# Can a bond's market price rise above its lifetime value?

I'm just learning about bonds, reading an introductory book about investing in German. Please correct me if terms are wrong, and if this question can be improved.

Consider a bond:

• Nominal value: 100 USD

• Yearly interest rate: 5%

If I buy that bond, then I assume after three years, I get my money back from the issuer, and in the meantime, I've earned:

3 × 5% × 100 USD = 15 USD

I understand that if I want to sell the bond before the end of its lifetime, then I may get less than 100 USD, for example if it is now competing with a comparable bond with 8% interest rate. Also, I can imagine selling the bond for up to its nominal value plus outstanding interest. In the first year that would be: 115 USD In this case, the buyer would not make any profit.

Are there circumstances where the market price of a bond rises beyond its lifetime value, i.e. beyond its nominal value plus interest?

• As you point out, I can't see any way it could rise above purchase price plus interest unless the buyer was being remarkably stupid or there was some sort of scam in progress... – keshlam Sep 28 '14 at 21:05
• Keshlam, that is correct (as far as I can see). You should convert that into an answer. – ChrisInEdmonton Sep 29 '14 at 0:53
• The present value of the bond is the value of the promise of the future payments. If the discount rate were negative, the present value would be greater than the sum of the future payments. Typically the discount rate is the interest rate of a "risk-free" investment such as a government bond. And in unusual circumstances, that rate can go negative. – The Photon Sep 29 '14 at 5:43
• The discount rate should have a floor of zero-- when a "risk-free" investment has a negative interest rate you're better off holding cash. – serakfalcon Sep 29 '14 at 10:41

The answer is yes. And the reason is if today's interest rates are lower than the interest rate (coupon) at which the bond was issued.

The bond's "lifetime value" is 100 cents on the dollar. That's the principal repayment that the investor will get on the maturity date.

But suppose the bond's coupon rate is 4% while today's interest rate is 3%. Then, people who bought the bond at 100 would get 4% on their money, while everyone else was getting 3%.

To compensate, a three year bond would have to rise to almost 103 so that the so-called yield to maturity" would be 3%. Then there would be a "capital loss" (from almost 103 to 100) that would exactly offset the extra interest, that is 1% "more" for three years.

If today's interest rates are negative (as they were from time to time in the 1930s, and in the present decade), the "negative" interest rates will prevent the buyer from getting the "lifetime value" (as defined by the OP) of principal plus interest over the original life of the bond. This happens in a "flight to quality" situation, where people are willing to take a (small) capital loss on Treasuries in order to prevent a large possible loss from bank failures like those that took place in 2008.

• That makes sense. However, it isn't an answer to my question because you use a different definition for "lifetime value". My definition includes interest being paid over the lifetime of the bond. In my example, that would be 115 USD. Sorry for the confusion. As I wrote in my question: Please correct me if terms are wrong […] – feklee Oct 1 '14 at 13:39
• @feklee: See my new last paragraph. – Tom Au Oct 1 '14 at 13:49
• Indeed, searching the web for "bonds with negative interest rate" gave me plenty of results. Quote from an Aug. 7, 2014 Business Insider article: "Earlier Thursday, the yield on Germany's two-year bond actually went negative, touching -0.004%. In other words, investors are effectively paying the German government to hold their money." – feklee Oct 1 '14 at 14:54