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Inverse Relationship between Bond Price and Gross Redemption Yield

A

Acronym Lover

Member
Would someone be able to explain the inverse relationship between bond price and gross redemption yield in a practical sense (I've looked at the mathematical example in the course notes which makes sense but struggling to think of this situationally).

I understand that if the price of the bond goes down, then the yield would increase but I can't seem to get my head around why the opposite relationship is also true (i.e. if the gross redemption yield increases, then the price of a bond goes down).
 
Hi @Acronym Lover ,

Start off with a zero-coupon bond redeemable at par. The equation relating to the price and the GRY

P = 100/ (1+i)^n

Suppose, you pay $90 today and n=5, then the yield = 2.13%. You would agree that asset prices will change every day due to the forces of demand and supply in the market. Suppose tomorrow, the price goes down to $89, then the yield for a 5 year zero coupon bond = 2.36%.
Hence, if the price goes down, GRY goes up. Intuitively, this makes sense because if you are paying less for a fixed nominal return(at par), your expected return should be higher.
 
The poster above gave a good explanation, but I just wanted to add a little more.

The way you’re thinking about how price and yield “affect” each other doesn’t seem right to me. The yield of a bond is an artificial construct based on price. It’s not that yields go up, hence the price goes down as a result.

It’s that yields going up is exactly the same thing as the price going down, because that’s how the yield is defined. Given the other information about the bond - the coupons, the duration, etc. - quoting a yield to someone is equivalent to quoting a price.
 
Great answer posts above - thank you both!

I agree that you shouldn't really be thinking about how the GRY 'affects' the price, as the GRY is driven by the price: it's (broadly speaking) what you would earn to maturity if you bought the bond at that price.

However, just to extend the reply a little further: you might be getting this muddled up with thinking about how interest rates might impact the price of a bond? Expectations theory posits that the yield curve (of GRYs) is driven by the market's expectations of future short-term interest rates.

If interest rates are expected to be higher in the future, this will reduce the attractiveness of fixed-interest bonds since these pay out a fixed known coupon and that coupon rate will look less generous if market interest rates are expected to be higher than previously. If the bonds are less attractive in the market, this will reduce their value or price - all else being equal. Lower price -> higher GRY. Hence the link between interest rate expectations and GRYs.

So that might be what you are thinking about in the final line of your question (ie interest rates rather than GRYs)?
 
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