HW 3 finance

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Colorado State University, Fort Collins *

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530

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Finance

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Apr 3, 2024

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docx

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Question 1 1.5 / 1.5 pts The figure shown below is similar to a figure shown in the assigned reading in the textbook. The vertical axis shows the standard deviation in the portfolio returns. The horizontal axis tracks the number of assets (n) in the portfolio. The downward sloping curve tracks the decrease in total risk in the portfolio as additional assets are added. What are the synonyms for the "diversifiable risk" shown in the figure? Select all terms below that are synonyms of this type of risk. (If you would like to look at the textbook version of this figure see Figure 6.1 or 7.1 depending on the edition of the textbook that you are using. The figure appears in the section titled Diversification and Portfolio Risk.) unique risk firm-specific risk nonsystematic risk systematic risk market risk

credit risk default risk Partial Question 2 3 / 4 pts The x-axis shown in the figure below measures standard deviation in portfolio returns and the y-axis measures the expected return. The curve represents the investment frontier. The frontier was created using 2 underlying risky portfolios based on stocks (#11, square portfolio) and bonds (#2, circle portfolio). The correlation between the stock and bond portfolios in this example was -0.25. Assumptions:  Expected return for portfolio #11 = 10%  Expected return for portfolio #2 = 7%  Risk free rate = 5%  Expected return on tangency portfolio = 8%, standard deviation for tangency portfolio = 7%  You have $10,000 of investment equity

 Portfolio 13 is on the CAL tangent to the frontier and has an expected return of 10.3%. Which assets would you use to create portfolio 13? [ Select ] ["Portfolio #13 can be created using a combination of just the risk-free asset and the tangency portfolio.", "Portfolio #13 can be created using a combination of just the risk-free asset and the stock portfolio.", "Portfolio #13 can be created using a combination of just the risk- free asset and the bond portfolio.", "Portfolio #13 can be created using a combination of just the stock and bond portfolios."]  Portfolio 8 is on the investment frontier and has an expected return of 9.1%. How much money would you need to invest in portfolio #11 if you wanted to create portfolio #8? Assume you can only invest in portfolios 2 and 11 and that you want to use all of your investment equity. [ Select ] ["We would invest $7,000 in portfolio #11 and the rest in portfolio #2 to create portfolio #8.", "We would invest $3,000 in portfolio #11 and the rest in portfolio #2 to create portfolio #8", "We would invest $5,000 in portfolio #11 and the rest in portfolio #2 to create portfolio #8.", "We would invest $1,000 in portfolio #11 and the rest in portfolio #2 to create portfolio #8."]  When we talk about portfolio weights we use the word "shorting" synonymously with the idea of "borrowing" and this appears in the math as negative investment weights. Assume we can invest in the risk-free asset, the tangency

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portfolio, the bond portfolio, and/or the stock portfolio. Which of the statements below are true? Only portfolio 13 requires shorting in some asset to create.  True/False: Portfolios 1 and 2 are on the "efficient frontier". False Answer 1: Portfolio #13 can be created using a combination of just the risk-free asset and the tangency portfolio. E[r 8 ] = (w 2 )E[r 2 ] + (w 11 )E[r 11 ] E[r 8 ] = (1-w 11 )E[r 2 ] + (w 11 )E[r 11 ] .091 = (1-w 11 )E[r 2 ] + (w 11 )E[r 11 ] <-- plug in the values for the expected returns from the assumptions and solve for w 11 and then multiply w 11 by the investment equity Answer 2: We would invest $7,000 in portfolio #11 and the rest in portfolio #2 to create portfolio #8. All portfolios on the frontier are created by combining the bond and stock portfolio. This means that portfolio #8 would be created using the stock and bond portfolio. We are given the information that the portfolio #8 has an expected return of 9.1% so we would start with the formula for portfolio return. E[r 8 ] = w 11 *E[r 11 ] + w 2 *E[r 2 ] = w 11 *E[r 11 ] + (1-w 11 )*E[r 2 ] <- general expression for the return on a 2 asset portfolio 0.091 = w(0.10) + (1-w)(0.07) <- fill in the values we know 0.091 = 0.10w + 0.07 - 0.07w <- multiply the 0.07 by the terms in the paranthesis 0.091 = 0.03w + 0.07 subtract 0.07 from both sides of equation 0.021 = 0.03w divide both sides by 0.03 0.021/0.03 = w = .7 This means that 70% of our investment equity should be invested in the stock portfolio and 30% in the bond portfolio to create portfolio 8. Answer 3: Only portfolio 13 requires shorting in some asset to create. Answer 4: False Only the upper portion of the curve are considered the "efficient frontier". Question 3

1 / 1 pts The figure shown below is similar to a figure shown in the assigned reading in the textbook. The vertical axis shows the standard deviation in the portfolio returns. The horizontal axis tracks the number of assets (n) in the portfolio. The downward sloping curve tracks the decrease in total risk in the portfolio as additional assets are added. What are synonyms for the "market risk" shown in the figure? Select all terms below that are synonyms of this type of risk. (If you would like to look at the textbook version of this figure see Figure 6.1 or 7.1 depending on the edition of the textbook that you are using. The figure appears in the section titled Diversification and Portfolio Risk.) unique risk firm-specific risk nonsystematic risk systematic risk nondiversifiable risk credit risk

default risk Question 4 1 / 1 pts True/False: The tangency portfolio is the minimum variance portfolio. True False Partial Question 5 1 / 2 pts The figure shown below was discussed as part of the lecture. The vertical axis in the figure is the expected portfolio return. The horizontal axis in the figure is the standard deviation in portfolio returns. The E portfolio is a portfolio of risky stocks (equity), and the D portfolio is a portfolio of risky bonds (debt). The frontier shown with the solid blue curve requires a correlation between D and E of 0.30. This question is about the blue "dotted" and black "solid" frontiers shown in the figure. The labels "dotted" and "solid" appear in the figure to clarify which frontiers to look at. Which of these statements are false ? Select all that are false. (Remember in my class that the statement needs to be unconditionally true in order for it to be true. If you find yourself needing to add words to the statement to make it true then it is false as written).

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The correlation between D and E would need to be less than 0.3 to create the dotted frontier. The correlation between D and E would need to be 1 to create the solid frontier. The correlation between D and E would need to be more than 0.3 to create the dotted frontier. The correlation between D and E would need to be less than 0 in order for the dotted frontier to curve left instead of right. The correlation between D and E would need to be -1 to create the the dotted frontier. The correlation between D and E would need to be 0 to create the solid frontier.

Question 6 1.5 / 1.5 pts There are 2 tables shown below. The first table reports the mean returns and standard deviation in returns to stocks in the US, UK, France, Germany, Japan, and China using historical data. The third column in the first table reports the Sharpe ratios for these 6 country-based portfolios. The second table reports the correlations between each of these country-based portfolios. (A) Assume you can invest in the risk-free asset and in one of these 6 country-based portfolios. So your final portfolio will be made up of some amount of money in the risk-free asset and some amount of money in one of the 6 country-based portfolios (i.e., your final portfolio will include 1 risk-free asset and 1 risky asset). Which country's portfolio would you use as the risky asset in your final portfolio and why? Assume the historical data is similar to what you expect to see going forward. You would use the US portfolio as the risky asset because the Sharpe ratio is highest for the US portfolio. (B) For this question assume that you can create a final portfolio that includes several risky assets together from multiple countries (i.e., you are not limited to just one country's stocks).  True/False: You would want to include some investments in each of the 6 countries in your final portfolio because none of the correlations are equal to -1 or to 1 which suggests there would be a

reduction in risk to your final portfolio by investing across all 6 assets. True  True/False: The Chinese assets would be the least likely to improve the risk-return characteristics of an underlying portfolio primarily focused on US stocks because the correlation between US and Chinese stocks is the lowest correlation of any of the other countries with the US. False Answer 1: You would use the US portfolio as the risky asset because the Sharpe ratio is highest for the US portfolio. Answer 2: True Answer 3: False Question 7 1 / 1 pts (The remaining questions in HW3 all rely on the same Excel file. It is recommended that you do these questions in order. This question is the first of 8 that use the Excel file. You can download the Excel file here: HW3.xlsx Open this document with ReadSpeaker docReader Download HW3.xlsx Open this document with ReadSpeaker docReader . The subsequent questions will also provide a link to the same Excel file but you only need to download it once.) The monthly returns for various assets are reported in columns B - J on the "Returns" tab corresponding with the dates shown in column A. Column B reports monthly returns for a portfolio of AAA corporate bonds and Column C reports monthly returns for a portfolio of High Yield bonds. Bonds are debt securities that investors can buy. The "AAA" credit rating indicates that this portfolio is created using the safest corporate bonds with the lowest risk of default. The "High Yield" designation means this portfolio is created using bonds with a high level of credit risk. Knowing that the AAA bonds are safer than the High Yield bonds, which portfolio do you expect to have higher returns over time? If there is a relationship between risk and return then you would expect the High Yield bonds should have a higher return on average over time.

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You can verify this intuition by looking at the average monthly returns for columns B and C.  You will see that the High Yield portfolio has a higher average monthly return over the 20 year period. If there is a relationship between risk and return then you would expect the AAA bonds should have a higher return on average over time. If there is a relationship between risk and return then you would expect the High Yield bonds should have a lower return on average over time. Question 8 1.5 / 1.5 pts (The remaining questions in HW3 all rely on the same Excel file. It is recommended that you do these questions in order. This question is the second of 8 that use the Excel file. You can download the Excel file here: HW3.xlsx Open this document with ReadSpeaker docReader Download HW3.xlsx Open this document with ReadSpeaker docReader . You only need to download the Excel file once.) This question builds on the prior question by having you calculate the arithmetic average return for the AAA and High Yield bond portfolios using the monthly return data from 2003-2023. To do this go to the "Returns" tab and enter the appropriate formulas in cells M4 and N4 to calculate the average monthly returns for the AAA and High Yield bonds, respectively. If you need to see an example of a similar calculation then look at cell O4 which shows the formula for the arithmetic average monthly returns on the S&P500 based on the returns in column D. After you have calculated the average returns answer the following 2 questions: What is the average monthly return over the last 20 years on the AAA bonds? What is the average monthly return over the last 20 years on the High Yield bonds? Choose the numbers closest to the correct answers. AAA average return = 0.00278, High Yield average return = 0.00579 The formula in M4 would be =AVERAGE(B2:B239). The formula in N4 would be =AVERAGE(C2:C239). AAA average return = 0.00706, High Yield average return = 0.00330

AAA average return = -0.004, High Yield average return = 0.014 Question 9 1.5 / 1.5 pts (The remaining questions in HW3 all rely on the same Excel file. It is recommended that you do these questions in order. This question is the third of 8 that use the Excel file. You can download the Excel file here: HW3.xlsx Open this document with ReadSpeaker docReader Download HW3.xlsx Open this document with ReadSpeaker docReader . You only need to download the Excel file once.) This question builds on the prior 2 questions. If High Yield bonds tend to be riskier than AAA bonds then we would expect to see the standard deviation (and variance) in monthly returns be higher for the High Yield bond returns than for the AAA bond returns. In this problem you will calculate the sample standard deviation in monthly returns for the AAA and High Yield portfolio returns using the data from 2003-2023. To do this go to the "Returns" tab and enter the appropriate formula in cells M6 and N6, respectively. If you need to see an example of a similar calculation look at cell O6 which shows the formula for the sample standard deviation in monthly returns on the S&P500. After you have calculated the average returns answer the following 2 questions: What is the sample standard deviation in monthly returns over the last 20 years on the AAA bonds? What is the sample standard deviation in monthly returns over the last 20 years on the High Yield bonds? Choose the numbers closest to the correct answers. AAA sample standard deviation = 0.01801, High Yield sample standard deviation = 0.02625 The formula for cell M6 would be =STDEV.S(B2:B239) AAA sample standard deviation = 0.00278, High Yield sample standard deviation = 0.00579 AAA sample standard deviation = 0.00032, High Yield sample standard deviation = 0.00069

Question 10 2 / 2 pts (The remaining questions in HW3 all rely on the same Excel file. It is recommended that you do these questions in order. This question is the 4th of 8 that use the Excel file. You can download the Excel file here: HW3.xlsx Open this document with ReadSpeaker docReader Download HW3.xlsx Open this document with ReadSpeaker docReader . You only need to download the Excel file once.) The earlier questions focused on the bond portfolio returns in columns B and C. The returns shown in columns D - J are from other assets. Each of these columns in the "Returns" tab are described below:  Column D reports monthly returns for a portfolio that tracks the S&P500 (the S&P500 index includes 500 large firms),  Column E reports monthly returns for a portfolio that tracks Gold and Platinum,  Column F reports monthly returns for a portfolio that tracks the S&P600 (the S&P600 index includes 600 small cap firms),  Columns G - I report monthly returns for 3 specific companies: Autozone (ticker: AZO), DollarTree (ticker: DLTR), and Netflix (ticker: nflx).  Column J reports the monthly returns to 1-month T-Bills. The average monthly returns and standard deviation in returns for all of these assets are reported in Columns M - U on the "Returns" tab using monthly data from 2003 - 2023. Using the information in the spreadsheet on the "Returns" tab answer the following questions:  Which of the assets had the highest average monthly return over the 20 years? Netflix  Which of the assets has the highest total risk based on the data from the 20 years? Netflix  Why would we expect the average returns to T-Bills to be smaller than the other assets? T-Bills are the least risky of these investments suggesting that their average returns would be less than the other riskier investments.  Why would we expect the standard deviation in returns to be smaller for the S&P500 portfolio than for the standard deviation in returns to Autozone, DollarTree, and Netflix? The S&P500 portfolio is well diversified with 500 different stocks. This means the idiosyncratic risk has been largely diversified away in the S&P500 portfolio. In contrast, the idiosyncratic risk hasn't been diversified away for investments in any of the 3 individual stocks alone.

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Answer 1: Netflix Answer 2: Netflix Answer 3: T-Bills are the least risky of these investments suggesting that their average returns would be less than the other riskier investments. Answer 4: The S&P500 portfolio is well diversified with 500 different stocks. This means the idiosyncratic risk has been largely diversified away in the S&P500 portfolio. In contrast, the idiosyncratic risk hasn't been diversified away for investments in any of the 3 individual stocks alone. Partial Question 11 0.5 / 1 pts (The remaining questions in HW3 all rely on the same Excel file. It is recommended that you do these questions in order. This question is the 5th of 8 that use the Excel file. You can download the Excel file here: HW3.xlsx Open this document with ReadSpeaker docReader Download HW3.xlsx Open this document with ReadSpeaker docReader . You only need to download the Excel file once.) The correlation coefficients are reported on the "Returns" tab. Use that information to answer the following questions:  Which two assets were the most correlated in the last 20 years? S&P500 and S&P600  Sometimes you hear people suggest that investments in gold do well during downturns. Does the correlation between the S&P500 and the Gold and Platinum portfolio support this idea? The negative correlation of -.041 suggests that when the overall market is down that gold is also down. The correlation is not strong but it suggests the returns move together on average. Answer 1: S&P500 and S&P600 Answer 2:

The negative correlation of -.041 suggests that when the overall market is down that gold is also down. The correlation is not strong but it suggests the returns move together on average. Question 12 5 / 5 pts (The remaining questions in HW3 all rely on the same Excel file. It is recommended that you do these questions in order. This question is the 6th of 8 that use the Excel file. You can download the Excel file here: HW3.xlsx Open this document with ReadSpeaker docReader Download HW3.xlsx Open this document with ReadSpeaker docReader . You only need to download the Excel file once.) During the lecture on regression we talked about how "excess returns" are calculated as an asset's raw return in a given period minus the risk-free return over the same time from. On the "Excess Returns, Scatter Plots" tab I've calculated the excess returns for the S&P600 portfolio, Autozone, DollarTree, Netflix, and the S&P500 portfolio in columns L - P. As discussed in the lecture the X variable in a CAPM-based regression is the excess return on the market (i.e., r m -r f or R m ). For this homework we will use the S&P500 as the "market" portfolio. The Netflix Scatter Plot graphs the historical monthly Netflix excess returns and the historical monthly market excess returns along with the trend line from the regression. This type of scatter plot with the trendline is called the "security characteristic line" or SCL. Each asset would have its own SCL. Using the information in the Netflix SCL plot answer the following questions:  What is the estimated beta for Netflix? Select the number closest to the correct number. 1.10  Which of the following statements best describes what this beta means? On average if the market is up 1% the Netflix is up 1.10% and if the market is down 1% Netflix is down 1.10%  What is the estimated intercept from the Netflix CAPM- based regression? Select the number closest to the correct number. 0.025  What is the R-square from the CAPM-based regression for Netflix? 0.0875  Which of the following statement best describes what this R-square value means? 8.75% of the variation in Netflix's returns is explained by the market. Answer 1: 1.10

Answer 2: On average if the market is up 1% the Netflix is up 1.10% and if the market is down 1% Netflix is down 1.10% Answer 3: 0.025 Answer 4: 0.0875 Answer 5: 8.75% of the variation in Netflix's returns is explained by the market. Question 13 1.5 / 1.5 pts (The remaining questions in HW3 all rely on the same Excel file. It is recommended that you do these questions in order. This question is the 7th of 8 that use the Excel file. You can download the Excel file here: HW3.xlsx Open this document with ReadSpeaker docReader Download HW3.xlsx Open this document with ReadSpeaker docReader . You only need to download the Excel file once.) The equation for the trendline is shown on each of the plots on the "Excess Returns, Scatter Plots" tab except for the lowest plot. In that plot the excess return on the market is plotted as the Y variable against the excess return on the market as the X variable. This plot is unlike the others because both the X and Y variables are excess returns on the S&P500.  What would the equation for the line on this plot be? y = 1x + 0  What would the R2 be for the lowest plot? 1 Answer 1: y = 1x + 0 Answer 2: 1 Question 14

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1.5 / 1.5 pts (This question is the 8th of 8 that use the Excel file. You can download the Excel file here: HW3.xlsx Open this document with ReadSpeaker docReader Download HW3.xlsx Open this document with ReadSpeaker docReader . You only need to download the Excel file once.) Go to Yahoo finance (finance.yahoo.com) and enter the Netflix ticker symbol (nflx) into the search bar and click enter. This should bring up a page that provides summary information about Netflix. The page should also report Netflix's beta.  Is the Netflix beta as reported by Yahoo the same as the beta shown on the Netflix Scatter Plot? no  The beta we estimated could be different than the one reported on the Yahoo website for a number of reasons. Select the statement below that would NOT provide a good reason for why the betas could be different. If both reasons could plausibly explain the difference in betas then select the option that indicates both statements could explain the differences. Both statements could explain the differences. Answer 1: no Answer 2: Both statements could explain the differences.