Question

On 12 October 2006 Rebecca bought a zero-coupon bond with maturity date of 12 October 2011. Rebecca sold the bond on 12 October 2008. The table below shows zero-coupon rates as at 12 October 2006 and 12 October 2008.

term(years) | zero-coupon rates (% pa) on 12 October 2006 | zero-coupon rates (% pa) on 12 October 2008 |

1 | 7.90 | 10.10 |

2 | 7.75 | 10.25 |

3 | 7.70 | 10.35 |

4 | 7.66 | 10.40 |

5 | 7.64 | 10.45 |

Rebecca's holding period rate of return is closest to:

a) -6.239% pa

b) 3.699% pa

c) 7.535% pa

d) 7.75% pa

Answer #1

To solve this lets take the face value of 1000$:

On 12 October 2006:

Expiry - 12 October 2011

Time - 5 years

Rate - 7.64%

Price - 1000/ ( 1+ 7.64/100)^5

= 1000 / 1.0764^5

= 1000 / 1.445

= 692.0415$

On 12 October 2008:

Expiry - 12 October 2011

Time - 3 years

Rate - 10.35%

Price - 1000/ ( 1+ 10.35/100)^3

= 1000 / 1.1035^3

= 1000 / 1.3437455

= 744.188539$

Rate of return = (744.188539 - 692.0415) / 692.0415 = 52.14704 / 692.0415 = 0.07535 for 2 years

Per year 0.07535/2 = 0.03768 or 3.768%

Which is closest to - b) 3.699%

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