FINC 331-WEEK 4: Bonds
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Bond Valuation
The Basics of Interest Rates
Additional Detail on Interest Rates
Key Characteristics of Bonds
Understanding Bonds
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Advantages and Disadvantages of Bonds
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Bond Valuation (continued)
Types of Bonds
Bond Markets
Valuing Bonds
Bond Risk
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Understanding the Cost of Money
Interest Rate Levels
Drivers of Market Interest Rates
The Term Structure
The Basics of Interest Rates
Bond Valuation > The Basics of Interest Rates
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The concept of the cost of money has its basis, as does the subject of finance in general, in the time value of money.
The time value of money refers to the fact that a dollar in hand today is worth more than a dollar promised at some future time.
The trade-off between money now (holding money) and money later (investing) depends on, among other things, the rate of interest you can earn by investing. Therefore, interest is the cost of money.
Understanding the Cost of Money
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Cost Of Money
Bond Valuation > The Basics of Interest Rates
In the U.S., the Federal Reserve (often referred to as 'The Fed') implements monetary policies largely by targeting the federal funds rate.
Expansionary monetary policy is traditionally used to try to combat unemployment in a recession by lowering interest rates in the hope that easy credit will entice businesses into expanding.
Contractionary monetary policy is intended to slow inflation in hopes of avoiding the resulting distortions and deterioration of asset values.
Crowding out is a phenomenon occurring when expansionary fiscal policy causes interest rates to rise, thereby reducing investment spending.
Interest Rate Levels
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Federal fund rates
Bond Valuation > The Basics of Interest Rates
A market interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender in the market.
Economists generally agree that the interest rates yielded by any investment take into account: the risk-free cost of capital, inflationary expectations, the level of risk in the investment, and the costs of the transaction.
A basic interest rate pricing model for an asset is presented by the following formula: in = ir + pe + rp + lp.
Drivers of Market Interest Rates
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Worldwide Inflation Rates 2009
Bond Valuation > The Basics of Interest Rates
Term structure of interest rates is often referred to as the yield curve.
The expectation hypothesis of the term structure of interest rates is the proposition that the long-term rate is determined by the market's expectation for the short-term rate plus a constant risk premium.
The liquidity premium theory asserts that long-term interest rates not only reflect investors' assumptions about future interest rates but also include a premium for holding long-term bonds.
In the segmented market hypothesis, financial instruments of different terms are not substitutable; therefore, supply and demand in the markets for short-term and long-term instruments is determined largely independently.
The Term Structure
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Yield curve for USD
Bond Valuation > The Basics of Interest Rates
The Yield Curve
Using the Yield Curve to Estimate Interest Rates in the Future
Macroeconomic Factors Influencing the Interest Rate
Additional Detail on Interest Rates
Bond Valuation > Additional Detail on Interest Rates
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In finance the yield curve is a curve showing several yields or interest rates across different contract lengths for a similar debt contract.
Based on the shape of the yield curve, we have normal yield curves, steep yield curves, flat or humped yield curves, and inverted yield curves.
There are three main economic theories that attempt to explain different term structures of interest rates, namely the expectation hypothesis, the liquidity premium theory, and the segmented market hypothesis.
The Yield Curve
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Israel Shekel yield curve
Bond Valuation > Additional Detail on Interest Rates
A normal yield curve tells us that investors believe the Federal Reserve is going to raise interest rates in the future.
A flat yield tells us that investors believe the Federal Reserve is going to be cutting interest rates.
An inverted yield curve tells us that investors believe the Federal Reserve is going to dramatically cut interest rates.
A flat curve expects unchanged interest rates in the future, sending signals of uncertainty in the economy.
An inverted yield curve occurs when long-term yields fall below short-term yields, indicating a fall in interest rates in the future.
Using the Yield Curve to Estimate Interest Rates in the Future
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Normal Yield Curve
Bond Valuation > Additional Detail on Interest Rates
In economics, the Taylor rule is a monetary-policy rule that stipulates how much the Central Bank should change the nominal interest rate in response to changes in inflation, output, or other economic conditions.
If the inflationary expectation goes up, then so does the market interest rate and vice versa.
If output gap is positive, it is called an "inflationary gap," possibly creating inflation, signaling a increase in interest rates made by the Central Bank; if output gap is negative, it is called a "recessionary gap," possibly signifying deflation and a reduction in interest rates.
Macroeconomic Factors Influencing the Interest Rate
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Interest Rates in Turkey
Bond Valuation > Additional Detail on Interest Rates
Par Value
Coupon Interest Rate
Maturity Date
Call Provisions
Sinking Funds
Other Features
Key Characteristics of Bonds
Bond Valuation > Key Characteristics of Bonds
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When a bond trades at a price above the face value, it is said to be selling at a premium. When a bond sells below face value, it is said to be selling at a discount.
A bond's price fluctuates throughout its life in response to a number of variables, including interest rates and time to maturity.
Pull to par is the effect in which the price of a bond converges to par value as time passes. At maturity, the price of a debt instrument in good standing should equal its par (or face value).
Par Value
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Temporary bonds for the state of Kansas issued in 1922
Bond Valuation > Key Characteristics of Bonds
Coupon interest rate is usually fixed throughout the life of the bond. It can also vary with a money market index.
Not all bonds have coupons. Zero-coupon bonds are those that pay no coupons and thus have a coupon rate of 0%.
Based on different coupon rates, there are fixed rate bonds, floating rate bonds, and inflation linked bonds.
Coupon Interest Rate
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Mecca Temple 1922 Bond Coupons
Bond Valuation > Key Characteristics of Bonds
As long as all due payments have been made, the issuer has no further obligations to the bond holders after the maturity date.
The length of time until the maturity date is often referred to as the term or tenor or maturity of a bond.
In the market for United States Treasury securities, there are three categories of bond maturities: short term, medium term, and long term.
Maturity Date
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Austrian war bond
Bond Valuation > Key Characteristics of Bonds
A callable bond is a type of bond that allows the issuer of the bond to retain the privilege of redeeming the bond at some point before the bond reaches its date of maturity.
If interest rates in the market have gone down by the time of the call date, the issuer will be able to refinance its debt at a cheaper level and so will be incentivized to call the bonds it originally issued.
Most callable bonds allow the issuer to repay the bond at par. With some bonds, the issuer has to pay a premium, known as the call premium.
Price of callable bond = Price of straight bond – Price of call option. Price of a callable bond is always lower than the price of a straight bond because the call option adds value to an issuer.
Call Provisions
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Redeemed Bonds
Bond Valuation > Key Characteristics of Bonds
Sinking fund provision of the corporate bond indenture requires a certain portion of the issue to be retired periodically.
A sinking fund reduces credit risk but presents reinvestment risk to bondholders.
For the creditors, the fund reduces the risk the organization will default when the principal is due: it reduces credit risk. However, if the bonds are callable, this comes at a cost to creditors, because the organization has an option on the bonds.
Sinking Funds
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Farm bond
Bond Valuation > Key Characteristics of Bonds
The yield is the rate of return received from investing in the bond. It usually refers either to the current yield, or to the yield to maturity or redemption yield.
The market price of a tradeable bond will be influenced by the amounts, currency and timing of the interest payments and capital repayment due, the quality of the bond, and the available redemption yield of other comparable bonds which can be traded in the markets.
Some bonds give the holder the right to force the issuer to repay the bond before the maturity date on the put dates. These are referred to as retractable or putable bonds.
Other Features
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San Francisco Pacific Railroad Bond
Bond Valuation > Key Characteristics of Bonds
The Nature of Bonds
Duration
Indenture
Ratings
Understanding Bonds
Bond Valuation > Understanding Bonds
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A bond is an instrument of indebtedness of the bond issuer to the holders. The issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay them interest (the coupon) and/or to repay the principal at a later date, termed the maturity.
Bonds provide the borrower with external funds to finance long-term investments, or, in the case of government bonds, to finance current expenditure.
Bonds and stocks are both securities, but the major difference between the two is that (capital) stockholders have an equity stake in the company (i.e. they are owners), whereas bondholders have a creditor stake in the company (i.e. they are lenders).
The Nature of Bonds
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A bond from the Dutch East India Company
Bond Valuation > Understanding Bonds
A good approximation for bond price changes due to yield is the duration, a measure for interest rate risk.
The Macaulay duration is the name given to the weighted average time until cash flows are received and is measured in years. It really makes sense only for an instrument with fixed cash flows.
The modified duration is the name given to the price sensitivity and is the percentage change in price for a unit change in yield. It really makes sense only for an instrument with fixed cash flows.
The modified duration is a derivative (rate of change) or price sensitivity and measures the percentage rate of change of price with respect to yield. The concept of modified duration can be applied to interest-rate sensitive instruments with non-fixed cash flows.
Duration
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Macaulay duration
Bond Valuation > Understanding Bonds
Terms of indentures include the interest rate, maturity date, repayment dates, convertibility, pledge, promises, representations, covenants, and other terms of the bond offering.
A bond indenture is held by a trustee. If the company fails to live up to the terms of the bond indenture, the trustee may bring legal action against the company on behalf of the bondholders.
The offering memorandum, also known as a prospectus, is a document that describes a financial security for potential buyers.
Indenture
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Indenture
Bond Valuation > Understanding Bonds
Ratings play a critical role in determining how much companies and other entities that issue debt, including sovereign governments, have to pay to access credit markets; for example, the amount of interest they pay on their issued debt.
The ratings are assigned by credit rating agencies such as Moody's, Standard & Poor's, and Fitch. Ratings to have letter designations (such as AAA, B, CC), which represent the quality of a bond.
A bond is considered investment-grade (IG) if its credit rating is BBB- or higher by Standard & Poor's, or Baa3 or higher by Moody's, or BBB(low) or higher by DBRS. Bond ratings below BBB/Baa are not considered to be investment grade; such bonds are called junk bonds.
Ratings
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Credit Rating Equivalents
Bond Valuation > Understanding Bonds
Advantages of Bonds
Disadvantages of Bonds
Advantages and Disadvantages of Bonds
Bond Valuation > Advantages and Disadvantages of Bonds
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Bonds are a debt security under which the issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay them interest (the coupon) and or repay the principal at a later date, which is termed the maturity.
The volatility of bonds (especially short and medium dated bonds) is lower than that of equities (stocks). Thus bonds are generally viewed as safer investments than stocks.
Bonds are often liquid – it is often fairly easy for an institution to sell a large quantity of bonds without affecting the price much.
Bondholders also enjoy a measure of legal protection: under the law of most countries, if a company goes bankrupt, its bondholders will often receive some money back (the recovery amount).
There are also a variety of bonds to fit different needs of investors.
Advantages of Bonds
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San Francisco Pacific Railroad Bond
Bond Valuation > Advantages and Disadvantages of Bonds
A bond is an instrument of indebtedness of the bond issuer to the holders. It is a debt security under which the issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay them interest and possibly repay the principal at a later date, which is termed the maturity.
Fixed rate bonds are subject to interest rate risk, meaning that their market prices will decrease in value when the generally prevailing interest rates rise.
Bonds are also subject to various other risks such as call and prepayment risk, credit risk, reinvestment risk, liquidity risk, event risk, exchange rate risk, volatility risk, inflation risk, sovereign risk, and yield curve risk.
A company's bondholders may lose much or all their money if the company goes bankrupt. There is no guarantee of how much money will remain to repay bondholders.
Some bonds are callable. This creates reinvestment risk, meaning the investor is forced to find a new place for his money. As a consequence, the investor might not be able to find as good a deal, especially because this usually happens when interest rates are falling.
Disadvantages of Bonds
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Bond
Bond Valuation > Advantages and Disadvantages of Bonds
Government Bonds
Zero-Coupon Bonds
Floating-Rate Bonds
Other Types of Bonds
Types of Bonds
Bond Valuation > Types of Bonds
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A government bond is a bond issued by a national government, generally promising to pay a certain amount (the face value) on a certain date, as well as periodic interest payments. Such bonds are often denominated in the country's domestic currency.
In the primary market, Government Bonds are often issued via auctions at Stock Exchanges. In the secondary market, government bonds are traded at Stock Exchanges.
Although, government bonds are usually referred to as risk-free, there are currency, inflation, and default risks for government bondholders.
Government Bonds
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Government Bond
Bond Valuation > Types of Bonds
Zero-coupon bonds may be created from fixed rate bonds by a financial institution separating ("stripping off") the coupons from the principal. In other words, the separated coupons and the final principal payment of the bond may be traded separately.
Zero coupon bonds have a duration equal to the bond's time to maturity, which makes them sensitive to any changes in the interest rates.
Pension funds and insurance companies like to own long maturity zero-coupon bonds since these bonds' prices are particularly sensitive to changes in the interest rate and, therefore, offset or immunize the interest rate risk of these firms' long-term liabilities.
Zero-Coupon Bonds
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SMAC bond
Bond Valuation > Types of Bonds
FRBs are typically quoted as a spread over the reference rate. At the beginning of each coupon period, the coupon is calculated by taking the fixing of the reference rate for that day and adding the spread. A typical coupon would look like three months USD LIBOR +0.20%.
FRBs carry little interest rate risk. A FRB has a duration close to zero, and its price shows very low sensitivity to changes in market rates. As FRBs are almost immune to interest rate risk. The risk that remains is a credit risk.
Securities dealers make markets in FRBs. They are traded over the counter, instead of on a stock exchange. In Europe, most FRBs are liquid, as the biggest investors are banks. In the United States, FRBs are mostly held to maturity, so the markets aren't as liquid.
Floating-Rate Bonds
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Municipal bond
Bond Valuation > Types of Bonds
Bonds directly linked to interest rates include fixed rate bonds, floating rate bonds, and zero coupon bonds.
Convertible bonds are bonds that let a bondholder exchange a bond to a number of shares of the issuer's common stock. Exchangeable bonds allows for exchange to shares of a corporation other than the issuer.
Asset-backed securities are bonds whose interest and principal payments are backed by underlying cash flows from other assets.
Subordinated bonds are those that have a lower priority than other bonds of the issuer in case of liquidation.
Foreign currency bonds are issued by companies, banks, governments, and other sovereign entities in foreign currencies, as it may appear to be more stable and predictable than their domestic currency.
Other Types of Bonds
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Government Bond
Bond Valuation > Types of Bonds
Purchase Process
Price Transparency
Bond Markets
Bond Valuation > Bond Markets
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Buying a bond involves setting up an account with a broker and requesting that the broker buy bonds on the buyer's behalf.
An individual can also purchase bonds by investing in bond funds, which hold baskets of bonds rather than competing for individual bond sales.
Most bond funds pay out dividends more frequently than individual bonds.
Purchase Process
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Bond Brokers
Bond Valuation > Bond Markets
A market is transparent if much is known–by many–about what products, services, or capital assets are available at what price and where.
In most developed bond markets, such as the United States, Japan, and western Europe, bonds trade in decentralized, dealer-based, over-the-counter markets.
Poor transparency contributes to investor differences in bond valuations, as well as other inefficiencies that may lead to economic losses for market participants and, ultimately, inhibit business development.
Price Transparency
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New York Stock Exchange
Bond Valuation > Bond Markets
Present Value of Payments
Par Value at Maturity
Yield to Maturity
Inflation Premium
Differences Between Real and Nominal Rates
Time to Maturity
Calculating Yield to Maturity Using the Bond Price
Impact of Payment Frequency on Bond Prices
Deciding to Refund Bonds
Valuing Bonds
Bond Valuation > Valuing Bonds
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The bond price can be summarized as the sum of the present value of the par value repaid at maturity and the present value of coupon payments.
The present value of coupon payments is the present value of an annuity of coupon payments.
The present value of an annuity is the value of a stream of payments, discounted by the interest rate to account for the payments being made at various moments in the future.
Present Value of Payments
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Bond Price
Bond Valuation > Valuing Bonds
A bond selling at par has a coupon rate such that the bond is worth an amount equivalent to its original issue value or its value upon redemption at maturity.
A typical bond makes coupon payments at fixed intervals during the life of it and a final repayment of par value at maturity. Together with coupon payments, the par value at maturity is discounted back to the time of purchase to calculate the bond price.
Par value of a bond usually does not change, except for inflation-linked bonds whose par value is adjusted by inflation rates every predetermined period of time.
Par Value at Maturity
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Bond Price Formula
Bond Valuation > Valuing Bonds
The Yield to maturity is the internal rate of return earned by an investor who bought the bond today at the market price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule.
Yield to maturity(YTM) = [(Face value/Present value)1/Time period]-1.
If the YTM is less than the bond's coupon rate, then the market value of the bond is greater than par value (premium bond). If a bond's coupon rate is less than its YTM, then the bond is selling at a discount. If a bond's coupon rate is equal to its YTM, then the bond is selling at par.
There are some variants of YTM: yield to call, yield to put, yield to worst...
Yield to Maturity
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Yield to Maturity
Bond Valuation > Valuing Bonds
Investors seek this premium to compensate for the erosion in the value of their capital due to inflation.
Actual interest rates (without factoring in inflation) are viewed by economists and investors as being the nominal (stated) interest rate minus the inflation premium.
Letting r denote the real interest rate, i denote the nominal interest rate, and let π denote the inflation rate, the Fisher equation is: i = r + π. In the Fisher equation, π is the inflation premium.
Inflation Premium
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Inflation rate graph
Bond Valuation > Valuing Bonds
Nominal rate refers to the rate before adjustment for inflation; the real rate is the nominal rate minus inflation.
Fisher equation states that the real interest rate is approximately the nominal interest rate minus the inflation rate: 1 + i = (1+r) (1+E(r)).
Simple equation between nominal rates and real rates: i = R - r.
Differences Between Real and Nominal Rates
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Real and nominal
Bond Valuation > Valuing Bonds
The maturity can be any length of time, but debt securities with a term of less than one year are generally not designated as bonds. Instead, they are considered money market instruments.
In the market for United States Treasury securities, there are three categories of bond maturities: short-term, medium-term and long-term bonds.
A bond that takes longer to mature necessarily has a greater duration. The bond price in this type of a situation, therefore, is more sensitive to changes in interest rates.
Time to Maturity
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Money market interest rates
Bond Valuation > Valuing Bonds
To achieve a return equal to YTM (i.e., where it is the required return on the bond), the bond owner must buy the bond at price P0, hold the bond until maturity, and redeem the bond at par.
If a bond's coupon rate is less than its YTM, then the bond is selling at a discount. If a bond's coupon rate is more than its YTM, then the bond is selling at a premium. If a bond's coupon rate is equal to its YTM, then the bond is selling at par.
Formula for yield to maturity: Yield to maturity(YTM) = [(Face value/Bond price)1/Time period]-1.
Calculating Yield to Maturity Using the Bond Price
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USD Yield Curve
Bond Valuation > Valuing Bonds
Payment frequency can be annual, semi annual, quarterly, monthly, weekly, daily, or continuous.
Bond price is the sum of the present value of face value paid back at maturity and the present value of an annuity of coupon payments. The present value of face value received at maturity is the same. However, the present values of annuities of coupon payments vary among payment frequencies.
The more frequent a bond makes coupon payments, the higher the bond price, given equal coupon, par, and face.
Impact of Payment Frequency on Bond Prices
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Bond price formula
Bond Valuation > Valuing Bonds
The issue of new, lower-interest debt allows the company to prematurely refund the older, higher-interest debt.
Bond refunding occurs when a) interest rates in the market are sufficiently less than the coupon rate on the old bond, b) the price of the old bond is less than par. and c) the sinking fund has accumulated enough money to retire the bond issue.
The decision of whether to refund a particular debt issue is usually based on a capital budgeting (present value) analysis.
Deciding to Refund Bonds
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French Bond
Bond Valuation > Valuing Bonds
Price Risk
Reinvestment Risk
Comparing Price Risk and Reinvestment Risk
Default Risk
Bond Rating System
Bankruptcy and Bond Value
Bond Risk
Bond Valuation > Bond Risk
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The market price of bonds will decrease in value when the generally prevailing interest rates rise and vice versa.
Unless you plan to buy or sell them in the open market, changing interest rates do not affect the interest payments to the bondholder.
Price changes in a bond will immediately affect mutual funds that hold these bonds. If the value of the bonds in their trading portfolio falls, the value of the portfolio also falls.
Price Risk
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Bond price and yield
Bond Valuation > Bond Risk
Reinvestment risk is more likely when interest rates are declining.
Reinvestment risk affects the yield-to-maturity of a bond, which is calculated on the premise that all future coupon payments will be reinvested at the interest rate in effect when the bond was first purchased.
Two factors that have a bearing on the degree of reinvestment risk are maturity of the bond and the coupon interest rate.
Reinvestment Risk
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Interest rates
Bond Valuation > Bond Risk
Price risk and reinvestment risk are both the uncertainty associated with the effects of changes in market interest rates.
Price risk and changes in interest rates are positively correlated.
Reinvestment risk and changes in interest rates are inversely correlated.
Comparing Price Risk and Reinvestment Risk
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Pacific Railroad Bond
Bond Valuation > Bond Risk
With default risk, the risk is primarily that of the bondholder and includes lost principal and interest, disruption to cash flows, and increased collection costs.
To reduce the bondholders' credit risk, the lender may perform a credit check on the prospective borrower and may require the issuer to take out appropriate insurance.
A company's bondholders may lose much or all their money if the company goes bankrupt. There is no guarantee of how much money will remain to repay bondholders.
Default Risk
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Prices of sovereign credit default swaps
Bond Valuation > Bond Risk
In investment, the bond credit rating assesses the credit worthiness of a corporation's or government debt issues.
The credit rating is a financial indicator to potential investors of debt securities, such as bonds. These are assigned by credit rating agencies such as Moody's, Standard & Poor's, and Fitch Ratings to have letter designations (such as AAA, B, CC) which represent the quality of a bond.
Bond ratings below BBB-/Baa are considered not to be investment grade and are colloquially called junk bonds.
Bond Rating System
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Bond rating
Bond Valuation > Bond Risk
When a business is unable to service its debt or pay its creditors, it or its creditors can file with a federal bankruptcy court for protection under either Chapter 7 or Chapter 11 of the Bankruptcy code.
If a company goes bankrupt, its bondholders will often receive some money back (the recovery amount).
In a bankruptcy involving reorganization or recapitalization, as opposed to liquidation, bondholders may end up having the value of their bonds reduced, often through an exchange for a smaller number of newly-issued bonds.
Bankruptcy and Bond Value
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Bankruptcy Courthouse
Bond Valuation > Bond Risk
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Appendix
Key terms
abscond To flee; to withdraw from.
annuity A specified income payable at stated intervals for a fixed or a contingent period, often for the recipient's life, in consideration of a stipulated premium paid either in prior installment payments or in a single payment. For example, a retirement annuity paid to a public officer following his or her retirement.
asset-backed securities An asset-backed security is a security that has value and income payments derived from and collateralized (or "backed") by a specified pool of underlying assets. The pool of assets is typically a group of small and illiquid assets that are unable to be sold individually.
bond funds A bond fund or debt fund is a fund that invests in bonds or other debt securities. Bond funds can be contrasted with stock funds and money funds.
call premium the additional cost paid by the issuer for the right to buy back the bond at a predtermined price at a certain time in the future
call provision the right for the issuer to buy back the bond at a predetermined price at a certain time in future
callable A callable bond (also called "redeemable bond") is a type of bond (debt security) that allows the issuer of the bond to retain the privilege of redeeming the bond at some point before the bond reaches its date of maturity.
clean price the price of a bond excluding any interest that has accrued since issue or the most recent coupon payment.
convertibility Quality of a bond that allows the holder to convert into shares of common stock in the issuing company or cash of equal value, at an agreed-upon price.
Convertible bonds A convertible bond is a type of bond that the holder can convert into shares of common stock in the issuing company or cash of equal value, at an agreed-upon price.
Convexity As interest rates change, the price does not change linearly, but rather is a convex function of interest rates. Convexity is a measure of the curvature of how the price of a bond changes as the interest rate changes. Specifically, duration can be formulated as the first derivative of the price function of the bond with respect to the interest rate in question, and the convexity as the second derivative.
corporate bonds A corporate bond is a bond issue by a corporation. It is a bond that a corporation issues to raise money effectively in order to expand its business.
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Bond Valuation
credit rating agencies A credit rating agency (CRA) is a company that assigns credit ratings to issuers of certain types of debt obligations, as well as to the debt instruments themselves.
debentures A debenture is a document that either creates a debt or acknowledges it, and it is a debt without collateral.
discount rate The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value.
discount rate The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value.
duration A measure of the sensitivity of the price of a financial asset to changes in interest rates, computed for a simple bond as a weighted average of the maturities of the interest and principal payments associated with it
duration A measure of the sensitivity of the price of a financial asset to changes in interest rates, computed for a simple bond as a weighted average of the maturities of the interest and principal payments associated with it
duration A measure of the sensitivity of the price of a financial asset to changes in interest rates, computed for a simple bond as a weighted average of the maturities of the interest and principal payments associated with it
Exchange rate risk The exchange rate risk is a financial risk posed by an exposure to unanticipated changes in the exchange rate between two currencies.
floating-rate bond a debt instruments with a variable coupon
gross domestic product A measure of the economic production of a particular territory in financial capital terms over a specific time period.
hedge funds An investment fund that can undertake a wider range of investment and trading activities than other funds, but which is generally only open to certain types of investors specified by regulators.
immunize In finance, interest rate immunization is a strategy that ensures that a change in interest rates will not affect the value of a portfolio. Similarly, immunization can be used to ensure that the value of a pension fund's or a firm's assets will increase or decrease in exactly the opposite amount of their liabilities, thus leaving the value of the pension fund's surplus or firm's equity unchanged, regardless of changes in the interest rate.
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Bond Valuation
indenture a document, written as duplicates separated by indentations, specifying such a contract
inflation An increase in the general level of prices or in the cost of living.
inflation-linked bonds Inflation-indexed bonds (also known as inflation-linked bonds or colloquially as linkers) are bonds where the principal is indexed to inflation. They are thus designed to cut out the inflation risk of an investment.
inflation-linked bonds Inflation-indexed bonds (also known as inflation-linked bonds or colloquially as linkers) are bonds where the principal is indexed to inflation. They are thus designed to cut out the inflation risk of an investment.
inflationary gap An inflationary gap, in economics, is the amount by which the real gross domestic product, or real GDP, exceeds potential GDP.
insolvent Unable to pay one's bills as they fall due.
interest rate The percentage of an amount of money charged for its use per some period of time. It can also be thought of as the cost of not having money for one period, or the amount paid on an investment per year.
interest rate risk the potential for loss that arises for bond owners from fluctuating interest rates
internal rate of return IRR. The rate of return on an investment which causes the net present value of all future cash flows to be zero.
LIBOR The London Interbank Offered Rate is the average interest rate estimated by leading banks in London that they would be charged if borrowing from other banks.
LIBOR The London Interbank Offered Rate is the average interest rate estimated by leading banks in London that they would be charged if borrowing from other banks.
liquidated In law, liquidation is the process by which a company (or part of a company) is brought to an end and the assets and property of the company redistributed.
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Bond Valuation
liquidation The selling of the assets of a business as part of the process of dissolving the business.
liquidity Availability of cash over short term: ability to service short-term debt.
Liquidity premium Liquidity premium is a term used to explain a difference between two types of financial securities (e.g. stocks), that have all the same qualities except liquidity.
market liquidity In business, economics or investment, market liquidity is an asset's ability to be sold without causing a significant movement in the price and with minimum loss of value.
monetary policy The process by which the monetary authority of a country controls the supply of money, often targeting a rate of interest for the purpose of promoting economic growth and stability.
money market A market for trading short-term debt instruments, such as treasury bills, commercial paper, bankers' acceptances, and certificates of deposit
municipal bonds A municipal bond is a bond issued by an American city or other local government, or their agencies.
mutual funds A type of professionally-managed collective investment vehicle that pools money from many investors to purchase securities. While there is no legal definition, the term is most commonly applied only to those collective investment vehicles that are regulated, available to the general public and open-ended in nature.
Opportunity cost The cost of an opportunity forgone (and the loss of the benefits that could be received from that opportunity); the most valuable forgone alternative.
par Equal value; equality of nominal and actual value; the value expressed on the face or in the words of a certificate of value, as a bond or other commercial paper.
par value the stated value or amount of a bill or a note
Pension funds A pension fund is any plan, fund, or scheme which provides retirement income.
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Bond Valuation
Pension funds Any plan, fund, or scheme which provides retirement income.
Preferred Stock Stock with a dividend, usually fixed, that is paid out of profits before any dividend can be paid on common stock. It also has priority to common stock in liquidation.
premium the price above par value at which a security is sold
premium bond a debt instrument bought at a price above par value
public debt offerings A public debt offering is the offering of debt securities of a government, a company or a similar corporation to the public.
purchasing power Purchasing power (sometimes retroactively called adjusted for inflation) is the amount of goods or services that can be purchased with a unit of currency.
purchasing power Purchasing power (sometimes retroactively called adjusted for inflation) is the amount of goods or services that can be purchased with a unit of currency.
purchasing power parity a theory of long-term equilibrium exchange rates based on relative price levels of two countries
puttable Puttable bond (put bond, putable, or retractable bond) is a bond with an embedded put option. The holder of the puttable bond has the right, but not the obligation, to demand early repayment of the principal.
quote To name the current price, notably of a financial security.
Real interest rate The "real interest rate" is the rate of interest an investor expects to receive after allowing for inflation. It can be described more formally by the Fisher equation, which states that the real interest rate is approximately the nominal interest rate minus the inflation rate.
recapitalization A restructuring of a company's mixture of equity and debt.
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Bond Valuation
Recessionary gap An inflationary gap, in economics, is the amount by which the real Gross domestic product, or real GDP, is less than the potential GDP.
Reinvestment risk The reinvestment risk is the possibility that the investor might be forced to find a new place for his money. As a consequence, the investor might not be able to find as good a deal, especially because this usually happens when interest rates are falling.
resale market The resale market, also called "secondary market" or "aftermarket," is the financial market in which previously issued financial instruments, such as stock, bonds, options, and futures, are bought and sold.
risk premium A risk premium is the minimum amount of money by which the expected return on a risky asset must exceed the known return on a risk-free asset, or the expected return on a less risky asset, in order to induce an individual to hold the risky asset rather than the risk-free asset.
sinking fund A sinking fund is a fund established by a government agency or business for the purpose of reducing debt by repaying or purchasing outstanding loans and securities held against the entity. It helps keep the borrower liquid so it can repay the bondholder.
straight bond A straight bond is a bond with no embedded options (call or put options).
systematic risks In finance and economics, systematic risk (sometimes called aggregate risk, market risk, or undiversifiable risk) is vulnerability to events which affect aggregate outcomes such as broad market returns, total economy-wide resource holdings, or aggregate income.
term structure of interest rates the relationship between the interest on a debt contract and the maturity of the contract
time value of money The value of money, figuring in a given amount of interest, earned over a given amount of time.
tranches One of a number of related securities offered as part of the same transaction.
transparency (figuratively) openness, degree of accessibility to view
treasury bill Treasury bills (or T-Bills) mature in one year or less. They do not pay interest prior to maturity; instead they are sold at a discount of the par value to create a positive yield to maturity.
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Bond Valuation
treasury bill A United States Treasury security is a government debt issued by the United States Department of the Treasury through the Bureau of the Public Debt. Treasury securities are the debt financing instruments of the United States federal government. They are often referred to simply as treasuries. There are four types of marketable treasury securities: Treasury bills, Treasury notes, Treasury bonds, and Treasury Inflation Protected Securities (TIPS), in which Treasury bills have the shortest maturity of one year or less.
Treasury bond Treasury bonds (T-Bonds, or the long bond) have the longest maturity of government securities, from 20 to 30 years. They have a coupon payment every six months, and are commonly issued with maturity of 30 years
Treasury bond A United States Treasury security is a government debt issued by the United States Department of the Treasury through the Bureau of the Public Debt. Treasury securities are the debt financing instruments of the United States federal government, and they are often referred to simply as Treasuries. There are four types of marketable treasury securities: Treasury bills, Treasury notes, Treasury bonds, and Treasury Inflation Protected Securities (TIPS), in which Treasury bonds have the longest maturity, from 20 years to 30 years.
Treasury bonds A United States Treasury bond is a government debt issued by the United States Department of the Treasury through the Bureau of the Public Debt, with a maturity of 20 years to 30 years.
yield curve the graph of the relationship between the interest on a debt contract and the maturity of the contract
Yield to maturity The yield to maturity (YTM) of a bond or other fixed-interest security, such as gilts, is the internal rate of return (IRR, overall interest rate) earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity and that all coupon and principal payments will be made on schedule.
Yield to maturity The internal rate of return on a bond held to maturity, assuming scheduled payment of principal and interest.
Yield to maturity The Yield to maturity (YTM) or redemption yield of a bond or other fixed-interest security, such as gilts, is the internal rate of return (IRR, overall interest rate) earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule.
Zero coupon bonds A zero-coupon bond (also called a discount bond or deep discount bond) is a bond bought at a price lower than its face value, with the face value repaid at the time of maturity.
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Bond Valuation
Eurozone Government Bonds Yield
Development of yield to maturity of bonds of 2019 maturity of a number of Eurozone governments.