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Unformatted text preview: MIT Sloan School of Management J. Wang 15.407 E52-456 Fall 2002 Solution to Final Exam Fall 2002 1. (a) False . Maximizing firms market value is equivalent to investing in projects with positive and greatest NPV. NPV of projects with high expected returns can be negative. (b) False . The arguments of market efficiency and no arbitrage imply that the NPV of both types of bonds should be zero. There is no way to tell if one is a better investment than the others without considering other factors such as interest rate risk or re-investment opportunity. (c) False . Growth stocks are companies with access to positive present value of growth opportunities. How these companies pay their dividends depends on their payout ratio and dividend policy. (d) False . Recall the futures pricing formula F = S (1 + r- y ) T If the convenience yield is greater than the interest rate, futures price for long-term contracts can be lower than that for short-term contracts. (e) Uncertain . For European options, the put-call parity C = P + S- PV( K ) = P + S- PV( S ) can easily show that the call options are more valuable if the interest rate is positive. Such relationship may not hold for American options when the options can be exercised early. (f) False . Diversification can reduce risk whenever the asset returns are not perfectly correlated. (g) False . Assets with more volatile returns but low correlation with the market may earn a low expected return according to CAPM. (h) False . The correct discount rate should be the cost of capital corresponds to the riskiness of the projects. Grade comments : I took points off for inaccurate comments or unclear answers. The answers of true or false would not affect the final credits. It is the explanation that counts. 1 2. (a) The present value of the liability is: PV = 9 . 756 + 9 . 518 + 9 . 286 = 28 . 56 million (b) The duration of the liability is: D = 1 28 . 56 (9 . 756 + 2 9 . 518 + 3 9 . 286) = 1 . 9835 (c) Let w 1 , w 2 and 1- w 1- w 2 be the amount invested in the 1-year, 2-year and 3-year STRIPS respectively. To eliminate interest rate risk, the value change of this portfolio should be the same as the value change of the liability in response to interest rate change, i.e. P = L P D P r = L D L r 20 ( w 1 + 2 w 2 + 3(1- w 1- w 2 )) = 28 . 56 1 . 9835 As you can see, there are multiple solutions to this equation. So, you can form different portfolios tailored to your preferences to achieve your hedging purposes. If you want to be fancy, you can consider portfolios with maximum convexity to benefit yourself from interest fluctuation. This solution will only demonstrate the case when w 1 = 0. The equation will become: 20 (2 w 2 + 3(1- w 2 )) = 56 . 65 w 2 = 0 . 1675 So, we should invest 16.75% in 2-year discount bonds and 83.25% in 3-year dis- count bonds....
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This note was uploaded on 01/19/2011 for the course 15 15.407 taught by Professor Wang during the Fall '03 term at MIT.
- Fall '03