Adjustment of Stock Prices

8/4/2019 Adjustment of Stock Prices

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Adjustment of Stock Prices tonew information

Arun TripathiBhadresh Thakkar

Chintan Jani

Rahul Pandya


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Adjustment of Stock Prices to

new information A paper by Eugene Fama, Lawrence Fisher, MichaelJensen & Richard Roll published in InternationalEconomic review (Feb-1969)

Examines the process by which stock prices

adjust to the information that is implicit in a stock split &more specifically addressing the following two questions

1) Is there some unusual behaviour in rates of return ona security in months surrounding the split?

2) If splits are associated with unusual behaviour ofsecurity returns, to what extent can this be accountedfor by relationships between splits and changes in

other more fundamental variables?Slide no.1


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Adjustment of Stock Prices

In answer to the 1st question, stock splits are precededby a period of high returns far in advance of the splitbecause these companies have experienced dramaticincrease in expected earnings and dividends.

However , as per the empirical study made by them ,highest avg monthly return on split shares occur in fewmonths immediately preceding the split which may leadus to believe that proposed split may itself be providingthe impetus for increased returns which actually is notthe case.

This actually reflect the markets anticipation ofsubstantial increases in dividends which , in fact ,usually occur.

Slide no.2


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Empirical Study-Sample & Methodology

A split security listed on NYSE for atleast12 months before and 12 months after

the split Split type: 5 for 4 24 successive months of price-dividend

data around the split date

940 splits meeting these criteria werecaptured from Jan-1927 to Dec-1959

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During the sample period of 33 years, the economic andhence the general stock market conditions were far fromstatic

Since our interest is to study the effects of split andassociated dividend history on returns in isolation, we need toadjust the security returns for general market conditions

This was done by expressing the monthly rates of returnprovided by individual security as a linear function ofcorresponding general market condition

i.e ln(Rjt)=j + jln(Lt) + ujt

Where ,Rjt is the price relative of jth security for month t

Ltis the Fishers index which represents a complicated average of Rjtfor all securities on NYSE

Ujt is the stochastic variable

Slide no.4


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Ujt accordingly should satisfy the following pertaining to a linear regressionmodel

E(Ujt) = 0 . i.e expected value is zero

Variance is independent of t

Ujt values are serially independent

Distribution of Uj is independent of ln(L)

Why the logarathmic form ?

Ln of the price relative is rate of return for given month on that security

Ln of the market index relative is the market return on entire portfolio

The distribution of above Ln values for a month are farily symmetricwhereas the distributions of relatives is skewed. Symmetry is desirablesince models involving symmetrically distributed variables present fewerestimation problems

Finally, when least square is used to estimate for j & j , the residuals

conform to the above assumptions for a simple linear regression model

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Hence the above formulation was found to be a satisfactorymethod for regressing the security returns on market returnsover time for abstracting the effects of general marketconditions on monthly rates of return on individual securities.

Using the available time series on Rjt & Ljt, least squares was

used to estimate j & j in below equation for each of the622 securities in sample of 940 splits.

ln(Rjt)=j + jln(Lt) + ujt

Now, if stock split is associated with abnormal behaviour inreturns during the months surrounding the split date, thisbehaviour should get reflected in the estimated regressionresiduals of the security for these months.

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Effects of Splits on Returns : Empirical Results

Since we are interested with whether the processof splitting is in general associated with specifictypes of return behaviour & not with effects of splits

for individual companies, cross-sectional averagesof estimated regression residuals in monthssurrounding the split dates should be used.

We term this average residual as um which can alsobe interpreted as the avg deviation of returns ofsplit stocks from their normal relationships withmarket.

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Effects of Splits on Returns : Empirical Results We also define a term called cumulative average

residual Um as sum total of abnormal return behaviourin months surrounding the split months which can alsobe interpreted as the cumulative deviation of returns ofsplit stocks.

Further, since we are also interested in dividendbehaviour of split stocks, we bring in um+, um-, Um+, Um-

where,

+ refers to dividend increases which are cases wheredividend change ratio of split stock > ratio for Exchangeas whole.

- refers to dividend decreases which include casesof relative dividend decline.

Slide no.8


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Adjustment of Stock PricesEmpirical results

AVERAGE RESIDUALS-ALL SPLITSSlide no.9


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AVERAGE RESIDUALS-FOR DIVIDEND INCREASESSlide no.10


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AVERAGE RESIDUALS-FOR DIVIDEND DECREASESSlide no.11


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Adjustment of Stock PricesEmpirical results As apparent in all of these plots, the average residuals (um) in29 months prior to the split are uniformly positive for all splits

and both class of dividend behaviour.

This cannot be completely considered as an impetusprovided by stock split announcement.

Moreover as per the finding from various random samples,

the gap between split announcement and effective date wasgenerally 1 to 1.5 months & only in 10% of cases exceeded 4months.

Hence, Split cannot account for the behaviour of regressionresiduals as far as 2.5 years in advance of split date.

The sharp improvement relative to market in preceding years

hence relates to the earnings prospects of the companyduring those years.

Based on this, it can be concluded that companies tend tosplit their shares during abnormally good times i.e whenprices of their shares have increased significantly.

Slide no.12


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The above conclusion gets validated in the above tablei.e no. of splits increases dramatically with increase in general rise in stock pricesSlide no.13


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Adjustment of Stock PricesEmpirical results Another important thing to note is that for

all splits examined together, the largestpositive average residuals occur in 3 to 4months preceding the split but that after

the split are randomly distributed about0.

Equivalently, the cumulative averageresiduals rise dramatically up to splitmonth, but there is almost no furthersystematic movement thereafter.

Slide no.14


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Slide no.15


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Adjustment of Stock PricesEmpirical results This is especially striking since 71.5% of all splitsexperienced greater % dividend increases in year after the

split than the average of all securities on the NYSE.

This can be explained from market interpretation of higherprobability that dividends will soon be substantially increased.

Since firms are reluctant to reduce dividends, then a split,which implies an increased expected dividend, is a signal tothe market that a companys directors are confident of futureearnings of the company.

Hence large price increases in months immediately precedinga split are due to altering expectations concerning the futureearning potential of firm rather than any intrinsic effects of thesplit itself.

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Cumulative Average Residuals Cumulative Average Residuals

(DIVIDEND INCREASES) (DIVIDEND DECREASES)

For both dividend cases, in the months preceding the split,cumulative average residuals rise sharply which is in line withour hypothesis that market recognizes that splits are usually

associated with higher divided payments.Slide no.17


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Adjustment of Stock PricesEmpirical results-Conclusion For the behaviour post split in case of dividend increases case, for the 1st year

where there is a slight upward drift, it can be attributed to the fact that in manycases dividend increases in the year after the split.

After the 1st year, the returns on stocks which had experienced dividend

increases, have resumed their normal relationships to market returns.

Contrary, in case of dividend decreases case, by the time it has become clear

that anticipated dividend increase is not forthcoming, the effect of split arecompletely wiped away which is supported by the plummeting values of theseresiduals.

Hence to sum up, The study suggests that once the information effects of associated dividend

changes are considered, a split per se has no net effect on common stockreturns.

This implies that on an average, market makes unbiased dividend forecastsfor split securities and these forecasts are fully reflected in the priceadjustments that take place to the extent of anticipated level of futuredividends.

Slide no.18


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Adjustment of Stock Prices