2 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?
3 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)
4 Can we earn profit from predictable returns? A traditional approach: Take a sample, e.g., RTSI in Run regression of RTSI on changes in oil price, USD/EUR, LIBOR Leave only the significant variables Check the quality of forecast –R 2, mean squared error, # correctly predicted signs Construct the trading strategy Compare its return with the market Whats wrong with this approach?
5 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
6 Data Monthly returns on S&P500 in 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)
7 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) / R 2 / 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%)
8 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
9 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 –R 2 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
10 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
11 Event study analysis How quickly does the market react to new information? 0+t-t Announcement Date
12 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
14 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
15 Methodology: modelling the return generating process Abnormal return: AR i,t = R i,t – E[R i,t | X t ] Prediction error: ex post return - normal return Normal return: expected if no event happened The mean-adjusted approach: X t is a constant The market model: X t includes the market return Control portfolio: X t 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
16 Methodology: testing the hypothesis AR=0 H 0 : the event has no impact on the firm's value For individual firm: Estimate the benchmark model during the estimation period [τ-t 1 -T: τ-t 1 -1]: R i,t = α i + β i R M,t + ε i,t, where ε ~ N(0, σ 2 (ε)) During the event period [τ-t 1 : τ+t 2 ], under H 0 : AR i,t = R i,t - a i - b i R M,t ~ N(0, V i,t ), var(AR i,t ) = s 2 (ε)[1+1/T+(R M,t -μ M ) 2 /var(R M )]
17 Methodology: testing the hypothesis AR=0 Aggregating the results across firms: Average abnormal return: AAR t = (1/N) Σ i AR i,t Computing var(AAR): –Using the estimated variances of individual ARs, or… –Cross-sectionally: var(AAR t ) = (1/N 2 ) Σ i (AR i,t - AAR i,t ) 2 Aggregating the results over time: Cumulative abnormal return: CAR[τ-t 1 : τ+t 2 ] = Σ t=τ-t1: τ+t2 AR i,t Similarly, average CAR: ACAR = (1/N) Σ i CAR i
18 Example: reaction to earnings announcements CLM, Table 4.1, Fig 4.2: 30 US companies, 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
19 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
20 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
21 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?