Notes. Page 1. Economics of Capital Markets. Page 1. Version 1.0 Outline. Bond
Duration and Convexity. Bond Duration and Convexity. Major Topics:.
Notes Economics of Capital Markets
Bond Bond Duration Duration and and Convexity Convexity Major Topics:
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Economics of Capital Markets
Introduction Introduction
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Notes Economics of Capital Markets
Bond Bond Duration Duration and and Convexity Convexity Introduction Introduction
We already know the relationship between bond prices and yields (or required rates of return) – Some others may be new
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Economics of Capital Markets
Bond Bond Duration Duration and and Convexity Convexity Introduction Introduction (Continued) (Continued)
1. The value of a bond is inversely related to changes in the investor’s required rate of return. –
The higher the required rate of return, the lower the bond value.
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Notes Economics of Capital Markets
Bond Bond Duration Duration and and Convexity Convexity Introduction Introduction (Continued) (Continued)
1. Prices and returns on bonds are inversely related $200
P0B =
Price
$150
C y
1 F + 1 − n (1 + y )n (1 + y )
$100 $50 $0 0%
2%
4%
6%
8%
10%
12%
Yield
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14%
16% Page 5
Economics of Capital Markets
Bond Bond Duration Duration and and Convexity Convexity Introduction Introduction (Continued) (Continued)
2 The market value of a bond will be less than the par value if the investor’s required rate is above the coupon interest rate
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Notes Economics of Capital Markets
Bond Bond Duration Duration and and Convexity Convexity Introduction Introduction (Continued) (Continued) Premium bonds Par bonds Discount bonds
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Economics of Capital Markets
Bond Bond Duration Duration and and Convexity Convexity Introduction Introduction (Continued) (Continued)
Price
3. Long-term bonds have greater interest rate risk than short term bonds. $250
20
$200
10
$150
5
10 Year 20 Year 5 Year 5 10 20
$100 $50 $0 0%
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2%
4%
6%
8% Yield
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10%
12%
14%
16%
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Notes Economics of Capital Markets
Bond Bond Duration Duration and and Convexity Convexity Introduction Introduction (Continued) (Continued)
Corollary: Low coupon bonds have greater interest rate sensitivity than high coupon bonds.
3.
Price
$200 $150
Coupon Zero
Zero Coupon
$100
Coupon
$50
Zero
15%
13%
9% Yield
11%
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7%
5%
3%
1%
$0 Page 9
Economics of Capital Markets
Bond Bond Duration Duration and and Convexity Convexity Introduction Introduction (Continued) (Continued)
The sensitivity of a bond’s value to changing interest rates depends on both the length of time to maturity and on the pattern of cashflows provided by the bond
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Notes Economics of Capital Markets
Duration Duration
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Economics of Capital Markets
Bond Bond Duration Duration and and Convexity Convexity Duration Duration
We want to know how the price of a bond changes as the yield changes
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Notes Economics of Capital Markets
Bond Bond Duration Duration and and Convexity Convexity Duration Duration (Continued) (Continued)
To derive the elasticity, use n
P =∑ B 0
t =1
C F + (1 + y)t (1 + y)n
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Economics of Capital Markets
Bond Bond Duration Duration and and Convexity Convexity Duration Duration (Continued) (Continued)
Take the first derivative with respect to y to get
