Financial Econometrics II

Lecture 2

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Up to now:

Tests for informational WFE assuming constant

expected returns

Autocorrelations

Variance ratios

Time series analysis

Why use different types of tests?

How to interpret the results?

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Plan for today:

Advanced topic: tests for operational SSFE

Regression analysis using public information variables to predict

returns

Measuring profitability of trading strategies exploring the predictability

New topic: event study analysis

High-frequency analysis of changes in security prices in response to

news (events)

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Can we earn profit from predictable returns?

A traditional approach:

Take a sample, e.g., RTSI in 1999-2006

Run regression of RTSI on changes in oil price, USD/EUR, LIBOR

Leave only the significant variables

Check the quality of forecast

– R2, mean squared error, # correctly predicted signs

Construct the trading strategy

Compare its return with the market

What’s wrong with this approach?

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Pesaran and Timmerman (1995 )

"Predictability of stock returns: Robustness and economic significance"

Examine profits from trading strategies using variables predicting future stock returns

Simulate investors’ decisions in real time using publicly available information Estimation of the parameters Choice of the forecasting model Choice of the portfolio strategy

Account for transaction costs

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Data

Monthly returns on S&P500 in 1954-1992

Forecasting variables Dividend yield, P/E ratio 1-month T-bill rate / 12-month T-bond rate Inflation rate Δ industrial production / money supply

Adjustments: 12-month moving averages 2-month lag for macro variables (1m for others)

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Methodology: Recursive approach

Each time t, using the data from the beginning of the sample period up to t-1: Choose (the best set of regressors for) the forecasting model using

one of the criteria:

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

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

Choose portfolio strategy

– Switching (100%) between stocks and bonds

Account for transaction costs

– Constant, symmetric, and proportional

– Zero, low (0.5% stocks / 0.1% bonds), or high (1% / 0.1%)

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Results

Robustness of the return predictability, Fig. 1-3 The volatility of predictions went up, esp after 1974 The predictability was decreasing, except for 1974

Predictors, Table 1 Most important: T-bill rate, monetary growth, dividend yield, and

industrial growth The best prediction model changed over time!

Predictive accuracy, Table 2 The market timing test (based on % of correctly predicted signs)

rejects the null– Mostly driven by 1970s

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Results (cont.)

Performance of the trading strategy, Table 3 Market is a benchmark:

– Mean return 11.4%, std 15.7%, Sharpe 0.35 Zero costs

– All but one criteria yield higher mean return, around 14-15%

– All criteria have higher Sharpe, from 0.7 to 0.8 High costs

– R2 and Akaike yield higher mean return

– Most criteria still have higher Sharpe, from 0.5 to 0.6 Results mostly driven by 1970s

Test for the joint significance of the intercepts in the market model: The null rejected, even under high transaction costs

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Conclusions

Return predictability could be exploited to get profit Using variables related to business cycles

Importance of changing economic regimes: The set of regressors changed in various periods Predictability was higher in the volatile 1970s

– Incomplete learning after the shock?

Results seem robust: Similar evidence for the all-variable and hyper-selection models Returns are not explained by the market model

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Event study analysis

How quickly does the market react to new information?

0 +t-t

Announcement Date

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Event study analysis

Measure the speed and magnitude of market reaction to a certain event High-frequency (usually, daily) data Ease of use, flexibility Robustness to the joint hypothesis problem

Experimental design Pure impact of a given event Role of info arrival and aggregation

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Reaction to the unexpected event

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Methodology: identification of the event and its date

Type of the event

Share repurchase / dividend / M&A

Date of the event τ=0

Announcement, not the actual payment

The event window: several days around the event date

Selection of the sample

Must be representative, no selection biases

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Methodology: modelling the return generating process

Abnormal return: ARi,t = Ri,t – E[Ri,t | Xt] Prediction error: ex post return - normal return

Normal return: expected if no event happened The mean-adjusted approach: Xt is a constant The market model: Xt includes the market return Control portfolio: Xt is the return on portfolio of similar firms (wrt

size, BE/ME)

The estimation window: period prior to the event window Usually: 250 days or 60 months

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Methodology: testing the hypothesis AR=0

H0: the event has no impact on the firm's value

For individual firm:

Estimate the benchmark model during the estimation period [τ-t1-T: τ-t1-1]:

Ri,t = αi + βiRM,t + εi,t, where ε ~ N(0, σ2(ε))

During the event period [τ-t1: τ+t2], under H0:

ARi,t = Ri,t - ai - biRM,t~ N(0, Vi,t),

var(ARi,t) = s2(ε)[1+1/T+(RM,t-μM)2/var(RM)]

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Methodology: testing the hypothesis AR=0

Aggregating the results across firms:

Average abnormal return: AARt = (1/N) Σi ARi,t

Computing var(AAR):

– Using the estimated variances of individual ARs, or…

– Cross-sectionally: var(AARt) = (1/N2) Σi (ARi,t - AARi,t)2

Aggregating the results over time:

Cumulative abnormal return:

CAR[τ-t1: τ+t2] = Σt=τ-t1: τ+t2 ARi,t

Similarly, average CAR: ACAR = (1/N) Σi CARi

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Example: reaction to earnings announcements

CLM, Table 4.1, Fig 4.2: 30 US companies, 1989-93

Positive (negative) reaction to good (bad) news at day 0

No significant reaction for no-news

The constant mean return model produces noisier estimates than the

market model

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Methodology: explaining abnormal returns

Relation between CARs and company characteristics:

Cross-sectional regressions

– OLS with White errors

– WLS with weights proportional to var(CAR)

Account for potential selection bias

– The characteristics may be related to the extent to which the event is

anticipated

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Strengths of the event study analysis

Direct and powerful test of SSFE Shows whether new info is fully and instantaneously incorporated in

stock prices The joint hypothesis problem is overcome

– At short horizon, the choice of the model usually does not matter In general, strong support for ME

Testing corporate finance theories Average AR measures market reaction to a certain type of the event

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Quiz

How to measure AR for a stock after IPO?

How to construct a control portfolio?

Why are tests usually based on CARs rather than ARs?

How to deal with infrequently traded stocks?

What are the problems with long-run event studies?