Reference no: EM132242784

You can do this quickly if you use the R help given!

The xx-indus-mon.csv files in the DATA directory contain the monthly returns on xx industries. Go to Ken French's web site to understand what the variables are. I cleaned up the files for you and added XRM = RM - RF and RF for you in the last two columns of each file.

Use the Risk free rate in the last column to compute excess returns for the industries. It's OK to leave all returns in % ala KF. You can now run the excess-returns regressions:

XR_it = R_it -R_Ft = α_I + β_IXR_Mt

For this entire problem, you can assume that the OLS assumption applies to each regression alone.

Problem: Sorting on Estimates

You are interested in the 2-pass approach because it has a predictive content and is used both for testing the models and by practitioners to control risk while attempting to forecast returns. This is why you are really excited about the upcoming lecture on Thursday Feb. 28th, where you will learn more about it. You heard a lot has to do with estimating risk from one period and using it for the next ... or something like that.

You wonder if βs arestable from period to period. There are two issues, estimates are noisy but maybe true βs move around. You know one thing: Since ∈ ∼ N(0,σ² I), the βs are estimated with no bias. So there should not be a bias from one period to the next .... unless true βs vary with time in a systematic manner.

You are going to use 47indus for this experiment.

a) Consider for period 1: 200901-201312 and period 2: 201401-201812. Estimate the β vector for each period. In Figure 1 plot β2 vs β1. Regress the 48 β2s against their first period counterparts. Write the estimates below:

β₂= ?? + ?? β^{^}₁

Add the regression line to your Figure 1, as well as the 45 degree line.

Using the regression. For β^1s = (0.5, 1, 1.5) what β^2 do you forecast in the next 60-month period?

Is there a bias here, which way, for what ranges of values of β^1?

What could be the reason?

b) This is puzzling! You wonder if it is specific to 2009-13, 2013-18. So you repeat the whole thing starting in 197401. This allows you to have exactly 9 periods of 5 years. Estimate the βs for each 5-year period. Then create two vectors: Oldbet and Newbet. Oldbet will have the βs estimated during the first 8 periods, Newbet the β estimates from periods 2 to 9. Each has 47x8 estimates to be sure. Then just redo the plot in Figure 2 and the regression.

β^{^}2 = ?? + ?? β^{^}₁

Any change?

What could be the reason for this?

A R help file will be posted with tips on fast ways to do some of the questions.