These Effects Suggest That The Abnormal Risk-Adjusted Returns Are Predictable In Equity Markets

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Homework 4
Chapter 11
7. These effects suggest that the abnormal risk-adjusted returns are predictable in equity markets, especially when findings are difficult to reconcile with the efficient market hypothesis.
a. P/E effect: some studies find that portfolios of low price-earnings (P/E) ratio stocks have higher returns than high P/E portfolios. The reason is that CAPM maybe not fully consider all the risk factors. If a firm believed risker, it may have a lower price, which lead to a higher P/E ratio.
b. Book-to-market effect: investors can earn excess returns by investing in companies with high book value to market value. Fama and French found that book-to-market ratios seem capable of predicting future returns because CAMP doesn’t include a risk factor reflected by book-to-market ratio.
c. Momentum effect: past performance of a stock is positively correlated with its future performance. Because investors are likely to underreact to new information, therefore if a stock did well in the past, it would keep doing well in the future. Some studies show that in momentum models, which included transaction costs, momentum traders are not likely to outperform the EMH strategy of buy and hold.
d. Small-firm effect: smaller firms produce higher returns than larger firms. Frpm 1926 to 2008 average annual returns are consistently higher on the small-firm portfolios. It is generally believed that small firms are risker than larger firms, so their perceived risk and return are higher than larger firms’. Another reason is the database doesn’t include the stock returns of those firms, which went bankrupt. Therefore this data has bias.

9. c. Because if the stock market is weakly efficient, there shouldn’t be a predictable pattern in returns.

14. d. Because there are semistrong-form efficient markets, information such as P/E ratio, recent price changes, is publicly known. Therefore it’s hard to earn abnormally high trading profits by using P/E ratios and recent price changes. On the other hand, if I have advance knowledge of an improvement in the management team which is not known by public, I can earn abnormally high trading profits.

19. a 1%+2*(1.5%-1%)=2%. Because the company won a $1 million lawsuit, which is 1% of initial equity, 2%+1%=3%. The total return should be 3%.

b. If the market had expected AmbChaser to win $2 million, the company’s nonsystematic return would be -1%. Therefore, 2%-1%=1%. The total return should be 1%.

Chapter 12
4. a. The principle of behavioral finance of overconfidence is most consistent with the investor’s statement. Even though he had been very satisfied with what he earned from Petrie stock over the past 2 years, he was too confident to make such a conclusion that the Petrie stock would continue to outperform in the future.

b. The principle of behavioral finance of mental accounting is most consistent with the investor’s statement, because the investor tended to separate his account into two accounts instead of considering the risk and return of whole investment. When he is considering the risk and return, he should include his “specific use money “ into the whole investment.

3.
(1a)
Book to market
Lo 10
5-Dec
Hi 10 α -0.000022
0.000013
0.000049
T stat
-2.4071
1.378872
3.10536026
P-value
0.0165
0.168651
0.00202619
β
0.011020
0.008932
0.009390
T stat
53.29625
41.7311
27.00226145
P-value
1.5E-191
2.7E-153
1.2387E-94

From this table, we can see that from low book to market ratio to high book to market ratio, the Alpha is growing, but the Beta has no trend. Most of the Alpha are significant. It is possible that CAPM beta not fully captured the size and relative value proxy for risks.

FF α β t Stat
P-value
Lo 10
0.000011

1.781527
0.075535
Mkt-Rf

0.009680
62.112982
3.0062E-216
SMB

-0.001564
-7.802259
4.69997E-14
HML

-0.005336
-23.069135
4.15258E-77

5-Dec
-0.000010

-1.126671