This summary outlines the main topics for the Part 2 Empirical Methods in Finance subject taught by Frank de Jong and Joost Driessen. Subjects: Event studies, Panel data, Time series and Machine Learning.
Empirical Methods in Finance
Block 1 - Event studies
• Event study: test of the change in stock or bond prices around specific “events”. Goal:
- Examine magnitude of some event on the wealth of the security holder
- To test that the market efficiently incorporates new information (EMH)
Efficient Market Hypothesis (EMH)
• Efficient market: market where prices always fully reflect available and relevant information
- Efficiency: two aspects of price adjustment: speed and quality of adjustment (direction and
magnitude)
• Weak ME: prices reflect all information contained in the record of past
- Return predictability
• Semi-strong ME: prices reflect past and all other published information
- Stock reaction on the day the announcement is made
• Strong ME: prices reflect public and private information
- Not suitable for event studies, don’t know the private information
Conducting an event study: Main steps
1. Identify event and timing
- Event time: t=0, every t is a day. Using daily return data
- Event window: starting before and after the event
o Estimation window: estimate NR, benchmark return,
before the event
2. Specify a “benchmark” model for normal stock return behaviour
- Normal return (NR): returns we expect in normal circumstances without an event. Need a
benchmark model:
o Own average return (mean adjusted) → inaccurate measure
o Market return (market adjusted)
o Market model (Rit= α + βi Rmt + eit) → simple linear regression model
o CAPM (Rit – Rft = βi + eit) -> imposes a restriction on the alpha of the market model
3. Calculate and analyse AR around the event date
- ARit = Rit – NRit
• Mean adjusted Return method:
• Market adjusted method: NRit = Rmt
• Market model: NRit = 𝛼̂𝑖 + 𝛽𝑖
̂ Rmt
- α and β are estimated over the estimation period
With And
• ̂ (Rmt – Rft)
CAPM: NRit = Rft + 𝛽𝑖
- Estimate over estimation period, beta from excess returns:
Testing for significance
• AAR= Average Abnormal Return
• H0: no abnormal price effects
- If ARs are independent, identically and normally distributed, the standardized AAR has a
𝑨𝑨𝑹𝒕
standard normal distribution: TS1= √𝑵 ~ N(0,1)
𝝈
o Where σ2 = VAR(ARit)
- Can be used as test statistics by comparing its value to quantiles of the standard normal
distribution
1
, • Estimate σ:
- σ is unknown: it is challenging to estimate the precise impact of an event on asset prices on
beforehand
𝑨𝑨𝑹𝒕
• Test for AR using t-statistic: TS1= √𝑵
𝑺𝒕
• Central Limit Theorem: for large N the t-statistic has approximately a standard normal distribution.
- N>30
Cumulative Abnormal Returns
• CAR over a window around the event and the outperformance measured by CAAR:
• Calculate CAR from the start of the event period to any day t ≤ t2 and CAAR for day t:
𝑪𝑨𝑨𝑹
• T-test: TS2= √𝑵 ≈ N(0,1) where
𝑺
Complications
• Event induced variance:
- Higher variance at or around event date, making it challenging to estimate their impact
accurately
- Cross-section estimators of standard deviation are robust against this
• Event clustering: multiple events in the same calendar time period.
- Induces cross-sectional correlation → makes t-test invalid
- Good benchmark often solves this problem, if not there are 2 solutions:
o Average all returns of the same calendar day into a portfolio return an treat as one
observation in the t-test
o Crude dependence adjustment of standard error: Estimating the variance of the
AAR directly from the time series of observations of AAR in the estimation period:
▪ where AR* is overall average of AR over the
estimation period
𝑨𝑨𝑹
▪ Test statistics now: TS5= ̅
≈ N(0,1)
𝑺
• Non-normality of return distribution:
- Skewness and outliers, mainly in small samples
- Rank or sign tests perform better than t-test
- Sign test: look whether returns are positive or negative
o More robust against outliers
o p= fraction of positive returns
o H0: E(p)=0.5
o TS9= 𝟐√𝑵 (p-0.5) ≈ N(0,1)
- Rank test: rank all returns if firm i in the estimation period + event period (lowest to highest)
o Ui: rank of the event-day returns on firm i in the full distribution of returns
o H0: E(Ui)=0.5
o where sut= SD of Ui
Long horizon event studies
• For long horizon event studies, IPO & SEO, use the Buy-and-hold abnormal returns (BHAR):
- . instead of using:
-
- BHAR gives a compounding effect over months (H) and implies the construction of portfolios
and keeping them until the end of the event period
- CAR assumes a monthly rebalancing of an equally weighted portfolio
2
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller juliareuvers. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $6.98. You're not tied to anything after your purchase.
