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AD 685 Project – Spring 2023

Instructions:

· Please complete the guided project by May 1, 11:59 PM (ET)

· Type your response in a separate “word doc” named LastName_FirstName.doc

· Also, you must upload the work files from R (LastName_FirstName.prg). One for Part 1 and one for Part 2. Excel is not suitable for this project, and it will not be accepted.

· Upload 3 files (Word doc and 2 R files) on Blackboard

This project consists of two parts:

· Part 1: Predicting Stock Returns.

· Part 2: Forecasting models for the rate of inflation.

Part 1: Predicting Stock Returns.

Data Description:

Documentation for Stock_Returns_1931_2002

This file contains 2 monthly data series over the 1931:1-2002:12 sample period.

· ExReturn: Excess Returns

· ln_DivYield: 100×ln(dividend yield). (Multiplication by 100 means the changes are interpreted as percentage points).

The data were supplied by Professor Motohiro Yogo of the University of Pennsylvania and were used in his paper with John Campbell:

· “Efficient Tests of Stock Return Predictability,” Journal of Financial Economics, 2006.

(Double click in the window below to access the data)


Some Background

exreturn: is the excess return on a broad-based index of stock prices, called the CRSP value-weighted index, using monthly data from 1960:M1 to 2002:M12, where “M1” denotes the first month of the year (January), “M2” denotes the second month, and so forth.

· The monthly excess return is what you earn, in percentage terms, by purchasing a stock at the end of the previous month and selling it at the end of this month, minus what you would have earned had you purchased a safe asset (a U.S. Treasury bill). The return on the stock includes the capital gain (or loss) from the change in price plus any dividends you receive during the month.

Calculating k-period stock returns:

One-period holding return:

Two-period holding return:

Other way

Three-period’s returns:

k-period’s returns:

When to apply a “buy and hold” strategy:

· If you have a reliable “forecast” of future stock returns then an active “buy and hold” strategy will make you rich quickly by beating the stock market.

· If you think that the stock market will be going up, you should buy stocks today and sell them later, before the market turns down. Forecasts based on past values of stock returns are sometimes called “momentum” forecasts: If the value of a stock rose this month, perhaps it has momentum and will also rise next month.

· If so, then returns will be autocorrelated, and the autoregressive model will provide useful forecasts. You can implement a momentum-based strategy for a specific stock or for a stock index that measures the overall value of the market.

· From another point of view, we can use autoregressive models to test a version of the efficient markets hypothesis (EMH). A strict form of the efficient markets hypothesis states that information observable to the market prior to period should not help to predict the return during period . If the (EMH) is false, then returns might be predictable. If so, then returns will be autocorrelated, and the autoregressive model will provide useful forecasts.

· For example, if you want to find out if returns are predictable (even if it is just a bit), estimate the following AR(1)

· A positive coefficient means “momentum,” past “good returns” mean higher future returns.

· A negative coefficient means “overreaction” or “mean reversion”. In this case, previous “good returns” mean lower future returns.

· Either way, if , then returns will be autocorrelated, and the autoregressive model will provide useful forecasts.

Note: In all your calculations use Huber-White heteroskedasticity consistent standard errors and covariance.

a. Repeat the calculations reported in Table 15.2, using the following regression specifications estimated over the 1960:M1–2002:M12 sample period.

AR(1) Model

rt = βo + βirt-1 +et

AR(2) Model

rt = βo+ βirt-1 + β2rt-2 +et

AR(4) Model

rt = βo + βirt-1 + β2rt-2 + β3rt-3 + β4rt-4 +et


Autoregressive Models of Monthly Excess Stock Returns, 1960:M1–2002:M12






Dependent variable: Excess returns on the CRSP value-weighted index

(1)


(2)


(3)

Specification

AR(1)

AR(2)

AR(4)

Regressors






Excess Ret(t-1)

Std. Error






p-value












Excess Ret(t-2)


Std. Error






p-value












Excess Ret(t-3)




Std. Error






p-value












Excess Ret(t-4)




Std. Error






p-value










Intercept

Std. Error






p-value












Adj R^2





Wald F-statistic

p-value






T=






b. Are these results consistent with the theory of efficient capital markets?

c. Can you provide an intuition behind this result?

d. Repeat the calculations reported in Table 15.6, using regressions estimated over the 1960:M1–2002:M12 sample period.

Autoregressive Distributed Lag Models of Monthly Excess Stock Returns, 1960:M1–2002:M12





Dependent variable: Excess returns on the CRSP value-weighted index



(1)


(2)


(3)

Specification

ADL(1,1)

ADL(2,2)

ADL(1,1)

Eatimation Period

1960:M1–2002:M12

1960:M1–2002:M12

1960:M1–1992:M12

Regressors






Excess Ret(t-1)






Std. Error






p-value












Excess Ret(t-2)




Std. Error






p-value












Change_ln_DP(t-1)





Std. Error





p-value












Change_ln_DP(t-2)




Std. Error





p-value












ln_DP(t-1)





Std. Error






p-value












Intercept






Std. Error






p-value