The Behavior of Market Interest Rates:

The required return on a bond has three components: the real rate of return (r*), an expected inflation premium (IP), and a risk premium (RP).

The behavior of interest rates is perhaps the single most important element in determining the level of return from a bond investment program. Interest rates affect the level of current income earned by conservative investors, as well as the amount of capital gains generated by aggressive bond traders. Whereas conservative investors are primarily concerned with the level of interest rates, aggressive investors are interested chiefly in movements in interest rates (the amount of interest rate volatility).

There is no single bond market or single interest rate that applies to all segments of the market. Some of the more important market yields and yield spreads (interest rate differentials) are:

Municipal bonds usually carry the lowest market rates because of their tax-exempt feature.

Issues that normally carry bond ratings generally display the same behavior: the lower the rating, the higher the yield.

There is generally a direct relationship between the coupon an issue carries and its yield. Discount (low-coupon) bonds yield the least, and premium (high-coupon) bonds yield the most.

In the municipal sector, revenue bonds yield more than general obligations bonds.

Bonds that are freely callable generally provide the highest returns.

Bonds with long maturities tend to yield more than short issues.

Some of the major determinants of interest rates include: inflation, changes in the money supply, the size of the federal budget deficit, the level of economic activity, actions of the Federal Reserve, and the level of interest rates in major foreign markets. Individual investors can monitor interest rates and formulate interest rate expectations on an informal basis through the use of reports obtained from their brokers, from investor services (e.g., S&P's Creditweek), and/or by following columns/articles in such business and financial publications as The Wall Street Journal or Business Week.

The Term Structure of Interest Rates and Yield Curves:

The term structure of interest rates is the relationship between the interest rate or yield and the time to maturity for any class of similar risk securities. The yield curve is just a graphic representation of the term structure of interest rates at a given point in time. To plot a yield curve, you need to know the yield-to-maturity for different maturities of similar risk bonds. As market conditions change, the yield curve's shape and location also change.

The upward-sloping yield curve indicates that yields tend to increase with longer maturities. The longer a bond has to go to maturity, the greater the potential for price volatility and the risk of loss. Thus, investors require higher yields on longer maturity bonds. Flat yield curves indicate that yields will be the same across maturities. Given that longer-term bonds have more default and maturity rate risk, a flat yield curve implies that inflation rates are expected to decline.

Analyzing the changes in yield curves over time provides investors with information about future interest rate movements and how they can affect price behavior and comparative returns. For example, if over a specific time period, the yield curve begins to rise sharply, it usually means that inflation is increasing. Investors can expect that interest rates, too, will rise. Under these conditions, most seasoned bond investors would turn to short or intermediate (three- to five-year) maturities. A downward-sloping yield curve would signal that rates have peaked and are about to fall. A downward-sloping yield curve occurs when short-term rates are higher than long-term rates that generally results from actions by the Federal Reserve.

The main theories that can explain the reasons for the general shape of the yield curve are the expectations hypothesis, the liquidity preference theory, and the market segmentation theory.

Expectations hypothesis: The yield curve reflects investor expectations above all else. Future behavior of interest rates with respect to the present is affected most by expectations regarding inflation. Higher expected inflation requires higher interest rates today. The result is an upward-sloping yield curve. To produce a downward-sloping yield curve under this hypothesis, the

expected future inflation would be lower, but the current rates would remain higher.

Liquidity preference theory: Long-term bond rates should be higher than shorter-term rates due to the condition that there are more liquid market rates in the short term. Uncertainty increases over time, causing the demand for a higher risk premium (bond interest rate). This theory expects upward-sloping yield curves. Downward-sloping curves would not occur in this theory since that would contradict the basic notion that uncertainty increases with time and the risk premium adjusts accordingly.

Market segmentation theory: The debt market is segmented according to length of maturity and preferences. An equilibrium exists in the short term between suppliers and demanders of funds.

There are different inhabitants in each segment with different motivations. In the short term, banks predominate, but in the long term, life insurance and real estate firms determine the equilibriums.In this theory, yield curves may be either upward- or downward-sloping, as determined by the general relationship between rates in each market segment.

Differences in yields on different maturities at a particular point in time, or the "steepness" of the curve, is an indication that long-term rates are likely to fall somewhat to narrow the spread,

providing an incentive to invest in longer-term securities. Steep yield curves are generally viewed as signs that long-term rates are near their peak.

Even among longer-term maturities, the spread between different longer-term maturities should be considered before making a decision to invest. For example, if the spread between 10 and 30-year maturities is not large enough (say, less than 20 basis points), then the investor should favor the 10-year bond because he would not gain enough to compensate for investing in the much riskier 30-year maturity. In any case, the investor would have to consider his or her own risk tolerance to determine whether the risk premium was sufficient for the additional risk of buying longer-term securities.

The Price of Bonds:

Bond prices are driven by market yields. In the marketplace, the appropriate yield at which the bond should sell is determined first, and then that yield is used to find the price of the bond. The yield is a function of certain market and economic forces, such as the risk-free rate and inflation, as well as key issue and issuer characteristics, such as the maturity of the issue and agency rating assigned to the bond. You cannot value a bond without knowing its market yield, which functions as the discount rate in the bond valuation process.

Po = [Ii / (1+i)t] + [PVn /(1+i)n]

= Present value of coupon payments + Present value of bond's par value

To determine the value of the bond, we need to know the number or periods remaining until maturity, the face value, the coupon and the market interest rate for similar bonds.

Bond Value = C x PVAIF + Face value paid at maturity x PVIF

Bonds are usually priced using semiannual compounding because in practice, most bonds pay interest every six months. Semiannual compounding makes discounting of semiannual coupon payments more precise, resulting in more accurate valuation. However, using annual compounding simplifies the valuation process a bit and does not make very much difference in value. With higher coupons and longer maturities, the difference increases more. Bonds offering semi-annual payments will be priced higher.

Bond price = Present value of annuity of annual interest income + Present value of the bond's par value

To generalize:

When r increases, Pbond decreases. Thus if the price of bond = $1000 and the coupon payment (C) is = $100 then the interest r will equal 10%. However for the same price of bond if coupon payment (C) is $10 the r will be lower 1%. Therefore there is a negative relationship between interest rate and the price of bonds. We can summarize this relations by the following expression.

Pbond = C / r

Measures of Yield and Return:

Current yield is a measure of a bond's current income. It is the amount of current income a bond provides relative to its prevailing market price.

Current yield = Annual interest income / Current market price of the bond

Yield-to-maturity is a more complete measure and evaluates both interest income and price appreciation. Yield-to-maturity indicates the fully compounded rate of return earned by an investor, given that the bond is held to maturity and all principal and interest payments are made in a prompt and timely fashion.

Promised yield is the same as yield-to-maturity. Promised yield is computed assuming the bond is held to maturity and the coupon cash flows are reinvested at the bond's computed promised yield.

Yield-to-call shows the yield on a bond if the issue remains outstanding not to maturity, but rather until its first call date.

Realized yield is the rate of return an investor can expect to earn by holding a bond over a period of time that is less than the life of the issue. Realized yield is used by bond traders who trade in and out of bonds over short holding periods.

When we are dealing with semi-annual cash flows, to be technically correct, we should find the bond's "effective" annual yield. However, the market convention for finding the annual yield is to double the semi-annual yield. This practice produces what the market refers to as the bond-equivalent yield. Thus, given a semi-annual yield of 4%, according to the bond-equivalent yield convention, the annual rate of return of this bond if held to maturity is 8%. This is also the same as the bond's promised yield or yield-to-maturity.

Conservative investors employ promised yield to value bonds, and aggressive investors use expected return to value bonds.

Duration and Immunization:

Duration is a measure of bond price volatility. It captures both price and reinvestment risks in a single measure and indicates how a bond's price will react to different interest rate environments. It is the effective maturity of a fixed-income security. On the other hand, the bond's actual maturity does not consider all of the bond's cash flows nor does it consider the time value of money. Duration is a far superior measure of the effective timing of a bond's cash flows because it explicitly considers both the time value of money and the bond's coupon and principal payments.

Duration = [PV(Ct) / Pbond x t]

When the market undergoes a big change in yield, duration will understate price appreciation when rates fall and overstate the price decline when rates increase. Modified duration is used to overcome this problem by linking interest rate changes to changes in bond price.

First, you can compute the modified duration using the bond's computed duration and the computed yield-to-maturity. Then, the change in bond price based upon a change in interest rates can be computed as follows:

Modified duration = Duration in years / 1 + Yield to maturity

Percent change in bond price = -1 x Modified duration x Change in interest rates

Market interest rate changes have two effects: the price effect and the reinvestment effect, which occur in opposite directions. When a bond portfolio is immunized, these two effects exactly offset each other and leave the value of the portfolio unchanged. This happens when the weighted average duration of the bond portfolio is exactly equal to the desired investment horizon. If a portfolio is constructed and continuously rebalanced such that the weighted average duration is equal to the desired investment horizon at any particular point in time, then the portfolio is said to be immunized from the effects of interest rate changes.

Effective duration = (The new price of the bond if market interest goes up - The new price of the bond if market interest goes down) / (2 x Price of the bond x The change in market interest rates)

Bond immunization allows an investor to derive a specified rate of return from bond investments regardless of what happens to market interest rates over the course of the holding period. That is, the investor's bond portfolio is "immunized" from the effects of changes in market interest rates over a given investment horizon.

Portfolio immunization is not a passive investment strategy; it requires continual portfolio rebalancing on the part of the investor in order to maintain a fully immunized portfolio. The composition of the portfolio should change every time interest rates change, and also with the

passage of time.

Bond Investment Strategies:

Bond ladders are a passive investment strategy whereby an equal amount of money is invested in a series of bonds with staggered maturities. Suppose an investor wants to confine her investing to fixed income securities with maturities of ten years or less. She could set up the ladder by investing in roughly equal amounts of 3-, 5-, 7-, and 10-year issues. When the 3-year issue matures, the proceeds would be reinvested in a new 10-year note. Similar rollovers would occur whenever a bond matures. Eventually, the investor would hold a full ladder of staggered 10-year notes. Rolling into new 10-year issues every 2 or 3 years allows the investor to dollar cost averaging and thereby lessen the impact of swings in market rates.

In a bond swap, an investor simultaneously liquidates one position and buys a different issue to take its place. Swaps can be executed to increase current yield or yield-to-maturity, to take advantage of shifts in interest rates, to improve the quality of a portfolio, or for tax purposes.

In a yield pickup swap, an investor switches out of a low-coupon bond into a comparable higher-coupon issue in order to realize an instantaneous pickup of current yield and yield-to-maturity.

Tax swaps involve replacement of a bond with a capital loss with a similar security. By selling the bond with the capital loss, an investor can offset a capital gain generated in another part of the portfolio and thereby reduce the overall tax liability. Identical issues cannot be used for this kind of swap; the IRS will rule such swaps as "wash sales" and therefore disallow the capital loss.

Having reviewed these topics please answer the following questions below:

1. Briefly define the following, use examples in your answers

a.) Term Structure of Interest Rates

b.) Yield Curve

c.)Negatively sloped yield curve

2. What do liquidity preference theory and market segmentation theory refer to?

3.) What is the difference between bond immunization and portfolio immunization?

4.) What kind of a relationship is there between price of bonds and interest rates? Use an example in your answer