Midterm paper for the course “Financial Econometrics” icef, 10/11/2010

1. (15 Points)

a.) Your colleague has found for US that dividend yield explains the corresponding stock index return over the next month rather poorly, but helps substantially to enhance forecast of the stock index return over the coming year. Please comment on novelty and possible grounds of this finding. (4 points)

b.) Another colleague of yours has made an event-study of the impact of seasonal public offerings, her sample containing 40 such events. She calculated abnormal returns as the return of each company under study minus the return of the stock market index. She used a two-day event window [-1,0] and cumulated the abnormal returns over it, then averaged across forty companies to obtain cumulated average abnormal returns. To test the significance cumulated average abnormal returns were divided by the root out of twice the variance of average abnormal returns, measured over the period [-68, -21]. Which problems do you see in such an approach and which modifications of the event study would you suggest? (7 points)

c.) Summarize briefly empirical evidence on predictability of monthly stock index returns (2-3 sentences) Mention thereby econometric techniques used. (4 points)

2. (15 Points) You observe statistical properties of a return series below.

a.) Can you say that these returns are normally distributed? Please provide formal reasoning for your answer. If not, which alternative distributions (assuming that returns are homoscedastic) would you suggest and why? (4 points)

b.) If you would like to fit a Student-t distribution (further assuming that the series is homoscedastic), which number of degrees of freedom would you choose and why (provide calculations where necessary) (4 points)

c.) If you suspect an ARCH(1)-process for the (demeaned) series under study, which α₀ and α₁ coefficients could yield some two of the observed central moments if you assume normal iid shock v_t (provide calculations)? (7 points)

3. (16 Points)

You obtain estimates of abnormal returns for seven stocks on a day on which some bad news concerning the companies arise:

	VW	DCX	DBE	CB	BMW	LIN	BSF
	-0.0296	-0.0294	0.0345	-0.0396	0.0008	-0.0357	-0.0669

You also know that the abnormal returns have been calculated using the market model. The standard errors of corresponding market model regressions for the stocks are:

	VW	DCX	DBE	CB	BMW	LIN	BSF
	0.0191	0.0149	0.0125	0.0136	0.0113	0.0111	0.0261

a.) Can you conclude using the abnormal returns and the standard errors that the news had a negative impact on the value of analyzed companies? Please provide all the calculations supporting your conclusion. (8 points)

b.) Which shortcoming has the approach suggested in a.)? Which statistics allows avoiding it? Calculate the latter and report whether your conclusion on the impact of the news has changed. (8 points)