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QBA25622: Finance Discipline- Quantitative Business Analysis Assignment
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A2. Based on your answers in A1, over the period from 2007 to 2016, which city experienced the lowest growth in value of established houses? Which city experienced the highest growth in value of established houses over the last 4 years?
A3. You have set your eyes on a house in (PICK A CITY FROM A1 ABOVE) that is going for $675,000 today [just above the national average]. You are very excited about the prospects of buying this house and negotiate a 25-year mortgage with 20% down and 6% interest rate. What will be the amount of your monthly payments?
A4. For each month for the duration of your mortgage calculate how much of your monthly payment goes to principal re-payment and how much of it is interest. Plot a graph showing a breakdown of your periodic payment into principal repayment and interest. What percentage of your monthly payment on the 24 th month of the mortgage contract goes towards repayment of the principal?
A5. What is the amount of total interest you will end up paying?
A6. You believe that the housing market will continue to grow at the same rate as in the past 4 years. How much will your house in (YOUR CITY SELECTION) be worth after 25 years? Will the house value appreciation (if any) be sufficient to cover the total interest you paid?
Question B - Stock Markets
Introduction
The Capital asset pricing model (CAPM) takes into account the stock's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset. CAPM shows that the cost of equity capital is determined only by beta. Despite it being invented in the 1960s, the CAPM still remains popular due to its simplicity and applicability in a variety of situations. It may be a good idea to check out Understanding Beta at http://www.investopedia.com/video/play/understanding-beta/ . The CAPM is a model for pricing an individual security or portfolio. The risk of a portfolio comprises systematic risk, also known as undiversifiable risk, and unsystematic risk which is also known as idiosyncratic risk or diversifiable risk. Systematic risk refers to the risk common to all securities—i.e. market risk. Unsystematic risk is the risk associated with individual assets. Unsystematic risk can be diversified away to smaller levels by including a greater number of assets in the portfolio (specific risks "average out"). The same is not possible for systematic risk within one market. Depending on the market, a portfolio of approximately 20 securities would be sufficiently diversified.
The beta from a single factor model in the form is a good approximation to the CAPM beta. The basic idea is that stocks tend to move together, driven by the same economic forces (the market). Here, the dependent variable, are percentage returns for stock , and independent variable, are percentage returns for a broad market index. is the intercept and is the slope of the linear relationship between the stock returns and the market. are the residual returns that cannot be explained by the market fluctuation (this is your idiosyncratic or firm-specific fluctuations).
In the file Assignment Data.xlsx, tab:ASX200 stocks (Prices), you will find prices for 152 stocks as well as the S&P/ASX 200 Index (a benchmark for the Australian stock market) from July 1, 2014 to June 30, 2017.
1. Pick any 3 securities (full name, industry and sector information are provided in column headings).
2. Convert your chosen security prices and the market index into percentage returns. For each asset/index, percentage returns are defined as . This will define your returns for the three stocks, , and the market return .
B1. Perform OLS regression for each stock separately and report regression outputs for the three models from Excel/Matlab including line fit plots and residual plots.
B2. For each stock, discuss the OLS assumptions and violations (if any) based on the results from B1.
B3. Discuss the estimated betas for your three stocks and their statistical significance. Are these betas in line with your expectations? Provide your reasoning. What does it mean if a stock has a beta equal to 1? What does it mean if a stock has a beta equal to zero?
B4. Discuss the measure of fit () of your regressions in B1. Are these in line with your expectations? Provide your reasoning. Note that gives the fraction of the variance of the dependent variable (the return on a stock/portfolio of stocks) that is explained by movements in the independent variable (the return on the market index).
B5. Construct an equally weighted portfolio consisting of your three chosen stocks (equally weighted portfolio returns are simply the average of individual stock returns in that portfolio, ) and find the portfolio beta. Report regression output (including line fit plots and residual plots), assess the OLS assumptions and violations (if any) and discuss the estimated portfolio beta and the measure of fit of your regression. How does the measure of fit for the portfolio compares with the measures of fit for your individual stocks? Comment on portfolio
diversification effect using your s.
Question C - Population Survey
Introduction
Each month the Bureau of Labor Statistics in the U.S. Department of Labor conducts the “Current Population Survey” (CPS), which provides data on labor force characteristics of the population, including the level of employment, unemployment, and earnings. Approximately 65,000 randomly selected U.S. households are surveyed each month. The sample is chosen by randomly selecting addresses from a database comprised of addresses from the most recent decennial census augmented with data on new housing units constructed after the last census. The exact random sampling scheme is rather complicated (first small geographical areas are randomly selected, then housing units within these areas randomly selected). The file Assignment Data.xlsx, tab: Population Survey contains the data from the survey. These data are for full-time workers, defined as workers employed more than 35 hours per week for at least 48 weeks in the previous year. Data are provided for workers whose highest educational achievement is (1) a high school diploma, and (2) a bachelor’s degree.
Series in Data Set:
FEMALE: 1 if female; 0 if male
YEAR: Year
AHE: Average Hourly Earnings
BACHELOR: 1 if worker has a bachelor’s degree; 0 if worker has a high school degree
Use the data in Assignment Data.xlsx, tab: Population Survey to answer the following questions:
C1. Run a regression of average hourly earnings (AHE) on age (Age). Repor Excel/Matlab output. What is the estimated intercept? What is the estimated slope?
C2. Run a regression of AHE on Age, gender (Female), and education (Bachelor). Report Excel/Matlab output. What is the estimated effect of Age on earnings? Construct a 95% confidence interval for the coefficient on Age in the regression.
C3. Are the results from the regression in C2 substantively different from the results in C1 regarding the effects of Age and AHE? What bias does the regression in C1 appear to suffer from?
C4. Bob is a 26-year- old male worker with a high school diploma. Predict Bob's earnings using the estimated regression in C2. Alexis is a 30-year- old female worker with a college degree. Predict Alexis's earnings using the regression.
C5. Compare the fit of the regression in C1 and C2 using the regression standard errors, and . Why are the and so similar in regression C2?
C6. Are gender and education determinants of earnings? Test the null hypothesis that Female can be deleted from the regression. Test the null hypothesis that Bachelor can be deleted from the regression. Test the null hypothesis that both Female and Bachelor can be deleted from the regression.
C7. A regression will suffer from omitted variable bias when two conditions hold. What are these two conditions? Do these conditions seem to hold here?
Quantitative Business Analysis Assignment:
Task: Question A – Australian Housing Market and Mortgage Loan Repayments Introduction Housing affordability is an enormous issue around the country. The average house price in Australia is now $656,800. In NSW, that average price jumps to $865,000, by far the highest price in the country; Victoria is next at $690,000, then the ACT at $642,000 and Western Australia at $536,000. If you're after a cheaper option, head south, because Tasmania's average price is $343,900. The Australian Bureau of Statistics releases its regular property price index and in this question we will try to analyse some of the issues on the Australia housing market. A1. File Assignment Data.xlsx, tab: Australian House Price Index, contains quarterly data on Australian House Price Index (HPI) for the eight capital cities as well as the weighted average HPI for the eight capital cities. Calculate compound annual growth rates (CAGR) and fill in the table below.
A2. Based on your answers in A1, over the period from 2007 to 2016, which city experienced the lowest growth in value of established houses? Which city experienced the highest growth in value of established houses over the last 4 years?
A3. You have set your eyes on a house in (PICK A CITY FROM A1 ABOVE) that is going for $675,000 today [just above the national average]. You are very excited about the prospects of buying this house and negotiate a 25-year mortgage with 20% down and 6% interest rate. What will be the amount of your monthly payments?
A4. For each month for the duration of your mortgage calculate how much of your monthly payment goes to principal re-payment and how much of it is interest. Plot a graph showing a breakdown of your periodic payment into principal repayment and interest. What percentage of your monthly payment on the 24 th month of the mortgage contract goes towards repayment of the principal?
A5. What is the amount of total interest you will end up paying?
A6. You believe that the housing market will continue to grow at the same rate as in the past 4 years. How much will your house in (YOUR CITY SELECTION) be worth after 25 years? Will the house value appreciation (if any) be sufficient to cover the total interest you paid?
Question B - Stock Markets
Introduction
The Capital asset pricing model (CAPM) takes into account the stock's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset. CAPM shows that the cost of equity capital is determined only by beta. Despite it being invented in the 1960s, the CAPM still remains popular due to its simplicity and applicability in a variety of situations. It may be a good idea to check out Understanding Beta at http://www.investopedia.com/video/play/understanding-beta/ . The CAPM is a model for pricing an individual security or portfolio. The risk of a portfolio comprises systematic risk, also known as undiversifiable risk, and unsystematic risk which is also known as idiosyncratic risk or diversifiable risk. Systematic risk refers to the risk common to all securities—i.e. market risk. Unsystematic risk is the risk associated with individual assets. Unsystematic risk can be diversified away to smaller levels by including a greater number of assets in the portfolio (specific risks "average out"). The same is not possible for systematic risk within one market. Depending on the market, a portfolio of approximately 20 securities would be sufficiently diversified.
The beta from a single factor model in the form is a good approximation to the CAPM beta. The basic idea is that stocks tend to move together, driven by the same economic forces (the market). Here, the dependent variable, are percentage returns for stock , and independent variable, are percentage returns for a broad market index. is the intercept and is the slope of the linear relationship between the stock returns and the market. are the residual returns that cannot be explained by the market fluctuation (this is your idiosyncratic or firm-specific fluctuations).
In the file Assignment Data.xlsx, tab:ASX200 stocks (Prices), you will find prices for 152 stocks as well as the S&P/ASX 200 Index (a benchmark for the Australian stock market) from July 1, 2014 to June 30, 2017.
1. Pick any 3 securities (full name, industry and sector information are provided in column headings).
2. Convert your chosen security prices and the market index into percentage returns. For each asset/index, percentage returns are defined as . This will define your returns for the three stocks, , and the market return .
B1. Perform OLS regression for each stock separately and report regression outputs for the three models from Excel/Matlab including line fit plots and residual plots.
B2. For each stock, discuss the OLS assumptions and violations (if any) based on the results from B1.
B3. Discuss the estimated betas for your three stocks and their statistical significance. Are these betas in line with your expectations? Provide your reasoning. What does it mean if a stock has a beta equal to 1? What does it mean if a stock has a beta equal to zero?
B4. Discuss the measure of fit () of your regressions in B1. Are these in line with your expectations? Provide your reasoning. Note that gives the fraction of the variance of the dependent variable (the return on a stock/portfolio of stocks) that is explained by movements in the independent variable (the return on the market index).
B5. Construct an equally weighted portfolio consisting of your three chosen stocks (equally weighted portfolio returns are simply the average of individual stock returns in that portfolio, ) and find the portfolio beta. Report regression output (including line fit plots and residual plots), assess the OLS assumptions and violations (if any) and discuss the estimated portfolio beta and the measure of fit of your regression. How does the measure of fit for the portfolio compares with the measures of fit for your individual stocks? Comment on portfolio
diversification effect using your s.
Question C - Population Survey
Introduction
Each month the Bureau of Labor Statistics in the U.S. Department of Labor conducts the “Current Population Survey” (CPS), which provides data on labor force characteristics of the population, including the level of employment, unemployment, and earnings. Approximately 65,000 randomly selected U.S. households are surveyed each month. The sample is chosen by randomly selecting addresses from a database comprised of addresses from the most recent decennial census augmented with data on new housing units constructed after the last census. The exact random sampling scheme is rather complicated (first small geographical areas are randomly selected, then housing units within these areas randomly selected). The file Assignment Data.xlsx, tab: Population Survey contains the data from the survey. These data are for full-time workers, defined as workers employed more than 35 hours per week for at least 48 weeks in the previous year. Data are provided for workers whose highest educational achievement is (1) a high school diploma, and (2) a bachelor’s degree.
Series in Data Set:
FEMALE: 1 if female; 0 if male
YEAR: Year
AHE: Average Hourly Earnings
BACHELOR: 1 if worker has a bachelor’s degree; 0 if worker has a high school degree
Use the data in Assignment Data.xlsx, tab: Population Survey to answer the following questions:
C1. Run a regression of average hourly earnings (AHE) on age (Age). Repor Excel/Matlab output. What is the estimated intercept? What is the estimated slope?
C2. Run a regression of AHE on Age, gender (Female), and education (Bachelor). Report Excel/Matlab output. What is the estimated effect of Age on earnings? Construct a 95% confidence interval for the coefficient on Age in the regression.
C3. Are the results from the regression in C2 substantively different from the results in C1 regarding the effects of Age and AHE? What bias does the regression in C1 appear to suffer from?
C4. Bob is a 26-year- old male worker with a high school diploma. Predict Bob's earnings using the estimated regression in C2. Alexis is a 30-year- old female worker with a college degree. Predict Alexis's earnings using the regression.
C5. Compare the fit of the regression in C1 and C2 using the regression standard errors, and . Why are the and so similar in regression C2?
C6. Are gender and education determinants of earnings? Test the null hypothesis that Female can be deleted from the regression. Test the null hypothesis that Bachelor can be deleted from the regression. Test the null hypothesis that both Female and Bachelor can be deleted from the regression.
C7. A regression will suffer from omitted variable bias when two conditions hold. What are these two conditions? Do these conditions seem to hold here?