The bond price and yield to maturity (YTM) have an inverse relation. Bonds issued in the past have a greater coupon rate, as compared to current market rates. The bond’s modified duration can assist us analyse the estimated impact of a 1% change in YTM on the bond price. However, the bond price and yield correlation is often convex, resulting in a small discrepancy in price computation. As a result, for greater variations in yield, the convexity principle should be utilised to calculate the sensitivity.
To recap, the relationship between bond price and Yield to Maturity (YTM) is inverse.
Source: Yubi Research
In the case of a downward interest rate scenario, bonds issued earlier would have a higher coupon rate than the current market rates. As the interest rates are falling, bonds with higher coupon rates become more valuable and hence the value of these bonds appreciate. Similarly, when the YTM is increasing, bonds issued earlier will have a lower coupon rate than the prevailing market rates and hence such bonds depreciate.
There are other factors like currency impact, credit risk, sovereign rating etc which would also affect the bond price.
What is Duration
Now that we have understood the relationship between interest rates and bond price, the next fundamental aspect is to decipher how much the bond price fluctuates on movement in interest rates which leads us to the concept of Duration.
Duration is the weighted average time period (in years) for the agreed cash flows (coupons and principal) to be repaid over the lifetime of the bond. This is also known as Macaulay Duration as this concept was introduced by Frederick Macaulay.
How to compute Macaulay Duration
Below is an illustration to calculate the duration of a four year 5% annual coupon bond trading at par.
Note that the duration of the bond (3.723) is lower than the tenor of the bond (4 years). Duration of the bond would always be lower than the tenor of the bond as there would be cash flows received during the lifetime of the bond. The only exception is a zero-coupon bond because as the name suggests this bond does not pay interest during the lifetime of the bond.
Modified Duration
Modified Duration of the bond can help us evaluate the approximate impact of the movement in the bond price for a change in YTM by 1%.
Key Takeaways
Duration / Modified provides a convenient way to compute the approximate change in bond price for movement in yield.
Impact of Duration on key factors:
Limitation of Duration
Duration is likely to be more efficient when there is minor movement in YTM. This is because Duration / Modified Duration considers the relationship between bond price and YTM to be linear. However, the bond price and yield relationship are typically convex leading to the minor inaccuracy in the computation of the price. Hence for larger movement in yield, the convexity principle is to be used for calculating the sensitivity.
Source: Yubi Research
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