Principles of Finance PDF

Introduction Theory Empirical test of market efficiency (Event study) Principles of Finance Lecture 12 & 13: Capital Market Efficiency (CWS ch. 10 & 11, MacKinley (1997)...

Introduction Theory Empirical test of market efficiency (Event study) Principles of Finance Lecture 12 & 13: Capital Market Efficiency (CWS ch. 10 & 11, MacKinley (1997) & Kothari and Warner (2004)) Rikke Sejer Nielsen 1 / 46 Introduction Theory Empirical test of market efficiency (Event study) Introduction Purpose of capital markets: Transfer funds between lenders and borrowers efficiently. ▶ Individuals lend out funds if few productive opportunities and great wealth. ▶ Individuals borrow funds if many productive opportunities and insufficient wealth. ⇒ BUT how efficient are these funds allocated? ⇒ Both lenders and borrowers are better off if capital markets are used efficiently to facilitate fund transfers 2 / 46 Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Capital Market Efficiency Definition of market efficiency To what degree, prices reflect all available relevant information ⇒ When assets are traded in an efficient market, prices are accurate signals for capital allocation. ⇒ Less restrictive than market perfection. 4 / 46 Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Capital Market Efficiency, cont. Three types of efficiency: 1 Weak-form efficiency: ▶ Prices fully reflect all past information ▶ No investor can earn excess/abnormal return using historical price/return information. 2 Semistrong-form efficiency: ▶ Prices reflect all publicly available information ▶ No investor can earn excess/abnormal return using publicly available information. 3 Strong-form efficiency: ▶ Prices reflect all information ▶ No investor can earn excess/abnormal return using any information Empirical evidence indicates that capital markets are efficient in the weak and semistrong forms. 5 / 46  Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Value of Information In a one-period setting Value of an information structure η (a set of messages m of various possible events e) X X V (η) ≡ q(m) max p(e|m)U(a, e) −V (η0 ) a m e | {z } maximize expected utility by choosing an action (’optimal’ action) given message m where q(m) = Prior prob. of receiving a message m, p(e|m) = Conditional prob. of an event e, given a message m, U(a, e) = Utility from an action a if an event e occurs ⇒ Benefit function, V (η0 ) = Expected utility of the decision maker without the information. 7 / 46  Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Value of Information In a one-period setting Value of information depends on 1 Utilities of the payoff to the decision maker, given an action, 2 Optimal action by the decision makers, given receipt of a message. 3 Probabilities of states of nature provided by the messages 8 / 46  Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Value of Information In a multi-period setting In the multi-period setting: Value of information ≈ the value of real option. ⇒ For a given message, a decision maker may or may not choose to take an action. 9 / 46 Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Value of information and market efficiency For the joint distributions of security prices Given information set at t − 1 used by the market (the representative investor) for pricing. m fm (P1t ,... , Pnt |ηt−1 ) Given all relevant information available at t − 1. f (P1t ,... , Pnt |ηt−1 ) In an efficient market: m fm (P1t ,... , Pnt |ηt−1 ) = f (P1t ,... , Pnt |ηt−1 ) ⇒ Information set used by the market = information set of all relevant information. 10 / 46 Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Value of information and market efficiency, cont. Information structure only adds value if it brings ’new’ relevant information ⇒ Not the case in the efficient market! In an efficient market, the utility value of the gain from information to the ith individual must be V (ηi ) − V (η0 ) ≡ 0 ⇒ No one can earn abnormal returns ⇒ No incentive to acquire information ⇒ Random selection of securities is just as effective. 11 / 46 Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Value of information and market efficiency, cont. Ex. a capital market with weak form of efficiency: Relevant information set, ηi , = set of historical prices So when the market is efficient: Information set used by the market, ηim , includes past price histories. ⇒ Security prices reflect past prices histories ⇒ Value of trading based on past prices = 0. 12 / 46 Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Rational Expectations and Market Efficiency For a given information structure, how is the decision-making process reflected in security prices on the market? Several hypotheses: Naı̈ve hypothesis: Asset prices are completely arbitrary Speculative equilibrium hypothesis: An individual’s investment decision is based on anticipations of the behavior of other investors. Intrinsic value hypothesis: Pricing of securities based on estimates of future payouts Rational expectations hypothesis: Pricing of securities based on exp. future payouts and resale value. ⇒ Rational expectations market is an efficient market 14 / 46 Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Market efficiency and Costly Information Market efficiency relies on arbitrageurs/analysts to search for information to make a profit ⇒ Ensures to drive prices back to equilibrium value consistent with available information. BUT why search for information when no one can earn an abnormal return? It is possible to make a profit for analysts But acquiring information is costly! Competition among analysts ⇒ the return from analysis equals the cost, on average ⇒ net of costs, abnormal return = 0 16 / 46  Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Market efficiency and Costly Information Example: Rational behavior of individuals when information is useful, but costly. Two strategies exist: 1 Random selection strategy w. fee c1 = 4% for the right to trade, 2 Analyst strategy w. fee c2 = 8% for acquiring info. ▶ Informational advantage doubles your competitive advantage/your return: d = 2. Additional information a ’normal’ return, r , of 6%, p is the probability to use analyst strategy. 17 / 46  Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Market efficiency and Costly Information Example: Rational behavior of individuals when information is useful, but costly. Expected payoff of trading: E(Payoff for analyst (A)) = p (r − c2 ) +(1 − p) (dr − c2 ) | {z } | {z } Payoff of A trading Payoff of A trading with another A with RS =−2% =4% r  E(Payoff to random selector (RS)) = p − c1 +(1 − p) (r − c1 ) d | {z } | {z } Payoff of RS trading Payoff of RS trading with another RS with an A =2% =−1% 18 / 46  Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Market efficiency and Costly Information Example: Rational behavior of individuals when information is useful, but costly. Expected payoff of trading: 19 / 46  Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Market efficiency and Costly Information Example: Rational behavior of individuals when information is useful, but costly. In equilibrium with anonymous trading E(Payoff to analysis strategy) =E(Payoff to random selection) r (1 − d) + c2 − c1 2 ⇔p= = 2r − rd − r /d 3 ⇒ No one will be tempted to change strategies ⇒ On average, the return from searching for information equals searching cost. ⇒ Net of costs, the abnormal return is zero. (as return of random selection = return of analysis strategy) ⇒ Investors may earn different gross returns because of different costs for acquiring information. 20 / 46  Introduction Theory Empirical test of market efficiency (Event study) Value of Information Rational Expectations Costly Information Market efficiency and Costly Information Example: Rational behavior of individuals when information is useful, but costly. For a mixed strategy (0 < p < 1) , we need (on the board) r (d − 1) > c2 − c1 and r (1 − 1/d) < c2 − c1 , If no net economic profit ⇒ No incentive to enter the capital market. E(Payoff to analysis strategy) =0 E(Payoff to random selection) =0 c2 rd − c2 ⇔d = and p= c1 rd − r ⇒ a stable mixed strategy where all net profits are zero. 21 / 46 Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Event Studies Testing market efficiency, we use an event study, defined as An event study measures the effect of economic events on the equity value of companies. Capital market valuation of economic events. ▶ Examples: capital increase, stock splits, investments, actions of financing, corporate governance changes etc. One of the most important and mostly used instruments in empirical research in the field of corporate finance. 23 / 46 Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Fundamentals of an Event Studies Assumptions and requirements: Event study requires semi-strong information efficiency. ▶ At least past historical prices and publicly available information have to be reflected in the prices on the capital market. Central element: Date when information about the event reaches the capital market for the first time (’announcement day’). Sample of as many cases as possible, in which the event occurred. ▶ Changes in market value on the announcement day may be caused by numerous idiosyncratic events. ▶ A large sample diversifies ⇒ only event triggers a price reaction on average. 24 / 46 Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Fundamentals of an Event Studies The relationship between event studies and the efficient market hypothesis: 25 / 46 Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Fundamentals of an Event Studies Example from MacKinlay A. (1997). 26 / 46 Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 General Procedure 27 / 46 Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Step 1 Time structure of an event study Estimation period: ▶ To determine the parameters of ’normal’ returns. Separation period: ▶ Period to ensure that estimation of the model for ’normal’ returns is not influenced by the event. 28 / 46 Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Step 1, cont. Time structure of an event study Event window: ▶ Period, in which information processing by the capital market takes place. Event day: ▶ Date, when information about the event reaches the capital market for the first(!) time. 29 / 46 Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Step 2: Normal return Normal return is the benchmark for the announcement effect of a single event. Use of capital market model (usually: single factor model) Rit − Rft = αi + βi (Rmt − Rft ) + εit Rit is the stock return of event firm i at time t, Rmt the return of the market portfolio proxy, εit an i.i.d. error term with E(εit ) = 0. ⇒ Use estimation period to find estimates for αi , and βi. To calculate the ’normal return’ at some point in time τ : ⇒ Use Rmτ , α̂i , and β̂i. In addition, the variance of the error term of this regression has to be calculated, as ’normal’ variation: var (εit ) = σi2 30 / 46 Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Step 3: Abnormal return Abnormal return (AR) is the difference between the ’observed’ and the ’normal’ return:
ARit = (Rit − Rft ) − α̂i + β̂i (Rmt − Rft ) Aggregation over time: Cumulative abnormal returns (CAR) over the event window period: v X CARi (u, v ) = ARit , t=u where u and u is the beginning and end of event window, respectively. Aggregation across securities/events: Average cumulative abnormal returns (ACAR) for N securities/events: N 1 X ACAR = CARi N i=1 31 / 46 Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Example The Excel ’EventStudies students.xlsx’ contains daily excess return data. All given returns are excess returns, i.e. they are already adjusted for the risk-free rate. Returns are given as decimals, e.g. 0.02 = 2%. All companies had one spin-off each during the given time frame. The announcement days, the estimated coefficients for the capital market model (α̂i and β̂i2 ) and the estimated variances of the error terms of the capital market model (σ̂i2 ) are given in the Excel sheet. Calculate the Normal Returns, Abnormal Returns, Cumulated Abnormal Returns (CAR) and Average Cumulated Abnormal Returns (ACAR) in the event window. 32 / 46  Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Step 4: Significance test of ACAR with independent events: Time series variance test (Brown/Warner 1985, JFE): Significance test of ACAR assuming independent time series variance of single AR N ACAR 1 X T1 = p ∼ N(0, 1) with var (ACAR) = 2 ET · var (εit ) var (ACAR) N i=1 where ET = Number of days in event window. Cross-sectional test: Significance test of ACAR with cross section variance N ACAR 1 X T2 = p ∼ N(0, 1) with var (ACAR) = (CARi − ACAR)2 var (ACAR) N2 i=1 Allows that event changes variance of AR. 33 / 46  Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Step 4: Significance test of ACAR, cont. with independent events: Non-parametric test: Significance test of ACAR without distribution assumption " #√ N+ N T3 = − 0.5 ∼ N(0, 1) N 0.5 where N + is number of positive CAR in the event window). 34 / 46 Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Example, cont. Back to example from before. Calculate the test statistic for the H0 -hypothesis that the estimated ACAR is zero using Time Series Variance (Brown/Warner) approach. 1 PN Hint: Use var (ACAR) = N2 i=1 ET · σ̂i2 , with ET = number of days in event window, and N = number of events as an estimator for the variance of the ACAR. 35 / 46  Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Step 4: Significance test of ACAR with correlated events: Event clustering: Events of different firms may occur at similar points in time (i.e. there are overlapping event windows) Correlations in returns occur e.g. through ▶ Systematic return factors ⇒ No problem, if these factors are included in the market model of ’normal’ returns. ▶ Industry- / Group effects etc. The previously presented significance tests for ACAR require independence of events. e.g. using Time series variance test: ⇒ A larger sample reduces influence of unrelated (other) events on event day. If the (other) events were not idiosyncratic (but correlated), these effects would not cancel out. ⇒ CAR-variance calculation for t-test assumes independence of variances. 36 / 46  Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Step 4: Significance test of ACAR, cont. with correlated events: Impact of correlation for the Cross-Sectional Test: ▶ Independence assumption is violated if events are correlated in cross section, after controlling for the market factor (September 11, Hot-issue-markets etc.). Non parametric test: ▶ Analogous to cross section test. Temporal dispersion of events reduces cross-sectional correlation. ▶ The biggest problem for the validity of significance tests is therefore temporal clustering of the events. 37 / 46  Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Step 4: Significance test of ACAR, cont. with correlated events: Two approaches generally used: 1 Regression analysis 2 Calendar-time portfolio approach 38 / 46  Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Step 4: Significance test of ACAR, cont. with correlated events: Regression analysis: The problem of clustering of events can be solved by regression analysis Step a: Translate the estimation problem into a regression model Step b: Use advanced regression estimators that account for clustering 39 / 46  Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Step 4: Significance test of ACAR, cont. with correlated events: Regression analysis (Step a): The standard event study approach can be expressed as a regression model, in which ▶ For each event firm i, a (separate) market model regression is conducted: rit = ai + bi rmt + di DEvent,i + eit ∀i = 1,..., N ▶ Regressors: Dummy-variable for the event window, return of market portfolio proxy, intercept. ∗ To get equivalent results compared to the Brown/Warner-approach, only estimation period (DEvent,i = 0) and event window (DEvent,i = 1) may be used. Alternative: Isolate separation period by additional dummy variables. 40 / 46  Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Step 4: Significance test of ACAR, cont. with correlated events: Regression analysis (Step b): Significance tests as Wald/F-Test of the average of event dummy coefficients for all equations. N 1 X di = 0 N i=1 Problems: ▶ AR are heteroscedastic by definition! ▶ F-Test of single OLS-equations requires independence assumption ∗ If there are common factors, that are not determined in the market model, the error terms of different regression equations are correlated. Specifically: Correlation of error terms that correspond to the same point in time. ⇒ Violation of independence assumption! 41 / 46  Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Step 4: Significance test of ACAR, cont. with correlated events: Calendar-time portfolio approach: Construct event portfolio ▶ In the observation period t = 1,..., T , find for all t the companies, for which an event took place at t (t ∈ τu,v ) ▶ Add up the returns of these event companies (equally weighted/value weighted). Time series of the event portfolio (EP) returns is regressed on factors of market model (excess returns!) REP,t − Rft = αEP + βEP (Rmt − Rft ) + εEP,t ⇒ Intercept is the average announcement effect 42 / 46  Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Step 4: Significance test of ACAR, cont. with correlated events: Calendar-time portfolio approach: Properties ▶ With sufficient observations of the event portfolio, highest power of all methods. ▶ Robust against cross-sectional correlation. ▶ Heteroscedasticity and autocorrelation can (should) be considered (e.g. using a White or Newey/West correction). 43 / 46 Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Example, cont. Back to example from before. Calculate the Calendar-Time Portfolio (CTP) returns for the event window [-1,+1] with equal weights for each security. Give the vector of values for the dependent variable y and the values of the matrix X which would be needed to run the OLS regression for the average Calendar-Time Portfolio announcement effect. 44 / 46 Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 Econometric challenges There are many econometric problems/challenges in event studies. Misspecifications of expected returns (wrong inference due to bias in the estimates of abnormal returns) Non-random sample, leading to non-normal distributions (wrong inference due to standard error calculations) 45 / 46 Introduction Theory Empirical test of market efficiency (Event study) Fundamentals Step 1 Step 2 Step 3 Step 4 References CWS, ch. 10 & 11. MacKinley (1997) Kothari and Warner (2004) 46 / 46