07_Yield1

07_Yield1 - Economics 251a John Geanakoplos Fall 2006 Yield 1 Cash Flow Yield The"yield of a ow of cash is one of the most famous concepts in nance

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Economics 251a John Geanakoplos Fall 2006 Yield 1 Cash Flow Yield The "yield" of a f ow of cash is one of the most famous concepts in F nance. But alas, it is often misleading. The cash f ows (say of a bond) are described by their maturity (the period in which thelastcash f ow comes), their price, and their precise payments each month. The "yield" is an e f ort to condense all this information into a single number, so that bonds with the highest yield are regarded as the most desirable.Sometimes this simpli F cation provides an accurate and vivid picture of what is really happening. But it is inevitable that something will be lost when so many numbers are summarized with just one number. If it were not for its wide usage, I would not bother telling you about yields at all! If every bond were priced at its present value, no bond would be more desireable than any other. A cheaper bond would cost less, but also deliver less (in present value). A raison d’etre of the concept of yield is that the present value pricing formula might be violated because a bond is mispriced. This could happen in the old days, because many people did not understand how to F nd the zero coupon prices π t , and thus were unable to compute present value. (Indeed it is not so obvious how to F nd the π t ; you shall learn how in the next chapter). Knowing that many bonds were mispriced, some more than their present value and some less, but unable to compute their present values, these people would assume that the bond with the highest yield (which is easy to compute without knowing the π t ) must have the highest present value, and therefore be the best buy. Even today a bond could also very easily be priced di f erently from the present value of its promises, because most traders might worry about the default risk of the bond, thus valuing it at less than the present value of its "promised" deliveries. A hedge fund manager who is convinced that the bond in fact has no chance of default will then be in a position similar to those traders in the old days when bonds with no default risk were mispriced. But should he judge the bond on its yield? Let us de F ne the concept of yield, and then explain its weakness. The word yield is used in di f erent ways. The most general concept is the internal rate of return, which becomes yield to maturity. It is also used in the term current yield. We shall show that both uses of yield give a misleading account of what is the value in a bond. We close by noting that yield depends on the length of the assumed time period. By convention, most bonds that promise coupons of C peryearpay C/n in n equal and equally spaced installments over the year. This kind of bond is worth more than one that just paid C per year. Its annualized yield is above C % . In fact, for large n it is approximately e C % . The limit is called continuous compounding.
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This note was uploaded on 12/08/2009 for the course ECON 251 at Yale.

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07_Yield1 - Economics 251a John Geanakoplos Fall 2006 Yield 1 Cash Flow Yield The"yield of a ow of cash is one of the most famous concepts in nance

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