Chapter 6 Chapter 6
Chapter 6 Chapter 6
Chapter 6 Chapter 6
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19<br />
Limitations of Modified Duration:<br />
Modified duration is a measure of rate of change in the bond price on change in<br />
yield to maturity. Suppose the modified duration is 2. It means for every 1<br />
percentage point change in YTM, the bond value will change inversely by 2%.<br />
Suppose the current value of a bond is Rs.90 and YTM is 10%; if YTM increases<br />
to 11% , the value of bond will be Rs.88.20; if the YTM decreases to 8%, the<br />
value of the bond will be Rs.91.80.<br />
Let us understand this point more clearly. Suppose (i) the current value of a bond<br />
is Rs.90 (ii) YTM is 10% and (iii) Modified duration is 1. The following table gives<br />
change in Bond price on various changes in YTMs.<br />
Change in YTM ( in terms % change in bond price Bond value<br />
of basis points)<br />
-100 + 1% 90.90<br />
+ 100 - 1% 89.10<br />
- 200 +2% 91.80<br />
+200 -2% 88.20<br />
-300 +3% 92.70<br />
+300 -3% 87.30<br />
-400 +4% 93.60<br />
+400 -4% 86.40<br />
The above data concludes that the relationship between YTM and bond value is<br />
linear and inverse i.e. if we draw graph using the above data (taking YTM on y-<br />
axis and bond value on x-axis), we will obtain a downward moving straight line<br />
i.e. the graph of the relationship between price and YTM is in the form of a down<br />
ward moving straight line.<br />
The realty (with respect to linearity), however, is different i.e. the true<br />
relationship between a change in price of bond and a change in YTM is not linear.<br />
Duration provides an approximation of this relationship. For a small change in<br />
YTM, duration estimates the changed price more or less accurately, but for<br />
larger changes duration becomes less accurate.<br />
Q. No. 29 : 10 % bond with maturity 5 years. Face value Rs.100. Current YTM is<br />
10%.<br />
(a)<br />
(i) Find value of the bond.<br />
(ii) What will be the value of the bond if the YTM increases from 10% to 11%<br />
(iii) What will be the value of the bond if the YTM decreases from 10% to 9%<br />
(iv) What will be the value of the bond if the YTM increases from 10% to 12%<br />
(v) What will be the value of the bond if the YTM decreases from 10% to 8%<br />
(b) Find modified duration. Using modified duration:
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