代写Empirical Finance、代做Java，c/c++，Python程序语言、代写Financial Econometrics

日期：2019-10-11 11:05

Financial Econometrics and Empirical Finance

Fall 2019

HW1

Due: Before October 14th, 7:00am

This assignment is designed to get you “acquainted” with one of the financial datasets that we will be

using in this class. All assignments must be completed using a programming language that allows you to

manipulate the data and to write your own procedures. No canned statistical packages are allowed. Please,

choose a software now and stick with it until the end of the class.

To complete this assignment, you will need the datafile Portfolios Formed on Size Daily.zip. The file

is zipped. Once unzipped it will be in text format, separated by tabs. The first column is the date, in

CRSP format, followed by three columns containing the year, month, and day of the data. The next 10

columns (5-14) report the returns of portfolios sorted by size deciles. For instance, column 5 presents the

return of companies that are in the first decile when sorted by market capitalization. Column 6 presents

the return of companies that are in the second decile when sorted by market capitalization, etc. The last

two columns provide the returns of the market-wide value and equal weighed portfolios for all stocks in

the NYSE-AMEX-NASDAQ. All data are at daily frequency. A header is included to help you with the

definition of the data.

1. Computing Means

(a) Compute the daily means and standard deviations of all portfolio returns, expressed in percents

(b) Express the daily means and standard deviations into monthly and annualized percents

(c) Can you compute the means using a simple regression? How

(d) Suppose you suspect that the means of the portfolio returns before and after 1945.01 are different.

Estimate the means of each portfolio for the pre-1945 and post-1945 subsamples. How would you

test the hypothesis that the pre-1945 and post-1945 means are equal to each other?

2. Efficient Markets

(a) Using each of the 11 portfolio returns (value-weighted and 10 decile portfolio returns), estimate:

where i = 1, 2, ...11, and t = 1, ...T.

(b) Test the hypothesis that markets are efficient, i.e. that returns are not serially correlated. This

is known as weak form efficiency (Fama (1970, 1990)). Please conduct the test for each portfolio,

separately.

(c) Explain your results.

3. Data-Mining

(a) You have no clear model in mind, but intuition tells you that the returns of small companies

might forecast market (value-weighted) returns. Therefore, you decide to run the regression:the return of the value-weighted (market?) portfolio, and rit?1

is the lagged return

of Decile 1 companies. Run similar regressions for Decile 2 and Decile 3 companies.

(b) Can the return of small companies forecast the market return?

4. Simulation: We will simulate an AR(1) process Yt = φYt?1 + εt.

(a) To start the recursion, we need an initial value Y0. Let Y0 = 0.

(b) Generate a sequence of Gaussian white noise, for φ = 0.1 and save it.

(d) Generate a new sequence of Gaussian white noise , for φ = 0.1 and save it.

(f) Repeat steps b and c, by generating nε, j = 3, ...,N, where N = 1000. Now you have N simulations of an AR(1) process, observed at T points in time.

(g) Using your knowledge, compute E(Yt) and V ar(Yt) using formulas discussed in class.

T = ?μT the means of Yt at each t from

cross sectional returns.

(j) Plot the histogram of the computed in part h.

(k) Plot the histogram of the computed in part i. Do they vary over time?

(l) How do the estimates in h and i compare with the theoretical mean E (Yt)?

(m) OPTIONAL: Do parts h-k for the second moments.

5. OPTIONAL: The dataset in questions 1-2 ends in 2018. But if you are curious whether the results

you obtained in that exercise continue to hold with more recent data, you are encouraged to go to Ken

French’s website, download the most recent vintage of the same dataset and re-run the regressions. Do

your results change significantly?

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