please see attached file and provide answers to the questions

FINC-UB.0002 FOUNDATIONS OF FINANCE Spring 2016 Problem Set #2 This problem set is due in class on Monday, March 21. You may collaborate with your classmates in preparing the solutions, but each student must hand in a separate assignment. If you do receive help or work with another student on the assignment, you must note this fact at the beginning of your solutions. Please remember to put your name at the top of the first page. Also, please staple your assignment if there are multiple pages and put your name on every page. You may find it useful to use Excel for a number of these problems. Assignments that are late but within 24 hours of the deadline, will receive credit. After 24 hours no assignments will be accepted! 1. Consider portfolios with positions in the US and Brazilian equity markets. The (annual) expected return and standard deviation of returns for the 2 markets are as follows: US Brazil E[r] 10% 15% SD[r] 20% 30% The correlation between the returns is 0.2. a. Calculate the expected returns and standard deviations of the following portfolios: (i) 80% in the US, 20% in Brazil (ii) 50% in the US, 50% in Brazil (iii) 20% in the US, 80% in Brazil b. Find the weights for a portfolio with an expected return of 25%? What is the standard deviation of this portfolio? c. Find the weights for a portfolio with the same standard deviation as the US market but a higher expected return? (Note: There is an analytical solution using the quadratic formula. You can also use the Solver tool in Excel under the Data tab in the Analysis group. In fact, this problem set is a great opportunity to familiarize yourself with this tool.) What is the expected return of this portfolio? d. What is the correlation between the returns on the portfolios in parts a(i) and a(iii)? (Recall that the correlation is the covariance divided by the product of the standard deviations. You may find some of the rules we went over in class useful) 2. In addition to the information in Q.1, assume that the (annual) risk-free (T-bill) rate is 5%. a. Calculate the expected returns and standard deviations of the following portfolios: (i) 50% in the risk-free asset, 50% in the US (ii) 50% in the risk-free asset, 50% in Brazil (iii) 50% in the risk-free asset, 50% in the portfolio in Q.1a(ii) b. Calculate the Sharpe ratios of (i) the US market (ii) the Brazilian market (iii) the portfolio in Q.1a(ii) (iv) the portfolio in Q.2a(iii) c. Find the weights (T-bill, US, Brazil) for a portfolio with the same expected return as Brazil, using only a combination of the risk-free rate and the portfolio in Q.1a(ii)? What is the standard deviation of this portfolio? What is the correlation of this portfolio with the portfolio in Q.2a(iii)? 1 3. Assume the risk-free rate is 5% (rf = 5%), the expected return on the market portfolio is 10% (E[rM] = 10%) and the standard deviation of the return on the market portfolio is 20% ( M = 20%). (All numbers are annual.) Assume the CAPM holds. a. What are the expected returns on securities with the following betas: (i) = 1.6 (ii) = 0.4 (iii) = -0.5 b. What are the betas of securities with the following expect returns: (i) 10% (ii) 5% (iii) -1% c. What are the portfolio weights (in the risk-free asset and the market portfolio) for efficient portfolios (portfolios on the efficient frontier/CML) with expected returns of (i) 6% (ii) 10% (iii) 20% d. What are the portfolio weights (in the risk-free asset and the market portfolio) for efficient portfolios (portfolios on the efficient frontier/CML) with standard deviations of (i) 8% (ii) 20% (iii) 25% 4. Consider a 4-year project with the following cash flows: 0 -100 1 0 2 40 3 40 4 40 a. What is the IRR of this project? (Use the IRR function.) b. What is the present value (NPV) of this project at a discount rate of 5%? (Use the NPV function in Excel, but be careful. The NPV function assumes that the first cash flow in the range is at time 1.) 5. Presentation Exercise You are to find a recent newspaper or business journal article that is related to one of the topics we have covered in class in wk 4, 5 or 6 (eg an article about asset allocation, CAPM or expected return of stocks or correlation between different asset classes). You will need to write a short summary of the article and how it relates to what we have covered in class. You will be required to present your article at the beginning of class, explaining the article to the class and how it relates to the course. This will be a verbal presentation only. There will be no need for any presentation materials. 2