Question 7) The sensitivity of a bond's price to a change in its yield is inversely related to the yield to maturity at which the bond currently is selling. What percentage does the price change of 3% yield to maturity, 6% coupon, 10-year bond if the yield goes to 2%?

A) 8.2%

B) 7.8%

C) 7.4%

D) 7.0%

48 49 50 51 52 53 6. The sensitivity of a bond's price to a change in its yield is inversely related to the yield to maturity at which the bond currently is selling. high YTM low YTM Par $1,000 $1,000 $1,000 $1,000 Coupon rate 6.0% 6.0% 6.0% 6.0% years to maturity 10 10 10 10 yield to maturity 6.0% 5.0% 3.0% 2.0% Price $1,000.00 $1,077.95 $1,257.53 $1,360.91 change in price due to 1% yield chan 7.8% 8.2% 54 55 56 57 58 59 60 61 Now Maturity Price Coupon Time Duration (and Convexity) in Excel 3/25/2020 Duration 7.6619 3/25/2030 Mduration 7.4387 $1,000.00 6.0% 10 6.0% 62 63 64 YTM 65 66 67 68 69 0.000889996 1 113.2075472 2 320.3987184 3 604.5258838 4 950.5123959 Convexity 1.769886566 70 Use Duration (and Convexity) to Approx. Change in Price YTM change to: 5.0% $ change in price % change in price ($74.39) -7.44% ($74.48) -7.43% 71 72 Duration Duration+Conv. 73 48 49 50 51 52 53 6. The sensitivity of a bond's price to a change in its yield is inversely related to the yield to maturity at which the bond currently is selling. high YTM low YTM Par $1,000 $1,000 $1,000 $1,000 Coupon rate 6.0% 6.0% 6.0% 6.0% years to maturity 10 10 10 10 yield to maturity 6.0% 5.0% 3.0% 2.0% Price $1,000.00 $1,077.95 $1,257.53 $1,360.91 change in price due to 1% yield chan 7.8% 8.2% 54 55 56 57 58 59 60 61 Now Maturity Price Coupon Time Duration (and Convexity) in Excel 3/25/2020 Duration 7.6619 3/25/2030 Mduration 7.4387 $1,000.00 6.0% 10 6.0% 62 63 64 YTM 65 66 67 68 69 0.000889996 1 113.2075472 2 320.3987184 3 604.5258838 4 950.5123959 Convexity 1.769886566 70 Use Duration (and Convexity) to Approx. Change in Price YTM change to: 5.0% $ change in price % change in price ($74.39) -7.44% ($74.48) -7.43% 71 72 Duration Duration+Conv. 73