Consider a small set of stocks to examine the size anomaly and the momentum anomaly. The file Data4.xls contains monthly returns on a set of U.S. stocks from July 1998 to December 2000. It also contains the stocks' market capitalization (cap, inmillions of USD) and cumulative 6-month past return measured at the end of June 1998 (pastret). Furthermore, the file contains the series of monthly market returns in excess of the risk-free rate (MKT_RF), the Fama-French factors (SMB and HML), and the risk-free rate (RF).

You are forming portfolios at the beginning of July 1998 (i.e. you are selecting stocks based on their characteristics as of the end of June 1998).

a) Based on information available at the end of June 1998, select the 3 largest stocks and the 3 smallest stocks. Form an equally weighted portfolio of large stocks and an equally weighted portfolio of small stocks. Calculate the average returns of these two portfolios starting in July 1998 until the end of the sample period. Using the Fama- French model, estimate the risk-adjusted returns for the portfolio of small stocks, the portfolio of large stocks, and the strategy that buys the small stocks and sells the large stocks.

Is there any evidence of a size anomaly?

b) Now consider the past 6-month cumulative return measured at the end of June 1998 to select the top 3 winner stocks and the bottom 3 loser stocks. Form a portfolio of winners and a portfolio of losers at the beginning of July 1998 and compute the average future returns to these portfolios. Using the Fama-French model, estimate the risk-adjusted returns for the winner and the loser portfolios.

Form a momentum portfolio starting in July 1998 and compute the average returns to this portfolio in the following 3, 6, 12 months. What do you notice?

Estimate alphas and factor loadings from the Fama-French model for the momentum portfolio. Is there evidence of momentum profits?