Question

a. Describe the relationship between the interest rates on bonds of different maturities.

b. If we follow the Expectation Hypothesis, calculate the interest rate on a 3-year bond if

a 1-year bond has an interest rate of 2% and is expected to have an interest rate of 3% next year, and 5% in two years.

c. How does the Liquidity Premium Theory explain an upward-sloping yield curve during normal economic environment?

d. Explain the economic implications of an inverted yield curve.

Answer 1

Part A

Before moving to understand the relationship between interest rates on bonds of different maturities, it is important to understand what constitutes a bond.

A bond is a conservative investment instrument that an investor buys for a fixed price with a promise of a pay-out at a future date (face value) at a pre-decided interest rate. Bonds also have a component of "coupon payments" which are periodic payments given during the course that the instrument is held.

For example: I own a INR 100 face value bond for 10 years with a coupon payment of 10% annually. Therefore, I receive INR 10 for 9 years and INR 110 [ i.e. 100+10] at the 10th year (maturity). Now, if after 5 years the interest rates on a 5 year bond are listed at 7%, my bond will have a higher value in the market since it is still drawing 10% i.e. it will be a premium bond.

Having understood the above base concept-

The bonds are inherently sensitive to interest rate changes. If the interest rates rise, the bond prices fall and vice versa. The long term bonds are more sensitive to interest rate changes than a shorter term bond (example: a 10 year treasury bond will be more sensitive than a 5 year bond) because more coupon payements are pending on a longer term bond.

The interest rates are subject to periodic changes over time and hence the longer duration bonds will have higher risk (volatility) attached to them [understand this as an inverse relation with interest rates]

In a snap shot: Interest Rates (up) -> Bond Price (down)

Interest Rates (down) -> Bond Price (up)

Part B

Expectation hypothesis calculates the future interest rates based on the present rates as well as expected future rates. The hypothesis says that the investor will have the same interest rate if he/she invests in a 3 year bond as he/she will have if he/she invests in 1 year bonds consequetively for 3 times.

Mathematically, the long term yield on the bond is the geometric mean of the short term interest rates on the said bond. As per the question:

Interest rate of 1 year bonds are:-

Year 1 = 2%

Year 2 = 3%

Year 3 = 5%

Geometric mean of the three = [(1+0.02)(1+0.03)(1+0.05)]^(1/3) - 1

Geometric mean Formula

= 3.326%

Please note that the combined bond value for a longer duration bond will be lower than individual values of the one year bonds.

Part 3

To understand the upward sloaping nature of yield curve, it is important to understand the following concepts first:

Liquidity Premium Theory: From liquidity we understand the ability to move around the asset at the quickest possible instance i.e. the asset can be bought or sold as quickly as possible without losing its value. The higher the risk attached with the said asset in liquidating it, the higher is the premium offered to the investor for holding it. Therefore, the theory suggests that a higher premium is offered for holding a relatively lower liquid asset.

Risk-Reward: Higher the risk, higher is the return on the asset.

As we have discussed in Part A above, the longer duration bonds are of higher risk than shorter duration, the premium offered on these bonds are higher. Even in normal conditions, there is a possibility of interest rate movement in the future since economic landscape is volatile. Hence, we can say that the yield curve has a normally upward sloping curve. (the shape of the curve is normally understood to be upward sloping. In fact it becomes a news if the shape changes!)

Graphically:

X axis- Years to Maturity

Y Axis- Interest Rates

Part D

In a snapshot- It means an impending economic recession

It simply means that the long term interest rates being offered on the bonds are lower than the short term interest rates (assuming that the credit quality is the same) - this is opposite of what we have seen above since the long term bonds usually are offered at a premium due to higher risk associated with them.

From market and economic perspective-> the long term outlook is poor for the economy

The alternate theory to an inverted yield curve can be linked to the law of " Supply and Demand" in the economy. It rests on the basic economic primciple : Higher demand creates upward pressure on prices since the supply is liimited in the short term. This can also cause the yield curve to get downward sloaping.

Inverted or downward sloping yield curves are rare but a cyclical part of the economic landscape since years.

How does an inverted curve form?

In the situation of an impending recession and failure of equity markets, the investors start looking for safer instruments to park their money in and hence opt for long term treasury bonds. This helps them in preservibg capital and keep away from impacts of the faiing market and economic conditions. Excessive buying causes the long-term interest rates to decline (demand supply rule- prices go up, yield comes down). This causes the yields to sometimes come down even below the levels of the short-term yields, thereby inverting the yield curve.

The economic implication (you can choose to use the below points as the starting point of the answer and then expand)

1. Recessionary mind-set

2. Lower short term liquidity in the market

3. Gives birth to expansionary policy by the government i.e. Quantitative easing