Investment Analysis and Portfolio Management Case2B

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Case 2B: The Small/Large Anomaly
Maastricht University
School of Business and Economics
Maastricht, 15 September 2009

Maastricht University
School of Business and Economics
Maastricht, 15 September 2009

Table of Content
Summary Statistics4
Spread Portfolio5
Evaluate the CAPM6


The Capital Asset Pricing Model (CAPM) is an equilibrium model that underlies all modern financial theory. It predicts the required rate of return of a security based on its risk, as measured by beta, and makes use of various simplifying assumptions. Hence, equilibrium condition would evolve with all investors choose to hold the same portfolio for risky assets, the “market” portfolio. However, following Fama and French’s study in 1992, numerous studies have suggested that beta is not sufficient in accounting for risk and recommend the inclusion of other variables. Most notably, Fama and French (1996) noted that stocks of smaller firms and stocks of firms with a higher book-to-market ratio have had higher stock returns than predicted by single factor models, and thus proposed a three-factor model that adds on firm size and book-to-market ratio to the market index. In this paper, we will focus on the small-large anomaly, and examine empirically if it still exists in today’s market. We use the Russell 1000, Russell 2000 and Russell 3000 to represent the large cap, small cap and general market respectively. Firstly, we will present the summary statistics of the 3 return series over the last 15 years. Next, we will build and analyze a spread portfolio over the same period, and discuss the effectiveness of such a strategy. Finally, this paper will test the CAPM and its accuracy in the pricing of both small and large styles, and the spread.

Summary Statistics

This section will shortly introduce the different indexes used for our analysis, elaborate on the outcomes of the statistical analysis to summarize the statistics of the data sets. For the statistical analysis we choose the Russell 1000, Russell 2000 and Russell 3000 to represent the small cap, large cap and general market respectively. The Russell 1000 lists the thousand US companies with the highest market capitalization and the Russell 2000 indexes the two thousand US companies with the smallest market capitalization. Therefore, the Russell 1000 index represents approximately 90% and the Russell 2000 only 10% of the market value. The Russell 3000 index is comparable with the Willshire 5000 or S&P 500 and represents the market portfolio. We will describe and compare the central tendency for the two return series using variables such as the mean, standard deviation, correlation coefficients and minimal and maximal returns. Over a period of 15 years (1996 – 2011), the average monthly mean return for the Russell 1000 and Russell 3000 are almost equal with 0.43% and 0.44% respectively. This can be explained by the dominance of approximately 90% of large cap firms in the Russell 3000. Additionally, the Russell 2000 (small cap index) had a slightly higher mean monthly return of 0.57%. According to Alex Kane (2008), the more a stock's returns vary from its average return, the more volatile the stock is reflected in a higher standard deviation. The higher standard deviation of the Russell 2000 of 6.09% compared to 4.79% and 4.81% of Russell 1000 and Russell 3000 respectively. These higher variations of the small cap index is reflected in the minimum and maximum returns of -353.061 and 202,591 respectively compared to -214.561 and 126.812 for the Russell 1000 index. These differences in the standard deviation can be tied to the lower liquidity levels and neglected-firm effect of small cap companies (Bodie, Kane & Markus, 2010). Furthermore, the correlation of 0.8313 between the Russell 2000 and Russell 1000 shows that these two indexes move largely in the same direction. Additionally,...
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