MIT Sloan Finance Problems and Solutions Collection Finance Theory I Part 1 Andrew W. Lo and Jiang Wang Fall 2008 (For Course Use Only. All Rights Reserved.) Acknowledgements The problems in this collection are drawn from problem sets and exams used in Finance Theory I at Sloan over the years. They are created by many instructors of the course‚ including (but not limited to) Utpal Bhattacharya‚ Leonid Kogan‚ Gustavo Manso‚ Stew Myers‚ Anna Pavlova‚ Dimitri Vayanos and Jiang Wang. Contents 1
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A commonwealth government bond (CGB) is a bond which pays semi-annual coupons‚ in which the maturity date/ coupon payment date is on the 15th of every month. A zero coupon bond is a bond with no coupons. The important information of a bond: 1. 2. 3. 4. 5. 6. • 1. 2. Transaction date: T Settlement date:T+2 Coupon payment dates Maturity date YTM Coupon rate Cum-interest or Ex-interest? If ex-interest If> 7 days to the next coupon payment-----> cum-interest YIELD TO MATURITY The Yield to Maturity
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Fixed Income Securities Chapter 2 Basics of Fixed Income Securities Problem Set (light version of the exercises in the text) Q3. You are given the following data on different rates with the same maturity (1.5 years)‚ but quoted on a different basis and different compounding frequencies: • Continuously compounded rate: 2.00% annualized rate • Continuously compounded return on maturity: 3.00% • Annually compounded rate: 2.10% annualized rate • Semi-annually compounded rate: 2.01% annualized
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different annual coupon rates (8% and 5%) and different maturities (5 years and 25 years)‚ starting with a common 8% yield-to-maturity (YTM)‚ and assuming successively a new yield of 5%‚ 7%‚ 7.99%‚ 8.01%‚ 9% and 11%. From this example‚ we can make the following observations. Using the bond valuation model‚ one can show the changes that occur in the price of a bond (i.e.‚ its volatility)‚ given a change in yields‚ as a result of bond variables such as time to maturity and coupon‚ and show that
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of a coupon bond is realized only if the bond coupons are reinvested at the same rate as the promised yield. As zero coupon bonds provide no coupons to be reinvested‚ the final value of the investor’s proceed from the bond is independent of the rate at which coupons could be reinvested. There is no reinvestment rate uncertainty with zeros. For default risk‚ the stated yield to maturity will be realized only if the firm meets the obligations of the bond issue. For a default-free zero coupon‚ there
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Part I: (1) Go to the Reserve Bank of Australia (RBA) website‚ find the statistic section‚ and then download the data file named “Zero-Coupon Interest Rates - Analytical Series -2009 to current”. (2) Plot the zero-coupon yield curve on October 1‚ 2009. (3) Based on the yield curve on October 1‚ 2009‚ calculate the expected rates on zero-coupon bonds with one-quarter maturity that are to be sold on the first day of the quarter that starts one‚ two‚ three and four quarters from Oct 1
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$1 to be delivered at a later date T : (1.1b) Z(t; T ) = zero coupon bond‚ maturity T ‚ as seen at t. These discount factors and zero coupon bonds are the ones obtained from the currency’s swap curve. Clearly D(T ) = Z(0; T ). We use distinct notation for discount factors and zero coupon bonds to remind ourselves that discount factors D(T ) are not random; we can always obtain the current discount factors from the stripper. Zero coupon bonds Z(t; T ) are random‚ at least until time catches up to
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UNIVERSITY OF TEXAS AT DALLAS SCHOOL OF MANAGEMENT FIN6310: INVESTMENT MANAGEMENT SOLUTIONS TO PROBLEM SET #1 PROF. ARZU OZOGUZ SPRING 2013 1. Calculate the value of the following two bonds. Assume that coupon payments are made semi-annually and that par value is $1‚000 for both bonds. Coupon rate Time to maturity Yield-to-maturity Bond A 5% 5 yrs 7.2% Bond B 5% 25 yrs 7.2% Recalculate the bonds’ values if the yield to maturity changes to 9.4%. Which bond is more sensitive to the changes in
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According to Section 45 (1)‚ any profits or gains earned by assessee during the previous year on the transfer of capital asset are called Capital Gains. The amount will be taxable under the head ‘Capital Gains’. There must be tree essential elements of capital gains are: A. Capital Assets B. Transfer of Capital Asset; and C. There must be profits or gains on such transfer‚ which will be known as capital gain (A). CAPITAL ASSETS Capital assets mean all types of assets either fixed or floating‚ movable
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Spot Rate and Forward Rate Spot Rate: It is nothing more than the YTM on bond. It is the rate of interest on bond maturing at any time in the future. It is also known as geometric average of 1 year forward rates in the future. Hence‚ YTM on bonds can be calculated as: When forward rates are given then; oS1 = oF1 oS2 = [(1+of1)(1+1F2)](1/2) -1 oS3 = [(1+of1)(1+1F2)(1+2F3)](1/3) -1 and so on. Forward Rates: It is the interest rate established today ‚ that will be paid on money to
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