Comparison of stock returns

Variables and Data Sources:

• PS&P = S&P 500 Price Index

This is the Standard and Poor index of 500 companies and will be used as a market portfolio. (You would use the return from this series as Market Return rM,t)

http://finance.yahoo.com/quote/%5egspc/history?p=^gspc

• PB = Boeing Company- BA's Stock Price

A particular stock we are interested in to determine how it behaves in response to market changes.

http://finance.yahoo.com/quote/BA/

• PGD = General Dynamics- GD's Stock Price

A particular stock we are interested in to determine how it behaves in response to market changes.

http://finance.yahoo.com/quote/GD/

• rf =Interest rate on 10 Year US-Treasury Note

This variable is given in percentage (with % sign omitted) and will serve as a risk-free interest rate. We will use this variable to compute excess returns on our preferred stock (either Boeing or GD) and Market excess returns.

http://finance.yahoo.com/quote/%5ETNX/

Task A: Downloading the data

Download the data for S&P 500 index, Boeing Stock Price, General Dynamics Corp. Stock Price, and US TN (10 Year), using the links provided above and choosing Monthly Historical Data for all variables covering the period related to a group your Student ID belongs to.

Data Group Data Period Students with ID Between (inclusive)

Start Date (day/month/year) End Date (day/month/year)

Group 01 01/03/2013 31/03/2018 16503281

19619593

Group 02 01/10/2012 31/10/2017 19619594

19841989

Group 03 01/03/2012 31/03/2017 19841990

19876048

Group 04 01/10/2011 31/10/2016 19876049

19888488

Group 05 01/03/2011 31/03/2016 19888489

20096775

Group 06 01/10/2010 31/10/2015 20096776

20193917

Example: Suppose a student's ID is 19855310. This ID falls in an interval corresponding to group 06 and therefore, this student would download monthly data covering the period 01/10/2010 to 31/10/2015.

Personal important note:

So my student id falls in interval corresponding to group 6 .

Task B: Perform the following.

1. Calculate returns for these three series in Excel or any software of your choice using the transformation: rt = 100*ln(Pt / Pt-1) and perform the Jarque-Berra test of normally distributed returns for each of Boeing and GD. What do you infer about the distribution of the two stock returns series? Describe also the risk and average return relationship in each of the two stocks.

Hints:

o We have performed a similar task in Workshop 01.

o If there are say -n+1- observations on prices, then the return series would have -n- observations.

o These numbers would represent percentages after multiplication with 100 in the formula above. But you would not put a percentage sign in your data. For example, returns for two periods are 0.35% and 0.41% but we would use 0.35 and 0.41 after omitting % sign in our excel worksheet.

2. Test a hypothesis that the average return on GD stock is different from 2.8%. Which test statistic would you choose to perform this hypothesis test and why? Also, specify the distribution of the test statistic under the null hypothesis, using 5% significance level.

3. Before investing in one of the two stocks, you first want to compare risk associated with each of the two stocks. Perform an appropriate hypothesis test using 5% significance level and interpret your results.

4. Besides, you want to determine whether both stocks have the same population average return. Perform an appropriate hypothesis test using information in your sample of 60 observations on returns, using 5% significance level. Report your findings and also mention which stock will you prefer and why?

5. Compute excess return on your preferred stock as yt = rt - rf,t and excess market return as xt = rM,t - rf,t and perform the following tasks.

a. Estimate the CAPM using linear regression by regressing the excess return on your preferred stock (yt) on excess market return (xt) and properly report your regression results.

b. Interpret the estimated CAPM beta-coefficient in terms of the stock's riskiness in comparison with the market.

c. Interpret the value of R2.

d. Interpret 95% confidence interval for the slope coefficient.

6. Using the confidence interval approach to hypothesis testing, perform the hypothesis test to determine whether your preferred stock is a neutral stock. (Note: You would not be given any marks if you do not use CI approach to test a hypothesis)

7. One of the assumptions of ordinary least squares (OLS) method is; normally distributed error term in the model. Perform an appropriate hypothesis test to determine whether it is plausible to assume normally distributed errors.

Analyse Data & Submit Report

Prepare your written report in two Parts:

Part A: Calculations

• Set out all your calculations for each of the tasks (listed above) using Data Analysis Tool in Excel. Present your results in graphs and charts as appropriate

Part B: Interpretation

• Explain what your results mean, in language that your client can understand. For example, what conclusions can you draw from each of your findings?

• Your written report must be no more than TWELVE (12) pages in total, including all appendices, graphs, tables and written answers. Answer the questions directly. Do not present unnecessary graphs or numerical measures, undertake inappropriate tests or discuss irrelevant matters.

Additional information and formulas:

The Capital Asset Pricing Model

The capital asset pricing model also known as CAPM is one of the fundamental models in the field of finance. The model explains variations in the rate of return on a security ( rt) as a function of the rate of return on a market portfolio (rM,t) consisting of all publicly traded stocks. Generally, the rate of return on any investment is measured relative to its opportunity cost, which is the return on a risk-free asset (rf,t). The difference between the return and risk-free rate is called the risk premium because it is the reward or punishment for making a risky investment. According to CAPM, the risk premium on a security, denoted by (rt - rf,t ), is proportional to the risk premium on the market portfolio, (rM,t - rf,t). Thus,

rt - rf,t = ßM (rM,t - rf,t)

where the coefficient provides security’s ‘‘beta’’ value.

Model in equation (1) is called economic model since it describes the relationship between excess stock return and the excess market return based on financial theory.

Why is CAPM important?

The CAPM beta is important to investors since it discloses the stock’s volatility. In particular, this beta measures the sensitivity of given security’s return to variation in the whole stock market. Value of beta determines whether the stock is a defensive, a neutral, or an aggressive stock.

Defensive stock: A stock is known as defensive stock if its beta value is less than 1. A defensive stock has its variation less than the market’s and therefore is considered as less risky than the market is.

Neutral Stock: A stock with beta equal to 1 is called neutral stock because it is as volatile as the market is.

Aggressive stock: A beta with a value greater than 1 is known as an aggressive stock since it has variation larger than the market’s and therefore is considered as more risky/volatile than the market is.

Since beta is an unknown parameter, therefore, investors usually require an estimate of a stock’s beta before purchasing it. However, the statistical model can be obtained by including an intercept (ß0) and an error term (ut) in the model, so that we have a simple linear regression model as

rt - rf,t = ß0 + ßM (rM,t - rf,t) +ut

By defining yt = rt -rf,t and xt = rM,t -rf,t , we can express CAPM model in above equation as

yt = ß0 + ß1 xt +ut

For further details, read the material available on:

https://www.investopedia.com/walkthrough/corporate-finance/4/return-risk/systematic-risk.aspx

Variables and Data Sources:

• PS&P = S&P 500 Price Index

This is the Standard and Poor index of 500 companies and will be used as a market portfolio. (You would use the return from this series as Market Return rM,t)

http://finance.yahoo.com/quote/%5egspc/history?p=^gspc

• PB = Boeing Company- BA's Stock Price

A particular stock we are interested in to determine how it behaves in response to market changes.

http://finance.yahoo.com/quote/BA/

• PGD = General Dynamics- GD's Stock Price

A particular stock we are interested in to determine how it behaves in response to market changes.

http://finance.yahoo.com/quote/GD/

• rf =Interest rate on 10 Year US-Treasury Note

This variable is given in percentage (with % sign omitted) and will serve as a risk-free interest rate. We will use this variable to compute excess returns on our preferred stock (either Boeing or GD) and Market excess returns.

http://finance.yahoo.com/quote/%5ETNX/

Task A: Downloading the data

Download the data for S&P 500 index, Boeing Stock Price, General Dynamics Corp. Stock Price, and US TN (10 Year), using the links provided above and choosing Monthly Historical Data for all variables covering the period related to a group your Student ID belongs to.

Data Group Data Period Students with ID Between (inclusive)

Start Date (day/month/year) End Date (day/month/year)

Group 01 01/03/2013 31/03/2018 16503281

19619593

Group 02 01/10/2012 31/10/2017 19619594

19841989

Group 03 01/03/2012 31/03/2017 19841990

19876048

Group 04 01/10/2011 31/10/2016 19876049

19888488

Group 05 01/03/2011 31/03/2016 19888489

20096775

Group 06 01/10/2010 31/10/2015 20096776

20193917

Example: Suppose a student's ID is 19855310. This ID falls in an interval corresponding to group 06 and therefore, this student would download monthly data covering the period 01/10/2010 to 31/10/2015.

Personal important note:

So my student id falls in interval corresponding to group 6 .

Task B: Perform the following.

1. Calculate returns for these three series in Excel or any software of your choice using the transformation: rt = 100*ln(Pt / Pt-1) and perform the Jarque-Berra test of normally distributed returns for each of Boeing and GD. What do you infer about the distribution of the two stock returns series? Describe also the risk and average return relationship in each of the two stocks.

Hints:

o We have performed a similar task in Workshop 01.

o If there are say -n+1- observations on prices, then the return series would have -n- observations.

o These numbers would represent percentages after multiplication with 100 in the formula above. But you would not put a percentage sign in your data. For example, returns for two periods are 0.35% and 0.41% but we would use 0.35 and 0.41 after omitting % sign in our excel worksheet.

2. Test a hypothesis that the average return on GD stock is different from 2.8%. Which test statistic would you choose to perform this hypothesis test and why? Also, specify the distribution of the test statistic under the null hypothesis, using 5% significance level.

3. Before investing in one of the two stocks, you first want to compare risk associated with each of the two stocks. Perform an appropriate hypothesis test using 5% significance level and interpret your results.

4. Besides, you want to determine whether both stocks have the same population average return. Perform an appropriate hypothesis test using information in your sample of 60 observations on returns, using 5% significance level. Report your findings and also mention which stock will you prefer and why?

5. Compute excess return on your preferred stock as yt = rt - rf,t and excess market return as xt = rM,t - rf,t and perform the following tasks.

a. Estimate the CAPM using linear regression by regressing the excess return on your preferred stock (yt) on excess market return (xt) and properly report your regression results.

b. Interpret the estimated CAPM beta-coefficient in terms of the stock's riskiness in comparison with the market.

c. Interpret the value of R2.

d. Interpret 95% confidence interval for the slope coefficient.

6. Using the confidence interval approach to hypothesis testing, perform the hypothesis test to determine whether your preferred stock is a neutral stock. (Note: You would not be given any marks if you do not use CI approach to test a hypothesis)

7. One of the assumptions of ordinary least squares (OLS) method is; normally distributed error term in the model. Perform an appropriate hypothesis test to determine whether it is plausible to assume normally distributed errors.

Analyse Data & Submit Report

Prepare your written report in two Parts:

Part A: Calculations

• Set out all your calculations for each of the tasks (listed above) using Data Analysis Tool in Excel. Present your results in graphs and charts as appropriate

Part B: Interpretation

• Explain what your results mean, in language that your client can understand. For example, what conclusions can you draw from each of your findings?

• Your written report must be no more than TWELVE (12) pages in total, including all appendices, graphs, tables and written answers. Answer the questions directly. Do not present unnecessary graphs or numerical measures, undertake inappropriate tests or discuss irrelevant matters.

Additional information and formulas:

The Capital Asset Pricing Model

The capital asset pricing model also known as CAPM is one of the fundamental models in the field of finance. The model explains variations in the rate of return on a security ( rt) as a function of the rate of return on a market portfolio (rM,t) consisting of all publicly traded stocks. Generally, the rate of return on any investment is measured relative to its opportunity cost, which is the return on a risk-free asset (rf,t). The difference between the return and risk-free rate is called the risk premium because it is the reward or punishment for making a risky investment. According to CAPM, the risk premium on a security, denoted by (rt - rf,t ), is proportional to the risk premium on the market portfolio, (rM,t - rf,t). Thus,

rt - rf,t = ßM (rM,t - rf,t)

where the coefficient provides security’s ‘‘beta’’ value.

Model in equation (1) is called economic model since it describes the relationship between excess stock return and the excess market return based on financial theory.

Why is CAPM important?

The CAPM beta is important to investors since it discloses the stock’s volatility. In particular, this beta measures the sensitivity of given security’s return to variation in the whole stock market. Value of beta determines whether the stock is a defensive, a neutral, or an aggressive stock.

Defensive stock: A stock is known as defensive stock if its beta value is less than 1. A defensive stock has its variation less than the market’s and therefore is considered as less risky than the market is.

Neutral Stock: A stock with beta equal to 1 is called neutral stock because it is as volatile as the market is.

Aggressive stock: A beta with a value greater than 1 is known as an aggressive stock since it has variation larger than the market’s and therefore is considered as more risky/volatile than the market is.

Since beta is an unknown parameter, therefore, investors usually require an estimate of a stock’s beta before purchasing it. However, the statistical model can be obtained by including an intercept (ß0) and an error term (ut) in the model, so that we have a simple linear regression model as

rt - rf,t = ß0 + ßM (rM,t - rf,t) +ut

By defining yt = rt -rf,t and xt = rM,t -rf,t , we can express CAPM model in above equation as

yt = ß0 + ß1 xt +ut

For further details, read the material available on:

https://www.investopedia.com/walkthrough/corporate-finance/4/return-risk/systematic-risk.aspx

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