Relationship Between Price, Yield and Duration

If you plot the graph of price versus yield of a bond, you would get a convex curve that falls as it moves towards the right. The curvature of this graph, referred to as convexity, signifies the sensitivity of the yield of the bond to its price. Moreover, at any given point on the graph, a tangent drawn on the curve represents the Macaulay Duration of the bond.

An important advantage of understanding convexity is that it allows you to compare different bonds. Even if two bonds have the same term and the same yield, the one with higher convexity will be less sensitive to changes in interest rates. This can be a desirable attribute as it means lesser uncertainty when you invest in that bond. Another key distinction is that whether interest rates fall or rise, the bond with higher convexity will end up having a higher price than a bond with lower convexity.

You can visualize this relationship by thinking of the shape of the two graphs. The price-yield graph of the bond with higher convexity will always curl upwards as compared to the graph of the bond with lesser convexity, which will be much flatter. So the moment you move by an equal amount on the yield curve, the price will rise by a higher amount (or fall by a lower amount if interest rates rise) for the bond with higher convexity.

There are some special characteristics of convexity that you should keep in mind. First of all, convexity has an inverse relationship with the coupon rate of the bond. Bonds with higher coupon rates have lower convexity, while zero coupon bonds have the highest convexity.

The price yield graph of a straight bond always have a positive convexity. The slope of the tangent to the graph will increase when yield decreases. This means that the duration of such a bond will increase as yield decreases.

On the other hand, callable bonds can have negative convexity for a part of the price yield graph. This means that for some yield values, the duration of these bonds increases as yield increases. There is a certain point on the curve beyond which it will not make sense for the company to call the bonds as it would be more expensive to raise fresh money from the market.

Beyond this point, the curve will behave just like a noncallable bond. Before this point, there is a strong possibility that the bond issuer will choose to call the bond, as the company can raise fresh money from the market at a cheaper interest rate.

Conclusion
Making investments in bonds can be a lucrative financial opportunity for those who put in the effort to understand how this market functions. There are many complicated and simple concepts that are used to assess the value of a bond and the state of the market.
Although some of these concepts will be difficult to understand initially, as you start investing in bonds and analyze different bonds more carefully, you will realize how useful this understanding can be.
Besides getting a good grasp of these concepts, you should also make sure that you stay updated with any major news about the issuer. After all, the biggest risk to your investment is that the issuer will default on its payments. If you are risk averse and want to prevent such situations, you’ll have to accept a more moderate return and choose risk free treasury bonds or high credit rating corporate bonds.

Those who are willing to take a risk to get a higher return also need to stay up to date with news from the economy and particularly about the issuer. It will allow you to choose the right entry and exit points for the investment, and quickly shift to other alternatives when the need arises, which can ultimately be the difference between making a profit or a loss on your investment.

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