Bond Yields, Returns, and Duration

Financial Institutions and Markets
Jim Wilcox

Bond Yields, Returns, Risks, and Duration
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Bonds and Loans
Yields and Returns
Price Volatility and Risk in Default-Free Bonds
Measuring Interest Rate Risk
Duration: Types, Calculation, Meaning, Uses

• Next Time: Chapter 11 re: Duration
Week # 2
January 28, 2014

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Coming Soon!
What We Did
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Week # 2
January 28, 2014

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Yield to Maturity (YTM):
A Result, Not a Cause!
• YTM = percentage rate that equates (known) bond price to PV of all promised (via bond) payments
• If the price of a coupon bond = its principal (or FV), then YTM = the bond’s coupon rate (C/FV)
– If bond price exceeds its face value, YTM < coupon rate

Week # 2
January 28, 2014

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Yields on U.S. Treasury Bonds, 2003-2012:
Short-Term Yields (but not Prices) Varied More

Week # 2
January 28, 2014

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Bond Yields Differ from Returns, in Concept and in the Data
• Returns (over some time span) = current yield (via coupon) plus percentage change in the bond’s price (over time span)
• Longer-maturity-bond prices fall more increase in YTM
– A measure called Duration, D, will conveniently show us how much

Week # 2
January 28, 2014

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in case we want a blank slide…

Week # 2
January 28, 2014

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Relation of a Bond’s Price to Its Yield:
Negative and Non-Linear
Because?

Price
(of a bond)

Actual Price

Tangent Line at y*
(use to approximate price)

p*

y*
Week # 2
January 28, 2014

Yield

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Bond Price Changes, Volatility, and Durations
• “Volatility”, V, as used in Fabozzi, text chapter 11:
V = ((%∆P)/(∆y))/(1+y), when y = yield to maturity, P = bond price

• 3 measures of price sensitivity to yield changes
– DV01 = dollar value (of ∆P) of yield change, ∆y, = 1 basis point
– Yield value, ∆y, of price change of 1 = ∆y/∆P
– D = Duration = (approximate) %∆P per ∆y

• Some duration measures
– MacD: Macaulay duration
– ModD: