Practice Midterm Questions Foundations of Finance1Foundations of Finance Practice Midterm QuestionsProf. Anthony LynchI. [15 points] You will be making 20 annual contributions of $75 to a bank account (thefirst is made at the end of year 1) that pays an APR of 5.90% compounded semiannually. What will be the balance of the bank account at the end of year 20?II. [10 points] I have available $5M to invest today. The continuously compounded annualinterest rate is 10%. How much will I have in 6 months?III. [15 points] One year ago XYZ stock had just run up from $12 per share to $25 per share. With a net worth of $20000, you bought $40000 worth of XYZ stock on margin at $25per share. The call money rate (which was the rate at which your broker would lend toyou) was 8.5% per annum EAR. The stock recently declared its first dividend: $1 pershare. (The dividend is payable in 10 days. The ex dividend date is tomorrow.) Thestock is presently trading at $27 per share. Commissions are $0.50 per share (each way),payable when you close out your position. If you close out your position today, what isyour total profit or loss on the entire transaction. IV. [30 points] Consider the following data:Economy Probability Return on ArcticStockReturn on ZebraStockGood 0.6 15% 30%Bad 0.4 -10% -15% Stock Expected Return StandardDeviation ofReturnArctic 5% 12.25%Zebra ? ?A. What is the expected return on Zebra?B. What is the return standard deviation on Zebra?C. What is the covariance between Arctic’s return and Zebra’s return?D. What are the expected return and standard deviation of return on a portfolio that is20% invested in Zebra and 80% in Arctic?Practice Midterm Questions Foundations of Finance2V. [15 points] Consider the following data for QDF stock (1/29 is a Friday):Date 1/29 2/1 2/2 2/3 2/4 2/5ClosingPrice-QDFshare41 42.5 41.125 41.75 43.25 43Dividendper QDF ShareDeclared Ex-date Record Date Payable Date0.5 1/20 2/1 2/4 3/5Calculate the daily return on QDF stock (buy at the close of the previous day and sell onthe close of the current day) for the following dates:A. 2/1.B. 2/2.C. 2/3.VI. [15 points] You are saving to buy a $150000 house. At the end of each of the next fiveyears, you will deposit $5000 into a bank account . At the end of five years you will usethe money as a down payment on the house. You will finance the balance of thepurchase price with a thirty-year annual-payment mortgage. If the investing rate is 5%per annum EAR and the borrowing rate is 7% per annum EAR, what is the size of yourannual mortgage payments (which are made at the end of each year of the mortgage). VII. [20 points] Consider the following:Expected Return Standard Deviation of ReturnJapanese Stock Fund 15% 20%U.S. Stock Fund 12% 10%The correlation between the return on the U.S. stock fund and the Japanese stock fund is0.2. The rate on T-bills is 5%. A. Suppose that Sure-thing Brokers’ recommended portfolio is 70% in the U.S. stockfund and 30% in the Japanese stock fund. What is the expected return andstandard deviation of return for this portfolio?B. An investor is trying to allocate a $20000 investment between Sure-thing’srecommended portfolio and T-bills to achieve a portfolio return standarddeviation of 5%. What dollar amounts should be invested in the Japanese stockfund, the U.S. stock fund and T-bills.Practice Midterm Questions Foundations of Finance3VIII. [30 points] Consider the following data:Expected Return Standard Deviation of ReturnBull Fund 16% 15%Hosem Fund 12% 8%The correlation between the return on the Bull fund and the Hosem fund is 0.7. The rateon T-bills is 8%. A. Suppose I am trying to decide whether to hold Bull in combination with T-bills orHosem in combination with T-bills. Which should I choose? (Show calculationsto support your answer.)B. Suppose instead that I can combine Bull and Hosem into a portfolio P which Iwould then combine with T-bills to obtain my final portfolio.1. What are the weights of Bull and Hosem in portfolio P?2. What is the expected return and standard deviation of return for portfolioP?Foundations of FinancePractice Midterm AnswersProf. Anthony LynchI. EAR = (1+0.059/2)2 -1 = 0.05987.FV20 = 75 FVAF5.987%,20 = 75 {[(1.05987)20 -1]/0.05987} = 75 x 36.7342 = 2755.07.II. FV0.5 = 5M x e0.1x½ = 5M x 1.051271 = 5.2564M.III.Borrow at 8.5% one year ago 20000Buy 1600 shs of XYZ @ $25 one year ago -40000Repay loan ($20000 x 1.085) today -21700Sell 1600 shs of XYZ @ $27 today 43200Commission (2x1600 x $0.50) -1600Total Profit -100So the total loss is $100.(Dividend is not paid until tomorrow and so is irrelevant; the price run up prior topurchase is also irrelevant.)Practice Midterm Questions Foundations of Finance4IV. Answer.A. Expected Return Zebra = 0.6 x 30% + 0.4 x -15% = 12%.B. Variance of Return Zebra = 0.6 x (30x30) + 0.4 x (-15x-15) - (12x12) = 486. Std Dev of Return Zebra = 22.0454%.C. Covariance Arctic & Zebra = 0.6 x (15x30) + 0.4 x (-10x-15) - (5x12) = 270.D. Expected Portfolio Return = 0.8 x 5% + 0.2 x 12% = 6.4%.Variance of Portfolio Return = (0.8x0.8) x (12.25x12.25) + (0.2x0.2) x 486 + 2 x (0.8x0.2) x 270 = 201.88.Std Dev of Portfolio Return = 14.2084%.V. Answer.A. Return 2/1 = {42.5 + 0.5 - 41}/41 = 4.878%.B. Return 2/2 = {41.125 - 42.5}/42.5 = -3.2353%.C. Return 2/3 = {41.75 - 41.125}/41.125 = 1.5198%.VI. Savings at time 5 will be $5000 x FVAF5%,5 = $5000 x {[(1.05)5-1]/0.05} = $27628.16.Amount to be borrowed at time 5 is $150000 - $27628.16 = $122371.84.So letting C be the mortgage repayment:$122371.84 = C x PVAF7%,30 = C x {[1-(1.07)-30]/0.07}.Thus, C = $122371.84 / 12.40904 = $9861.51.VII. Let P be Sure-thing’s recommended portfolio.A. Expected Return for P = 0.7 x 12% + 0.30 x 15% = 12.9%.Variance of Return for P = (0.7x0.7) x (10x10) + (0.3x0.3) x (20x20) + 2 x (0.7x0.3) x(0.2x10x20) = 49 + 36 + 16.8 = 101.8Standard Deviation of Return for P = 10.0896.B. Let Q be the investor’s portfolio with a standard deviation of 5% which consistsof portfolio P and T-bills. Let ωP,Q be the weight of portfolio P in portfolio Q.Know σ[RQ] = |ωP,Q | σ[RP] and since the expected return for P exceeds the T-billrate, we know that the investor wants to hold a positive weight in P. So ωP,Q = 5/10.0896 = 0.4956. So the weight of T-bills in Q is (1- ωP,Q) = 0.5044 which implies a dollarinvestment in T-bills of $20000 x 0.5044 = $10088. The weight of the U.S stock fund in Q is (0.7 ωP,Q) = 0.7 x0.4956 = 0.34692which implies a dollar