Quantitative Portfolio Management

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3.1.1 General Relationship between E/P Ratio and Realized Return

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Figure 3-1-1 Averaged realized return vs. E/P Ratio

As shown in figure 3-1-1, when the portfolio has a negative E/P ratio, it provides investors with an abnormal return of 41%, which is even higher than the realized return brought by portfolio with highest E/P ratio. And as the E/P ratio of portfolio increases, the average realized return of portfolio rises from 25% to 41%, which is consistent with the hypothesis theory that portfolio with higher E/P ratio tends to generate a higher return. Hence, it is advisable of investors to buy the portfolio with a high E/P ratio and sell the portfolio with a relatively low E/P ratio. Besides, investors who are risk-seeking can also consider to buy portfolio with negative E/P ratio. Although the portfolio with negative E/P ratio has higher risk, it is more likely for it to give rise to higher return.

3.1.2 Average Realized Return of Highest and Lowest E/P Ratio

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Figure 3-1-2 Average Realized Return of Highest and Lowest E/P Portfolio

We can further verify the hypothesis that portfolio with higher E/P ratio generally has a higher realized return than portfolio with lower E/P ratio. As shown in figure 3-1-2, portfolios with higher E/P ratio generate higher realized return than portfolios with lower E/P ratio from 1981 to 1995, except for year 1991,1992, and 1994. In these three years, portfolios with higher E/P ratio generate lower realized return than portfolios with lower E/P ratio.

3.1.3 Difference between Average Realized Returns of Highest and Lowest E/P Ratio

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Figure 3-1-3 Difference between Average Realized Returns of Highest and Lowest E/P Ratio

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Figure 3-1-4 Difference between highest and lowest E/P Ratio from 1981 to 1995

As we can see from figure 3-1-3 and 3-1-4, when the difference between high E/P ratio and low E/P ratio fell to around 0.18 in year 1991, 1992, and 1994, gaps between average realized returns of portfolio with high E/P ratio and low E/P ratio tends to be narrowed or even become negative, which were -26%, -7% and -3% respectively. Thus, the smaller the gap between high and low E/P ratios of different portfolio, the less likely that portfolio with higher E/P ratio can generate higher return. As a result, we can not make the conclusion that portfolio with higher E/P ratio will definitely generate higher return in all cases.

On the other hand, difference between high E/P ratio and low E/P ratio of portfolios is not perfectly correlated with the difference between their realized returns even when the difference between high E/P ratio and low E/P ratio of portfolio is relatively high. For example, in 1983, even though the difference between high E/P ratio and low E/P ratio of portfolios was 0.2713, which was relatively large, these portfolios had same level of realized return in that year. Similar situations existed in year 1988, 1989 and 1995. When differences between high and low E/P ratio were 0.2404, 0.2815 and 0.2747, gaps of realized return were only 4%, 5% and 4% respectively.

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3.2 Book-to-Market Ratio and Realized Return

3.2.1 General Relationship between B/M ratio and Realized Return

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Figure 3-2-1 Average realized return vs. B/M Ratio

The book-to-market (B/M) ratio is used to find the value of a company by comparing the book value of a firm to its market value. As we can see from Figure 3-2-1, the average realized return are proportional to B/M ratio in the below five groups. The lowest B/M ratio brings the lowest average realized return of 19% versa the highest B/M ratio gives rise to the highest average realized return of 46%. It means if the firm has a high book value compared with its market value, it has the more chances to obtain the higher realized return.

3.2.2 Average Realized Return of Highest and Lowest B/M Ratio

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Figure 3-2-2 Average realized return of highest and lowest B/M portfolio

We can further verify the hypothesis that portfolio with higher B/M ratio generally has a higher realized return than portfolio with lower B/M ratio. As shown in figure 3-2-2, portfolios with higher B/M ratio is more likely to generate higher realized return than portfolios with lower B/M ratio from 1981 to 1995. However, exceptions existed in year 1983, 1994 and 1995. In these three years, portfolios with higher B/M ratio generate lower realized return than portfolios with lower B/M ratio.

3.2.3 Difference between Average Realized Returns of Highest and Lowest B/M Ratio

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Figure 3-2-3 Difference between averages realized returns of highest and lowest B/M portfolio

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Figure 3-2-4 Difference of B/M Ratio

As we can see from Figure 3-2-3 and 3-2-4, from 1981 to 1995, portfolio with higher B/M ratio generate higher realized return than portfolio with low B/M ratio in most cases. In year 1983, 1994 and 1995, differences between average realized returns of portfolio with high B/M ratio and low B/M ratio became negative, which were -21%, -2%, and -9% respectively. It is noticeable that differences between high B/M ratio and low B/M ratio of portfolios dropped to 1.82 in year 1994. Thus, the smaller the gap between high and low B/M ratios of different portfolio, the less likely that portfolio with higher B/M ratio can generate higher returns. On the other hand, while differences between high B/M ratio and low B/M ratio of portfolios remained relatively high in year 1983 and 1995, portfolio with high B/M ratio still generated lower realized return. Therefore, we can not make the proportional conclusion for the relationship between higher B/M ratio and higher average realized return.

Part 4 Combined Analysis of E/P and B/M Ratio Strategy