L11_bond_portfolio

# L11_bond_portfolio - FINANCE431 INVESTMENTS Lecture 11...

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FINANCE 431 INVESTMENTS Lecture 11: Managing Bond Portfolios

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FIN 431: Investments 2 Interest Rate Risk When interest rates fall, bond prices rise When interest rates rise, bond prices fall Therefore, fluctuating interest rates represents a risk for bondholders. How to measure this risk?
FIN 431: Investments 3 Duration “Duration” can be used as a measure of interest rate sensitivity. To calculate duration, First, you need to know the yield to maturity Discount the bond’s cash flows, one at a time Divide the PV of each cash flow by the bond price These are your “weights” For each cash flow, take the number of years until the cash flow and multiply by the weight Then add them up

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FIN 431: Investments 4 Duration also known as Macaulay’s duration Duration of a zero coupon bond is equal to its maturity Duration is shorter than maturity for all coupon bonds For a perpetuity, D = (1+y) / y Formally it is defined as follows: where w t = [CF t / (1+y) t ] / Price D t w t t T = × = 1
FIN 431: Investments 5 Calculating Duration Example 5% bond, annual coupons, YTM = 4% Cash flows: 50 50 1050 PV(Cash flows): 50/(1.04) 50/(1.04) 2 1050/(1.04) 3 =48.08 46.23 933.44 Bond Price: = 48.08+46.23+933.44 = 1027.75

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FIN 431: Investments 6 Calculating Duration Example, Continued Weights: W1+W2+W3 = 1 W1 = 48.08/1027.75 = .0468 W2 = 46.23/1027.75 = .0450 W3 = 933.44/1027.75 = .9082 Duration = (.0468) (1Y) + (.0450) (2Y) + (.9082)(3Y) Duration = 2.86 Years
FIN 431: Investments 7 Modified Duration If the duration of a bond is D And its Yield to Maturity is y Modified Duration: D* = D/(1+y) For our example: D* = 2.86 / 1.04 = 2.75

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FIN 431: Investments 8 Modified Duration and Bond Price  Changes
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L11_bond_portfolio - FINANCE431 INVESTMENTS Lecture 11...

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