Chapter 13 - Term Structure of Interest Rates

Term Structure of Interest Rates

The variation of interest rates by term.

Reasons Why Interest Rates Vary Over Time:

• Supply and Demand

• Interest Rates in Other Countries

• Expected Future Inflation

• Tax Rates

• Risk associated with Changes in Interest Rates

Why Interest Rates Vary Over Time: Supply and Demand

Interest rates are determined by market forces - the interaction between borrowers and lenders. If cheap finance is easy to obtain or there is little demand for finance, this will push interest rates down.

Why Interest Rates Vary Over Time: Interest Rates in Other Countries

The interest rates in a particular country will also be influenced by the cost of borrowing in other countries because major investment institutions have the alternative of borrowing from abroad

Why Interest Rates Vary Over Time: Expected Future Inflation

Lenders will expect the interest rates they obtain to outrstrip inflation. So periods of high inflation tend to be associated with higher interest rates.

Why Interest Rates Vary Over Time: Tax Rates

If tax rates are high, interest rates may also be high, because investors will require a certain level of return after tax

Why Interest Rates Vary Over Time: Risk Associated with Changes in Interest Rates

In general, rates of interest tend to increase as the term increases because the risk of loss due to a change in the interest rates is greater for longer-term investments. This is the idea behind liquidity preference theory

Expectations Theory

The relative attraction of short and longer-term investments will vary according to the expectations of future movements in interest rates. An expectation of a fall in interest rates will make short-term investments less attractive and longer-term investments are more effective.

• In these circumstances yields on short-term investments will rise and yields on long-term investments will fall.

• An expectation of a rise in interest rates will have the converse effect.

Liquidity Preference Theory

Longer-dated securities are more sensitive to interest rate movements than short dated bonds. It is assumed that risk averse investors will require compensation (in the form of higher yields) for the greater risk on longer bonds. This may explain some of the excess return offered on longer term bonds.

Market Segmentation Theory

Argues that the term structure emerges from different forces of supply and demand.

Bonds of different terms are attractive to different investors, who will choose assets that are similar in term to their liabilities. The liabilities of banks are very short term; hence they invest in very short-term bonds. Many pension funds have liabilities that are very-long term, so pension funds are more interested in the longer-dated bonds. The demand for bonds will therefore differ for different terms.

Yield to Maturity

The effective rate of interest at which the discounted value of the proceeds of a bond equals the price of the bond.

Par Yield

The n-year par yield represents the coupon per 1 nominal that would be payable on a bond with term years, which would give the bond a current price under the current term structure of 1 per 1 nominal, assuming the bond is redeemed at par.

• Alternative measure of the relationship between the yield and term of investments

Volatility/ Discounted Mean Term

Measure of the average life on an investment.

• important when considering the effect of changes in interest rates on investment, portfolios with a longer term will be more affected by a change in interest rates.

Convexity

A measure of the change in duration of a bond when the interest rate changes.

• Positive convexity implies that τ(i) is a decreasing function of i meaning that P increases more when there is a decrease in interest rates than it falls when there is an increase of the same magnitude in interest rates.

Immunisation

Selecting portfolio assets such that it will protect the surplus against small changes in the interest rate.

Reddington’s Immunisation Conditions

1. The value of the assets at the starting interest is equal to the value of the liabilities

2. The volatilities of the asset and liability cashflow series are equal or the DMT’s are equal

3. The convexity of the asset cashflow series is greater than the convexity of the liability cashflow series.