HW 2 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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HW 2 JYflE_BQ@ut (?){http://www.acns.colostate.edulsingle-sign-on-using-shibboleth/#1471272725675-5603b487 -ebab) Due Oct 30 at 11:59pm Points 25 Questions 19 Available after Oct 23 at 8am Time Limit None Attempt History Attempt Time Score LATEST Attempt 1 66 minutes 24 out of 25 () Correct answers will be available on Oct 31 at 8am. Score for this quiz: 24 out of 25 Submitted Oct 30 at 3:53pm This attempt took 66 minutes. Question 1 1/1 pts You observe the following IBM annual returns over the last 3 years: 10%, -5%, 2%. What is the best description of this formula? .10—.05+-.02 3 T r-bar is the arithmetic mean r-bar is the geometric mean r-bar is the variance r-bar is the standard deviation
Question 2 171 pts You observe the following IBM annual returns over the last 3 years: 10%, -5%, 2%. What is the best description of the formula shown below? .10—.05+.02 3 when answering this question. Assume 1 = (10 7)* (=05 7)*+(:02—7)" _ . = This is the sample variance This is the population variance This is the standard deviation This is the geometric mean Question 3 1/1 pts You observe the following IBM annual returns over the last 3 years: 10%, -5%, 2%. What is the best description of this formula? (1 +.10) (1 —.05) (1 +.02)](5) —1 This is the geometric return This is the arithmetic return This is the cumulative return over 3 years This is the additive return over 3 years
Question 4 171 pts Assume that your portfolio has an expected return of 22% and a standard deviation of returns of 41.6%. What is the 5% Value-at-Risk (VaR)? -46.22% —_— 0.22 - 1.64*0.416 = - 46.22% -23.15% 23.15% 46.31% Question 5 1.5/1.5 pts A stock has an expected return of 16% with a standard deviation of 0.20. Assume you can borrow and lend risk-free at 5%. Assume your portfolio can include this one risky asset and/or the risk-free investment. What is the expected return and standard deviation of a portfolio for an investor with 50% of her wealth in the risky asset and 50% in the risk-free investment? E[r] = 10.5%, sigma=10% ' E[r] = .5*.16 + .5*.05 = 10.5% E[r] = 10.5%, sigma=20% E[r] = 16%, sigma=10%
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E[r] = 16%, sigma=20% Question 6 1.5/1.5 pts A stock has an expected return of 16% with a standard deviation of 0.20. Assume you can borrow and lend risk-free at 5%. Assume your portfolio can include this one risky asset and/or the risk-free investment. What is the expected return and standard deviation of a portfolio for an investor with 150% of her wealth in the risky asset and the rest in the risk-free investment? E[r] = 21.5%, sigma=30% ' E[r] = 1.5*.16 + -.5*.05=21.5% - sigma = 1.5%/20 = 30% E[r] = 21.5%, sigma=9% E[r] = 16%, sigma=20% E[r] = 16%, sigma=30% Question 7 1.5/1.5 pts Assume the price of a Schwab Small-Cap index fund is $45 per share, the annual expected return is 16%, and the annual standard deviation is 0.25. Assume you have $10,000 of investment equity and that you want to buy the Schwab Small-Cap fund using your money and some of the broker's money such that your total expected annual return on your portfolio is 22%. Assume you can borrow at 7% annually. What is the portfolio weight in the Small-Cap index fund such that the expected return on your portfolio is 22%7
1.66 22 = w(.16) + (1-w)(.07) w = 1.6666 -.666 Question 8 1.5/ 1.5 pts Assume that you have $10,000 of your own money in your account. Assume you use these funds and some margin to create a portfolio with investment weights of 1.4 in a risky asset and -.4 in a risk-free asset. How much money do you need to borrow? $4,000 410,000 = 4,000 The negative sign on the .4 indicates that you are borrowing J $7,143 $10,000 $14,000 Question 9 2/ 2 pts
A stock has an expected return of 20% with a standard deviation of 0.15. Assume you can borrow and lend risk-free at 5%. Assume you are considering investing in this one risky asset and/or the risk-free investment and considering different investment weights. The table below reports the expected return and the standard deviation of 4 portfolios given different investment weights. All 4 of these portfolios are created by including the same stock and the risk free assets in the portfolio but with different investment weights. e What is the y-intercept for the CAL traced out by these portfolios? 5% e What is the Sharpe ratio for the CAL traced out by these portfolios? 1 Weight in (Weight in |Expected |Standard risky risk-free |returnto |deviation asset asset portfolio |of portfolio 0 1 .05 0 5 5 125 075 1 0 20 15 1.5 -.5 275 225 Answer 1: 5% Answer 2: | slope = rise/run = (E[r_risky asset] - risk free rate)/(sigma for risky asset) Question 10 1.5/1.5 pts
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Assume you have a portfolio with 1.25 investment weight in a risky asset and -.25 investment weight in a risk-free asset. If your account has $10,000 of your own money. How many dollars are invested in the risky asset? $12,500 —_— \ 1.25*10000 = 12,500 $10,000 $7,500 $2,500 Question 11 2 /2 pts A friend asks your advice about her investments. She holds in her brokerage account $20,000 worth of a Blackrock mutual fund and $5,000 in risk-free bonds. She asks you whether she should re-allocate her assets. You are analyzing the returns of the Blackrock fund and you compare them with the Vanguard index fund. You expect the Blackrock fund to have an expected return of 13% and a standard deviation of 30%. The Vanguard fund has an expected return of 10% and a standard deviation of 20%. Risk-free bonds currently yield 2%. Assume that borrowing and lending rates differ. In particular, the borrowing rate equals 8% and the lending rate equals 2%. o What is the expected return and standard deviation of your friend's current portfolio? E[r] = .108, sigma = .24 e Can you find a new portfolio investing in the Vanguard fund and the risk- free bond (but not the Blackrock fund) that has higher expected return and same standard deviation as your friend’s current portfolio? It is not possible to create a portfolio using Vanguard and the risk free asset that has a higher expected return and the same risk as the current portfolio. Answer 1:
E[r] = .108, sigma = .24 ElF] = (20125)(.13) + (5/25)"(.02)= 108 ' sigma = (20/25)(.3) = .24 Answer 2: It is not possible to create a portfolio using Vanguard and the risk free asset that has a higher expected return and the same risk as the current portfolio. 1. Total risk of current portfolio: (20/25)*.30=0.24 2. Weight needed in Vanguard fund to attain this same level of risk: solve 0.24=w*.20. This implies w=1.2 3. The weight needed in Vanguard is greater than 1.0. This implies that to attain a portfolio standard deviation of 0.24 using Vanguard, you will have to borrow at 8%. The expected return of this portfolio using Vanguard is 1.2*.10+(-.2)*.08=10.4%. This is less than the current portfolio expected return (10.4<10.8). Question 12 1.5/1.5 pts Assume the price of the Schwab Small-Cap index fund is $50 per share, the annual expected return is 18%, and the annual standard deviation is 0.24. Assume you have $10,000 of investment equity and you want to buy the Schwab Small-Cap fund on margin such that your total portfolio standard deviation is 0.30. Assume you can borrow at 8% annually. What is the portfolio weight in the Small-Cap index fund such that the standard deviation of your portfolio is 0.307 1.25 —————\ w(.24)=0.30 implies w=1.25 § 1S -.25
Question 13 1/1 pts True/False: The capital allocation line (CAL) can be thought of as a plot of the set of expected risk-return outcomes that are available to an investor by investing in a risky asset and in a risk-free asset. The various positions on the line are created by varying the investment weights that the investor uses for the 2 assets. True False Question 14 1/1 pts During the lecture | showed you a spreadsheet with historical returns. As part of that discussion we talked about several different Excel functions. Using the rows and columns of data shown below, identify which formula would calculate each of the summary statistics. The screenshot shown below shows stock prices in column B and daily returns in column C. The stock prices appear in rows 2 through 1259.
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Stock (P1 - Po)/Po Returns -0.0094 0.0007 0.0079 -0.0030 Date Price 8/6/2018 49.95 8/7/2018 49.48 8/8/2018 49.52 8/9/2018 49.91 8/10/2018 | 49.76 (PEYd 8/2/2023 192.58 (P&Ys] 8/3/2023 191.17 Z&ye] 8/4/2023 181.99 arithmetic average daily price sample standard deviation of daily returns population variance of daily returns -0.0155 -0.0073 -0.0480 =average(B2:B1259) v =stdev.s(C3:C1259) v =var.p(C3:C1259) v Question 15 1/1 pts True/False: The expected shortfall return will be less than the 5%VaR return. True False
Question 16 1.5/1.5 pts Assume you think a stock will give you a 25% return if the economy is good this year and a 10% loss if there is a recession. You think there is an 80% chance of a good economy and a 20% chance of a recession. What is your expected return on this stock? 25% because this is the most likely outcome 18% | Elf] = .80*25+.20%(-~10)=0.18 \ J -10% Question 17 1.5/1.5 pts The expected return on a Vanguard fund is 12% and the standard deviation is 0.16. The risk-free rate is 7%. Assume you can borrow and lend at the risk-free rate and that you have $1,000 investment equity. How much money would you need to invest in Vanguard to create a portfolio with an expected return of 17%? $2,000 J Start with formula targeting expected return: E[r,] = .17 = w(.12) + (1-w) - (.07) « W =2 which means that (1-w)= -1 e 200% in Vanguard and -100% of investment equity in risk free $1,000 Not enough information provided to answer this questions
Question 18 1/1 pts True/False: If you are using standard deviation as your measure of risk then some stocks that have experienced strong price appreciation over recent years will appear to be risky investments. neerrest - Question 19 0/1pts True/False: Variance is a measure of total risk in finance. True False Quiz Score: 24 out of 25
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