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?

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.

a. To calculate the expected return of each stock, we can use the following formula:

Expected Return = Expected Liquidating Dividend / Market Capitalization

Using this formula, we can calculate the expected return for each stock:

For Stock A:
Expected Return = 1000 / 800 = 1.25

For Stock B:
Expected Return = 1000 / 750 = 1.33

For Stock C:
Expected Return = 1000 / 950 = 1.05

For Stock D:
Expected Return = 1000 / 900 = 1.11

Therefore, the expected returns for the stocks are as follows:
Stock A: 1.25
Stock B: 1.33
Stock C: 1.05
Stock D: 1.11

b. To determine the sign of correlation between the expected return and market capitalization of the stocks, we need more information on the correlation coefficient or the covariance between the two variables. The given data only provides information about the expected liquidating dividend, market capitalization, and beta, which is a measure of volatility relative to the market.

Without additional information, it is not possible to accurately determine the sign of correlation between expected return and market capitalization.

To calculate the expected return of each stock, you can use the formula:

Expected Return = (Expected Liquidating Dividend - Current Market Capitalization) / Current Market Capitalization

a. Let's calculate the expected return for each stock:

For Stock A:
Expected Return = (1000 - 800) / 800 = 0.25 or 25%

For Stock B:
Expected Return = (1000 - 750) / 750 = 0.3333 or 33.33%

For Stock C:
Expected Return = (1000 - 950) / 950 = 0.0526 or 5.26%

For Stock D:
Expected Return = (1000 - 900) / 900 = 0.1111 or 11.11%

b. To determine the sign of correlation between the expected return and market capitalization of the stocks, we need to find the relationship between the two variables.

If the correlation is positive, it means that as the market capitalization increases, the expected return also increases. Conversely, if the correlation is negative, it means that as the market capitalization increases, the expected return decreases.

Since we do not have information about the correlation between the expected return and market capitalization in the given data, we cannot determine the sign of correlation.