honeycfa

A non-callable bond with 10 years remaining maturity has an annual coupon of 5.5% and a $1,000 par value. The current yield to maturity on the bond is 4.7%. Which of the following is closest to the estimated price change of the bond using duration if rates rise by 75 basis points?

A) -$47.34.

B) -$5.68.

C) -$61.10.

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First, compute the current price of the bond as: FV = 1,000; PMT = 55; N = 10; I/Y = 4.7; CPT → PV = –1,062.68. Then compute the price of the bond if rates rise by 75 basis points to 5.45% as: FV = 1,000; PMT = 55; N = 10; I/Y = 5.45; CPT → PV = –1,003.78. Then compute the price of the bond if rates fall by 75 basis points to 3.95% as: FV = 1,000; PMT = 55; N = 10; I/Y = 3.95; CPT → PV = –1,126.03.

The formula for effective duration is: (V_-–V₊) / (2V₀Δy). Therefore, effective duration is: ($1,126.03 – $1,003.78) / (2 × $1,062.68 × 0.0075) = 7.67.

The formula for the percentage price change is then: –(duration)(Δy). Therefore, the estimated percentage price change using duration is: –(7.67)(0.75%) = –5.75%. The estimated price change is then: (–0.0575)($1,062.68) = –$61.10

honeycfa

An $850 bond has a modified duration of 8. If interest rates fall 50 basis points, the bond's price will:

A) increase by $34.00.

B) increase by $4.00.

C) increase by 22.5%.

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ΔP = (-)(P)(MD)(Δi)

ΔP = (-)(8)(850)(-0.005) = +$34