The Term Structure of Interest Rates



WEEK 5

Bonds and the Term Structure of Interest Rates

The Real Rate of Interest

Assume a perfect world in which there is no inflation and in which funds suppliers and demanders are indifferent to the term of loans or investments because they have no liquidity preference and all outcomes are certain.' At any given point in time in that perfect world, there would be one cost of money—the real rate of interest.

The real rate of interest creates an equilibrium between supply of savings and the demand for investment funds.

Nominal or Actual Rate of Interest (Return)

The Nominal rate of interest is the actual rate of interest charged by the supplier of funds and paid by the demander.

The nominal rate of interest differs from the real rate of interest, k*, as a result of two factors:

[pic]Inflationary expectations reflected in an inflation premium (IP)

and

[pic]issuer and issue characteristics, such as default risk and contractual

provisions,

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The Term Structure of Interest Rates

[pic] YIELD

The rate of return for a debt security is equal to the rate of interest or the YIELD.

[pic] YIELD TO MATURITY

The rate of return that will be earned if the security is held to maturity.

[pic] TERM STRUCTURE OF INTEREST RATES

The relationship between a debt security’s yield (rate of return) and the length of time until the debt matures.

It represent a cross section of yields for a category of bonds that are comparable in all aspects but maturity.

Specifically, the quality of the issues should be constant

Shapes of the Yield Curve

[pic] Normal or Positive Yield Curve

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[pic] Inverse or Negative Yield Curve

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[pic] Flat Yield Curve

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[pic] Hump-backed Yield Curve

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EXPLAINING THE SHAPE OF THE

TERM STRUCTURE

THE UNBIASED EXPECTATIONS THEORY

The term structure is determined by an investor’s expectations about future interest rates.

Holds that a forward rate represents the average opinion of the expected future spot rate for the time period in question.

f(expectations of investors for future rates)

Long term interest rates are geometric averages of the short term rates.

(1 + tRn) = [(1 + tR1)(1 + t+1r1)..... (1 + t+n-1r1)]1/N

Where:

Rn = actual current rate for the bond of maturity N

N = term to maturity

tR1 = current one year rate

t+1r1 = one year rate expected to hold at some future time t + 1

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• Future interest rates are implicit in today’s actual or observed interest rates for different maturities.

The expectations hypothesis can explain any shape of the yield curve:

Upward sloping: expectation of rising short term rates.

Falling yield: expectation of falling rates.

Flat yield: expectation of rates staying constant.

Humped yield: expectation that rates will rise then fall.

[pic] LIQUIDITY PREFERENCE THEORY

Holds that the term structure is a result of the preference of investors for short-term securities (less volatile).

Investors require liquidity premiums to compensate them for buying securities that expose them to the rates of fluctuating interest rates.

Investors are willing to sacrifice some yields to invest in short-term obligations to avoid higher price volatility of long-maturity bonds.

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Can you be indifferent in terms of risk between these two choices.

You might decide that you will only expose yourself to the uncertainty of future interest rates only if you can reasonably expect to earn an additional premium for taking the risk.

The Liquidity Preference Hypothesis maintains that long term bonds should carry a higher yield than short term in order to attract investors away from shorter term, more liquid bonds.

According to the liquidity preference mode, the yield curve should always be upward sloping.

Actual long term rates tend to be above those predicted by the expectations model, also lending support to the liquidity preference model.

[pic] MARKET SEGMENTATION THEORY

Holds that investors and borrowers are restricted by law, preference, or custom to certain maturity ranges.

The market segmentation theory implies that the spot rate of interest for a particular maturity is determined solely by the demand and supply for a given maturity

The Segmented Market Hypothesis, also referred to as the preferred habitat, the institutional, or hedging pressure theory, contends that institutional investors have different maturity structures that must be met differently and they tend to confine themselves to particular segments of the yield curve.

Certain clienteles hold positions of short and long term maturities premised on the structure and nature of their businesses.

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❑ Institutions with short term liabilities, such as banks, will tend to invest in short term securities, while life insurance companies, with longer term liabilities, will invest in long term assets.

❑ The term structure is a result of the investment policies of major financial institutions.

❑ The various maturity sectors of the term structure are to a greater or lesser extent set apart from one another, so that factors that affect one maturity might not affect another directly. The supply of and demand for funds in each segment will determine the interest rate in that section.

Corporate Bonds

A corporate bond is a long-term debt instrument indicating that a corporation has borrowed a certain amount of money and promises to repay it in the future under clearly defined terms.

Legal Aspects of Corporate Bonds

Bondholders are protected primarily through the bond trust deed and the trustee.

[pic]Bond Trust Deed

A bond trust deed is a legal document that specifies both the rights of the bondholders and the duties of the issuing corporation. Included in the deed are descriptions of the amount and timing of all interest and principal payments, various standard and restrictive provisions and, frequently, sinking-fund requirements and security interest provisions.

[pic] Standard Provisions

The standard debt provisions in the bond deed specify certain record-keeping and general business practices that the bond issuer must follow.

The borrower commonly must

❑ Maintain satisfactory accounting records;

❑ Periodically supply audited financial statements;

❑ Pay taxes and other liabilities when due;

❑ Maintain all facilities in good working order.

[pic] Restrictive Provisions

Bond deeds also normally include certain restrictive covenants that place operating and financial constraints on the borrower. Without them, the borrower could increase firm's risk but not have to pay increased interest to compensate for the increased risk.

The most common restrictive covenants do the following:

• Require a minimum level of liquidity, to ensure against loan default.

• Impose non-current restrictions. The borrower must maintain a specified level of non-current assets to guarantee its ability to repay the bonds.

• Constrain subsequent borrowing. Additional long-term debt may be prohibited, or additional borrowing may be subordinated to the original loan.

• Limit the firm's annual cash dividend payments to a specified percentage or amount.

The violation of any standard or restrictive provision by the borrower gives the bondholder the right to demand immediate repayment of the debt.

[pic]Trustee

A trustee is a third party to a bond deed.

The trustee is paid to act as a 'watchdog' on behalf of the bondholders and can take specified actions on behalf of the bondholders if the terms the deed are violated.

Cost of Bonds to the Issuer

The major factors that affect the cost, which is the rate of interest paid by the bond issuer are:

[pic] Impact of bond maturity on bond cost

Generally, as noted earlier, long-term debt pays higher interest rates than short-term debt. In practical sense, the longer the maturity of a bond, the less accuracy there is in predicting future interest rates and, therefore, the greater the bondholders' risk of giving up an opportunity to lend money at a higher rate. In addition, the longer the term the greater the chance that the issuer might default.

[pic] Impact of offering size on bond cost

The size of the bond offering also affects the interest cost of borrowing, but in an inverse manner: bond flotation and administration costs per dollar borrowed are likely to decrease with increasing offering size. On the other hand, the risk to the bondholders may increase because larger offering result in greater risk of default.

[pic] Impact of issuer's risk

The greater the issuer's default risk, the higher the interest rate.

[pic] Impact of the cost of money

The cost of money in the capital market is the basis for determining a bond's coupon interest rate. Generally, the rate on Treasury securities of equal maturity is used as the lowest-risk cost of money. To that basic rate is added a risk premium (described above) that reflects the factors mentioned above (maturity, offering size and issuer's risk).

General Features of a Bond Issue.

[pic]Conversion Feature

A feature of convertible bonds that allows bondholders to change each bond into a stated number of shares.

[pic]Call Feature

A feature included in nearly all corporate bond issues that gives the issuer the opportunity to repurchase bonds at a stated call price prior to maturity.

[pic]Call Price

The stated price at which a bond may be repurchased, by use of a call feature, prior to maturity.

[pic]Call Premium

The amount by which a bond's call price exceeds its par value.

[pic]Share Purchase Warrants

Instruments that give their holders the right to purchase a certain number of shares at a specified price over a certain period of time.

Bond Ratings

Independent agencies such as Moody's and Standard & Poor's assess the riskiness of publicly traded bond issues.

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Popular Types of Bonds

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Characteristics of Contemporary Types of Bonds

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WHAT DETERMINES THE PRICE VOLATILITY OF BONDS?

In addition to yield behaviour, bond price changes are also a function of:

[pic] Par value

[pic] Coupon

[pic] Time to maturity

[pic] Prevailing market rate

Malkiel proved the following theorems.

Bond prices move inversely to bond yields. (Interest rates)

[pic]The Yield Level Effect.

A constant percentage change in yield will not produce a constant percentage change in price.

For a given change in yields (interest rates), longer maturity bonds post larger price changes.

❑ Longer the time to maturity, the greater the percentage price change.

[pic]The Maturity Effect.

Bond price volatility is directly related to term to maturity, but price volatility (percentage of price change) increases at a diminishing rate as time to maturity increases.

[pic]Direction of Change.

Price movements for a given change in interest rates aren’t symmetrical.

A constant percentage change in yield, whether an increase or decrease, will not produce the same percentage price change.

❑ A decrease in the yield raises bond prices by more than an increase in yield of the same amount lowers price

[pic]The Coupon Effect

Higher coupon bonds have smaller percentage price changes for a given fluctuation in yield.

❑ Bond price volatility is inversely related to the coupon rate

Some Trading Strategies

If market rates are expected to rise, bond prices will fall.

❑ Invest in short term, high coupon bonds to minimize price volatility and capital loss.

If market rates are expected to decline, bond prices will rise.

❑ Buy bonds with maximum price volatility.

❑ Maximum price increase (capital gain) results from long term, low coupon bonds.

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FINANCIAL MANAGEMENT

An upward-sloping yield curve is referred to as being normal or positive.

This occurs where short-term rates are lower than longer-term rates, and are said to reflect expectations that interest rates will rise in the future.

We have a flat yield curve when future interest rates are not expected to change; that is, short-term and long-term rates are the same.

A hump-backed yield curve is a combination of the preceding three types of curve. In this example short-term rates may be expected to fall over the next few years then to remain steady for a while but increasing in the longer term. The curve can also be humped high in the middle and lower at the short and longer ends.

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