Question

Consider a 10 year bond with a coupon rate of 7% and annual coupon payments. Draw a graph showing the relationship between the price and the interest on this bond. The price should be on the y-axis and the interest rate on the x-axis. To compute the various prices, consider interest rates between 2% and 12% (use 0.5% increments). So your x-axis should go from 2%, then 2.5% … until 11.5% and then 12%. Is the relationship linear (i.e. is the slope constant)? Start at 7%. If interest rates go up or down by 0.5% is the price changing by the same amount? What type of relationship do we observe between prices and interest rates (liner, concave, convex or something else)?

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Answer #1

1.

Interest Rate | Price |

2.00% | $1,449.13 |

2.50% | $1,393.84 |

3.00% | $1,341.21 |

3.50% | $1,291.08 |

4.00% | $1,243.33 |

4.50% | $1,197.82 |

5.00% | $1,154.43 |

5.50% | $1,113.06 |

6.00% | $1,073.60 |

6.50% | $1,035.94 |

7.00% | $1,000.00 |

7.50% | $965.68 |

8.00% | $932.90 |

8.50% | $901.58 |

9.00% | $871.65 |

9.50% | $843.03 |

10.00% | $815.66 |

10.50% | $789.48 |

11.00% | $764.43 |

11.50% | $740.45 |

12.00% | $717.49 |

No, the relationship is not linear i.e., the slope is not constant

No the price changes by different amount

Convex relationship

a) First, consider a 10 year bond with a coupon rate of 7% and
annual coupon payments. Draw a graph showing the relationship
between the price and the interest on this bond. The price should
be on the y- axis and the interest rate on the x-axis. To compute
the various prices, consider interest rates between 2% and 12% (use
0.5% increments). So your x-axis should go from 2%, then 2.5% ...
until 11.5% and then 12%.
Is the relationship...

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