Relationship between bond prices, the stock market and interest rates

To illustrate the relationship between bond prices and interest rates consider a 19th century bond issued by the British government called a consul. This bond paid a set nominal rate of interest forever. For example, a $1000 consul with a 5% interest rate would pay the owner $50 each year forever.

The interest rate a government must pay to obtain buyers for its bonds depends on the supply and demand of competing financial assets. Governments desire to sell their bonds at the lowest interest rate possible. Suppose the government sells a large number of consuls at 5% interest. The next year the demand for consuls drops and the government has to raise the interest rate to 10% to attract buyers. What happens to the price of the consuls issued at 5% interest. To see what happens suppose a buyer of a 5% consul tried to sell his consul in a market where buyers could buy 10% consuls. If a buyer bought a 10% $1000 consul he would receive $100 a year. The price of the 5% $1000 consul would have to fall to $500 in order for the buyer to obtain 10% interest. The buyer would be indifferent between purchasing two of the old 5% $1000 consuls at $500 each or one of the new 10% $1000 consuls. In either case he would receive $100 a year for his $1000 investment. The price of consuls adjusts such the interest payment equals the market rate of interest.

The purpose in introducing consuls was to eliminate the problem with the time horizon of current bills, notes and bonds. Currently at the end of the stated time horizon, for example a 30 year bond, the government pays back the principal in full. What this means the longer the time horizon before repayment of principal the more the bond acts like a consul. For short term debt the price changes only slightly with varying interest rates. The longer the time horizon the greater the change. New 30 year bonds act approximately like consuls.

The higher the interest rates the lower the value of the stock market. To clearly understand why this is so consider the choice of an investor. The higher the interest rate the government is willing to pay on its bonds the more investors forgo the stock market to obtain sure thing rewards from the government. The price/earnings ratio of stock falls until stocks are competitive (based on earnings) with bonds at higher interest rates.

Bank expansion problem

Note: The theory of bank expansion and contraction is adequately covered in the text. The following problem is an exam type problem:

1. Given a very large number of standard banks whose initial position is:

_____ Assets _____ Liabilities
____________ ___ _______________

R____ $10M _____ DD $100M

GS____ 30M

L_____ 60M

where R is reserves, GS is government securities, L are loans, DD is demand deposits and the required reserve ration is 10%

_____ 1. To expand the money supply should the FED buy or
_______ sell securities?

_____ 2. What will happen to interest rates?

_____ 3. Assuming the FED's transaction to expand the money supply is $10M and to maximize profits the banks kept reserves down to the legal minimum explain numerically what happens if the FED transaction is with a bank. consider a plausible course of action at the first two banks. (The first two terms of the geometric series.)

_____ 4. Explain in words the mechanism which causes the
_______ expansion.

_____ 5. Briefly discuss a contraction.

_____ 6. What is the money multiplier resulting from part 3.
_______ What is Þ(M)? (Change in the money supply)

_______ Why is this multiplier larger than the
_______ empirical monetary expansion multiplier? Discuss _______with words or symbols.