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The Valuation of Bonds
The Fundamentals of Bond Valuation
The Present Value Model
P = Ct / (i t 1)
Where: it = required return “may sell at discount or premium”
The Yield Model
P = Ct / (i 1)
i = discount rate needed to solve equation for market price P
Interest Rate at Return (IRR) is i
Computing Bond Yields
• Nominal Yield: stated coupon rate
• Current Yield: CY = Ci / Pm
• Promised Yield to Maturity: P = Ct / (i 1)
Solve for i
Assumes all interim cash flows (interest payments) are reinvested at the YTM
Works if
1. ... Interim cash flows at YTM
• Realized yield will differ if 1 or 2 is violated “Expect to sell before maturity”
• Promised Yield to Call
YTC relevant when bond sells above par
Crossover point: approximately par plus one year’s interest
At crossover YTC will produce lowest yield
Yield Adjustments for Tax Exempt Bonds
FTEYI / (1-t) “Yield Adjustments for Tax Exempt Bonds”
What Determines Interest Rates? ... investors) prefer the lower price volatility of shorter-term issues
They must be induced into the longer-term market with a premium rate
Segmented Market Hypothesis
Preferred habitat, institutional theory, hedging pressure
Trading Implications of the Term Structure
Yield curve can help predict future rates
Yield Spreads: Difference in promised yields between bonds or market segments
Four major yield spreads
1. ... Maturity
What Determines the Price Volatility of Bonds? ... Longer-term bonds are affected more by changes in rates than are shorter-term bonds
3. ... Keeping these interest rate changes in mind, when analyzing individual bonds or fixed income portfolios, duration and convexity are two sensitivity measures that help illustrate exposure to parallel changes in interest rates. ... However, instruments such as mortgage backed securities and callable bonds can have negative duration. For instruments that pay fixed cash flows, such as non-callable bonds, there is Macaulay’s duration. ...
With securities that do not pay fixed cash flows, such as callable bonds or mortgage-backed securities, the Macaulay formula for duration is insufficient because it fails to evaluate the varying cash flows. ... Hence, convexity, like duration, is greater for higher long-term coupon-bearing bonds and smaller for shorter-term lower coupon bonds. Typically, fund managers and investors prefer bonds with higher convexity. This is because these bonds will rise higher than other bonds when interest rates fall and they decline less than other bonds, when interest rates rise. ...
Summary
In a climate of volatile interest rate swings, in which bonds may be priced to the call date or to maturity, one must consider investment strategies that will protect a portfolio against these up and down movements.
Approximate Word count = 2090
Approximate Pages = 8.4
(250 words per page double spaced)
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