Need help with finance investment homework. Deadline is in 15 hours. Thank you.

1 Investments - Finance 460AB Homework #4, Due Friday February 10, 2017 at 6 PM For all assignments: Please place your answer first within the yellow format. Please justify your work within the light yellow format when specified (by giving a reason, a formula, and/or a description of the calculation as appropriate). Chapter 8 Problems: 8.1. Distinguish between the Single-Index Model and the Single-Factor Model, as they are presented in Chapter 8. @Answer: 8.2. The market index has standard deviation of 18% in a financial market that satisfies the single-index model with just three stocks having the following properties: a. Find the expected excess return on the market portfolio @Answer: @Justification: b. Find the firm-specific risk of stock B as both a variance and as a standard deviation. @Answer: @Justification: c. Find and interpret the alpha of stock A @Answer: @Justification: 8.3. Choose an asset whose symbol begins with the first letter of your last name. Download historical data (from http://finance.yahoo.com/ , instructions are in Canvas, "Financial Data and Information Sources") for this asset and for the SP500 index (^GSPC, to be used as a benchmark index), weekly since January 2, 2014 and compute weekly rates of return for each series from the adjusted close. Do your work in Excel, then paste the results (one by one) into your homework assignment as a Word Document; I recommend that you use "Paste Special as Picture (Enhanced Metafile)" for Windows, Paste Special as Picture for Mac. Hint: type your letter into the search box at the top of http://finance.yahoo.com/q to bring up a list of potential choices, perhaps choosing \"show all results for ...\" near the bottom of the list (without hitting Enter) looking closely at the asset 2 symbol (not the name). Hint: you may find the worksheet from Canvas \"Chap 08 Regression Analysis of Microsoft.xlsx\" to be helpful. a. Create a scatter diagram for this situation @Answer: b. Insert the Security Characteristic Line on your scatterplot, with its equation. @Answer: c. Find the estimated beta for your chosen asset. @Answer: @Justification: d. Assess the estimation error in beta for your chosen asset by reporting and interpreting its 95% confidence interval. @Answer: @Justification: 8.4. A portfolio manager has identified an active portfolio (hoping to improve upon the Sharpe Ratio of the market portfolio) which has a beta of 0.8, an alpha of 2.19%, a total risk (yearly standard deviation) of 31%, and a nonsystematic risk of 28.8%. The market index portfolio has a Sharpe Ratio of 0.406 and a yearly standard deviation of 14.2%. a. Find the information ratio of this active portfolio. @Answer: @Justification: b. Find the Sharpe Ratio of the optimal portfolio P formed by combining the market portfolio with the active portfolio. @Answer: @Justification: 8.5. What is the role of alpha in active portfolio management? @Answer: Chapter 9 Problems: 9.1. You have carefully constructed a portfolio that has a beta of exactly zero. You did this by combining a few stocks together with some put options on other stocks. Assuming that the CAPM holds for these assets, what can you say about the expected return of this risky portfolio? Please ignore the fact that option betas change over time for this question by concentrating on the short-term behavior. @Answer: @Justification: 9.2. Regression analysis shows that a stock's beta is 1.17. Separately, it was determined that the stock's total risk is 36.1%. The market risk premium is estimated as 8.96%, the risk-free rate is 1.1%, and the market portfolio's total risk is 16.2%. a. Estimate the expected return of this stock, assuming that the CAPM holds. @Answer: @Justification: b. Find the correlation of this stock with the market portfolio, assuming that the CAPM holds. 3 @Answer: @Justification: c. If you believe that this stock has an actual expected rate of return of 13.9%, find its alpha. @Answer: @Justification: d. Your co-worker agrees that the stock has an actual expected rate of return of 13.9%, but claims that the alpha is zero and that this can happen because beta was mis-estimated. Assuming that your co-worker is correct, find the beta of this stock. @Answer: @Justification: e. Find the market price of risk in this situation. @Answer: @Justification: 9.3. What is the beta of the risk-free asset? @Answer: @Justification: Chapter 10 Problems: 10.1. In a two-factor model a security has sensitivities 1=1.59 and 2=0.48 to the two factors and a firm-specific standard deviation of 28.3%. The risk premiums of the factors are ( RP )1=9.2 and ( RP )2=3.4 . The risk-free rate is 1.48% and the risk premium of the market portfolio is 11.6%. a. Find the expected return of this security. @Answer: @Justification: b. If you have the additional information that the factor values are F1=2.90 and F2 =3.80 , find the security's expected return given this new information. @Answer: @Justification: 10.2. All morning you have been watching prices of a particular security as it rises and falls. Based on what you have seen, you are ready to try a trading strategy whereby you would buy the stock, wait for its price to rise by $1, then sell it. Because you would purchase on margin, borrowing the funds from your broker, and would post margin using funds from your savings account (whose funds are just sitting there), this is starting to look like a costless way to make money. Ignoring trading commissions, is this an arbitrage opportunity? @Answer: @Justification: 10.3. Assume a single-factor model describes security returns and that you have figured out a way to construct two well-diversified portfolios where portfolio P has an expected return of 10.6% (over the next time period) and has P =1 with respect to the factor F, and portfolio Q has an expected return of 13.8% and (also) has 4 Q=1 with respect to the factor F. You have decided to buy $1 million worth of one portfolio, and sell short $1 million of the other, a net investment of zero. Please assume no costs of trading or of selling short for this problem. a. Which portfolio (P or Q) should you buy? Which should you sell short? Why? @Answer: @Justification: b. What is the risk in your position in the next time period? @Answer: @Justification: c. How much money will you make next period @Answer: @Justification: d. If this were actually possible, would it be an arbitrage opportunity? @Answer: @Justification: 1 Investments - Finance 460AB Homework #4, Due Friday February 10, 2017 at 6 PM For all assignments: Please place your answer first within the yellow format. Please justify your work within the light yellow format when specified (by giving a reason, a formula, and/or a description of the calculation as appropriate). Chapter 8 Problems: 8.1. Distinguish between the Single-Index Model and the Single-Factor Model, as they are presented in Chapter 8. @Answer: single index model is an asset pricing model which according to it, the returns on a security can be represented as a linear relationship with any economic variable that is relevant to the security while single factor model is A model of security returns that recognizes only one common factor. The single factor is normally the market return 8.2. The market index has standard deviation of 18% in a financial market that satisfies the single-index model with just three stocks having the following properties: a. Find the expected excess return on the market portfolio @Answer: 7.33% @Justification: Excess return = 0.06+0.11+0.05/3=0.0733*100=7.33% b. Find the firm-specific risk of stock B as both a variance and as a standard deviation. @Answer: 3.67 @Justification: Variance =(Er-r)^2 (7.33-11)^2=13.4689 SD= 13.4689=3.67 c. Find and interpret the alpha of stock A @Answer: 1.32. this means that on adjusted basis, the risk of stock A is high and this means that the stock is highly volatile as compared to a number of stock in the market. @Justification: Alpha =(Rm-Rf) 2 Alpha =0.66(20-18) Alpha =1.32 8.3. Choose an asset whose symbol begins with the first letter of your last name. Download historical data (from http://finance.yahoo.com/ , instructions are in Canvas, "Financial Data and Information Sources") for this asset and for the SP500 index (^GSPC, to be used as a benchmark index), weekly since January 2, 2014 and compute weekly rates of return for each series from the adjusted close. Do your work in Excel, then paste the results (one by one) into your homework assignment as a Word Document; I recommend that you use "Paste Special as Picture (Enhanced Metafile)" for Windows, Paste Special as Picture for Mac. Hint: type your letter into the search box at the top of http://finance.yahoo.com/q to bring up a list of potential choices, perhaps choosing \"show all results for ...\" near the bottom of the list (without hitting Enter) looking closely at the asset symbol (not the name). Hint: you may find the worksheet from Canvas \"Chap 08 Regression Analysis of Microsoft.xlsx\" to be helpful. a. Create a scatter diagram for this situation @Answer: b. Insert the Security Characteristic Line on your scatterplot, with its equation. @Answer: c. Find the estimated beta for your chosen asset. @Answer: @Justification: d. Assess the estimation error in beta for your chosen asset by reporting and interpreting its 95% confidence interval. @Answer: @Justification: 8.4. A portfolio manager has identified an active portfolio (hoping to improve upon the Sharpe Ratio of the market portfolio) which has a beta of 0.8, an alpha of 2.19%, a total risk (yearly standard deviation) of 31%, and a nonsystematic risk of 28.8%. The market index portfolio has a Sharpe Ratio of 0.406 and a yearly standard deviation of 14.2%. a. Find the information ratio of this active portfolio. @Answer: 0.5833 @Justification: IR=(31-14.2)%/28.8%=0.5833 b. Find the Sharpe Ratio of the optimal portfolio Pformed by combining the market portfolio with the active portfolio. @Answer: @Justification: 8.5. What is the role of alpha in active portfolio management? @Answer: Alpha is a measure of the active return on an investment, the performance of that investment compared to a suitable market index. 3 Chapter 9 Problems: 9.1. You have carefully constructed a portfolio that has a beta of exactly zero. You did this by combining a few stocks together with some put options on other stocks. Assuming that the CAPM holds for these assets, what can you say about the expected return of this risky portfolio? Please ignore the fact that option betas change over time for this question by concentrating on the short-term behavior. @Answer: @Justification: 9.2. Regression analysis shows that a stock's beta is 1.17. Separately, it was determined that the stock's total risk is 36.1%. The market risk premium is estimated as 8.96%, the risk-free rate is 1.1%, and the market portfolio's total risk is 16.2%. a. Estimate the expected return of this stock, assuming that the CAPM holds. @Answer: @Justification: Rr=rf+(rm-rf) Rr =1.1%+1.17(8.96-1.1) Rr=10.2962% b. Find the correlation of this stock with the market portfolio, assuming that the CAPM holds. @Answer: 2.23 @Justification: corr=36.1/16.2=2.23 c. If you believe that this stock has an actual expected rate of return of 13.9%, find its alpha. @Answer: 3.6038% @Justification: Alpha is the excess return =13.9%-10.2962%=3.6038% d. Your co-worker agrees that the stock has an actual expected rate of return of 13.9%, but claims that the alpha is zero and that this can happen because beta was mis-estimated. Assuming that your co-worker is correct, find the beta of this stock. @Answer: @Justification: b = (R - Rf) / (Rm - Rf) b=(13.9-1.1)/(8.96-1.1) b= 1.62850 e. Find the market price of risk in this situation. @Answer: @Justification: market price risk = (E[r] - rf)/ standard deviation (10.2962-1.1)/16.2=0.5677 9.3. What is the beta of the risk-free asset? @Answer: Zero @Justification: The beta of a risk free asset is zero since there is no anticipated risk in the respective asset. 4 Chapter 10 Problems: 10.1. In a two-factor model a security has sensitivities 1=1.59 and 2=0.48 to the two factors and a firm-specific standard deviation of 28.3%. The risk premiums of the factors are ( RP )1=9.2 and ( RP )2=3.4 . The risk-free rate is 1.48% and the risk premium of the market portfolio is 11.6%. a. Find the expected return of this security. @Answer: @Justification: RR=Rf+ 1 (Rm-Rf) RR= 1.48%+1.59(9.2%-1.48%) RR=1.48%+12.2748=13.7548% Factor 2 Rr=1.48%+0.48(-3.4%-1.48%) Rr= 1.48%-4.88%=-3.4% b. If you have the additional information that the factor values are F1=2.90 and F2 =3.80 , find the security's expected return given this new information. @Answer: @Justification: 10.2. All morning you have been watching prices of a particular security as it rises and falls. Based on what you have seen, you are ready to try a trading strategy whereby you would buy the stock, wait for its price to rise by $1, then sell it. Because you would purchase on margin, borrowing the funds from your broker, and would post margin using funds from your savings account (whose funds are just sitting there), this is starting to look like a costless way to make money. Ignoring trading commissions, is this an arbitrage opportunity? @Answer: Yes @Justification: An arbitrage opportunity arises when one purchase and sell underlying assets at a profit from the existing price differences, since am buying and waiting for the price to rise by $1 then sell, it qualifies to be a an arbitrage opportunity. 10.3. Assume a single-factor model describes security returns and that you have figured out a way to construct two well-diversified portfolios where portfolio P has an expected return of 10.6% (over the next time period) and has P =1 with respect to the factor F, and portfolio Q has an expected return of 13.8% and (also) has Q=1 with respect to the factor F. You have decided to buy $1 million worth of one portfolio, and sell short $1 million of the other, a net investment of zero. Please assume no costs of trading or of selling short for this problem. a. Which portfolio (P or Q) should you buy? Which should you sell short? Why? @Answer: You should buy portfolio Q and sell short portfolio P @Justification: You should buy portfolio Q because it has a high anticipated expected return hence profitable and you should sell portfolio P because of low anticipated return. b. What is the risk in your position in the next time period? @Answer: @Justification: Er=0.5*10.6%+0.5*13.8=12.2 Risk =(13.8-12.2)^2=2.56 5 SD= 2.56=1.6 c. How much money will you make next period @Answer: $138,000 @Justification: 13.8/100*1,000,000=$138,000 d. If this were actually possible, would it be an arbitrage opportunity? @Answer: Yes @Justification: it would be an arbitrage since there is evaluation of the portfolio movement in profitability and making a profitable decision. For instance portfolio P will result to 10.6/100*1,000,000=$106,000 while portfolio Q will result to 13.8/100*1,000,000=$138,000 hence making a decision that Q is more profitable than P hence an arbitrage opportunity. 1 Investments - Finance 460AB Homework #4, Due Friday February 10, 2017 at 6 PM For all assignments: Please place your answer first within the yellow format. Please justify your work within the light yellow format when specified (by giving a reason, a formula, and/or a description of the calculation as appropriate). Chapter 8 Problems: 8.1. Distinguish between the Single-Index Model and the Single-Factor Model, as they are presented in Chapter 8. @Answer: single index model is an asset pricing model which according to it, the returns on a security can be represented as a linear relationship with any economic variable that is relevant to the security while single factor model is A model of security returns that recognizes only one common factor. The single factor is normally the market return 8.2. The market index has standard deviation of 18% in a financial market that satisfies the single-index model with just three stocks having the following properties: a. Find the expected excess return on the market portfolio @Answer: 7.33% @Justification: Excess return = 0.06+0.11+0.05/3=0.0733*100=7.33% b. Find the firm-specific risk of stock B as both a variance and as a standard deviation. @Answer: 3.67 @Justification: Variance =(Er-r)^2 (7.33-11)^2=13.4689 SD= 13.4689=3.67 c. Find and interpret the alpha of stock A @Answer: 1.32. this means that on adjusted basis, the risk of stock A is high and this means that the stock is highly volatile as compared to a number of stock in the market. @Justification: Alpha =(Rm-Rf) 2 Alpha =0.66(20-18) Alpha =1.32 8.3. Choose an asset whose symbol begins with the first letter of your last name. Download historical data (from http://finance.yahoo.com/ , instructions are in Canvas, "Financial Data and Information Sources") for this asset and for the SP500 index (^GSPC, to be used as a benchmark index), weekly since January 2, 2014 and compute weekly rates of return for each series from the adjusted close. Do your work in Excel, then paste the results (one by one) into your homework assignment as a Word Document; I recommend that you use "Paste Special as Picture (Enhanced Metafile)" for Windows, Paste Special as Picture for Mac. Hint: type your letter into the search box at the top of http://finance.yahoo.com/q to bring up a list of potential choices, perhaps choosing \"show all results for ...\" near the bottom of the list (without hitting Enter) looking closely at the asset symbol (not the name). Hint: you may find the worksheet from Canvas \"Chap 08 Regression Analysis of Microsoft.xlsx\" to be helpful. a. Create a scatter diagram for this situation @Answer: b. Insert the Security Characteristic Line on your scatterplot, with its equation. @Answer: c. Find the estimated beta for your chosen asset. @Answer: @Justification: d. Assess the estimation error in beta for your chosen asset by reporting and interpreting its 95% confidence interval. @Answer: @Justification: 8.4. A portfolio manager has identified an active portfolio (hoping to improve upon the Sharpe Ratio of the market portfolio) which has a beta of 0.8, an alpha of 2.19%, a total risk (yearly standard deviation) of 31%, and a nonsystematic risk of 28.8%. The market index portfolio has a Sharpe Ratio of 0.406 and a yearly standard deviation of 14.2%. a. Find the information ratio of this active portfolio. @Answer: 0.5833 @Justification: IR=(31-14.2)%/28.8%=0.5833 b. Find the Sharpe Ratio of the optimal portfolio Pformed by combining the market portfolio with the active portfolio. @Answer: 0.154 @Justification: (31-28.8)/14.2=0.154 8.5. What is the role of alpha in active portfolio management? @Answer: Alpha is a measure of the active return on an investment, the performance of that investment compared to a suitable market index. 3 Chapter 9 Problems: 9.1. You have carefully constructed a portfolio that has a beta of exactly zero. You did this by combining a few stocks together with some put options on other stocks. Assuming that the CAPM holds for these assets, what can you say about the expected return of this risky portfolio? Please ignore the fact that option betas change over time for this question by concentrating on the short-term behavior. @Answer: The expected return on risky portfolio is expected to vary. @Justification: A risky portfolio is the one whose return vary more often in the market than the risk free asset. Therefore it is anticipated to vary greatly in the market. 9.2. Regression analysis shows that a stock's beta is 1.17. Separately, it was determined that the stock's total risk is 36.1%. The market risk premium is estimated as 8.96%, the risk-free rate is 1.1%, and the market portfolio's total risk is 16.2%. a. Estimate the expected return of this stock, assuming that the CAPM holds. @Answer: 10.2962% @Justification: Rr=rf+(rm-rf) Rr =1.1%+1.17(8.96-1.1) Rr=10.2962% b. Find the correlation of this stock with the market portfolio, assuming that the CAPM holds. @Answer: 2.23 @Justification: corr=36.1/16.2=2.23 c. If you believe that this stock has an actual expected rate of return of 13.9%, find its alpha. @Answer: 3.6038% @Justification: Alpha is the excess return =13.9%-10.2962%=3.6038% d. Your co-worker agrees that the stock has an actual expected rate of return of 13.9%, but claims that the alpha is zero and that this can happen because beta was mis-estimated. Assuming that your co-worker is correct, find the beta of this stock. @Answer: 1.62850 @Justification: b = (R - Rf) / (Rm - Rf) b=(13.9-1.1)/(8.96-1.1) b= 1.62850 e. Find the market price of risk in this situation. @Answer: 0.5677 @Justification: market price risk = (E[r] - rf)/ standard deviation (10.2962-1.1)/16.2=0.5677 9.3. What is the beta of the risk-free asset? @Answer: Zero @Justification: 4 The beta of a risk free asset is zero since there is no anticipated risk in the respective asset. Chapter 10 Problems: 10.1. In a two-factor model a security has sensitivities 1=1.59 and 2=0.48 to the two factors and a firm-specific standard deviation of 28.3%. The risk premiums of the factors are ( RP )1=9.2 and ( RP )2=3.4 . The risk-free rate is 1.48% and the risk premium of the market portfolio is 11.6%. a. Find the expected return of this security. @Answer: -3.4% @Justification: RR=Rf+ 1 (Rm-Rf) RR= 1.48%+1.59(9.2%-1.48%) RR=1.48%+12.2748=13.7548% Factor 2 Rr=1.48%+0.48(-3.4%-1.48%) Rr= 1.48%-4.88%=-3.4% b. If you have the additional information that the factor values are F1=2.90 and F2 =3.80 , find the security's expected return given this new information. @Answer: -37.972% @Justification: RR= 1.48%+-2.90(9.2%-1.48%) RR=1.48%+-19.428=-20.908% Rr=1.48%+3.80(-3.4%-1.48%) Rr= 1.48%+-18.544%=-17.064 -17.064+-20.908=-37.972% 10.2. All morning you have been watching prices of a particular security as it rises and falls. Based on what you have seen, you are ready to try a trading strategy whereby you would buy the stock, wait for its price to rise by $1, then sell it. Because you would purchase on margin, borrowing the funds from your broker, and would post margin using funds from your savings account (whose funds are just sitting there), this is starting to look like a costless way to make money. Ignoring trading commissions, is this an arbitrage opportunity? @Answer: Yes @Justification: An arbitrage opportunity arises when one purchase and sell underlying assets at a profit from the existing price differences, since am buying and waiting for the price to rise by $1 then sell, it qualifies to be a an arbitrage opportunity. 10.3. Assume a single-factor model describes security returns and that you have figured out a way to construct two well-diversified portfolios where portfolio P has an expected return of 10.6% (over the next time period) and has P =1 with respect to the factor F, and portfolio Q has an expected return of 13.8% and (also) has Q=1 with respect to the factor F. You have decided to buy $1 million worth of one portfolio, and sell short $1 million of the other, a net investment of zero. Please assume no costs of trading or of selling short for this problem. 5 a. Which portfolio (P or Q) should you buy? Which should you sell short? Why? @Answer: You should buy portfolio Q and sell short portfolio P @Justification: You should buy portfolio Q because it has a high anticipated expected return hence profitable and you should sell portfolio P because of low anticipated return. b. What is the risk in your position in the next time period? @Answer: 1.6 @Justification: Er=0.5*10.6%+0.5*13.8=12.2 Risk =(13.8-12.2)^2=2.56 SD= 2.56=1.6 c. How much money will you make next period @Answer: $138,000 @Justification: 13.8/100*1,000,000=$138,000 d. If this were actually possible, would it be an arbitrage opportunity? @Answer: Yes @Justification: it would be an arbitrage since there is evaluation of the portfolio movement in profitability and making a profitable decision. For instance portfolio P will result to 10.6/100*1,000,000=$106,000 while portfolio Q will result to 13.8/100*1,000,000=$138,000 hence making a decision that Q is more profitable than P hence an arbitrage opportunity. 1 Investments - Finance 460AB Homework #4, Due Friday February 10, 2017 at 6 PM For all assignments: Please place your answer first within the yellow format. Please justify your work within the light yellow format when specified (by giving a reason, a formula, and/or a description of the calculation as appropriate). Chapter 8 Problems: 8.1. Distinguish between the Single-Index Model and the Single-Factor Model, as they are presented in Chapter 8. @Answer: single index model is an asset pricing model which according to it, the returns on a security can be represented as a linear relationship with any economic variable that is relevant to the security while single factor model is A model of security returns that recognizes only one common factor. The single factor is normally the market return 8.2. The market index has standard deviation of 18% in a financial market that satisfies the single-index model with just three stocks having the following properties: a. Find the expected excess return on the market portfolio @Answer: 7.33% @Justification: Excess return = 0.06+0.11+0.05/3=0.0733*100=7.33% b. Find the firm-specific risk of stock B as both a variance and as a standard deviation. @Answer: 3.67 @Justification: Variance =(Er-r)^2 (7.33-11)^2=13.4689 SD= 13.4689=3.67 c. Find and interpret the alpha of stock A @Answer: 1.32. this means that on adjusted basis, the risk of stock A is high and this means that the stock is highly volatile as compared to a number of stock in the market. @Justification: Alpha =(Rm-Rf) 2 Alpha =0.66(20-18) Alpha =1.32 8.3. Choose an asset whose symbol begins with the first letter of your last name. Download historical data (from http://finance.yahoo.com/ , instructions are in Canvas, "Financial Data and Information Sources") for this asset and for the SP500 index (^GSPC, to be used as a benchmark index), weekly since January 2, 2014 and compute weekly rates of return for each series from the adjusted close. Do your work in Excel, then paste the results (one by one) into your homework assignment as a Word Document; I recommend that you use "Paste Special as Picture (Enhanced Metafile)" for Windows, Paste Special as Picture for Mac. Hint: type your letter into the search box at the top of http://finance.yahoo.com/q to bring up a list of potential choices, perhaps choosing \"show all results for ...\" near the bottom of the list (without hitting Enter) looking closely at the asset symbol (not the name). Hint: you may find the worksheet from Canvas \"Chap 08 Regression Analysis of Microsoft.xlsx\" to be helpful. a. Create a scatter diagram for this situation @Answer: b. Insert the Security Characteristic Line on your scatterplot, with its equation. @Answer: c. Find the estimated beta for your chosen asset. @Answer: @Justification: d. Assess the estimation error in beta for your chosen asset by reporting and interpreting its 95% confidence interval. @Answer: @Justification: 8.4. A portfolio manager has identified an active portfolio (hoping to improve upon the Sharpe Ratio of the market portfolio) which has a beta of 0.8, an alpha of 2.19%, a total risk (yearly standard deviation) of 31%, and a nonsystematic risk of 28.8%. The market index portfolio has a Sharpe Ratio of 0.406 and a yearly standard deviation of 14.2%. a. Find the information ratio of this active portfolio. @Answer: 0.5833 @Justification: IR=(31-14.2)%/28.8%=0.5833 b. Find the Sharpe Ratio of the optimal portfolio Pformed by combining the market portfolio with the active portfolio. @Answer: @Justification: 8.5. What is the role of alpha in active portfolio management? @Answer: Alpha is a measure of the active return on an investment, the performance of that investment compared to a suitable market index. 3 Chapter 9 Problems: 9.1. You have carefully constructed a portfolio that has a beta of exactly zero. You did this by combining a few stocks together with some put options on other stocks. Assuming that the CAPM holds for these assets, what can you say about the expected return of this risky portfolio? Please ignore the fact that option betas change over time for this question by concentrating on the short-term behavior. @Answer: @Justification: 9.2. Regression analysis shows that a stock's beta is 1.17. Separately, it was determined that the stock's total risk is 36.1%. The market risk premium is estimated as 8.96%, the risk-free rate is 1.1%, and the market portfolio's total risk is 16.2%. a. Estimate the expected return of this stock, assuming that the CAPM holds. @Answer: @Justification: Rr=rf+(rm-rf) Rr =1.1%+1.17(8.96-1.1) Rr=10.2962% b. Find the correlation of this stock with the market portfolio, assuming that the CAPM holds. @Answer: 2.23 @Justification: corr=36.1/16.2=2.23 c. If you believe that this stock has an actual expected rate of return of 13.9%, find its alpha. @Answer: 3.6038% @Justification: Alpha is the excess return =13.9%-10.2962%=3.6038% d. Your co-worker agrees that the stock has an actual expected rate of return of 13.9%, but claims that the alpha is zero and that this can happen because beta was mis-estimated. Assuming that your co-worker is correct, find the beta of this stock. @Answer: @Justification: b = (R - Rf) / (Rm - Rf) b=(13.9-1.1)/(8.96-1.1) b= 1.62850 e. Find the market price of risk in this situation. @Answer: @Justification: market price risk = (E[r] - rf)/ standard deviation (10.2962-1.1)/16.2=0.5677 9.3. What is the beta of the risk-free asset? @Answer: Zero @Justification: The beta of a risk free asset is zero since there is no anticipated risk in the respective asset. 4 Chapter 10 Problems: 10.1. In a two-factor model a security has sensitivities 1=1.59 and 2=0.48 to the two factors and a firm-specific standard deviation of 28.3%. The risk premiums of the factors are ( RP )1=9.2 and ( RP )2=3.4 . The risk-free rate is 1.48% and the risk premium of the market portfolio is 11.6%. a. Find the expected return of this security. @Answer: @Justification: RR=Rf+ 1 (Rm-Rf) RR= 1.48%+1.59(9.2%-1.48%) RR=1.48%+12.2748=13.7548% Factor 2 Rr=1.48%+0.48(-3.4%-1.48%) Rr= 1.48%-4.88%=-3.4% b. If you have the additional information that the factor values are F1=2.90 and F2 =3.80 , find the security's expected return given this new information. @Answer: @Justification: 10.2. All morning you have been watching prices of a particular security as it rises and falls. Based on what you have seen, you are ready to try a trading strategy whereby you would buy the stock, wait for its price to rise by $1, then sell it. Because you would purchase on margin, borrowing the funds from your broker, and would post margin using funds from your savings account (whose funds are just sitting there), this is starting to look like a costless way to make money. Ignoring trading commissions, is this an arbitrage opportunity? @Answer: Yes @Justification: An arbitrage opportunity arises when one purchase and sell underlying assets at a profit from the existing price differences, since am buying and waiting for the price to rise by $1 then sell, it qualifies to be a an arbitrage opportunity. 10.3. Assume a single-factor model describes security returns and that you have figured out a way to construct two well-diversified portfolios where portfolio P has an expected return of 10.6% (over the next time period) and has P =1 with respect to the factor F, and portfolio Q has an expected return of 13.8% and (also) has Q=1 with respect to the factor F. You have decided to buy $1 million worth of one portfolio, and sell short $1 million of the other, a net investment of zero. Please assume no costs of trading or of selling short for this problem. a. Which portfolio (P or Q) should you buy? Which should you sell short? Why? @Answer: You should buy portfolio Q and sell short portfolio P @Justification: You should buy portfolio Q because it has a high anticipated expected return hence profitable and you should sell portfolio P because of low anticipated return. b. What is the risk in your position in the next time period? @Answer: @Justification: Er=0.5*10.6%+0.5*13.8=12.2 Risk =(13.8-12.2)^2=2.56 5 SD= 2.56=1.6 c. How much money will you make next period @Answer: $138,000 @Justification: 13.8/100*1,000,000=$138,000 d. If this were actually possible, would it be an arbitrage opportunity? @Answer: Yes @Justification: it would be an arbitrage since there is evaluation of the portfolio movement in profitability and making a profitable decision. For instance portfolio P will result to 10.6/100*1,000,000=$106,000 while portfolio Q will result to 13.8/100*1,000,000=$138,000 hence making a decision that Q is more profitable than P hence an arbitrage opportunity. 1 Investments - Finance 460AB Homework #4, Due Friday February 10, 2017 at 6 PM For all assignments: Please place your answer first within the yellow format. Please justify your work within the light yellow format when specified (by giving a reason, a formula, and/or a description of the calculation as appropriate). Chapter 8 Problems: 8.1. Distinguish between the Single-Index Model and the Single-Factor Model, as they are presented in Chapter 8. @Answer: single index model is an asset pricing model which according to it, the returns on a security can be represented as a linear relationship with any economic variable that is relevant to the security while single factor model is A model of security returns that recognizes only one common factor. The single factor is normally the market return 8.2. The market index has standard deviation of 18% in a financial market that satisfies the single-index model with just three stocks having the following properties: a. Find the expected excess return on the market portfolio @Answer: 7.33% @Justification: Excess return = 0.06+0.11+0.05/3=0.0733*100=7.33% b. Find the firm-specific risk of stock B as both a variance and as a standard deviation. @Answer: 3.67 @Justification: Variance =(Er-r)^2 (7.33-11)^2=13.4689 SD= 13.4689=3.67 c. Find and interpret the alpha of stock A @Answer: 1.32. this means that on adjusted basis, the risk of stock A is high and this means that the stock is highly volatile as compared to a number of stock in the market. @Justification: Alpha =(Rm-Rf) 2 Alpha =0.66(20-18) Alpha =1.32 8.3. Choose an asset whose symbol begins with the first letter of your last name. Download historical data (from http://finance.yahoo.com/ , instructions are in Canvas, "Financial Data and Information Sources") for this asset and for the SP500 index (^GSPC, to be used as a benchmark index), weekly since January 2, 2014 and compute weekly rates of return for each series from the adjusted close. Do your work in Excel, then paste the results (one by one) into your homework assignment as a Word Document; I recommend that you use "Paste Special as Picture (Enhanced Metafile)" for Windows, Paste Special as Picture for Mac. Hint: type your letter into the search box at the top of http://finance.yahoo.com/q to bring up a list of potential choices, perhaps choosing \"show all results for ...\" near the bottom of the list (without hitting Enter) looking closely at the asset symbol (not the name). Hint: you may find the worksheet from Canvas \"Chap 08 Regression Analysis of Microsoft.xlsx\" to be helpful. a. Create a scatter diagram for this situation @Answer: b. Insert the Security Characteristic Line on your scatterplot, with its equation. @Answer: c. Find the estimated beta for your chosen asset. @Answer: @Justification: d. Assess the estimation error in beta for your chosen asset by reporting and interpreting its 95% confidence interval. @Answer: @Justification: 8.4. A portfolio manager has identified an active portfolio (hoping to improve upon the Sharpe Ratio of the market portfolio) which has a beta of 0.8, an alpha of 2.19%, a total risk (yearly standard deviation) of 31%, and a nonsystematic risk of 28.8%. The market index portfolio has a Sharpe Ratio of 0.406 and a yearly standard deviation of 14.2%. a. Find the information ratio of this active portfolio. @Answer: 0.5833 @Justification: IR=(31-14.2)%/28.8%=0.5833 b. Find the Sharpe Ratio of the optimal portfolio Pformed by combining the market portfolio with the active portfolio. @Answer: 0.154 @Justification: (31-28.8)/14.2=0.154 8.5. What is the role of alpha in active portfolio management? @Answer: Alpha is a measure of the active return on an investment, the performance of that investment compared to a suitable market index. 3 Chapter 9 Problems: 9.1. You have carefully constructed a portfolio that has a beta of exactly zero. You did this by combining a few stocks together with some put options on other stocks. Assuming that the CAPM holds for these assets, what can you say about the expected return of this risky portfolio? Please ignore the fact that option betas change over time for this question by concentrating on the short-term behavior. @Answer: The expected return on risky portfolio is expected to vary. @Justification: A risky portfolio is the one whose return vary more often in the market than the risk free asset. Therefore it is anticipated to vary greatly in the market. 9.2. Regression analysis shows that a stock's beta is 1.17. Separately, it was determined that the stock's total risk is 36.1%. The market risk premium is estimated as 8.96%, the risk-free rate is 1.1%, and the market portfolio's total risk is 16.2%. a. Estimate the expected return of this stock, assuming that the CAPM holds. @Answer: 10.2962% @Justification: Rr=rf+(rm-rf) Rr =1.1%+1.17(8.96-1.1) Rr=10.2962% b. Find the correlation of this stock with the market portfolio, assuming that the CAPM holds. @Answer: 2.23 @Justification: corr=36.1/16.2=2.23 c. If you believe that this stock has an actual expected rate of return of 13.9%, find its alpha. @Answer: 3.6038% @Justification: Alpha is the excess return =13.9%-10.2962%=3.6038% d. Your co-worker agrees that the stock has an actual expected rate of return of 13.9%, but claims that the alpha is zero and that this can happen because beta was mis-estimated. Assuming that your co-worker is correct, find the beta of this stock. @Answer: 1.62850 @Justification: b = (R - Rf) / (Rm - Rf) b=(13.9-1.1)/(8.96-1.1) b= 1.62850 e. Find the market price of risk in this situation. @Answer: 0.5677 @Justification: market price risk = (E[r] - rf)/ standard deviation (10.2962-1.1)/16.2=0.5677 9.3. What is the beta of the risk-free asset? @Answer: Zero @Justification: 4 The beta of a risk free asset is zero since there is no anticipated risk in the respective asset. Chapter 10 Problems: 10.1. In a two-factor model a security has sensitivities 1=1.59 and 2=0.48 to the two factors and a firm-specific standard deviation of 28.3%. The risk premiums of the factors are ( RP )1=9.2 and ( RP )2=3.4 . The risk-free rate is 1.48% and the risk premium of the market portfolio is 11.6%. a. Find the expected return of this security. @Answer: -3.4% @Justification: RR=Rf+ 1 (Rm-Rf) RR= 1.48%+1.59(9.2%-1.48%) RR=1.48%+12.2748=13.7548% Factor 2 Rr=1.48%+0.48(-3.4%-1.48%) Rr= 1.48%-4.88%=-3.4% b. If you have the additional information that the factor values are F1=2.90 and F2 =3.80 , find the security's expected return given this new information. @Answer: -37.972% @Justification: RR= 1.48%+-2.90(9.2%-1.48%) RR=1.48%+-19.428=-20.908% Rr=1.48%+3.80(-3.4%-1.48%) Rr= 1.48%+-18.544%=-17.064 -17.064+-20.908=-37.972% 10.2. All morning you have been watching prices of a particular security as it rises and falls. Based on what you have seen, you are ready to try a trading strategy whereby you would buy the stock, wait for its price to rise by $1, then sell it. Because you would purchase on margin, borrowing the funds from your broker, and would post margin using funds from your savings account (whose funds are just sitting there), this is starting to look like a costless way to make money. Ignoring trading commissions, is this an arbitrage opportunity? @Answer: Yes @Justification: An arbitrage opportunity arises when one purchase and sell underlying assets at a profit from the existing price differences, since am buying and waiting for the price to rise by $1 then sell, it qualifies to be a an arbitrage opportunity. 10.3. Assume a single-factor model describes security returns and that you have figured out a way to construct two well-diversified portfolios where portfolio P has an expected return of 10.6% (over the next time period) and has P =1 with respect to the factor F, and portfolio Q has an expected return of 13.8% and (also) has Q=1 with respect to the factor F. You have decided to buy $1 million worth of one portfolio, and sell short $1 million of the other, a net investment of zero. Please assume no costs of trading or of selling short for this problem. 5 a. Which portfolio (P or Q) should you buy? Which should you sell short? Why? @Answer: You should buy portfolio Q and sell short portfolio P @Justification: You should buy portfolio Q because it has a high anticipated expected return hence profitable and you should sell portfolio P because of low anticipated return. b. What is the risk in your position in the next time period? @Answer: 1.6 @Justification: Er=0.5*10.6%+0.5*13.8=12.2 Risk =(13.8-12.2)^2=2.56 SD= 2.56=1.6 c. How much money will you make next period @Answer: $138,000 @Justification: 13.8/100*1,000,000=$138,000 d. If this were actually possible, would it be an arbitrage opportunity? @Answer: Yes @Justification: it would be an arbitrage since there is evaluation of the portfolio movement in profitability and making a profitable decision. For instance portfolio P will result to 10.6/100*1,000,000=$106,000 while portfolio Q will result to 13.8/100*1,000,000=$138,000 hence making a decision that Q is more profitable than P hence an arbitrage opportunity