    ? More complicated model: time-varying expected

    returns E

    [R] = E[R] + E[RiskPremium] tt+1tF,t+1tt+1

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    Econometrics of Financial Markets, NES 2006/7

    o Changing preferences / risk-free rate / risk premium

    o Decline in interest rate => increase in prices

    ? If temporary, then positive autocorrelation in SR, mean reversion in LR

Conclusions:

    ? Reliable evidence of return predictability at short horizon

    o Mostly among small stocks, which are characterized by low liquidity and high trading costs

    ? Weak evidence of return predictability at long horizon

    o May be related to business cycles (i.e., time-varying returns and variances)

Harvey, 1991, The world price of covariance risk

Objective:

    ? Investigate predictability of developed countries‟ stock index returns

Methodology:

    ? Time series regressions

    o Consider dollar-denominated excess returns

    o Use global and local instruments

Data:

    ? Monthly returns on MSCI stock indices of 16 OECD countries and Hong Kong, 1969-1989

    o The indices are value-weighted and dividend-adjusted

    o Only investable domestic companies are included

    o Investment and foreign companies are excluded (to avoid double counting)

    ? Risk-free rate: US 30-day T-bill

    ? Common instruments:

    o Lagged world excess return

    o Dummy for January

    o Dividend yield of S&P500

    o Term spread for US: 3month 1month T-bill rates

    o Default spread for US: Moody‟s Baa – Aaa yields

    ? Local instruments:

    o Lagged own-country return

    o Country-specific dividend yield

    o Change in FX rate

    o Local short-term interest rate

    o Local term spread

Results: 2? Common instruments, Table 3 )

    o Reject SSFE for most countries (F-test based on R? 13 out of 18 at 5% level, 10 at 1% level

    2o The world ptf is most predictable: R = 13.3% a

    o Strongest predictors:

    ? Dividend yield: + for 11 countries

    ? Term spread + for 7 countries

    ? Default spread + for US and world, - Austria

    ? January dummy + Hong Kong and Norway, - Austria (16 positive)

    ? Adding local instruments to common instruments, Table 4

    o Overall improvement in R2 is small 2? The largest increase in adjusted R for Norway and Austria

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    Econometrics of Financial Markets, NES 2006/7

    o Surprisingly small impact of FX rate and local interest rates

    o Most important: local return and dividend yield

Conclusions:

    ? Stock indices of developed countries are predictable

    ? Common information variables capture most of the predictable variation

    ? Later they will be used as instruments in conditional asset pricing tests

Pesaran&Timmerman, 1995, Predictability of stock returns: Robustness & economic significance

Objective:

    ? Examine profits from trading strategies using variables predicting future stock returns

    ? Simulate investors‟ decisions in real time using publicly available info

    o Estimation of the parameters

    o Choice of the forecasting model

    o Choice of the portfolio strategy

    ? Account for transaction costs

Methodology: recursive approach, each time t

    ? Using the data from the beginning of the sample period to t-1,

    ? Choose (the best set of regressors for) the forecasting model using one of the criteria:

    o Statistical: Akaike / Schwarz (Bayes) / R2 / sign

    ? Sign criterion: maximize proportion of correctly predicted signs

    o Financial: wealth / Sharpe (adjusted for transaction costs!)

    ? Maximize profit from the switching strategy / Sharpe coefficient ? Choosing portfolio strategy:

    o Switch (100%) between stocks and bonds based on the forecast

    ? No short sales

    ? No leverage

    ? Accounting for transaction costs

    o Constant (over time), symmetric (wrt buying and selling), proportional (to the price)

    o Three scenarios: zero, low (0.5% stocks / 0.1% bonds), or high (1% / 0.1%)

Results:

    ? Robustness of the return predictability, Figures 1-3

    o The volatility of predictions went up, esp. after 1974

    o The predictability was decreasing, except for a large increase in 1974

    ? Main predictors, Table 1

    o Most important: T-bill rate, monetary growth, dividend yield, and industrial growth

    o The best prediction model changed over time

    ? Dividend yield: after 1970

    ? Monetary and industrial growth: after 1965

    ? Inflation: after the oil shock

    ? Interest rates: excluded in 1979-82, when the Fed did not target % ? Predictive accuracy, Table 2

    o The market timing test (based on % of correctly predicted signs) rejects the null

    ? Mostly driven by 1970s ? Performance of the trading strategy, Table 3

    o Market is a benchmark:

    ? Mean return = 11.4%, std = 15.7%, Sharpe = 0.35

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    Econometrics of Financial Markets, NES 2006/7

    o Zero costs

    ? All criteria except for Schwarz yield higher mean return, around 14-15%

    ? All criteria have higher Sharpe, from 0.7 to 0.8 (0.5 for Schwarz)

    o High costs

    ? R2 and Akaike yield higher mean return

    ? Financial criteria esp. suffer from transaction costs

    ? Most criteria still have higher Sharpe, from 0.5 to 0.6 ? Test for the joint significance of the intercepts in the market model:

    o Returns are not fully explained by the market risk, even under high transaction costs

Conclusions:

    ? Return predictability could be exploited to get profit

    o Using variables related to business cycles

    ? Importance of changing economic regimes:

    o The set of regressors changed in various periods

    o Predictability was higher in the volatile 1970s

    ? Incomplete learning after the shock?

    ? Results seem robust:

    o Similar evidence for the all-variable and hyper-selection models

    o Returns are not fully explained by the market model

    Lecture 5. Event study analysis

Plan

    ? Methodology of event studies

    o Problems and solutions

    ? Performance of event study tests

    ? Specifics of modelling illiquid stocks

    ? Specifics of long-run event studies

Event studies (tests for rapid price adjustment): most important tool to test SSFE

    ? Measure the speed and magnitude of market reaction to a firm-specific event

    o High-frequency (usually, daily) data

    o Ease of use, flexibility

    o Robustness to the joint hypothesis problem

    ? Experimental design

    o Pure impact of a given event

    o Role of info arrival and aggregation

Methodology:

    ? Identification of the event and its date

    o Type of the event:

    ? Share repurchase / dividend / M&A / change in gvt policy

    o Date of the event η=0

    ? Announcement, not the actual payment

    ? The event window: several days around the event date

    o Selection of the sample

    ? Must be representative, no selection biases

    ? Modelling the return-generating process

    Why include several days o Abnormal return: AR

    in the event window?

     = R E[R | X] i,ti,ti,tt

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    Econometrics of Financial Markets, NES 2006/7

    ? Prediction error: ex post return - normal return

    o Normal return: expected if no event happened Which approach is ? The mean-adjusted approach: X is a constant tthe best for IPOs? ? The market model: X includes the market return t

    ? Control portfolio: X is the return on portfolio of similar firms (wrt size, BE/ME) t

    o The estimation window: period prior to the event window

    ? Usually: 250 days or 60 months

    ? Testing the hypothesis H: AR=0, the event has no impact on the value of the firm 0

    o For an individual firm:

    ? Estimate the benchmark model during the estimation period [η-t-T: η-t-1]: 112R = α + βR + ε, where ε ~ N(0, ζ(ε)) i,tiiM,ti,ti,tWhy are ARs ? During the event period [η-t: η+t], under H: 120

    ARauto-correlated? = R - a - bR~ N(0, V), i,ti,tiiM,ti,t22where var(ARR) = s(ε)[1 + 1/T + (R-)/var(R)] Mi,tM,tM

    o Aggregating the results across N firms:

    ? Average abnormal return: AAR = (1/N) Σ AR tii,t

    ? Computing var(AAR):

    ? Using the estimated variances of individual ARs, or…

    22? Cross-sectional approach: var(AAR) = (1/N) Σ (AR - AAR) tii,ti,t

    o Aggregating the results over time:

    ? Cumulative abnormal return: CAR(η-t: η+t) = Σ AR 12t=η-t1: η+t2i,t

    ? Similarly, average CAR: ACAR = (1/N) Σ CAR ii? Relation between CARs and company characteristics:

    o Cross-sectional regressions

    ? OLS with White errors

    ? WLS with weights proportional to var(CAR)

    o Account for potential selection bias

    ? The characteristics may be related to the extent to which the event is anticipated

    ? Long-run impact of the event

    o The estimation error is much larger

Asquith&Mullins, 1983, The impact of initiating dividend payments on shareholder wealth

Objective:

    ? Measure stock price reaction to dividend announcements

    o Costs vs clientele vs signaling vs other theories

    ? Sample of companies initiating dividend payments

    o No need to model investors‟ expectations

    ? Explicitly control for other news

    ? Relate ARs to the magnitude of dividends

    o The first cross-sectional analysis of factors explaining ARs

    ? Compare reaction to initial and subsequent dividends

Data:

    ? 168 firms that initiated dividend payments to common stockholders in 1963-1980

    o 114 increased dividends within 3 years

    o 7 decreased dividends

    ? The announcement date:

    o Publication in the Wall Street Journal

    ? Other announcements in +/- 10 day interval around the event date

    ? Daily stock returns

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    Econometrics of Financial Markets, NES 2006/7

Methodology:

    ? Normal return: on control portfolio with similar beta + AR -10o Each year, stocks traded in NYSE and ASE were grouped into 10 portfolios ranked by beta ? Cross-sectional approach to compute std: t(ACAR) = ?N ACAR / std(CAR) tti,t? Event window: [-1:0] o To capture cases when the news was published on the next day after the announcement Results: ? Main variable: CAR[-1:0] = AR? Table 1, all firms in the sample

    o AR = 2.5%, AR= 1.2%, both with t>3 -10

    o Two-day ACAR = 3.7% with t=6.6

    o Almost 70% of firms experienced positive market reaction

    o Other ARs are small and insignificant

    ? Consistent with ME

    ? No leakage of info prior to div announcement ? Table 3, subsamples of firms

    o 88 firms with no other new info: two-day ACAR = 4.7% with t=5.9

    ? Dividend and earning announcements may be partial substitutes!

    o Firms that subsequently raised dividends: smaller and marginally (in)significant ACARs

    ? No expectation model for subsequent dividends! ? Table 4, CS regression of CARs on the change in payout yield

    o Slope coefficient: captures the effects of an unexpected div increase

    ? Positive relation for both initial and subsequent dividends

    ? The reaction is stronger for subsequent dividends

    o The intercept: captures the expected div increase (with negative sign)

    ? Negative for subsequent dividends (they are partially forecast)

Conclusions:

    ? The first clean test of the market reaction to dividends

    ? The positive effects of dividends overweigh the negative ones

    o Support for the signaling model

    ? Market efficiency is not rejected

Strengths of the event study analysis

    ? Direct and powerful test of SSFE

    o Shows whether new info is fully and instantaneously incorporated in stock prices

    o The joint hypothesis problem is overcome

    ? At short horizon, the choice of the model usually does not matter

    o In general, strong support for ME

    ? Testing corporate finance theories

    o Average AR measures market reaction to a certain type of the event

    o E.g., wealth effects of M&A, financing decisions, etc.

Event studies: problems and solutions

    ? Uncertain event date

    o Use cumulative abnormal return

    ? Event-induced variance

    o Use cross-sectional approach to compute var(ACAR)

    ? Heteroscedasticity

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