Price Yield Relationship – Concept

A basic property of a bond is that its price varies inversely with yield. The reason is simple. As the required yield increases, the present value of the cash flow decreases; hence the price decreases. On the contrary, when the present value of the cash flow decreases, the present value of the cash flow increases; hence the price increases. The graph of the price-yield relationship for any callable bond has a convex shape as shown in the diagram below:


The relationship of bond price and yield can be summed up pretty simply.  As yield goes up, price goes down.  And vice versa.  But why?

The government issues bonds on a fairly regular basis.  Let’s say it issues a $1,000 bond with a 5% yield.  That yield looks good so you buy a bond, hoping to hold it to maturity.  Next month rolls around and the government plans on issuing some more bonds only interest rates have risen in the past month.  So it has to issue a $1,000 bond with a 6% yield.  You think this is a great deal, so you try to sell that old bond, to buy the new one.

Here’s where the problem lies.  No one wants to pay $1,000 for a 5% bond yield, when they can get a 6% bond yield for the same amount.  In order to sell that old bond, you’d have to discount it to a lower price that will yield about 6%, just to make it worthwhile to other buyers.

The opposite is also true.  Let’s say you still have that 5% bond, only this time interest rates fall, so the government issues a $1,000 bond with a 4% yield.  The lower rate isn’t that appealing to you, but bond buyers are pounding down your door to buy your old 5% bond.  It’s in high demand so you can charge a premium for that old bond and make a profit.

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