ECON2210-KPU Copyright: Rabia Aziz Spring Econ2210-HO3-Top5-ch6 Homework Assignment Ch 6

- Explain using the diagrams for bonds markets why does the risk premium (spread) becomes bigger during recessions?

- If the interest rate on a brand-new one-year bond is 4% and people expect the one-year bond rate to rise to 5% next year, 6% the year after, 7% the year after that, and 8% the year after that, then: * the interest rate on a 1-year bond sold today is ____ * What will the interest rates on 2-, 3-, 4-, and 5-year bonds be based on the expectations hypothesis. Draw the yield curve for these set of bonds.

- Suppose that the current i on 1-year bonds is 2% and the expected interest rate on all oneyear bonds to be issued in the next five years is also 2%. Suppose that the illiquidity premium is: ln,t = (0.1)(n-1) (%) What will the interest rates on 2-, 3-, 4-, and 5-year bonds: a. be based on the expectations hypothesis of term structure of interest rates? b. based on the liquidity-premium theory? • Draw the yield curve for both part a and b.

- Based on the YC for question 3 part b, forecast what do you expect about future Real GDP and inflation over the next 5 years. How would you evaluate the stance of current monetary policy?

Money and Banking

**1.**

During cycle recessions, corporates are more likely to go bankrupt and default on their bonds. Therefore, recessions are likely to be characterized by high default risks. For lending institutions to combat the high risk of defaulting, they charge a higher risk premium, as shown in figure 1. Conversely, when the economy booms, corporations are less likely to go bankrupt. Therefore, the default risks and risk premium would be lower.

As shown in figure 1, an economic recession triggers an increase in borrowing to sustain businesses, from D0 to D1. However, as the demand for bonds increases, the risk of default also increases, leading to a rise in the risk premium.

The brand-new one-year bond has an interest rate of 4%, and the rate is expected to rise to 5% next year, 6% the year after, 7% the year after, and 8% the year thereafter.

Calculate the interest rate of the one-year bond:

- Add one to the brand-new one-year bond’s rate: 1+4%= 1.04
- Square the results 1.04
^{2}= 1.0816 - Divide the results obtained by the current interest rate and add one

(0.010816/0.04) +1= 1.2704

Therefore, the interest rate on a 1-year bond sold today is 12.7%

Interest rates on 2-, 3-, 4- and 5- year bonds based on the expectations hypothesis.

The expectations hypothesis provides that investors can forecast future interest rate changes by observing the current yield spread. Therefore, in this scenario, an investor can use the expectations hypothesis to predict the 2-5- year bonds’ interest rate.

Formula:

Interest rates for bonds with long-dated maturities such as 2, 3, 4 years can be calculated using the formula:

I_{nt}=( i_{t}+ i^{e}_{t+1 + }i^{e}_{t+2}+ i_{t+ (n-1)})/n

In this scenario; the interest rate for the two-year bond would be:

(4%+5%)/2= 4.5%

For the three-year bond, it would be:

(4%+5%+6%)/3= 5%

For the four-year bond, it would be:

(4%+5%+6%+7%)/4= 5.5%

For the five-year bond, it would be:

(4%+5%+6%+7%+8%)/5=6%

The rising trend of the bond’s interest rates produces an upward sloping yield curve, as shown in figure 2.

**Figure 2: The Yield Curve**

**3.**

- Interest rate based on the expectations hypothesis

For the two-year bond, the interest rate would be:

(2%+2%)/2= 2%

For the three-year bond, the interest rate would be:

(2%+2%+2%)/3= 2%

For the four-year bond, the interest rate would be:

(2%+2%+2+2%)/4= 2%

For the five-year bond, the interest rate would be:

(2%+2%+2%+2%+2%)/5= 2%

Constant bond’s interest rates produce a horizontal sloping yield curve.

Interest rates based on the liquidity-premium theory

The liquidity-premium theory posits that investors are more inclined to purchase highly liquid and short-term securities that are easily disposable than long-dated securities.

In this scenario, the interest rate for the 2-, 3-, 4- and 5- year bonds can be calculated based on the liquidity-premium theory using the same formula as the expectations hypothesis;

Therefore, the interest rate on:

Two-year bond is (2%+2%)/2= 2%

Three-year bond is (2%+2%+2%)/3= 2%

Four-year bond is (2%+2%+2+2%)/4= 2%

Five-year bond is (2%+2%+2%+2%+2%)/5= 2%

**Yield Curve for Parts a and b**

**4.**

In essence, the bond market, notably the yield curve, is a good predictor of the economic direction and a country’s inflation. In this scenario, the yield curve is flat, indicating uncertainties in the country’s inflation and economy over the next five years.

One can evaluate the current monetary policy by determining whether its contribution to the economy is appropriate to the objectives set by the federal government.