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1464 Words Oct 4th, 2013 6 Pages
LECTURE 10: DURATION
BONDS III

FIN300 (Matt Marcinkowski, Fall '13)

DURATION
• Consider two bonds with 10 years to maturity and $1,000 face value (assume annual coupons/compounding): • Bond A: Coupon rate = 10% • Bond B: Coupon rate = 0% (discount paper)
Yield Bond 8% A B $1,134.20 (+13.4%) $463.19 (+20%) 10% $1,000 $385.54 12% 887.00 (-11.3%) $321.97 (-16.5%)

FIN300 (Matt Marcinkowski, Fall '13)

DURATION
• Now, consider two bonds with 10 percent coupon rate and $1,000 face value (assume annual coupons/compounding): • Bond C: Time to maturity = 5 years • Bond D: Time to maturity = 25 years
Yield Bond 8% C D $1,079.85 (+8%) $1,213.50 (+21.4%) 10% $1,000 $1,000 12% $927.90 (-7.2%) $843.14 (-15.7%)

FIN300 (Matt
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Calculate the duration of that bond. (The price of the bond is…) • Do this in Excel:
Time 1 2 3 4 5 CF 100 100 100 100 1,100 Disc factor 1/1.1=0.91 1/(1.1)2=0.83 0.75 0.68 0.62 PVCF 91 83 75 68 682 Weights 91/1,000=0.091 0.083 0.075 0.068 0.683 Weights x Time 1x0.091=0.091 2x0.083=0.165 0.225 0.273 3.145

SUM = D= 4.17
FIN300 (Matt Marcinkowski, Fall '13)

DURATION: SELF-TEST

• Question 1: What is the duration of a zero-coupon bond with 5 years until maturity and a YTM of 3%?

• Question 2: What happens to the duration of a stream of payments when interest rates increase?

FIN300 (Matt Marcinkowski, Fall '13)

DURATION AND BONDS
• Back to last week’s lecture example: 10-year bond, 10% coupon, annual payments, purchase at issue.  Duration for a 10% YTM = 6.7590238 years • Case A: YTM stays the same throughout the bond’s life
Years Total Interest I2 Bond Price Capital G/L Total Income Real. Return Real. Yield

1 $100 $0 $1,000.00 $0.00 $100.00 10.00% 10.00%

5 $500 $110.51 $1,000.00 $0.00 $610.51 10.00% 10.00%

6.7590238 $675.90 $228.57 $1,000.00 $0.00 $904.47 10.00% 10.00%

10 $1,000 $593.7 $1,000.00 $0.00 $1,593.74 10.00% 10.00%

FIN300 (Matt Marcinkowski, Fall '13)

DURATION AND BONDS
• Case B: YTM

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