Fidelity provides data on the risk and return of its funds atwww.fidelity.com.

• Click on the News and Research link, then choose Mutual Funds from the submenu.

• Scroll down and click “View 3411 Funds”.

• On the left panel of the next screen, click Volatility and choose Beta.

• Under Beta, there are two cells termed “Min” and “Max”, enter 0.5 in the Max cell (keep Min unchanged), which means we choose low Beta funds.

• Select five funds from the resulting list and click Compare Funds. Rank the five funds according to their betas and then according to their standard deviations. (You will have to click on Risk to get more detailed information on each fund.) Report your rankings in a table then answer the following questions: Do both lists rank the funds in the same order? How would you explain any difference in the rankings?

• Click “Back to Research Results”, repeat the exercise to compare five funds that have betas greater than or equal to 1.50 (you enter 1.50 in the Min cell, and keep Max unchanged), i.e. we look at high Beta funds. Note: before you choose new set of five funds, you need de-select the previous ones (Next to Compare Funds, it shows “5 Funds selected”, click “show funds”, and then remove them). Similarly, report your rankings in a table and then answer the following questions: Why might the degree of agreement when ranking funds by beta versus standard deviation differ when using high versus low beta funds?

Financial AnomaliesUse data from finance.yahoo.com to answer the following questions: Collect the following data for 25 firms of your choosing.

i. Book-to-market ratio.

ii. Price–earnings ratio.

iii. Market capitalization (size).

iv. Price–cash flow ratio (i.e., market capitalization/operating cash flow).

v. Another criterion that interests you (optional).

(a) You can find this information by choosing a company and then clicking on Statistics. Rank the firms based on each of the criteria separately, and divide the firms into five groups based on their ranking for each criterion. Calculate the average rate of return for each group of firms.

Do you confirm or reject any of the anomalies cited in the Chapter 11? Can you uncover a new anomaly? Note: For your test to be valid, you must form your portfolios based on criteria observed at the beginning of the period. Why?

Hint:To test the anomalies, you need to construct a zero-cost portfolio based on each criterion. For exmple, we use book-to-market ratio to construct the zero-cost portfolio.

(1) Rank all 25 stocks according to book-to-market ratio on 12/31/2020, with highest on the top and lowest on the bottom;

(2) Choose top 5 and bottom 5 stocks;

(3) Using the prices of each stock on 12/31/2020 (if holiday or weekend, use the most recent business day price) to calculate the weights:

for each of the top 5 stocks, weight= +(individual price/sum(all 5 top stock prices)

for each of bottom stocks, weight = - (individual price/sum(all 5 bottom stock prices)

That is, positive for top 5 stock, and negative for bottom 5 stocks;

(4) Calculate the returns for each stock from 12/31/2020 to 6/30/2021 (We suppose hold the portfolio for 6 months);

(5) Calculate the portfolio return, which is the weighted average of the 10 returns, again, positive for the top ones and negative for the bottom ones.

(6) Compare portfolio return to the S&P500 return during the same period, if significantly better (say >2%), anomaly exists.

(b) (Optional) Now form stock groups that use two criteria simultaneously. For example, form a portfolio of stocks that are both in the lowest quintile of price–earnings ratio and in the highest quintile of book-to-market ratio. Does selecting stocks based on more than one characteristic improve your ability to devise portfolios with abnormal returns? Repeat the analysis by forming groups that meet three criteria simultaneously. Does this yield any further improvement in abnormal returns?

1. Choose 10 firms that interest you and download their financial statements from any of these Web sites: finance.yahoo.com, finance.google.com, or money.msn.com.

a. For each firm, find the return on equity (ROE), the number of shares outstanding, the dividends per share, and the net income. Record them in a spreadsheet.

b. Calculate the total amount of dividends paid (Dividends per share × Number of shares outstanding), the dividend payout ratio (Total dividends paid/Net income), and the plowback ratio (1 − Dividend payout ratio).

c. Compute the sustainable growth rate, g = b × ROE, where b equals the plowback ratio.

d. Plot the P/E ratios of the firms against the growth rates in a scatter diagram. Is there a relationship between the two?

e. Plot the price-to-book ratios against the price-earnings ratio for your sample of firms. Are the two variables correlated? What about price-to-sales versus price-earnings?

f. For each firm, compare the 3-year growth rate of earnings per share with the growth rate you calculated above. Is the actual rate of earnings growth correlated with the sustainable growth rate you calculated?

2. Now calculate the intrinsic value of three of the firms you selected in the previous question. Make reasonable judgments about the market risk premium and the risk-free rate.

a. What is the required return on each firm based on the CAPM? You can find the beta of each firm from its Statistics page.

b. Try using a two-stage growth model, making reasonable assumptions about how future growth rates will differ from current growth rates. Compare the intrinsic values derived from the two-stage model to the intrinsic values you find assuming a constant-growth rate. Which estimate seems more reasonable for each firm?