a. To calculate the expected return of each stock, we first need to determine the dividend yield for each stock. Dividend yield is the expected liquidating dividend divided by the market capitalization. Then, we can multiply the dividend yield by the beta to get the expected return.
Stock A:
Dividend Yield = 1000 / 800 = 1.25
Expected Return = 1.25 * 0.77 = 0.9625 or 96.25%
Stock B:
Dividend Yield = 1000 / 750 = 1.33
Expected Return = 1.33 * 1.46 = 1.9418 or 194.18%
Stock C:
Dividend Yield = 1000 / 950 = 1.05
Expected Return = 1.05 * 1.25 = 1.3125 or 131.25%
Stock D:
Dividend Yield = 1000 / 900 = 1.11
Expected Return = 1.11 * 1.07 = 1.1877 or 118.77%
b. To determine the sign of the correlation between the expected return and market capitalization, let's first look at the expected return and market capitalization values:
Stock A: Expected Return = 96.25%, Market Cap = $800M
Stock B: Expected Return = 194.18%, Market Cap = $750M
Stock C: Expected Return = 131.25%, Market Cap = $950M
Stock D: Expected Return = 118.77%, Market Cap = $900M
Generally, the stocks with lower market capitalization tend to have a higher expected return, while the stocks with higher market capitalization tend to have a lower expected return. This suggests that there might be a negative correlation between expected return and market capitalization of the stocks. However, to be sure, we would need to calculate the correlation coefficient between the two sets of values, but the information given is not enough to do that.
5. Consider the following stocks, all of which will pay a liquidating dividend in a year and nothing in the interim:
Market Capitalization ($ million) Expected Liquidating Dividend ($ million) Beta
Stock A 800 1000 0.77
Stock B 750 1000 1.46
Stock C 950 1000 1.25
Stock D 900 1000 1.07
a. Calculate the expected return of each stock.
b. What is the sign of correlation between the expected return and market capitalization of the stocks?
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