Finance and bonds?

Question

An investor holds an 8 percent coupon bond and a 12 percent coupon bond. Both bonds mature in five years and have a face value of $1000. If interest rates fall by two percent the percentage increase in the value of the 12 percent coupon bond is greater than the 8 percent coupon bond. True or false and why

Answer 1

When the interest rate falls the the percentage increase in the value of the bond with the higher coupon rate increase more than lowe coupon rate. So the answer to your first question is TRUE.

Now your answer for the WHY. This can only be explained using graph. The graph for the value of the bond and interest rate is convex and sloping downwards. Value of bond on the Y-axis and IR on the X-axis. (DO THIS: draw a circle O, now draw + in the circle so the circle is now divided into 4 parts, the graph looks like bottom left part of the circle)

If the maturity is constant (5 years in this case) then as the coupon rate increases the graph SHIFTS to the right. Therefore, the graph for 12% coupon rate is TO THE RIGHT the 8% coupon rate (since they are parallel, it looks as if the 12% is ABOVE the 8%). At ANY given interest rate the TANGENT of the graph with higher coupon rate (i.e. the graph above) is steeper than the lower coupon rate (DO THIS: once you have two graphs, 12% above the 8%, mark one point on the IR (X-axis). Draw a vertical line, which will cross the two graphs. Now draw a TNAGENT at the point where this vertical line crosses each graph). You will notice that the TANGENT of the 12% graph is STTEPER (as in more downward sloping) than the 8% graph.

A TANGENT represents the gradient of a graph at that particular point (as you probably know gradient is the change in Y to change in X). Therefore, since the TANGENT of the 12% STEEPER than 8%, it can be said that the CHANGE in the value of the 12% will be higher than the change in 8% at any given IR.

Hope this has helped