Final 2 solution

# Final 2 solution - MGCR 341 Finance 1 Summer 2010 Vadim di...

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MGCR 341: Finance 1 Summer 2010 Vadim di Pietro Final Exam: Version A Solutions Student Name:____________________________________ Student Number:__________________________________ Time: Do not turn past this page until the exam has begun. The exam will be 180 minutes in length, from 6:05pm to 9:05pm . Show your work: In order to receive credit for your answers, you must show your work. Correct answers with no work shown will not receive any credit. Incorrect answers with partial correct work may receive partial credit. The exception to this rule is the True or False section, where no explanations are required. Answer questions directly on the exam sheet. If you need more space, use the back side of the pages. Formula sheet: The exam is closed book, and you may not bring any notes into class. A formula sheet is provided on the last 2 pages of this exam. You may detach the formula sheets if you like. You do not need to hand in the formula sheets at the end of the exam. Calculator: You are allowed a non-programmable calculator with nothing stored in memory. This exam has a total of 13 pages, including the cover page and formula sheets. The exam is worth a total of 100 points. GOOD LUCK!

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1) (10 points, 20 mins) You are given the following information about two coupon paying bonds. Bond A Face value = 200 Maturity = 2 years Coupon rate = 10% YTM = 6% Bond B Face value = 1000 Maturity = 1 year Coupon rate = 5% YTM = 4% Also, the forward rate for borrowing or lending between t = 2 and t = 3 , f 2,1 = 10% . Based on the above information, what is the price of a 3-year , 4% coupon bond, with face value \$200 ? The price of the bond is given by P = 4%(200)/(1+r 1 ) + 4%(200)/(1+r 2 ) 2 + [200+4%(200)]/(1+r 3 ) 3 Bond B has only 1 cash flow at t = 1, so its YTM of 4% is equal to r 1 . Bond A’s price can be determined as B a = 20/1.06 + 220/1.06 2 But it can also be expressed as
B a = 20/1.04 + 220/(1+r 2 ) 2 Setting these two equations equal and isolating for r 2 gives r 2 = 6.01% r 3 satisfies the following equation (1+r 3 ) 3 = (1+r 2 ) 2 (1+f 2,1 ) = (1.0601) 2 (1.1) r 3 = 7.38% Substituting the values for r 1 , r 2 , and r 3 into the equation for P, gives P = 182.78 2) (10 points, 20 mins) Stocks A and B have expected returns of 10% and 20% , respectively, and standard deviations of 20% and 30% , respectively. The correlation between stocks A and B is 0 . The risk free rate is 5% , and the market risk premium is 10% . The standard deviation of the market portfolio is 10% . Assume the CAPM holds. a) Portfolio X is composed of 25%, 25%, and 50% in stocks A , B , and the risk free asset, respectively. What is the expected return of portfolio X ? 0.25(10%) + 0.25(20%) + 0.5(5%) = 10%

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b) What is the standard deviation of portfolio X ? (Hint: one way to think of this is that portfolio X as a combination of the risk free asset and a risky portfolio.) Portfolio X is a 50-50 portfolio of the risk free asset and a risky portfolio that is itself a 50-50 portfolio of stocks A and B. A 50-50 portfolio of stocks A and B has a standard
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## This note was uploaded on 08/31/2010 for the course MANAGEMENT MGCR 341 taught by Professor Jassim during the Summer '09 term at McGill.

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Final 2 solution - MGCR 341 Finance 1 Summer 2010 Vadim di...

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