< Calculating Expected Return: Dividend Yield Regressions > Suppose you are consulting a customer whose investment horizon is one year. This customer would like to invest in an equally weighted portfolio consisting of all firms in NYSE and AMEX and in Treasury Bill. You will perform mean variance analysis and you need to calculate expected return for the risky asset. You will use dividend yield to calculate expected return of the risky asset. (a) (4%) Regression Model: You would like to estimate expected return using a regression of the following form using the data obtained for question 2: rt= a+ b dt-1/pt-2 + et [1] where t 'rt' is equally weighted portfolio return (includes distributions) and dt-1 / pt-2 is the previous year's dividend yield calculated using the method described in question 1. This implies that your first return observation in [1] is 1927's return and your first dividend yield observation is 1926's dividend yield. Your last return observation for this regression analysis should be the return of 2021 and the dividend yield of 2020 even though you have 2022's return in the sample. What is the arithmetic average and standard deviation of Y variable? (b) (4%) Run the regression (using the return data from 1927 to 2021 and the dividend yield data from 1926 to 2020) with Excel and report the coefficient estimate and its t-statistic. By examining t-statistic or p-value of beta, can you conclude that the coefficient is significant with 10% significant level (p-value of 10%)? Note) In addition to t-statistic, you can use p-value to evaluate the significance of the result. If p-value is smaller than 5% (10%), then we say that results are meaningful at 5% (10%) significance level. Approximately, p-value of 5% corresponds to t statistics of 2. p-value will be discussed in class. (c) (4%) Suppose you would like to calculate the expected return for 2022 using estimated coefficients obtained in (b). Given the dividend yield of 2021 in the data, what is the expected return of 2022? How does it compare with the actual return of 2022 in the data? (NOTE: Regardless of whether the estimate of , , is significant or not, expected return should be + 2021.) (d) (4%) Now instead of annual return, you would like to use 10 year return as your Y variable. Let the first X variable be dividend yield of 1926. Then, the first Y variable is 10 year return measured between 1927 and 1936. Let the last X variable be dividend yield of 2011 and the last Y variable be 10 year return measured between 2012 and 2021 (Thus, as in (a), we do not use 2022's return for this question). 10 year return is defined as follows. For example, your first Y variable is (1+ r1927 )(1+ r1928 )(1+ r1936 ) 1 [2] Recall that this is a 10 year return. What is the arithmetic average and standard deviation of Y variable? (e) (4%) Run the regression with Excel and report the coefficient estimate beta and its t-statistic. By examining t-statistic or p-value of beta, can you conclude that this relationship is reliable with 10% p-value (or in other words, significant at 10%)? (f) (5%) Try to explain the difference in the magnitude of coefficient for X based on Shiller's mispricing story. (i.e., which coefficient is larger and why?)