Bonds: Price vs Yields

This post and the next post will be dedicated to a question that was asked yesterday on the blog regarding Bond market's bubble speculations. I will try to address the question in the following format:

1- Question
2- Define Bonds
3- Mathematical definition
4- When/why Bond prices rise or fall?
5- U.S. Bond market
6- Relationship of U.S. bond market and U.S. stock market
7- Conclusion

Question:
"I still don't get it. I've seen and heard that bonds are getting bubbly. So, if they explode, are interest rates going up down? and stocks go up?"

What is a Bond:

In finance, a bond is an instrument of indebtedness of the bond issuer to the holders. It is a debt security, under which the issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay them interest (the coupon) and/or to repay the principal at a later date, termed the maturity.Interest is usually payable at fixed intervals (semiannual, annual, sometimes monthly). 

Thus a bond is a form of loan: The holder of the bond is the lender (creditor), the issuer of the bond is the borrower (debtor), and the coupon is the interest. Bonds provide the borrower with external funds to finance long-term investments, or, in the case of government bonds, to finance current expenditure. 

Bonds and stocks are both securities, but the major difference between the two is that (capital) stockholders have an equity stake in the company (i.e. they are owners), whereas bondholders have a creditor stake in the company (i.e. they are lenders). As a result, if a company goes bankrupt creditors are repaid first and then owners are paid.

Pricing Formula:

Below is the formula for calculating bond's price, which uses the basic present value formula for a given discount (interest/yield) rate: 

P = (C/ 1+i   +   C/(1+i)^2    +   .....    +   C/(1+i)^n) + M/(1+i)^n

where:

F = face value

i_F = contractual interest rate

C = F * i_F = coupon payment (periodic interest payment)

n = number of payments

i = market interest rate, or required yield

M = value at maturity (usually equals face value)

P = market price of bond.

To summarize: 

• Price of Bond is inversely related to the yield: Prices go down as interest rates go up
• This inverse relationship is true for all Bond, Government or Private

In the next update, I will present various reasons why Bond Market acts can differently under different circumstances. It will also summarize the Bond market discussion in regards with current market action.

If anyone wants a similar explanation on any other topic, please leave a comment, and I will try to address it on the blog (if time permits).