# How can the bond market be overvalued when the value of a bond is a function of interest rates?

I seem to have a major misconception in my understanding of the bond market and how interest rates and demand and supply influence valuation levels. I hope someone will be able to clarify.

My thinking is as follows. If the fair value of a bond is the present value of the cash flows resulting from coupons and principal repayment, discounted at an interest rate that depends on a policy interest rates, how can the bond market be overvalued, given a specific set of interest rate levels?

I understand the idea of overvaluation in equity markets, where demand and supply freely determine prices, and demand may be artificially high in expectation of fiscal stimulus or because investors buy into unrealistic success narratives of specific companies. But in bond markets, the situation is a little more complex because both the policy interest rate and demand and supply feature in the valuation mechanism.

So my questions are the following:

• How to interest rate levels on the one hand and demand and supply on the other hand interact to determine the market price of bonds?
• Can the bond market be overvalued or can bond market valuations be inferred perfectly from policy interest rates?
• How can it be that bond markets are referred to in the media as overvalued when valuations depend on interest rates? Do they mean that market participants are assuming inappropriately low spreads to discount bond-related cashflows in valuation?

Thank you in advance for any clarifications you may be able to provide!

How can the bond market be overvalued?

To value a bond, you need, as you mention, to discount future cash flows. The cash flows (or coupons) are fixed, but the discount rate is not, and every investor may have a different view on interest rates and hence price bonds differently.

Therefore, someone thinking that interest rates will remain at rock-bottom levels will find different prices for bonds from someone who thinks that interest rates will rise sharply in the near future (the first investor will find higher prices).

So, in your case, someone thinking that the bond market is overvalued simply has a different view on interest rates than the consensus on the market. To be more precise, they expect interest rates to increase faster than the market consensus.

Bond Prices and interest rates

Taking into account what we have said above, you can view the bond market as follows: every investor forms a view on discount rates, for a given bond. Doing so, they actually compute the yield, that is the discount rate that makes the NPV of the cash flows of the bond equal to 0.

However, investors disagree on where the yield should be. They will thus trade the bond between them until they all agree.

Let's take a numerical example :

• Investor A owns a Bond, which has a face value of 100, a coupon of 1 and will mature in one year.
• Investor A thinks that the yield of this bond should be 2%
• Investor B thinks that the yield of this bond should be 0.5%

The value of this Bond to Investor A is : $$(100 + 1) / 1.02 = 99.02$$ The value of this Bond to Investor B is : $$(100 + 1) / 1.005 = 100.50$$

Therefore investor A and Investor B will both improve their current state by trading the bond anywhere between \$99 and \$100.5, ie. Investor A should sell the Bond to Investor B.

If the market price of the bond is \\$100, then Investor A thinks that the bond is overvalued, and Investor B thinks that the bond is undervalued.