A calendar effect is an observed pattern in stock prices based on the calendar-f

Question

A calendar effect is an observed pattern in stock prices based on the calendar-for example, a rise or fall associated with a particular weekday or month. The most well-known effect is the January effect, a tendency for prices to increase (especially for small-capitalization stocks) in the first few weeks of January. One explanation is that investors sell poor-performing stocks at year-end to reduce their capital gains taxes, thus depressing the prices. This prompts investors to buy undervalued stocks during the first few weeks of January, causing their prices to go up. In recent years, what has been observed instead is a rise in stock prices in the last week of December, between the Christmas and New Year holidays. This December effect may reflect stock buyers' anticipation of the January effect. Consider the returns on XYZ stock. A researcher uses an extended market model to determine whether the January and December effects are present for this stock. (To simplify the model, he assumes that the January effect occurs in the first week of January.) His regression model is as follows: where y the daily return on XYZ stock x1 the daily return on the Dow Jones Industrial Average 1 if the return occurs in the first week of January; 0 otherwise X2 1 if the return occurs in the last week of December; 0 otherwise X3 The model predicts returns on XYZ stock using returns on a market portfolio, represented by the Dow Jones Industrial Average (DJIA), and a categorical variable that has three levels; that is, whether the return occurs in the first week of January, in the last week of December, or in any other week besides these two. The two dummy variables, x2 and x3, represent the three levels of the categorical variable. A return that occurs outside the first week of January and last week of December is represented by X1. 0 and x2 0 x2 0 and x 0 uation for this case can be written as X1. 0 and x3 0 two weeks) Bo B1x1 X2 1 and x3 1

Explanation / Answer

In the first week of January

Outside the last week of December

Negtaive

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The estimated coeffcient of "First week of January" is negative.

And the p-value is 0.016.

Since p-value is less than 0.05 so we reject the null hypothesis. It is not signficant. You can conclude that

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The estimated coeffcient of "last week of December" is positve.

And the p-value is 0.026.

Since p-value is less than 0.05 so we reject the null hypothesis. It is not signficant. You can conclude that

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X1 = 0.032, X2=1, X3=0

So required predicted value is

y' = 0.011 +1.325*X1-0.012*X2+0.049*X3 = 0.011+1.325 *0.032 -0.012*1+0 = 0.0414

So requried predicted value is 4.1%.

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