Tutorial for chapter 4: behavior of interest rates.

1. Explain why would you be more or less willing to buy a share of Polaroid stock in the following situation:

a) Your wealth falls;

b) You expect the stock to appreciate in value;

c) The bond market becomes more liquid;

d) Prices in the bond market become more volatile.

2. Explain why would you be more or less willing to buy a house under the following circumstances:

a) You just inherited $100 000;

b) Real estate commissions fall from 6% of the sales price to 4% of the sale price;

c) You expect Polaroid stock to double in value next year;

d) Prices in the stock market become more volatile;

e) You expect housing prices to fall.

Answer:

(a) More, because your wealth has increased;

(b) more, because it has become more liquid;

(c) less, because its expected return has fallen relative to Polaroid stock;

(d) more, because it has become less risky relative to stocks;

(e) less, because its expected return has fallen.

3. An important way in which the Federal Reserve decreases the money supply is by selling bonds to the public. Using the supply and demand analysis for the bonds, show what effect this action has on interest rates. You must draw the diagram to justify your answer.

Answer:

When the Fed sells bonds to the public, it increases the supply of bonds, thus shifting the supply curve B^s to the right. The result is that the intersection of the supply and demand curves B^s and B^d occurs at a higher equilibrium interest rate, and the interest rate rises. With the liquidity preference framework, the decrease in the money supply shifts the money supply curve M^s to the left, and the equilibrium interest rate rises. The answer from the loanable funds framework is consistent with the answer from the liquidity preference framework.

4. Using supply and demand for bonds framework, show why interest rates are pro-cyclical (rising when the economy is expanding and falling during recessions).

Answer:

When the economy booms, the demand for bonds increases: the public’s income and wealth rises while the supply of bonds also increases, because firms have more attractive investment opportunities. Both the supply and demand curves (B^d and B^s) shift to the right, but as is indicated in the text, the demand curve probably shifts less than the supply curve so the equilibrium interest rate rises. Similarly, when the economy enters a recession, both the supply and demand curves shift to the left, but the demand curve shifts less than the supply curve so that the interest rate falls. The conclusion is that interest rates rise during booms and fall during recessions: that is, interest rates are procyclical.

5. What effect will a sudden volatility of gold prices have on interest rates?

Answer:

Interest rates fall. The increased volatility of gold prices makes bonds relatively less risky relative to gold and causes the demand for bonds to increase. The demand curve, B^d, shifts to the right and the equilibrium interest rate falls.

6. How might a sudden increase in people expectations of future real estate prices affect interest rates?

Answer:

Interest rates would rise. A sudden increase in people’s expectations of future real estate prices raises the expected return on real estate relative to bonds, so the demand for bonds falls. The demand curve B^d shifts to the left, and the equilibrium interest rate rises.

7. The President of the US announces in a press conference that he will fight the higher inflation rate a new anti-inflation program. Predict what will happen to interest rates if the public believes him?

Answer:

If the public believes the president’s program will be successful, interest rates will fall. The president’s announcement will lower expected inflation so that the expected return on goods decreases relative to bonds. The demand for bonds increases and the demand curve, B^d, shifts to the right. For a given nominal interest rate, the lower expected inflation means that the real interest rate has risen, raising the cost of borrowing so that the supply of bonds falls. The resulting leftward shift of the supply curve, B^s, and the rightward shift of the demand curve, B^d, causes the equilibrium interest rate to fall.

Problems:

1. You own a $1000-par zero-coupon bond that has five years of remaining maturity. You plan on selling the bond in one year, and believe that the required yield next year will have the following probability distribution.

a. What is your expected price when you sell the bond?

b. What is the standard deviation of the bond price?

Solution:

Probability	Required Yield	Price	Prob ´ Price	Prob *(Price – Exp. Price)2
0.1	6.60%	$774.41	$77.44	12.84776241
0.2	6.75%	$770.07	$154.01	9.775668131
0.4	7.00%	$762.90	$305.16	0.013017512
0.2	7.20%	$757.22	$151.44	6.862609541
0.1	7.45%	$750.20	$75.02	16.5903224
			$763.07	46.08937999

a)

The expected price is $763.07.

b) The variance is $46.09, or a standard deviation of $6.79.

2. An economist has concluded that, near the point of equilibrium, the demand curve and supply curve for one-year discount bonds can be estimated using the following equations:

B^d: Price =

B^s: Price = Quantity + 500

a) What is the expected equilibrium price and quantity of bonds in this market?

b) Given your answer to part a), which is the expected interest rate in this market?

Solution:

(a) Solve the equations simultaneously:

This implies that P = 814.2857.

(b)