Question

Both Bond Sam and Bond Dave have 6.5 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 3 years to maturity, whereas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam? Of Bond Dave? If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Sam be then? Of Bond Dave? All bond price answers should be dollar prices.

Answer 1

Price at current YTM:

Price of Bond Sam = 1000

Price of Bond Dave = 1000

Price if YTM increases:

Price of Bond Sam = 948.00

Price of Bond Dave = 809.23

% change in Bond Sam = -5.2%

% change in Bond Dave = -19.07%

Price if YTM decreases:

Price of Bond Sam = 1055.54

Price of Bond Dave = 1261.94

% change in Bond Sam = 5.54%

% change in Bond Dave =26.19%

Inserting screenshots for excel formulas:

6.5%) Bond Sam Coupon rate Settlement Date maturity Date redemption % of par Freq 01-01-2000) 01-01-2003) 100 par value Current Ytm New YTM New YTM 1000 6.50% 8.50% 4.50% ] Value of Bond as % of par =PRICE(05,06,04,013,07,08,0)| Value of Bond in Dollars 1055.54

Bond Sam Coupon rate Settlement Date maturity Date redemption % of par 6.5%) 01-01-2000) 01-01-2003) 100! 21 Freq par value Current Ytm New YTM New YTM 1000 6.50% 8.50%! 4.50% Value of Bond as % of par =PRICE(T5,76,T4,112,17,18,0)| Value of Bond in Dollars 948.00

Bond Dave Coupon rate Settlement Date maturity Date redemption % of par Freq 6.5% | 01-01-2000) 1 01-01-2020 100) par value Current Ytm New YTM New YTM 1000 6.50%) 8.50% 4.50% Value of Bond as % of par =PRICE(220,221,J19,326,322,323,0)|| Value of Bond in Dollars 1000

Bond Dave Coupon rate Settlement Date maturity Date redemption % of par Freq 6.5% 01-01-2000! 01-01-20201 1001 par value Current Ytm New YTM New YTM 1000 6.50% 8.50% 4.50%) Value of Bond as % of par =PRICE(020,021,019,028,022,023,0) Value of Bond in Dollars 1261.94

6.5% Bond Dave Coupon rate Settlement Date maturity Date redemption % of par Freq 01-01-2000) 01-01-2020) 1001 par value Current Ytm New YTM New YTM 1000 6.50% 8.50%) 4.50% Value of Bond as % of par =PRICE(T20, T21, T19,T27,122,123,0)| Value of Bond in Dollars 809.23

Bond Sam Coupon rate Settlement Date maturity Date redemption % of par Freq 6.5% 01-01-2000 | 01-01-2003) 100! par value Current Ytm New YTM New YTM 1000 6.50%! 8.50% 4.50% Value of Bond as % of par =PRICE(35,16,14,111,37,38,0) Value of Bond in Dollars 1000