Expectations Theory

The three forms of the expectations theory (the pure expectations theory, the liquidity preference theory, and the preferred habitat theory) assume that the forward rates in current long-term bonds are closely related to the market’s expectations about future short term rates. The three forms of the expectations theory differ on whether or not other factors also affect forward rates, and how.

Pure Expectations Theory

The pure expectations theory postulates that no systematic factors other than expected future short-term rates affect forward rates. According to the pure expectation theory, forward rates exclusively represent expected future spot rates. Thus, the entire term structure at a given time reflects the market’s current expectations of the family of future short-term rates. A rising term structure must indicate that the market expects short-term rates to rise throughout the relevant future. A flat term structure reflects an expectation that future short-term rates will be mostly constant. A falling term structure must reflect an expectation that future short-term rates will decline. Because forward rates are not perfect predictors of future interest rates, the pure expectations theory neglects the risks (interest rate risk and reinvestment risk) associated with investing in Treasury securities.Advocates of the pure expectations theory argue that forward rates are the market’s consensus of future interest rates. Forward rates have not been found to be good predictors of future interest rates; however, an understanding of forward rates is still extremely important because of their role as break-even rates and rates that can be locked in.

Liquidity Preference Theory

The liquidity preference theory and the preferred habitat theory assert that there are other factors that affect forward rates and these two theories are therefore referred to as biased expectations theories. The liquidity preference theory states that investors will hold longer-term maturities only if they are offered a risk premium and therefore forward rates should reflect both interest rate expectations and a liquidity risk premium. According to the liquidity preference theory, forward rates will not be an unbiased estimate of the market’s expectations of future interest rates because they contain a liquidity premium. Thus, an upward-sloping yield curve may reflect expectations that future interest rates will 1) either rise 2)or be unchanged or even fall. But with a liquidity premium increasing fast enough with maturity so as to produce an upward-sloping yield curve. Any shape for either the yield curve or the term structure of interests rates can be explained by pure expectation and liquidity preference theory jointly. Not by liquidity preference theory individually

Preferred Habitat Theory

The preferred habitat theory, in addition to adopting the view that forward rates reflect the expectation of the future path of interest rates as well as a risk premium, argues that the yield premium need not reflect a liquidity risk but instead reflects the demand and supply of funds in a given maturity range. If there is an imbalance between the supply and demand for funds within a given maturity range, investors and borrowers will shift their investing and financing activities out of their preferred maturity sector to take advantage of any imbalance

Gap Analysis

A traditional measure of interest risk is the maturity gap between assets and liabilities, which is based on the repricing interval of each component of the balance sheet. To compute the maturity gap, the assets and liabilities must be grouped according to their repricing intervals. Within each category, the gap is then expressed as the rand amount of assets minus those of liabilities. Altough the maturity gap suggests how a bank's condition will respond to a given change in interest rate, and thus permits the analyst to get a quick and simple overview of the profile of exposure, the downside of this approach is that it doesn't offer a single summary statistic that expresses the bank's interest rate risk. It also omits some important factors, for example, cash flows, unequal interest rates on assets and liabilities, and initial net worth.

Gap Analysis

A traditional measure of interest risk is the maturity gap between assets and liabilities, which is based on the repricing interval of each component of the balance sheet. To compute the maturity gap, the assets and liabilities must be grouped according to their repricing intervals. Within each category, the gap is then expressed as the rand amount of assets minus those of liabilities. Altough the maturity gap suggests how a bank's condition will respond to a given change in interest rate, and thus permits the analyst to get a quick and simple overview of the profile of exposure, the downside of this approach is that it doesn't offer a single summary statistic that expresses the bank's interest rate risk. It also omits some important factors, for example, cash flows, unequal interest rates on assets and liabilities, and initial net worth.

Duration analysis

Duration can also be used and is usually presented as an account's weighted average time to repricing, where the weights are discounted components of cash flow. A bank will be perfectly hedged when the duration of its assets, weighted by rands of assets, equals to the durations is called the duration gap, and the larger the bank's duration gap is, the more sensitive a bank's net worth will be to a given change in interest rates. The advantages of duration analysis is that it proviedes a simple and accurate basis for hedging portfolios, it can be used as a standard of compariosn for business development and funding strategies, and it provides the essential elemets for the calculation of interest rate elasticity and price elasticity. Several technical factors however, make it difficult to apply duration analysis correctly. First, the detailed information on cash flows required for duration analysis presents a computation and accounting burden. Second, the true cash flow patterns are not well known for certain types of accounts, such as demand deposits, and they arel ikely to vary withthe size or timing of a change in market interest rates, making it harder to quantify the associated interest rate risk. Finally, a more complex version of duration is needed to reflect the fact that, long-term interest rates are not always equal to short-term interest rates and may move independetly from each other.

Duration analysis

Duration can also be used and is usually presented as an account's weighted average time to repricing, where the weights are discounted components of cash flow. A bank will be perfectly hedged when the duration of its assets, weighted by rands of assets, equals to the durations is called the duration gap, and the larger the bank's duration gap is, the more sensitive a bank's net worth will be to a given change in interest rates. The advantages of duration analysis is that it provides a simple and accurate basis for hedging portfolios, it can be used as a standard of comparison for business development and funding strategies, and it provides the essential elements for the calculation of interest rate elasticity and price elasticity. Several technical factors however, make it difficult to apply duration analysis correctly. First, the detailed information on cash flows required for duration analysis presents a computation and accounting burden. Second, the true cash flow patterns are not well known for certain types of accounts, such as demand deposits, and they are likely to vary with the size or timing of a change in market interest rates, making it harder to quantify the associated interest rate risk. Finally, a more complex version of duration is needed to reflect the fact that, long-term interest rates are not always equal to short-term interest rates and may move independently from each other.

Simulation analysis

Some banks simulate the impact of various risk scenarios on their portfolios (Schaffer, 1991). In other words, simulation analysis involves the modelling of changes in the bank’s profitability and value under alternative interest rate scenarios (Payne et al., 1999). The advantages of this technique are that it permits an easy examination of a bank’s interest rate sensitivities and strategies (Cade, 1997), and it replicates the same bottom line as duration theory while bypassing the more sophisticated mathematical deviations. The drawback of this approach is that the need for detailed cash flow data for assets and liabilities are not satisfied and computers alone cannot solve the problem of forecasting cash-flow patterns for some assets and liabilities (Shaffer, 1991).

Scenario analysis

Another approach is to choose interest rate scenarios within which to explore portfolio effects (Schaffer, 1991). Different scenarios must thus be set out and it must be investigated what the bank stand to loose or gain under each of them. Advantages of this approach are that it can be applied to most kinds of risks and that it is less limited by data availability. Schaffer (1991) states that this approach is thus more flexible and it requires less effort. Unfortunately traditional measures of interest rate risk, while convenient, provide only rough approximations at best (Shaffer, 1991) and derivatives must be used in addition.

Cash flow hedge:

This is a hedge against forecasted transactions or the variability in the cash flow of a recognized asset or liability (Landsberg, 2002, p. 11). In this hedge, a variable rate loan can, for example, be converted to a fixed rate loan. It can also hedge the cash flows from returns on securities to be purchased in the future, the cash flow from the future sale of securities, or the cash flow of interest received on an existing loan (Rasch & Colquitt, 1998).

Market value hedge

This is a hedge against exposure to changes in the value of a recognized asset or liability (Landsberg, 2002). In this type of hedge a fixed-rate can, for example, be converted to a variable rate (Rasch & Colquitt, 1998).

Foreign currency hedge:

A forward contract entered into to sell the foreign currency of the foreign operation would, for example, hedge the net investment. Therefore, if the exchange rate decreases, the net investment would also decrease. The forward contract would however increase in value because the currency could be purchased at a lesser amount than the locked-in selling price (Jones et al., 2000).

Other ways to manage interest rate risks.

x Forward contract: This is a legal agreement between two parties to purchase or sell a specific quantity of a commodity, government security or foreign currency or other financial instrument at a price specified now, with delivery and settlement at a specified future date. x Futures contract: This is an agreement to buy and sell a standard quantity and quality of a commodity, financial instrument, or index at a specified future date and price. x Interest rate swap: This is an agreement between two parties to exchange interest payments on a specified principal amount for a specified period. x Option: This is a contract conveying the right, but not the obligation to buy or sell a specified item at a fixed price within a specified period. The buyer of the option pays a non-refundable fee, called a premium, to the writer of the option and the maximum loss is the premium paid for the option. Options can be divided into caps, collars and floors:

DEFINITION OF 'TERM STRUCTURE OF INTEREST RATES'

The relationship between interest rates or bond yields and different terms or maturities. The term structure of interest rates is also known as a yield curve and it plays a central role in an economy. The term structure reflects expectations of market participants about future changes in interest rates and their assessment of monetary policy conditions. In general terms, yields increase in line with maturity, giving rise to an upward sloping yield curve or a "normal yield curve." One basic explanation for this phenomenon is that lenders demand higher interest rates for longer-term loans as compensation for the greater risk associated with them, in comparison to short-term loans. Occasionally, long-term yields may fall below short-term yields, creating an "inverted yield curve" that is generally regarded as a harbinger of recession.

Definition of Current Yield

Annual income (interest or dividends) divided by the current price of the security. This measure looks at the current price of a bond instead of its face value and represents the return an investor would expect if he or she purchased the bond and held it for a year. This measure is not an accurate reflection of the actual return that an investor will receive in all cases because bond and stock prices are constantly changing due to market factors. Current Yield = Annual Cash Inflows / Market Price

Yield Curve Spread

The spread between long-term Treasury yields and short-term Treasury yields is referred to as the steepness or slope of the yield curve

Yield Curve Shift

A shift in the yield curve refers to the relative change in the yield for each Treasury maturity. A parallel shift in the yield curve refers to a shift in which the change in the yield for all maturities is the same; a nonparallel shift in the yield curve means that the yield for all maturities does not change by the same number of basis points.

Yield Curve Shift

A shift in the yield curve refers to the relative change in the yield for each Treasury maturity. A parallel shift in the yield curve refers to a shift in which the change in the yield for all maturities is the same; a nonparallel shift in the yield curve means that the yield for all maturities does not change by the same number of basis points.

Yield to Maturity

YTM is the most popular measure It is the interest rate that will make the present value of the bond’s cash flow equal to its market price plus accrued income. It is the same as the Internal Rate of Return (IRR) Calculations: Trial and error / approximations Calculator Spreadsheet (Excel) The yield to maturity takes into account all three sources of return but assumes that the coupon payments and any principal repayments can be reinvested at an interest rate equal to the yield to maturity. The yield to maturity will only be realized if the interim cash flows can be reinvested at the yield to maturity and the bond is held to maturity. Reinvestment risk is the risk an investor faces that future reinvestment rates will be less than the yield to maturity at the time a bond is purchased.

For a bond selling at a discount (premium), the coupon rate is bigger or smaller than... (current yield and YTM)

For a bond selling at a discount (premium), the coupon rate is ) the current yield, and ) the yield to maturity.

For a bond selling at a discount (premium), the coupon rate is bigger or smaller than... (current yield and YTM)

For a bond selling at a discount (premium), the coupon rate is ) the current yield, and ) the yield to maturity.

Limitations of YTM

YTM is better than current yield because it considers the coupon, capital gain/loss, and reinvestment income. It is also based on the time value of money concepts. However, it assumes that the coupon payments from a bond can be reinvested at an interest rate equal to the yield to maturity. This assumption can be highly misleading because of reinvestment risk We have seen that a term structure of interest rates exists, which can result in different yields at different points in time.

Factors Affecting Reinvestment Risk

Reinvestment risk is the risk an investor faces that future reinvestment rates will be less than the yield to maturity at the time a bond is purchased. Interest rate risk is the risk that if a bond is not held to maturity, an investor may have to sell it for less than the purchase price. The longer the maturity and the higher the coupon rate, the more a bond’s return is dependent on reinvestment income to realize the yield to maturity at the time of purchase.

DEFINITION OF 'BOND EQUIVALENT YIELD - BEY'

A calculation for restating semi-annual, quarterly, or monthly discount-bond or note yields into an annual yield. For a fixed income security with a par value of $1000, the calculation is as follows: ((1000-Purchase Price) / Purchase Price) x (365 / Days to maturity) The BEY allows fixed-income securities whose payments are not annual to be compared with securities with annual yields. The BEY is the yield that is quoted in newspapers. Alternatively, if the semi-annual or quarterly yield to maturity of a bond is known, the APR calculation may be used.

Yield to Call

For callable bonds, the practice has been to calculate a YTM and a yield to call (YTC) The YTC assumes the issuer will call the bond on the call date at the specified call price Investors calculate the yield to first call, yield to next call, yield to first par call, and a yield to refunding. Yield to refunding is used when bonds are currently callable buthave some restrictions on the source of the funds used to buy back the debt when a call is exercised.

Yield to Call

For callable bonds, the practice has been to calculate a YTM and a yield to call (YTC) The YTC assumes the issuer will call the bond on the call date at the specified call price Investors calculate the yield to first call, yield to next call, yield to first par call, and a yield to refunding. Yield to refunding is used when bonds are currently callable buthave some restrictions on the source of the funds used to buy back the debt when a call is exercised.

Yield to Put

When a bond is putable, the yield to the put date is computed. The yield to put is computed assuming that the issue will be put on the first put date. The yield to put is the interest rate that will make the present value of the cash flows to the first put date equal to the price plus accrued interest. Like other yield measures, the yield to put assumes that any interim coupon payments can be reinvested at the yield calculated.

Theoretical Spot Rates

The theoretical spot rate is the interest rate that should be used to discount a default-free cash flow. Because there are a limited number of on-the-run Treasury securities traded in the market, interpolation is required to obtain the yield for interim maturities; hence, the yield for most maturities used to construct the Treasury yield curve are interpolated yields rather than observed yields. Default-free spot rates can be derived from the Treasury yield curve by a method called bootstrapping. The basic principle underlying the bootstrapping method is that the value of a Treasury coupon security is equal to the value of the package of zero- coupon Treasury securities that duplicates the coupon bond’s cash flows.

Spot Rate and forward rates for Fixed Income Securities

A spot rate is a rate agreed upon today, for a loan that is to be made today. (e.g. r1 = 5% indicates that the current rate for a one-year loan is 5%)

A forward rate is a rate agreed upon today, for a loan that is to be made in the future. (e.g. _{2}f_{1} = 7% indicates that we could contract today to borrow money at 7% for one year, starting two years from today).

General Formulas for Forward Rates

Straight Bond

A bond that pays interest at regular intervals, and at maturity pays back the principal that was originally invested. Straight bonds are debt instruments because they are essentially loaning money (creating debt) to an entity. The entity (government, municipality, or organization) promises to pay the interest on the "debt" and at maturity pay back the original loan.

A straight bond is the most basic of debt investments. It is also knows as a plain vanilla bond because there are no additional features that other bonds might have. For example, some bonds can be converted into shares of common stock. As with all bonds there is default risk, which is the risk that the company could go bankrupt and no longer honor its debt obligations.

DEFINITION OF 'DURATION'

A measure of the sensitivity of the price (the value of principal) of a fixed-income investment to a change in interest rates. Duration is expressed as a number of years. Rising interest rates mean falling bond prices, while declining interest rates mean rising bond prices.

The duration number is a complicated calculation involving present value, yield, coupon, final maturity and call features. Fortunately for investors, this indicator is a standard data point provided in the presentation of comprehensive bond and bond mutual fund information. The bigger the duration number, the greater the interest-rate risk or reward for bond prices.

It is a common misconception among non-professional investors that bonds and bond funds are risk free. They are not. Investors need to be aware of two main risks that can affect a bond's investment value: credit risk (default) and interest rate risk (rate fluctuations). The duration indicator addresses the latter issue.

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