Fixed Income notes

# Fixed Income notes - Fixed Income Securities Fixed Income...

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Fixed Income Securities Fixed Income Securities, FIRE 314, Fall 2009 THE GOLDEN RULE OF VALUATION The Golden Rule of valuation for all assets is: Equivalent assets should have equivalent prices . A simpler version of this is the “Law of one Price” from economics: the same asset should not sell for two different prices. But often we must value assets that are dissimilar in many ways, but still equivalent, so that the dollar values will be different. The easy example is a difference in size. Consider two annuities: one of \$10, one of \$100. Assume the timing and risk of both annuities is the same. How can we apply the Golden Rule in such cases? The approach is to find the rate of return required of annuities of the given level of risk. Then, equivalent price means the price that will result in both assets having the same rate of return. So, we could restate the Golden Rule as: Equivalent assets should have the same rate of return. The “equivalent price” found by equating the rates of return of equivalent assets is sometime called the intrinsic value or the economically justified price. For the moment we will assume that the “required rate of return” is known. Once we get a feel for how assets are valued given the required rate, we will turn to a discussion of risk and the required rate. BOND VALUATION AND YIELD VALUATION IMMEDIATELY AFTER PAYMENT DATE From the above discussion of time value, the intrinsic value of a bond is the present value of the cash flows at the required rate of return: EXAMPLE: What is the value of a 20 year, 10%, annual pay bond, if the true annual yield to similar bonds is 10.6%? Using the calculator, we can find the present value of the cash flows at a rate of 10.6%. On an HP-12C, you would enter: 20 = N, 10.6 = %I, 100 = PMT, 1000 = FV On a Texas Instruments BA-35 calculator, you would enter: 20 = N, 10.6 = %I, 100 = PMT, 1000 = FV, CPT = PV. This gives the value of the bond as \$950.94. Bonds prices are generally not given in dollar terms but rather as a per cent of face value. This bond would typically be quoted as “95.094.” ACCRUED INTEREST The seller of the bond is probably not a total dummy, however, and will want his/her share of the next interest payment. Thus, bond prices are understood to include payment of accrued interest (unless specifically said to be trading "flat"). You get this back, since you get all of the next interest payment. The method of computing accrued interest differs between corporate (360 day year of twelve 30 day 1

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Fixed Income Securities months) and Treasury bonds (actual number of days in period and actual number of days in the year), but both are based on “simple interest.” Simple interest is computed at a constant daily rate equal to the annual rate divided by the number of days in a year. E.g., if a 10% corporate bond pays interest semiannually, and it has been 45 days since the last interest payment, the accrued interest would be (45/180)x\$50. Note that this can get complicated for corporates, because not all months have 30 days.
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## This note was uploaded on 12/07/2009 for the course FIRE 314 taught by Professor Upton during the Spring '09 term at VCU.

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Fixed Income notes - Fixed Income Securities Fixed Income...

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