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Summer 2022

Investment and Portfolio Management

PROJECT DESCRIPTION

Autocorrelation Regression

In this project, you can design a simple model used for regressing the return of an ETF on one or two explanatory variables.

NYSE Symbols

International ETF

Bond ETF

Sector/ Industry ETF

Commodity ETF

EIS=    Israel   ,

HYG = High Yield Bond

Utilities = XLU

Oil = USO

GXC= Shanghai ,  

JNK = High Yield Bond 2

Energy Large Cap = XLE

Natural Gas = UNG

EEM = Emerging Market

LQD = Investment Grade Corporate Bond

Financial = XLF

Copper = CPER

 JPP =   Japan  ,

IEF = 10 year Treasury Bond

Oil and Gas = XOP

Gold = GLD

EWU= Britain

TLT = 20 year Treasury

Growth (ex: Technology)  = IWF, QQQ

Silver = SLV

EWQ= France

SHY = Short Term Treasury

Real Estate = IYR

UUP = U.S. Dollar Index

EWG= Germany

TIP =  Inflation Protected Bond

Gold Miners = GDX

Oil = USO

Table 1  Sample of models

Y

X1

X2

 

Gold Return

Dollar Return

Bond Return

 

Copper Return

SP Return

 

 

Gold Miner Return

Gold  Return

Bond Return

 

Energy Large Cap Return

Oil Commodity return

Bond Return

 

You can choose to do daily or monthly returns.  But economics data are released only monthly.

To generate return, you need to first download historical prices of stocks from yahoo finance.  (use adjusted stock price data from Yahoo).  You may also download interest rate data from St. Louis FederalReserve. Paste all your data into one single Excel spreadsheet.  Make sure all you data are aligned correctly by date and that the oldest data are on top of the spreadsheet. Convert your date in scientific format.  For example, April 1, 2015 should be written as 20150401.  This can be done using the formatting cell function in Excel and choose Custom and type in yyyymmdd.  

You can try different combinations of variables and variations of model structure. You can use one X or even three X’s.   See which version has the best explanatory power for the Y you are focusing (as revealed by Adjusted R2 and t-stats.)  

Writing Format

In your paper, you should have three parts (one or two pages plus the TSP output) written as follows:

1) Objective-  Explain what you hope to find in this project (one short paragraph) 

2) Data Description-  the financial theories behind the relationship between Y and X.     Describe data used (daily or monthly, source of data, etc)     

Calculations-  (show how variables are calculated, ex: return = (Pt –Pt-1)/Pt-1,   )    

(half page)

3) Regression Results-  must be written in the form of estimated coefficient values  and their corresponding t-stats in parenthesis below the coefficients as follows:

Energy Large Cap Returnt  =  1.2 +  .05 Oil ETF Returnt  - .01 ΔTreasuryRate t  -  .2  e t-1      

                                                                        (.01)                        (-5.2)                          (-1.5)     

             TSP Command for above :  AR1  RXOP C  RUSO CHANGER ;

Explain all your variable names (ex: TreausryRate t  ) in a clear way so that the notations used by you would be understood by readers.

Please copy the section of your TSP output results (estimated coefficients and t-stats) and paste it here in this section.       

Coefficient Analysis- Based on the t-stats, which coefficients are statistically significant? Are the signs of the coefficients consistent with your expectation?    (half page)

Please copy the original TSP command and output and paste them to your written report.  Since the data are long, you can delete the data to save paper.  For the output, you only need to copy the regression result (where TSP shows the estimated coefficients and T-statistics) and paste only that part onto your written report.

Common errors or omissions:

Did not use X variables in change form to predict return (which is in change form).

Using values of X that share the same variable as Y.  Ex:  Y = Return    X = P/E change.  In this case,  price appears in both Y and X, thus creating accounting (self-fulfilling) correlation rather than stochastic correlation.

In your TSP program, type”?” at the beginning of each line that you want to write documentation or descriptions of your TSP statements.  Such lines are not part of the program but are in the program to help readers understand the symbols, commands, and the methodology you are using.

I will be glad to help you along the way in this exciting adventure of regression.

I am hopeful that you will find regressing financial data to be both interesting and exciting.