Q4. A bond with a semi-annually coupon rate of 3% sells for $850. It has a modified duration of 10 and is priced at a yield to maturity (YTM) of 8.5%. If the YTM increases to 9.5%, the predicted change in price, using the duration concept decreases by:

A)   $77.56.

B)   $79.92.

C)   $85.00.

Q5. A bond has the following characteristics:

• Modified duration of 18 years
• Maturity of 30 years
• Effective duration of 16.9 years
• Current yield to maturity is 6.5%

If the market interest rate decreases by 0.75%, what will be the percentage change in the bond's price?

A)   0.750%.

B)   +12.675%.

C)   -12.675%.

Q6. Par value bond XYZ has a modified duration of 5. Which of the following statements regarding the bond is TRUE? If the market yield:

A)   increases by 1% the bond's price will increase by $50.

B)   increases by 1% the bond's price will decrease by $50.

C)   increases by 1% the bond's price will decrease by $60.

Q7. Given a bond with a modified duration of 1.93, if required yields increase by 50 basis points, the expected percentage price change would be:

A)   -1.025%.

B)   -0.965%.

C)   1.000%.

Q8. What happens to bond durations when coupon rates increase and maturities increase?

       As coupon rates increase, duration:           As maturities increase, duration:

A)         increases                                                              increases

B)         decreases                                                            decreases

C)        decreases                                                              increases

Q9. 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)   -$61.10.

B)   -$47.34.

C)   -$5.68.

Q4. A bond with a semi-annually coupon rate of 3% sells for $850. It has a modified duration of 10 and is priced at a yield to maturity (YTM) of 8.5%. If the YTM increases to 9.5%, the predicted change in price, using the duration concept decreases by:fficeffice" />

A)   $77.56.

B)   $79.92.

C)   $85.00.

Correct answer is C)

Approximate percentage price change of a bond = (-)(duration)(Δy)

Δy = 9.5% ? 8.5% = 1%

(-10)(1%) = -10%

($850)(-0.1) = -$85

Q5. A bond has the following characteristics:

• Modified duration of 18 years
• Maturity of 30 years
• Effective duration of 16.9 years
• Current yield to maturity is 6.5%

If the market interest rate decreases by 0.75%, what will be the percentage change in the bond's price?

A)   0.750%.

B)   +12.675%.

C)   -12.675%.

Correct answer is B)

Approximate percentage price change of a bond = (-)(effective duration)(Δy)

= (-16.9)(-0.75%) = +12.675%

Q6. Par value bond XYZ has a modified duration of 5. Which of the following statements regarding the bond is TRUE? If the market yield:

A)   increases by 1% the bond's price will increase by $50.

B)   increases by 1% the bond's price will decrease by $50.

C)   increases by 1% the bond's price will decrease by $60.

Correct answer is B)

Approximate percentage price change of a bond = (-)(Duration)(Δy)

(-5)(1%) = -5%

($1000)(-0.05) = $50

Q7. Given a bond with a modified duration of 1.93, if required yields increase by 50 basis points, the expected percentage price change would be:

A)   -1.025%.

B)   -0.965%.

C)   1.000%.

Correct answer is B)

Approximate percentage price change of a bond = (-)(duration)(Δ y)

(-1.93)(0.5%) = -0.965%

Q8. What happens to bond durations when coupon rates increase and maturities increase?

       As coupon rates increase, duration:           As maturities increase, duration:

A)         increases                                                              increases

B)         decreases                                                            decreases

C)        decreases                                                              increases

Correct answer is C)

As coupon rates increase the duration on the bond will decrease because investors are recieving more cash flow sooner. As maturity increases, duration will increase because the payments are spread out over a longer peiod of time.

Q9. 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)   -$61.10.

B)   -$47.34.

C)   -$5.68.

Correct answer is A)

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

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