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Review of Pricing, Spreads and
Volatility Measures FIN 428
Prof. Hood Pricing p= tE(CF,) • ,"I r = Expected Return When dealing with Treasury bonds, E(CF)
With Treasuries ONLY, (1 + r)' = CF Expected Return '" Yield With risk of default, E(CF) not equal to CF and Expected
Return is different from Yield
Formula for pricing bonds with periodic yield Yield Measures
US Treasuries and Corporates pay semi-annual coupons. So the period yield = semi-annual yield
Convention is to multiply the semi-annual to get the bond-equivalent yield yield by 2 Y-""2- Since we are accounting for all coupon payments,
this is the Yield to Maturity
Other Measures: Yield to call, Yield to put, Yield to worst
Current yield = Annual Coupon / Price • Effective Annual Yield accounts for compounding (l+yYZ. 1 -------- ---------- Reasons Bond Prices Change Over Time
1) There is a change in the required yield. 2) The bond is selling at a discount or premium and the bond is
moving closer to maturity, but required yield does not 3) The price intreases betwee~ coupon payments then drops
again after the payment is made (Accrued Interest) change. ~o.y 'j;:lJ\ \ "'cO For part 1 there are several components to why this may change.
_ Risk free rate [market _ Risk premium (market driven) drlvenl Risk of default chanBes (Individual security driven) Sources of Realized Return
l} Changes in yield over time => causes changes in the
price 2) Coupons received
3) Interest on coupons received Ifyield changes and we can't reinvest at the VTM,
then our return will not be YTM.
lfwe hold to maturity and there is no default,
take away the risk that the bond will decrease • we
in price. Measuring Price Sensitivity to Changes
in Yield I I View price as a function of yield. We can approximate
with a Taylor series expansion.
We want percent change in price which is capital gain dP
1 d' P,
(dy) - error
dP = dP .!.d +.!- d'P .!.(d )'
P dy P Y 2 dy' P Y I Duration part i Conyexity part + error
2 J ...
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This note was uploaded on 09/06/2011 for the course FIN 428 taught by Professor Hood during the Fall '11 term at Iowa State.
- Fall '11