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Suppose that you have the following utility function:
U=E(r) – ½ Aσ2 and A=3
Suppose that you have $10 million to invest for one year and you want to invest that money into ETFs tracking the S&P 500 (US) and S&P/TSX 60 (Canada) index, which are often used as proxies for the US and Canadian stock markets, respectively, and the Canadian one-year T-bill. Assume that the interest rate of the one-year T-bill is 0.35% per annum.
You have found two ETFs that you are interested in. From a set of their historical data between 2001 and 2019, you have estimated the annual expected returns, standard deviations, and covariance as follows:
ETFUS :
E(r)= 0.070584
0.173687
ETFCDA :
E(r)= 0.073763
0.16816
Covariance between ETFUS and ETFCDA = 0.02397
Answer the following questions using Excel:
- What is the optimal portfolio of ETFUS and ETFCDA?
Also submit an Excel file to show your work.
Step by step
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- Suppose that you have the following utility function: U=E(r) – ½ Aσ2 and A=3 Suppose that you have $10 million to invest for one year and you want to invest that money into ETFs tracking the S&P 500 (US) and S&P/TSX 60 (Canada) index, which are often used as proxies for the US and Canadian stock markets, respectively, and the Canadian one-year T-bill. Assume that the interest rate of the one-year T-bill is 0.35% per annum. You have found two ETFs that you are interested in. From a set of their historical data between 2001 and 2019, you have estimated the annual expected returns, standard deviations, and covariance as follows: ETFUS : E(r)= 0.070584 0.173687 ETFCDA : E(r)= 0.073763 0.16816 Covariance between ETFUS and ETFCDA = 0.02397 Answer the following questions using Excel: Determine your optimal asset allocation among ETFUS , ETFCDA , and T-bill, in percentage and in dollar amounts. Also submit an Excel file to show your…An analyst has modeled the stock of a company using the Fama-French three-factor model. The market return is 10%, the return on the SMB portfolio (rSMB) is 3.2%, and the return on the HML portfolio (rHML) is 4.8%. If ai = 0, bi = 1.2, ci = 20.4, and di = 1.3, what is the stock’s predicted return?Consider the following information about the various states of the economy and the returns of various investment alternatives for each scenario. Answer the questions that follow. Question 1 Fill in the parts in the above table that are empty. Using the data generated in the previous question (Question 1); Plot the Security Market Line (SML) 2. Superimpose the CAPM’s required return on the SML % Return on T-Bills, Stocks, and Market Index State of the Economy Probability T- Bills Phillips Pay- up Rubber- made Market Index Recession 0.2 7 -22 28 10 -13 Below Average 0.1 7 -2 14.7 -10 1 Average 0.3 7 20 0 7 15 Above Average 0.3 7 35 -10 45 29 Boom 0.1 7 50 -20 30 43 Mean Standard Deviation Coefficient of Variation Covariance with MP…
- Suppose that in a two-period Arrow-Debreu economy with three states, the state probabilities are T₁ = 0.1, 7₂ = 0.55, 73=0.35 and the state prices are 9₁ = 0.2, 9₂=0.5, 93 = 0.8 for states 1, 2, and 3 respectively. Assume that an asset has the state-contingent dividend given in the following table, and the observed price of the asset is 4.1. State-contingent dividend State 1 State 2 State 3 Asset's dividend 5 3 2 According to information above, which one of the following statements regarding arbitrage opportunities is correct? O A. In this case, arbitrage opportunities do not exist. O B. In this case, arbitrage opportunities exist because the asset is over-priced. O c. In this case, arbitrage opportunities exist because the asset is under-priced. O D. Due to insufficient information, it is inconclusive whether arbitrage opportunities exist or not.Assume that you are using the Capital Asset Pricing Model (CAPM) to find the expected return for a share of common stock. Your research shows the following: Beta = βi = 1.54 Risk free rate = Rf = 2.5% per year Market return = E(RM) = 6.5% per year Based on this information, answer the following: A. Based on the beta, how does the stock's risk compare to the market overall? On what do you base your answer? B. Based on the beta, how would you expect the stock's returns to react to a decrease in returns in the market overall? Why? C. According to the CAPM and the information given above, what is the expected return E(Ri) for this stock? D. If the required rate of return on this stock were 7% per year, would you invest? Why or why not?Suppose TRF = 4%, TM = 9%, and b = 1.1. a. What is n, the required rate of return on Stock i? Round your answer to one decimal place. % b. 1. Now suppose rar increases to 5%. The slope of the SML remains constant. How would this affect ry and n? I. ry will increase by 1 percentage point and n will remain the same. II. Both ry and r, will decrease by 1 percentage point. III. Both rm and r, will remain the same.. IV. Both r and r, will increase by 1 percentage point. V. r will remain the same and r, will increase by 1 percentage point. -Select- v 2. Now suppose rar decreases to 3%. The slope of the SML remains constant. How would this affect ry and n? I. TM will decrease by 1 percentage point and n will remain the same. II. rs will remain the same and n will decrease by 1 percentage point. III. Both ry and r, will increase by 1 percentage point. IV. Both ry and r, will remain the same. V. Both ry and r, will decrease by 1 percentage point. Select
- Capital asset pricing model (CAPM) For the asset shown in the following table, use the capital asset pricing model to find the required return. (Click on the icon here O in order to copy the contents of the data table below into a spreadsheet.) ne Risk-free Market rate, R return, rm Beta, b nts 4% 0.7 1% The required return for the asset is %. (Round to two decimal places.) eТext edia Librai ial Calculat er Resource Enter your answer in the answer box and then click Check Answer. Check Answer mic Study ules Clear All All parts showing 10: DExercise(14); ools > This course (Introduction to Finance (FIN-101-D02) Distance Spring 2021) is hased on Zutter/Smart Princinles of Managerial Finance Rrief Re 4/13 O Type here to search insertYou live in a world where assets are priced by the CAPM. The following information is given to you regarding stock X. The expected payoff from the stock X=£105.00 Expected return of stock X = 18% Risk-free rate =5% Market Risk Premium = 9% Assume there are no other changes, except that the correlation between the returns of Stock X and the market becomes twice what it is currently. How would this change affect the current price of Stock X? Explain why the change of the correlation causes the observed change in the stock price. [hint: Provide a risk-based explanation]Consider 1-factor model and assume that the price of a certain fixed income security P(y) for y=9%, 9.05% and 8.95% is given by P(0.09)=$5,000; P(0.0905)=$4,980; P(0.0895)=$5,030. Find the estimate for DV01, Duration, and Convexity of this security. Keep at least 4 decimal digits while performing your calculations.
- Using CAPM to determine the expected rate of return for risky assets, consider the following example stocks, assuming that you have already compute the betas Stock Beta A 0.70 B 1.00 C 1.15 D 1.40 E -0.30 Assume that we expect the economy’s RFR to be 5 percent (0.05) and the expected return on the market portfolio (E(RM)) to be 9 percent (0.09), 1, what would this imply? With these inputs, what would the be the following required rate of returns for these five stocks, show the formula for each in your calculations.This question assumes the standard mean-variance utility function. You are allocating your investments between a the NZX50 and a holding of (New Zealand) T-bills. The expected return on the NZX50 is 7.50%, with volatility 12.80%. In contrast, there is no risk investing in T-bills, and they will earn you a return of 4.70%. Your risk-aversion is 7. What percentage of your wealth should you allocate to Treasury bills? 34.61% 96.88% 96.51% 75.59%b) You are given the following information about Stock X and the market: The annual effective risk-frec rate is 5%. The expected return and volatility for Stock X and the market are shown in the table below: Expected Return Volatility Stock X 5% 40% Market 8% 25% The correlation between the returns of stock X and the market is -0.25. Assume the Capital Asset Pricing Model holds. Calculate the required return for Stock X and determine if the investor should invest in Stock X.