Empirical Finance Spring II 2022
Assignment 1
Data are from the Center for Research in Security Prices (CRSP). The two monthly series from CRSP are the value-weighted with-, RNt, and without-dividend nominal returns, RXt, of CRSP stock market indexes (NYSE/AMEX/NASDAQ/ARCA). The sample period is from 1946:M1 to 2020:M12. The monthly nominal dividend series are constructed as follows.
• A normalized nominal value-weighted price series is produced by initializing P0 = 1 and recursively setting Pt = (1 + RXt)Pt-1,
• A normalized nominal dividend series, Dt, is obtained by recognizing that Dt = (RNt − RXt)Pt-1 .
You will find “dividends.xlsx” that explains how to construct Pt (Price) and Dt (Div).
Q1. (70pts) Constructing dividend growth rates and log pd ratio
1. (10pts) Compute log dividend growth rates, Ad= In(D/Dt-1), and plot Ad.
2. (10pts) Compute the sample average and standard deviation of Ad in the range between 1947:M1 and 2020:M12.
3. (20pts*) Discuss the time series properties of △d.
4. (10pts) Aggregate the monthly dividends Dat = Σi11=o Dt-i. It is important to understand that for each December, we are aggregating the 12-months of dividends. Thus, T runs in annual frequency (i.e., December of each year) while t runs in monthly frequency. Compute the annual log growth rates Adta = In(D/Dat-1) and provide its sample average and standard deviation.
5. (10pts*) Plot the time series of Ad and compare with Ad (you could evenly distributeAd over the 12 months). Discuss the sample standard deviation of the two series.
6. (10pts) Consider the December value of price P as P. Therefore, the length of time series of P matches that of D. Construct the log pd ratio pd- = In(P/D) and compute its sample average and standard deviation in the range of 1948 to 2020.
Q2. (60pts) Predictability
1. (20pts) Run the following OLS regression
∆dτ+h = αh + βhpdτ+ τ+h (1)
for h ∈ { 1, 2, 3, 4, 5} using the most available sample. For example, ∆dτ+5 is available from 1953 to 2020 whereas pdτ is available from 1948 to 2015. Report the estimate of βh and the implied R2 value for each h.
Q3. (20pts) Reading on dividend/return predictability
Read Binsbergen and Koijen (2010) and summarize the paper. The summary should be not more than two paragraphs
Q4. (50 pts) Correlation between stock and bond returns
You will find "returns.csv" that includes two daily series of stock returns and bond returns (of maturity 1-year) which range from 1971 to 2020.
1. (20pts) Compute the rolling correlation between stock returns and bond returns bysetting window interval to w. That is, you are to compute corr(R, Ro,) for each t where 2/w + 1 ≤ t ≤ T - 2/w
Plot the time series of rolling correlation for w=60 and =900.
2. (30pts*) Describe the correlation pattern and provide potential explanations. (Hint:feel free to search online). The explanation should be not more than two paragraphs.