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Ex.: Suppose that a corporate bond, originally offering investors an 8% coupon rate for 10 years and issued at 1,000 par, is called 5 years after its issue date when going market interest rates on investments of comparable risk are 6 percent. What is this bond’s 10-year holding-period yield (h) if its call price equals par ($ 1,000) plus one year’s worth of coupon income ($ 80).

The investor in callable securities encounters two major uncertainties:

(1) When and if securities will be called (value of k);

(2) Market yield (Reinvestment rate) at time of call.

Therefore, the investor demands for callable securities depends upon:

(1) Investor Rate Expectations.

The investor’s expectations regarding future changes in interest rates, especially decreases in rates, during the term of the security

(2) Length of Call Deferment.

The length of the deferment period before the security is eligible to be called.

(3) The call price (par value plus call penalty) the issuer is willing to pay to redeem the security.

c. Advantages and Disadvantages of the call privilege:

(1) Gives Issuer greater financial flexibility

(2) Creates call risk for the investor due to a possible decline in holding period yield

(3) Call privilege limits potential capital gains (usually to no more than the call price).

The call privilege is an advantage to the issuer because it gives him or her greater flexibility and the potential to reduce future interest rate by exercising the call privilege, then reinssuing a new security at a lower current interest rate.

This is a disadvantage to the investor who is paid off because he or she will be forced to reinvest in lower yielding securities if market rates have fallen.

Calling in security also limits the potential increase in a security’s market price, and therefore, the chance investors will earn capital gains.

Call risk is higher when R are expected to fall because borrowers may find it advantageous at those times to call and issue new securities at lower rates.

d. Call premium and Interest rate expectations:

( Callable securities generally sell at lower prices and higher rates (particularly if interest rates are expected to fall) relative to non-callable securities in order to compensate an investor for call risk

( Securities with long call deferments generally have lower rates than those with short deferments.

Call risk is highest when interest rates are expected to fall because borrowers may find it advantageous at those times to call and issue new securities at lower rates.

e. Research evidence:

(1) Inverse relationship between rate expectations + the value of the call price

(2)Call provisions influence the yield spread between corporate bonds and government securities

f. Effects of Coupon Rates on Call Risk:

The coupon rate on a bond is closely related to the investor’s call risk

(1) Greater call risk with higher coupon bonds.

High coupon rates mean that a bond issuer is forced to pay high interest costs as long as the bond is outstanding. Therefore, there is a strong incentive to call in such bonds and replace them with lower coupon securities.

(2) Less potential capital gain with high coupon securities.

This is true because the market value of a high –coupon security is usually close to its call price ceiling. In contrast, bonds with more modest coupon rates sell at lower prices and carry considerably more potential for capital gains before hitting their call price

Thus there is more risk of call and less potential gain to the investor who chooses high coupon securities.

As a result, the issuer of such securities must pay a higher yield to induce investors to buy them and accept greater call risk.

6. Prepayment Risk and the Interest Rate on Loan back securities:

Prepayment risk is the probability that a loan or security (especially securities that draw their earnings from payment of loans) will be paid off ahead of schedule, lowering investor’s yield from the instrument.

Factors that result in an increase in prepayment risk often involve: (1) earlier than expected loan repayments (“prepayments”) due to loan refinancing or, (2) in the case of mortgage-backed securities, home owner turn over.

The greater the prepayment risk, the higher the yield tends to rise and the lower the loan backed security’s price tends to go.

7. Event Risk:

Event Risk describes the possible effect that a public announcement by a company could have on the price of its market traded securities.

Announcement of stock splits or increased stock dividends seem to lead towards an increase in a company’s stock price.

Whereas announcements of new securities issues or a debt equity swap (a company’s bonds are replaced by stocks) may trigger a decrease in stock price.

Many financial analysts believe that events such as the foregoing trigger changes in security prices and about the probable future performance of these institutions.

8. Taxation of Security Returns:

Taxes imposed by federal, state, and local governments have a profound effect on the returns earned by investors on financial assets.

U.S. tax laws are used to redirect savings and investment to those areas considered to be of critical social need. Under the Tax Reform Act of 1986, many provisions in the tax code that provided tax breaks to investors in or issuers of securities were eliminated or curtailed.

Net losses on security investments are deductible for tax purposes.

Currently one of the few sectors that maintains a preferred status in the tax code is the municipal sector.

Interest on municipal bonds is, under a wide range of circumstances, tax exempt, particularly if the municipal securities are issued for public, rather than private purposes.

All interest income from municipal bonds is tax exempt, but not most capital gains. This exemption is designed to encourage investment in local government projects and ease the burden on local tax payers.

Effect of Marginal tax rates on After-tax yields:

Before-tax yield (1- Investor’s marginal tax rate) = After tax yield

Taxable yield (1- Investor’s marginal tax rate) = equivalent tax exempt yield

Suppose an investor is in 28% tax bracket (t):

YTM on taxable bonds = 12%

Tax exempt yield on municipal bonds of comparable quality + rating = 9%

The investor would prefer the tax-exempt municipal bond

=> Tax has an effect

At what rate would an investor be indifferent as to whether securities are taxable or tax exempt? In other words, what is the break-even point between these 2 types of financial instruments?

Tax exempt yield = (1-t) * taxable yield

where t is the investor’s marginal tax rate

t* = 1 – (tax exempt yield/ taxable yield)

Clearly, if the current yield tax-exempt securities is 8% and 10% on taxable issues, the break-even tax rate is 1- 0.80= 20%

An investor in a marginal tax bracket above 20% would prefer the yield on a tax-exempt security to a taxable one at these prevailing interest rates, other things equals (other factors held equal).

Investors whose marginal tax bracket is greater than t would receive higher after-tax yields if they invested in municipal securities. If their marginal tax bracket is less than t, then they should invest in taxable securities.

Comparing taxable and tax-exempt securities:

The taxed investor must convert all expected yields to an after tax basis. In the case of the YTM on a security,

P0 -> market value of security

Ii -> interest expected each year

t -> marginal income tax

Pn ->reduced price at maturity

(Pn - P0) measures the expected capital gain

a -> the after-tax YTM

Suppose:

Pn = $ 1,000

P0 = $ 900 (with par value of $ 1,000)

n= 10 years

Coupon rate = 10%

t = 28%

· a = 8.54%

9. Convertibility:

Convertibility is the option given to holders of special corporate bonds or preferred stock to exchange these securities for the issuing firm’s common stock.

Convertibles are called hybrid securities because they offer the investor the prospect of both stable income from interest or dividend plus capital gains on common stocks if the conversion privilege is exercised.

Convertible bonds carry lower yields because the investor must pay a premium to purchase the hedge against future risk which convertibles offer.

G. THE STRUCTURES OF INTEREST RATES:

The concept that the interest rate or yield attached to any loan or security consists of the risk-free (or pure) rate of interest plus risk premiums for the security holder’s exposure to various forms of risk.

These is a relationship among the interest rates or yields on securities in the market. The foundation of the structure of interest rates is the risk-free rate. This rate is determined by the supply and demand for loanable funds. All other interest rates add premiums to compensate investors for bearing additional risk due to:

1) lack of liquidity

2) potential for default

3) inflation

4) call privilege

5) low marketability

6) low convertibility

7) prepayment risk

8) taxability

9) interest rate risk, maturity

Forecasting rates is very difficult task. The interest rate on a given security can change for any number of reasons, including a change in any of the risk factors.

Forecasting the risk-free rate is also difficult since it is driven by the supply + the demand for loanable funds.

H. INTEREST RATE FORECASTING AND HEDGING AGANST INTEREST RATE RISK

We have looked thus far at several of the most important factors that cause R and security prices to change over time. Even this impressive list of influential factors does not account for all the changes in interest rates and security prices we observe daily in the real world.

Political developments at home and abroad

Changes in government policy

Changes in corporate earnings and business conditions

Announcements of new security offerings

And Thousands of other bits of information flood

The financial markets daily and bring about fluctuations in interest rates and security prices.

In fact, for actively traded securities, demand and supply forces are continually shifting, minute by minute, so that investors interested in these securities must constantly stay a breast of the latest developments in the financial market place.

1. Influence of the business cycle in shaping interest rate:

a. Rising and falling of rates in economic expansion + recession:

Demand of loanable funds lower => interest rates lower. Interest rates are pro-cyclical.

Business cycle = fluctuations in economic activity, with the economy experiencing expansionary (boom) and recessionary (contracting) periods.

Interest rates tend to rise and fall with the level of economic activity. Economic expansions (booms) generally lead to increases in both short-term and long-term interest rates, while recessions generally result in a decline in all rates, sooner or later.

This pattern apparently reflects shifting demand for credit as credit demands fall relative to the supply of loanable funds in periods of recession and increase relative to loanable-funds supply in expansion.

b. Relative movements in short and long-term interest rates and security prices over business

Both long term and short term R tend to rise and fall together, though lags observed with short-term rate changes often preceding long-term rate changes. Over the course of the business cycle short-term rates tend to rise faster than long-term rates in a period of expansion and decline faster than long-term rates in a recession.

The result is marked changes in the shape of the yield curve with each cyclical phase. These changes probably reflect the influence of public expectations and the fact that long-term rates can be expressed as geometric averages of short-term interest rates.

Also longer-term securities have more cash flow terms to be affected by changing interest rates than do short-term securities.

c. Seasonality in interest rates:

Patterns in the behavior of interest rates, with rate increases during certain period of the year and decreases during other seasons. Short-term rates tend to be pushed somewhat higher through summer and fall due to rising seasonal demand for short term funds, especially as businesses stock their shelves with inventory for the fall and for the major holidays that come late in the year.

From January through May, on the other hand, slackening demand for short-term credit encourages short-term interest rates to fall, other factors held equal.

Long-term interest rates, on the other hand, tend to experience upward pressure in the late spring through midsummer (June or July), related to heavy construction activity during this time of the year, and often approach seasonal lows in the winter month.

Several notes of caution should be added here, however. First, these seasonal patterns are easily overriden by other factors, such as changes in the economy or in government policy.

For example, central banks like the Fed frequently use their monetary policy tools to counteract seasonal changes in the supply + demand for loanable funds.

Second, research evidence suggests that seasonal patterns are not necessarily stable over time.

Third, unpredictable events, such as droughts, change in laws and regulations, and political turmoil often create false signals of seasonal interest rate pressures. In general, we can say that seasonal interest rate patterns exist, but they are usually of minor importance in explaining most interest rate movements.

2. Advantages and disadvantages of Interest Rate forecasting:

a. Problems:

Interest rates are influenced by the borrowing and lending decisions of thousands of individuals and institutions. No forecasting model complex enough to reflect the complexity of such decisions working their way through the financial system.

b. Advantages:

Of course, being to forecast where interest rates are going would be a distinct advantage to both borrowers + lenders of funds. Borrowers could choose to borrower when the “price” of credit was lowest, while lenders could more fully take advantage of high-rate periods.

3. Approaches to Modern Interest Rate Forecasting:

The interest difficulties in interest rates and price forecasting has not stopped many financial analysts from attempting to predict the future. They are impressed by the continuing presence of broad trends in interest rates, particularly those related to the business cycle and to central bank monetary policy.

A number of forecasting models have been developed in recent years, some have performed slightly better than pure chance for short-periods of time. Several of the more popular forecasting approaches are reviewed below.

a. Money Supply Approaches:

Many financial analysts attempt to forecast short-term changes in R by tracking money supply figures.

Changes in Ms can be linked in theory to R changes in several different ways:

The money supply liquidity effect argues that increases in the money supply or money stock (relative to money demand) cause R to fall with the changing supply of liquid funds.

The money supply expectations effect (a method for forecasting R that compares actual growth of the money supply with the market’s expectation for money supply growth) asks to forecasters to consider what money supply growth rate the public expects versus the actual money growth rate. If money growth is faster than expected, R will tend to rise other factors held constant, because a more restrictive monetary policy would be expected in future periods (perhaps due to the public’s fear of more info).

The money supply income effect links R changes to changes in income and prediction levels. Rising income tends increase money demand, while falling income leads to reduced money demand. Other things held constant, rising incomes will eventually generate higher R and falling incomes will result in lower R.

b. The Fisher Effect:

The Fisher Effect focuses on the connection between inflation and interest rates. Other factors held constant, a forecast of mere rapid inflation is a forecast of higher interest rates.

Lenders of funds anticipating higher prices for goods + services, will attempt to increase their revenues from loans by raising loan rates. A key approach is to estimate the rate of inflation expected by lenders. Unfortunately, there is little agreement on the most accurate method for making such an estimate.

One commonly used approach is to calculate a weighted average of past rates of inflation and use that average as a proxy for expected inflation. This is a crude approximation because we do not know exactly what factors the public considers in formulating its inflation forecast.

More recently, periodic surveys of economists and investors have been used to represent inflationary expectations in the marketplace.

For example, each quarter of the year, the Fed of Philadelphia surveys 33 professionals forecasters regarding their outlook for real GDP growth, inflation, and interest rates. However, such an approach suffers from being incomplete and possibly irrelevant. Expectations can change so fast that any opinion survey could be outdated before its results are published.

c. Econometric Models :

The use of systems of equation and statistical estimation methods to explain or forecast changes in R or other variables.

These econometric models often employ current and lagged values money, income or total spending, and past rates of inflation. To predict short and long term interest rates through the application of statistical regression techniques.

Interest rates in econometric models typically are linked to monetary and fiscal policy factors, security supplies, foreign demand for loanable funds, and change in income or production activity.

These models suffer from simplicity while trying to represent an exceedingly complex institution. The modern market economy. They also cannot anticipate external shocks such as wars or sudden shifts in government policy.

d. The Forward Calendar:

The foreward calendar lists new security issues (usually marketable notes and bonds) expected to come to the market within the next few weeks or months. Such listings are representations of the future supply of securities coming to the markets that is, future demand for credit. If the future supplies are expected to be tight (with demand unchanged), interest rates should fall. Conversely, an increased future supply of security offerings should lead to higher interest rates, other factors held equal.

e. Market Expectations and Implied Rate forecasting:

The financial markets reveal the public’s expectations at any given moment regarding the future course of R. These expectations are reflected most directly in the shape of the yield curve and in the prices and yields on securities traded for future delivery in the financial in the financial futures market. Upward sloping yield curves generally point to an expectation of rising R, for example, while declining yields on securities whose futures contracts are being priced today suggest lower R between now and when those futures contracts mature.

The biggest problem with such implied market forecasts is that current expectations about the future may turn out to be incorrect.

Moreover, expectations often change rapidly, sometimes in a matter of minutes or hours, as new info reaches the markets.

f. The Consensus forecast:

Because any one forecasting technique can generate spacious forecasts due to change or due to the impact of factors not taken into account by that particular technique, many forecasters “check out” their predictions using more than one forecasting method.

The outlook that arises from the application of several different forecasting methods is often called the consensus forecast.

A prediction of interest rates or economic conditions based on a variety of projections derived from several different forecasting methods.

I. INTEREST RATE RISK HEDGING STRATEGIES

1. What is hedging?

The increasingly volatile interest rates in recent years, coupled with the inherent difficulties of rate forecasting, have led many individuals and institutions to find ways to insulate themselves from interest rate changes. Hedging is the attempt to protect oneself from adverse movements in prices, and in particular adverse changes in interest rates. Some of the instruments and techniques of hedging are described in the following.

2. Duration

Duration is defined as a weighted average measure of the maturity of a financial instrument that takes into account the amount and timing of all cash flows associated with the instrument. Duration can be used as a hedging strategy. An investor could immunize his or her portfolio against interest rate changes (interest rate risks) by setting

Duration of a financial asset portfolio = Length of the investor’s planned holding period

With this investment strategy, a rise in interest rates will reduce the market value of our investor’s portfolio, but the interest return on reinvested cash flows from the portfolio will increase by an offsetting amount. The investor’s total return will be stabilized. Similarly, falling interest rates reduce the interest return from reinvesting earnings form loans or securities, but with a duration set equal to holding period length, the market value of those financial assets will rise by the corresponding amount. Again, the total return will be stabilized.

For a financial institution (such as a bank) that borrows and lends funds simultaneously, a good immunizing strategy is to set

Asset duration = Liability duration

3. Stripped securities

Interest-bearing financial instruments (usually bonds) that have been split up into multiple discount securities, each composed of one interest payment (known as an IO) or one promised principal payment (known as a PO). They are security issues whose separate interest and principal payments are each separated into a zero-coupon security by itself, which pays cash only on its maturity date.

4. GAP management

This is a technique for protecting a financial institution’s earnings from losses due to changes in interest rates which requires setting the volume of interest-sensitive assets equal to the volume of interest-sensitive liabilities. If the interest rates rise, the increase in costs would be matched by an increase in revenues.

5. Interest rate caps, floors, and collars

Interest rate caps limit how high the interest on a loan can rise. The borrower pays a fee to the lender for the protection the cap provides against rising interest rates.

A Rate floor limits how low the interest rate on a loan can fall. If market rates fall below the minimum agreed-upon rate, the borrower will reimburse the lender for the difference between the minimum loan rate and the actual market interest rate.

Rate collars are loan agreements containing both a minimum and a maximum loan rate to protect both borrower and lender against excessive interest rate risk. Rate collars place limits on both how high interest rates can go and how low interest rates can fall. Thus, both the lender and the borrower have some protection against interest rates moving in the wrong direction.

6. Interest rate insurance

Here, a borrower will pay a premium to an insurer in order to be protected against interest rates rising above some level. If rates exceed this maximum, the insurer pays the additional interest expense incurred by the borrower.

7. Loan options

Loan options are contracts entitling a borrower to take out a loan at a guaranteed interest rate over a stipulated time period. If rates rise above the guaranteed rate and borrowing is necessary, the borrower will use the loan option and borrow at the guaranteed rate. On the other hand, if loan rates stay below the guaranteed rate, funds will be borrowed as needed at market interest rates and the option will not be used. An option fee is assesses by the lending institution regardless of whether is option is ever exercised.

8. Interest rate SWAPS

An interest rate SWAP refers to a contract between two or more firms in which interest payments are exchanged so that each participating firm saves on interest costs and gets a better balance between its cash inflows and outflows. For instance, a company with fixed rate assets may issue floating-rate debt, and then swap the payment on that debt with another firm that has issued fixed-rate debt.

The terminology of the SWAP market

The SWAP partner that pays out a floating (variable) interest rate is said to be in a short position sending a variable interest rate to its SWAP partner and receiving a fixed interest rate in return. In contrast, the SWAP partner that pays out a fixed interest rate and receives, in return, a floating interest rate is said to be in a long position in the SWAP market.

Financial intermediaries and other institutions frequently occupy a hedged position, meaning that the hedged institution both pays and receives both floating and fixed interest rates.

Derivatives (Forwards, futures, options, swaps, caps, and floors) are discussed in greater details later in the course.