Market Adjusted Model


Oil Nationalisation and Managerial Disclosure: The Case of Anglo-Iranian Oil Company, 1933-1951

Chapter 5: The AIOC’s Stock Market reaction to nationalisation: Event Analysis and empirical results

AUTHOR : NEVEEN ABDELREHIM | THE UNIVERSITY OF YORK

There are three different models used in event study literature to estimate ex ante expected returns[689]. These are Mean Adjusted Returns, Market Adjusted Returns and Market and Risk Adjusted Returns. The Mean Adjusted Returns assumes that the ex-ante expected return E (Rit) is constant for each security over time however it differs across securities[690]. It assumes that the return on security i at any point of time is a function of the average past time series of returns. The Mean Adjusted model is consistent with the Capital Asset Pricing Model (CAPM) which assumes that the stock has a constant systematic risk and thus the expected return is constant. The Market Adjusted Returns assumes that the ex-ante expected returns are constant across securities but not necessarily constant over time for a given security since all securities in the sample are assumed to be equal in terms of the size and the risk. The ex-ante expected returns for any security at a point of time E(Rit) equals the expected market return at that particular point of time, i.e. E(Rmt) = Σ Rit, where t = [1,2,3…,T] [691]. Finally, the Market and Risk Adjusted Returns model is based upon the market model estimates for each security in the sample and the abnormal returns are calculated as the difference between the actual stock return and the expected return relative to the market. Abnormal returns result when an event is unanticipated. It worth highlighting that CAPM controls for security risk as well as for the market and assumes non-zero intercept terms through the use of a single factor, β, to compare the excess returns of a portfolio with the excess returns of the market as a whole[692]. This in turn may lead to simplifying the complex market. However, Fama and French[693] added two factors to CAPM to reflect a portfolio’s exposure to these two classes:

but not equal to it. SMB measures the historic excess returns of small caps over big caps and of value stocks over growth stocks. These factors are calculated with combinations of portfolios composed by ranked stocks and available historical market data which can bias the results. There is no doubt that the Fama French model works better than the single factor market models in empirical tests. However, these tests are based on longer run windows for portfolios of large samples of stocks. In an event study of this kind, with a shorter window and single firm case study, there are insufficient observations of book value to operationalise the tests in a three factor framework. Brown and Warner (1980) argued that there are a variety of ways of measuring abnormal returns under different Asset Pricing models. They asserted that the Market Model and Market Adjusted Model had the same power where the specification and power of the actual tests for abnormal performance is similar to that obtained with the OLS market model[694]. They explained that the Market Adjusted Model takes into account market-wide movements which occurred at the same time as the firm experienced the event. Moreover, they asserted that the Market Adjusted Model is also consistent with the Asset Pricing model if all securities have a systematic risk of unity. When the return on a security and the return on the market index are each measured over a different trading interval, ordinary least squares (OLS) estimates of market model parameters are biased and inconsistent[695]. Furthermore, OLS estimates of market model β might be biased and inconsistent due to non-synchronous trading. By constructing OLS residuals for a security sum to zero in the estimation period, a bias in the estimate of β is compensated for by a bias in α[696]. Therefore, they assume that there is a stable linear relationship between the market return and the security return where market model parameters are adjusted as α=0 and β=1 assuming the same risk level among the market and sample security. Thus, the expected value of the difference between the return on a security and the return on market index should in an asset pricing model framework be equal to zero which indicates that the expected return is equal to the market return. Appraisal of the event‟s impact requires a measure of the abnormal return. A security‟s price performance is considered to be abnormal relative to a particular benchmark[697].

The abnormal return for a given security in any time period t is defined as the actual ex post return of the security minus the normal return of the firm over the event window. Estimates of daily abnormal returns (AR) for the ith firm will be calculated as follows:

Cumulative average abnormal returns (CAR) are then calculated by aggregating the abnormal returns over the event period whilst dividends are not ignored.

The basis for inference in event studies is a test statistic for the significance of the empirical results and there is no general agreement on the t-test formula. Therefore, the statistical significance of short term CARs over the event window applied in this study are adopted from Dodd and Warner[698], Kothari and Warner[699] and Goergen and Renneboog[700] who computed the test statistic as the ratio of the mean of CAR to the estimated standard deviation of abnormal returns over the estimation window as follows:

Brown and Warner (1985) explained the above t-statistic for testing one day
abnormal return. However, if the event window has multi day intervals, then the tstatistics will be calculated differently by multiplying the standard deviation of abnormal returns by the square root of the number of event windows as follows:

Where, T is the number of days in the event window and other terms are explained above. It is important to aggregate the abnormal returns for the event window and across observations of the event. The aggregation should be considered through time without any overlap in the event windows of the included security.


References
689. For more details about these models, see for example Mackinlay, Event studies in Economics and Finance; Brown and Warner , Measuring security price performance and Using daily stock returns.

690. Campbell et al., The Econometrics of Financial Market, 151.

691. Ibid.

692. Strong, Modelling abnormal returns: a review article, 536.

693. Fama and French, Common risk factors in the returns on stocks and bonds.

694. Brown and Warner, Using daily stock returns, 25.

695. Ibid, 5.

696. Ibid, 16.

697. Brown and Warner, Measuring security price performance, 207.

698. Dodd and Warner, On corporate governance- a study of proxy contests, 437.

699. Kothari and Warner, Measuring long-horizon security price performance, 308.

700. Goergen and Renneboog, Shareholder wealth effects of European Domestic and Cross-border takeover bids, 18.

 

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