59 YIELD-BASED BOND DURATION MEASURES AND PROPERTIES

The price value of a basis point (PVBP) for a 7-year, 10% semiannual pay bond with a par value of $1,000 and yield of 6% is closest to: A) $0.64. B) $0.92. C) $0.28.

$0.64. PVBP = initial price - price if yield changed by 1 bps. Initial price:Price with change:FV = 1000FV = 1000PMT = 50PMT = 50N = 14N = 14I/Y = 3%I/Y = 3.005CPT PV = 1225.92CPT PV = 1225.28 PVBP = 1,225.92 - 1,225.28 = 0.64

Consider a 25-year, $1,000 par semiannual-pay bond with a 7.5% coupon and a 9.25% YTM. Based on a yield change of 50 basis points, the approximate modified duration of the bond is closest to: A) 10.03. B) 12.50. C) 8.73.

A) 10.03. Calculate the new bond prices at the 50 basis point change in rates both up or down and then plug into the approximate modified duration equation: Current price: N = 50; FV = 1,000; PMT = (0.075/2) × 1,000 = 37.50; I/Y = 4.625; CPT → PV = $830.54. +50 basis pts: N = 50; FV = 1,000; PMT = (0.075/2)1,000 = 37.50; I/Y = 4.875; CPT → PV = $790.59. -50 basis pts: N = 50; FV = 1,000; PMT = (0.075/2)1,000 = 37.50; I/Y = 4.375; CPT → PV = $873.93. Approximate modified duration = (873.93 - 790.59) / (2 × 830.54 × 0.005) = 10.03.

When interest rates increase, the modified duration of a 30-year bond selling at a discount: A) decreases. B) does not change. C) increases.

A) decreases. The higher the yield on a bond the lower the price volatility (duration) will be. When interest rates increase the price of the bond will decrease and the yield will increase because the current yield = (annual cash coupon payment) / (bond price). As the bond price decreases the yield increases and the price volatility (duration) will decrease.

Compared to a bond's Macaulay duration, its modified duration: A) is lower. B) is higher. C) may be lower or higher.

A) is lower. Modified duration = Macaulay duration / (1 + YTM). Modified duration is lower than Macaulay duration unless YTM equals zero.

An investor finds that for a 1% increase in yield to maturity, a bond's price will decrease by 4.21% compared to a 4.45% increase in value for a 1% decline in YTM. If the bond is currently trading at par value, the bond's approximate modified duration is closest to: A) 43.30. B) 4.33. C) 8.66.

B) 4.33. Modified duration is a measure of a bond's sensitivity to changes in interest rates. Approximate modified duration = (V- - V+) / [2V0(change in required yield)] where: V- = estimated price if yield decreases by a given amount V+ = estimated price if yield increases by a given amount V0 = initial observed bond price Thus, duration = (104.45 - 95.79)/(2 × 100 × 0.01) = 4.33. Remember that the change in interest rates must be in decimal form.

On Monday, the yield curve is upward sloping with yields of 3%, 4%, and 5.5% on 1-year, 5-year, and 10-year government bonds, respectively. The following day, the yield curve experiences an upward parallel shift equal to 50 basis points. Other things equal, which of the following noncallable 6% coupon bonds is likely to experience the smallest percent change in price as a result of the yield curve shift? A) Zero coupon government bond maturing in five years. B) Par value government bond maturing in five years. C) Par value government bond maturing in ten years.

B) Par value government bond maturing in five years. The bond with the least percentage price change will be the bond with the lowest interest rate risk. Higher coupons or shorter maturities decrease interest rate risk. The coupon paying bond with only five years to maturity will have the lowest interest rate risk.

Which of the following statements about an embedded call feature in a bond is least accurate? The call feature: A) reduces the bond's capital appreciation potential. B) increases the bond's duration, increasing price risk. C) exposes investors to additional reinvestment rate risk.

B) increases the bond's duration, increasing price risk. A call provision decreases the bond's duration because a call provision introduces prepayment risk that should be factored in the calculation. For the investor, one of the most significant risks of callable (or prepayable) bonds is that they can be called/retired prematurely. Because bonds are nearly always called for prepayment after interest rates have decreased significantly, the investor will find it nearly impossible to find comparable investment vehicles. Thus, investors have to replace their high-yielding bonds with much lower-yielding issues. From the bondholder's perspective, a called bond means not only a disruption in cash flow but also a sharply reduced rate of return. Generally speaking, the following conditions apply to callable bonds: The cash flows associated with callable bonds become unpredictable, since the life of the bond could be much shorter than its term to maturity, due to the call provision. The bondholder is exposed to the risk of investing the proceeds of the bond at lower interest rates after the bond is called. This is known as reinvestment risk. The potential for price appreciation is reduced, because the possibility of a call limits or caps the price of the bond near the call price if interest rates fall.

Martina Whittaker runs a fixed-income portfolio that contains a $12 million full price position in the corporate bonds of Dewey Treadmills. Whittaker is concerned that interest rates are likely to rise and has calculated an annual modified duration of 8.0 for the Dewey bonds. The money duration of the position in Dewey bonds is closest to:

C) $96.0 million. Money duration = annual modified duration × portfolio value = 8 × $12 million = $96,000,000.

A non-callable bond with 10 years remaining maturity has an annual coupon of 5.5% and a $1,000 par value. The 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?

C) -$61.10. 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 approximate modified duration is: (V--V+) / (2V0Δy). Therefore, modified 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)(ΔYTM). 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

Which of the following is most likely to be the money duration of newly issued 360-day eurocommercial paper? A) 360 days. B) 4.3%. C) €25 million.

C) €25 million Money duration is expressed in currency units.