# Essay

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
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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