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FIN100 PRINCIPLES OF FINANCE WEEK 7 CHAPTER 11-12 HOMELESSON ASSIGNMENT CHAPTERS 11-12 Note: These are homelesson problems which are directly related to the finance concepts discussed in the course textbook, Chapter 12, Financial Risk and Return and similar to problems presented and discussed in the supplementary readings, Chapter 10 Capital Markets and the Pricing of Risk, Corporate Finance, Berk and DeMarzo, 2007 and Chapter 11 Systematic Risk and the Equity Risk Premium, Fundamentals of Corporate Finance, Berk and DeMarzo, 2000. Show all mathematical or quantitative calculations in Microsoft Excel or Microsoft Word. 1. Suppose your purchase Netflix stock (NFLX:US) which is currently trading close to $95.00. The probability of NFLX increasing to $105.00 is 35%. The probability of NFLX attaining $100.00 is 40%. There is also a 25% probability that NFLX will fall to $80.00. Determine the expected return on NFLX. In addition, determine the variance and standard deviation of NFLX, which provide some indication of the stock's riskiness or volatility. 2. Suppose you invest $158,000 and buy 2,000 shares of Microsoft (MSFT:US) at $25 per share ($50,000) and 3,000 shares of Pepsi (PEP:US) at $36 per share ($108,000). What are the portfolio weights for MSFT and PEP. If the expected returns are 12% on MSFT stock and 18% on PEP stock, which is the expected return on the investment portfolio? 3. Microsoft Excel spreadsheets are useful for computing statistics: average returns, standard deviation, variance, and coefficient of variation. Below is recent annual stock return data for ExxonMobil (XOM) and Microsoft (MSFT). Using Microsoft Excel, compute the average return, variance, standard deviation, and coefficient of variation on the returns for these stocks. As a risk adverse investor, provide a brief explanation as to which stock you would select for your investment portfolio? FIN100 PRINCIPLES OF FINANCE WEEK 7 CHAPTER 11-12 HOMELESSON ASSIGNMENT CHAPTERS 11-12 Note: These are homelesson problems which are directly related to the finance concepts discussed in the course textbook, Chapter 12, Financial Risk and Return and similar to problems presented and discussed in the supplementary readings, Chapter 10 Capital Markets and the Pricing of Risk, Corporate Finance, Berk and DeMarzo, 2007 and Chapter 11 Systematic Risk and the Equity Risk Premium, Fundamentals of Corporate Finance, Berk and DeMarzo, 2000. Show all mathematical or quantitative calculations in Microsoft Excel or Microsoft Word. 1. Suppose your purchase Netflix stock (NFLX:US) which is currently trading close to $95.00. The probability of NFLX increasing to $105.00 is 35%. The probability of NFLX attaining $100.00 is 40%. There is also a 25% probability that NFLX will fall to $80.00. Determine the expected return on NFLX. In addition, determine the variance and standard deviation of NFLX, which provide some indication of the stock's riskiness or volatility. 2. Suppose you invest $158,000 and buy 2,000 shares of Microsoft (MSFT:US) at $25 per share ($50,000) and 3,000 shares of Pepsi (PEP:US) at $36 per share ($108,000). What are the portfolio weights for MSFT and PEP. If the expected returns are 12% on MSFT stock and 18% on PEP stock, which is the expected return on the investment portfolio? 3. Microsoft Excel spreadsheets are useful for computing statistics: average returns, standard deviation, variance, and coefficient of variation. Below is recent annual stock return data for ExxonMobil (XOM) and Microsoft (MSFT). Using Microsoft Excel, compute the average return, variance, standard deviation, and coefficient of variation on the returns for these stocks. As a risk adverse investor, provide a brief explanation as to which stock you would select for your investment portfolio? Prob 12-1 From the information below, compute the average annual return, the variance, standard deviation, and coefficient of variation for each asset. Asset A B C D 5% -6% 12% 10% Average Return Asset A Asset B Asset C Asset D Prob 12-2 ASSET ANNUAL RETURNS 10% 20% 15% -10% 4% -5% 10% -15% 8% 5.07% 10.92% 2.52% 13.65% Coefficient of Variation 0.60 2.60 0.17 13.65 Standard Deviation Variance 8.50% 4.20% 14.67% 1.00% 15% 2% 17% 20% 0.26% 1.19% 0.06% 1.86% -7% Based upon your answers to question 1, which asset appears riskiest based on standard deviation? Based on coefficient of variation? Asset D appears to be riskiest based on the standard deviation and coefficient of variation. RCMP, Inc. shares rose 10 percent in value last year while the inflation rate was 3.5 percent. What was the real return on the stock? If an investor sold the stock after one year and paid taxes on the investment at a 15 percent tax rate, what is the real after-tax return on the investment? Prob 12-5 Real return on stock real after-tax return on investment 6.5% 5% Given her evaluation of current economic conditions, Ima Nutt believes there is a 20 percent probability of recession, a 50 percent chance of continued steady growth, and a 30 percent probability of inflationary growth. For each possibility, Ima has developed an interest rate forecast for long-term Treasury bond interest rates: 11. Ima is considering a purchase of Wallnut Company stock. Using the same scenarios and probabilities as in problem 10, she estimates Wallnut's return is -5 percent in a recession, 20 percent in constant growth, and 10 percent in inflation. Prob 12-10 Economic Forecast Recession Constant growth Inflation Interest Rate Forecast 6% 9% 14% Econ Recession Constant growth Inflation P I 20% 50% 30% P*I 6% 9% 14% 1.20% 4.50% 4.20% a. What is the expected interest rate under Ima's forecast? Expected interest rate under Ima's forecast 9.9% b. What is the variance and standard deviation of Ima's interest rate forecast? Variance Standard Deviation 8.49% 2.91% c. What is the coefficient of variation of Ima's interest rate forecast? Econ Recession Constant growth P I I - EI 20% 50% 30% Inflation 6.00 9.00 14.00 (I-EI)2 P*(I-EI)2 (3.90) 15.2100 (0.90) 0.8100 4.10 16.8100 3.04 0.41 5.04 8.49 variance Coefficient of variation of Ima's interest rate forecast 2.9137605 stand dev 0.29 d. If the current long-term Treasury bond interest rate is 8 percent, should Ima consider purchasing a Treasury bond? Why or why not? The expected interest rate of 9.90% is higher than the current interest rate of 8%. When interest rate goes up, bond prices will fall because they have an inverse relationship. So, if Ima buys a bond now, the value of the same is expected to decrease in future. Therefore, she should not consider buying the bond. a. What is Ima's expected return forecast for Wallnut stock? Forecast of expected return Prob 12-11 12% b. What is the standard deviation of the forecast? Standard Deviation Econ Recession Constant growth Inflation P R 20% 50% 30% P*R -5% 20% 10% -1.00% 10.00% 3.00% Econ Recession Constant growth Inflation P R 20% 50% 30% R - ER (R-ER)2 P*(R-ER)2 (5.00) (17.00) 289.00 57.80 20.00 8.00 64.00 32.00 10.00 (2.00) 4.00 1.20 91.00 variance 9.539392 stand dev 9.54% c. If Wallnut's current price is $20 per share and Wallnut is expected to pay a dividend of $0.80 per share next year, what price does Ima expect Wallnut to sell for in one year? Expected price $ 21.60 EXCEL Spreadsheets are useful for computing statistics: averages, standard deviation, variance, and correlation are included as built-in functions. Below is recent monthly stock return data for ExxonMobil (XOM) and Microsoft (MSFT). Using a spreadsheet and its functions, compute the average, variance, standard deviation, and correlation between the returns for these stocks. Prob 12-19 Month XOM Return November -4.6% October 0.1% September -1.9% August -3.3% July -4.4% June -1.6% May 0.7% April 9.4% March -0.1% February -3.2% MSFT Return 10.4% 13.6% -10.3% -13.8% -9.3% 5.5% 2.1% 23.9% -7.3% -3.4% XOM MSFT Average Return Variance Standard Deviation Correlation What does the correlation between the returns imply for a portfolio containing both stocks? There is moderate positive correlation between the two stocks. -0.89% 1.14% 0.00165 0.01482 4.07% 12.17% 67% Pr ob 12 -1 As se t A B From the information below, compute the average annual return, the variance, standard deviation, and coefficient of variation for each asset. ASSET ANNUAL RETURNS 15% 2% 12% 10% 15% -10% 17% 20% Varia nce Stan dard Devi ation 8.50% 0.26 % 5.07 % Coe ffici ent of Vari atio n 0.6 0 4.20% 1.19 % 10.9 2% 2.6 0 14.67% 0.06 % 2.52 % 0.1 7 1.00% As se t A As se tB As se tC 10% 20% Average Return C D 5% -6% 1.86 % 13.6 5% 13. 65 As se t D Pr ob 12 -2 4% -5% 15% 10 % 8 % 7 % Based upon your answers to question 1, which asset appears riskiest based on standard deviation? Based on coefficient of variation? Asset D appears to be riskiest based on the standard Pr ob 12 -5 deviation and coefficient of variation. RCMP, Inc. shares rose 10 percent in value last year while the inflation rate was 3.5 percent. What was the real return on the stock? If an investor sold the stock after one year and paid taxes on the investment at a 15 percent tax rate, what is the real after-tax return on the investment? Real return on stock real aftertax return on investment Given her evaluation of current economic conditions, Ima Nutt believes 6.5% 5% there is a 20 percent probability of recession, a 50 percent chance of continued steady growth, and a 30 percent probability of inflationary growth. For each possibility, Ima has developed an interest rate forecast for longterm Treasury bond interest rates: Pr ob 12 10 11. Ima is considering a purchase of Wallnut Company stock. Using Economic Forecast Recession Constant growth Inter est Rate Forec ast 6% Eco n P I P *I the same scenarios and probabilities as in problem 10, she estimates Rec essi on 20 % Wallnut's return is -5 percent in a recession, 20 percent in constant 9% Con stan t gro wth 50 % 6 1. % 2 0 % 9 4. % 5 0 % growth, and 10 percent in inflation. Inflation a. What is the expected interest rate under Ima's forecast? Expected interest rate under Ima's forecast b. What is the variance and standard deviation of Ima's interest rate forecast? Variance 14% Infl atio n 30 % 1 4. 4 2 % 0 % 9.9% c. What is the coefficient of variation of Ima's interest rate forecast? IEI (IEI )2 P*(I -EI)2 2 0 6. % 0 0 (3 .9 0) 1 5. 2 1 0 0 3.0 4 Con stan t gro wth Standard Deviation 8.49 % Eco n P 2.91 % Rec essi on I 5 0 9. % 0 0 (0 .9 0) 0. 8 1 0 0 0.4 1 Infl atio n 3 0 1 % 4. 0 0 4. 1 0 1 6. 8 1 0 0 5.0 4 8.4 v ar 2. 9 st a 9 Coefficient of variation of Ima's interest rate forecast d. If the current long-term Treasury bond interest rate is 8 percent, should Ima consider purchasing a Treasury bond? Why or why not? The expected interest rate of 9.90% is higher than the current interest rate of 8%. When interest rate goes up, bond prices will fall because they have an inverse relationship. So, if Ima buys a bond now, the value of the same is expected to decrease in 0.29 ia n c e 1 3 7 6 n d d e v future. Therefore, she should not consider buying the bond. a. What is Ima's expected return forecast for Wallnut stock? Eco n P R P * R Eco n P Pr ob 12 11 R E R (R E R) 2 P *( RE R) 2 Rec essi on Forecast of expected return R 12% b. What is the standard deviation of the forecast? 2 0 5 % % 1. 0 0 % Rec essi on 2 0 % Con stan t gro wth Infl atio n 5 2 0 0 % % 1 0. 0 0 % 3. 0 0 % Con stan t gro wth Infl atio n 5 0 % 3 1 0 0 % % 3 0 % (5 .0 0) (1 7. 0 0) 2 8 9. 0 0 5 7. 8 0 2 0. 0 0 8. 0 0 6 4. 0 0 3 2. 0 0 1 0. 0 0 (2 .0 0) 4. 0 0 1. 2 0 9.54 % va ri a n ce 9. 5 3 9 3 9 2 Standard Deviation 9 1. 0 0 st a n d d e v c. If Wallnut's current price is $20 per share and Wallnut is expected to pay a dividend of $0.80 per share next year, what price does Ima expect Wallnut to sell for in one year? Expected price EXCEL Spreadsheet s are useful for computing statistics: averages, standard deviation, variance, and correlation are included as built-in functions. Below is recent monthly stock return data for ExxonMobil (XOM) and Microsoft (MSFT). Using a spreadsheet $ 21.60 and its functions, compute the average, variance, standard deviation, and correlation between the returns for these stocks. Pr ob 12 19 Month XOM Retur n November -4.6% October 0.1% September -1.9% August -3.3% July -4.4% June May April -1.6% 0.7% 9.4% March -0.1% February -3.2% XOM Average Return 0.89 % MSF T Retu rn 10.4 % 13.6 % 10.3 % 13.8 % 9.3% 5.5% 2.1% 23.9 % 7.3% 3.4% MSF T 1.14 % Variance Standard Deviation Correlation 0.001 65 4.07 % 67% What does the correlation between the returns imply for a portfolio containing both stocks? There is moderate positive correlation between the two stocks. 0.01 482 12.1 7% FIN100 PRINCIPLES OF FINANCE WEEK 7 CHAPTER 11-12 HOMELESSON ASSIGNMENT CHAPTERS 11-12 Note: These are homelesson problems which are directly related to the finance concepts discussed in the course textbook, Chapter 12, Financial Risk and Return and similar to problems presented and discussed in the supplementary readings, Chapter 10 Capital Markets and the Pricing of Risk, Corporate Finance, Berk and DeMarzo, 2007 and Chapter 11 Systematic Risk and the Equity Risk Premium, Fundamentals of Corporate Finance, Berk and DeMarzo, 2000. Show all mathematical or quantitative calculations in Microsoft Excel or Microsoft Word. 1. Suppose your purchase Netflix stock (NFLX:US) which is currently trading close to $95.00. The probability of NFLX increasing to $105.00 is 35%. The probability of NFLX attaining $100.00 is 40%. There is also a 25% probability that NFLX will fall to $80.00. Determine the expected return on NFLX. In addition, determine the variance and standard deviation of NFLX, which provide some indication of the stock's riskiness or volatility. 2. Suppose you invest $158,000 and buy 2,000 shares of Microsoft (MSFT:US) at $25 per share ($50,000) and 3,000 shares of Pepsi (PEP:US) at $36 per share ($108,000). What are the portfolio weights for MSFT and PEP. If the expected returns are 12% on MSFT stock and 18% on PEP stock, which is the expected return on the investment portfolio? 3. Microsoft Excel spreadsheets are useful for computing statistics: average returns, standard deviation, variance, and coefficient of variation. Below is recent annual stock return data for ExxonMobil (XOM) and Microsoft (MSFT). Using Microsoft Excel, compute the average return, variance, standard deviation, and coefficient of variation on the returns for these stocks. As a risk adverse investor, provide a brief explanation as to which stock you would select for your investment portfolio? Question 1 Scenario Current Future Price Price $ 95 $ 105 $ 95 $ 100 $ 95 $ 80 Probability (P) 35% 40% 25% 100% Return 1 2 3 Total Standard deviation 10.53% 5.26% -15.79% Return Probability 3.68% 2.11% -3.95% 1.84% P (Return Mean)2 0.0119% 0.0003% 0.0838% 0.0959% 3.10% Expected return on NFLX Return i Probability i i Where Return i is the return in scenario i ; and Probabilityi is the probability of scenario i . Note, the return is calculated as follows: Return Future Price 1 Current Price Thus: Expected return on NFLX = (10.53% 35%) + (5.26% 40%) + (-15.79% 25%) = 1.84% Variance of Return on NFLX Probabilityi Return i Expected Return 2 i =35%(10.53%-1.84%)2 + 40%(5.26%-1.84%)2 + 25%(-15.79%-1.84%)2 = 0.0959% Standard deviation of Return on NFLX Variance of return on NFLX 0.0959% 3.10% Question 2 Stock MSFT PEP Total Number of shares 2 000 3 000 Price Value Weight $25 $36 $50 000 $108 000 $158 000 31.65% 68.35% 100.00% Expected Return 12.00% 18.00% Weight Expected Return 4% 12% 16.10% Expected return on investment portfolio Weight i Return i i Weight for MSFT = ($50,000)/($50,000 + $108,000) = 31.65% Weight for PEP = ($108,000)/($50,000 + $108,000) = 68.35%. Therefore, expected return on investment portfolio = 31.65%12% + 68.35%18% = 16.10%. Question 3 The Microsoft Excel results are shown in the table below. Month November October September August July June May April March February Average return Variance Standard deviation Coefficient of Variation XOM Monthly Returns 5.80% 0.10% 7.30% -3.30% -4.40% -1.60% 0.70% 10.70% -0.10% -3.20% 1.20% 0.26% 5.06% 4.22 MSFT Monthly Return 10.40% 13.60% -10.30% -13.80% -9.30% 5.50% 2.10% 23.90% -7.30% -3.40% 1.14% 1.48% 12.17% 10.68 As a risk averse investor, I will probably choose XOM given its lower coefficient of variance (COV). This suggests that XOM has a better risk-return tradeoff than MSFT. Furthermore, XOM had a higher average return and lower variance (risk) than MSFT. The above recommendation, however, should be taken with extreme caution because past performance of stocks (return and variance) is not necessarily a good guide to future performance. Thus, what matters more than assessing historical risk and return is my outlook. It may well be that my outlook on expected return on MSFT is higher than XOM. Furthermore, it may well be that XOM is likely to be more volatile than MSFT, in which case, I will prefer MSFT as a risk averse investor. Question 1 Current Future Probability Return Return P (Return - Mean)^2 Price Price (P) Probability 1 $ 95 $ 105 10.53% 35% 3.68% 0.0119% 2 $ 95 $ 100 5.26% 40% 2.11% 0.0003% 3 $ 95 $ 80 -15.79% 25% -3.95% 0.0838% Total 100% 1.84% 0.0959% Standard deviation 3.10% Scenario Question 2 Stock MSFT PEP Total Number of shares Price Value Weight 2,000 3,000 $25 $36 $50,000 $108,000 $158,000 31.65% 68.35% 100.00% Expected Return Weight X Expected Return 12.00% 18.00% 4% 12% 16.10% Question 3 Month November October September August July June May April March February Average return Variance Standard deviation Coefficient of Variation XOM Monthly MSFT Monthly Returns Return 5.80% 10.40% 0.10% 13.60% 7.30% -10.30% -3.30% -13.80% -4.40% -9.30% -1.60% 5.50% 0.70% 2.10% 10.70% 23.90% -0.10% -7.30% -3.20% -3.40% 1.20% 1.14% 0.26% 1.48% 5.06% 12.17% 4.22 10.68