Risk Free Interest Rates Spot Interest Rate Another term for a default free

Risk free interest rates spot interest rate another

This preview shows page 43 - 46 out of 46 pages.

Risk-Free Interest Rates ! Spot Interest Rate ! Another term for a default-free, zero-coupon yield ! Zero-Coupon Yield Curve ! A plot of the yield of risk-free zero-coupon bonds as a function of the bond’s maturity date Bond Par Yield ! Suppose that the following zero-coupon bonds are selling at the prices shown below per $100 face value. Determine the corresponding yield to maturity for each bond. Consider the following risk-free bond Face value: 100 Maturity:3 ans Coupon rate: 5% Frequency: annual Calculate the YTM of this bond Use this YTM to determine the price Bond. Comment. Maturité 1 an 2 ans 3 ans YTM 3,5% 4% 4,5%
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44 Bond Par Yield P = NPM (NPER) TAUX (RATE) VA (PV) VPM (PMT) VC (FV) Formule Excel (Excel Formula) GIVEN SOLVE FOR YTM NPM (NPER) TAUX (RATE) VA (PV) VPM (PMT) VC (FV) Formule Excel (Excel Formula) GIVEN SOLVE FOR PV Bond Par Yield 2 3 5 5 5 100 101,464 1 3,5% (1 4%) (1 4,5%) P + = + + = + + + NPM (NPER) TAUX (RATE) VA (PV) VPM (PMT) VC (FV) Formule Excel (Excel Formula) GIVEN 3 4,467% 5 100=RATE(3;5;-101,464;100) SOLVE FOR YTM -101,464 = TAUX(3;5;-101,464;100) NPM (NPER) TAUX (RATE) VA (PV) VPM (PMT) VC (FV) Formule Excel (Excel Formula) GIVEN 3 4,467% 5 100=PV(4,467%;3;5;100) SOLVE FOR PV -101,464 = VA(4,467%;3;5;100)
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45 Forward Rates ! One may represent the term structure of interest rates as set of implicit forward rates ! Consider two choices for a 2-year horizon: ! Choice A: Buy 2-year zero ! Choice B: Buy 1-year zero and rollover for 1 year ! What yield from year 1 to year 2 will make you indifferent between the two choices? ) 1 ( ) 1 ( 1 1 , 0 2 2 , 0 1 , 1 R R F + + = + Forward Rates (continued) ! They are ‘implicit’ in the term structure ! Rates that explain the relationship between spot rates of different maturity ! Example: ! Suppose the one year spot rate is 4% and the eighteen month spot rate is 4.5% % 51 . 5 ; ) 1 )( 04 . 1 ( ) 045 . 1 ( ) 1 )( 1 ( ) 1 ( 6 , 12 2 / 1 6 , 12 2 / 3 2 / 1 6 , 12 1 , 0 2 / 3 18 , 0 = + = + + = + m m m m m m m F F F R R
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46 Recap: Taxonomy of Rates ! Coupon Rate ! Current Yield ! Yield to Maturity ! Zero-Coupon Rate ! Bond Par Yield ! Forward Rate
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