Bond Question | YTM increases..

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Onestar

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Hello all,
I’ve really stuck on the question below, does anyone know how to work this question out? would really appreciate it!
Q) An investor purchases a newly issued 15-year bond at a YTM of 8% when the bond’s Macaulay duration is 10 years. Shortly after purchase, the market yield on the bond increases to 9% and remains there until maturity. Assuming the bond does not default, the investor can expect to earn an annual rate of return greater than 8%:
  • A. if the bond is sold after 7 years.
  • B. if the bond is sold after 12 years.
  • C. at no point during the bond’s life.
Answer: B
 
Ten years is the point of indifference: the point at which your investment will reach the same point (in this case, an 8% return) as it would have had the interest rate change not occurred. Thus, 7 years is too short – the loss on the value of the bond is greater than the additional reinvestment income – and any time longer than 10 years is long enough; thus, 12 years is the answer (from those offered).
 
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