Fixed Income
Content
TYPES PF BONDS
Types
The following descriptions are not mutually exclusive, and more than one of them may apply to a particular bond.
Fixed rate bonds have a coupon that remains constant throughout the life of the bond. Floating rate notes (FRNs) have a variable coupon that is linked to a reference rate of interest, such as LIBOR or Euribor. For example the coupon may be defined as three month USD LIBOR + 0.20%. The coupon rate is recalculated periodically, typically every one or three months.
Zero-coupon bonds pay no regular interest. They are issued at a substantial discount to par value, so that the interest is effectively rolled up to maturity (and usually taxed as such). The bondholder receives the full principal amount on the redemption date. An example of zero coupon bonds is Series E savings bonds issued by the U.S. government. 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. See IO (Interest Only) and PO (Principal Only).
Inflation linked bonds, in which the principal amount and the interest payments are indexed to inflation. The interest rate is normally lower than for fixed rate bonds with a comparable maturity (this position briefly reversed itself for short-term UK bonds in December 2008). However, as the principal amount grows, the payments increase with inflation. The United Kingdom was the first sovereign issuer to issue inflation linked Gilts in the 1980s. Treasury Inflation-Protected Securities (TIPS) and Ibonds are examples of inflation linked bonds issued by the U.S. government.
Asset-backed securities are bonds whose interest and principal payments are backed by underlying cash flows from other assets. Examples of asset-backed securities are mortgage-backed securities (MBS's), collateralized mortgage obligations (CMOs) and collateralized debt obligations (CDOs).
Subordinated bonds are those that have a lower priority than other bonds of the issuer in case of liquidation. In case of bankruptcy, there is a hierarchy of creditors. First the liquidator is paid, then government taxes, etc. The first bond holders in line to be paid are those holding what is called senior bonds. After they have been paid, the subordinated bond holders are paid. As a result, the risk is higher. Therefore, subordinated bonds usually have a lower credit rating than senior bonds. The main examples of subordinated bonds can be found in bonds issued by banks, and asset-backed securities. The latter are often issued in tranches. The senior tranches get paid back first, the subordinated tranches later.
Bearer bond is an official certificate issued without a named holder. In other words, the person who has the paper certificate can claim the value of the bond. Often they are registered by a number to prevent counterfeiting, but may be traded like cash. Bearer bonds are very risky because they can be lost or stolen. Especially after federal income tax began in the United States, bearer bonds were seen as an opportunity to conceal income or assets.[5] U.S. corporations stopped issuing bearer bonds in the 1960s, the U.S. Treasury stopped in 1982, and state and local tax-exempt bearer bonds were prohibited in 1983.[6]
Treasury bond, also called government bond, is issued by the Federal government and is not exposed to default risk. It is characterized as the safest bond, with the lowest interest rate. A treasury bond is backed by the “full faith and credit” of the federal government. For that reason, this type of bond is often referred to as risk-free. Municipal bond is a bond issued by a state, U.S. Territory, city, local government, or their agencies. Interest income received by holders of municipal bonds is often exempt from the federal income tax and from the income tax of the state in which they are issued, although municipal bonds issued for certain purposes may not be tax exempt.
A mortgage-backed security (MBS) is an asset-backed security that represents a claim on the cash flows from mortgage loans through a process known assecuritization. Types
A residential mortgage-backed security (RMBS) is a pass-through MBS backed by mortgages on residential property. A commercial mortgage-backed security (CMBS) is a pass-through MBS backed by mortgages on commercial property.
A stripped mortgage-backed security (SMBS) where each mortgage payment is partly used to pay down the loan's principal and partly used to pay the interest on it. An interest-only stripped mortgage-backed security (IO) is a bond with cash flows backed by the interest component of property owner's mortgage payments. A principal-only stripped mortgage-backed security (PO) is a bond with cash flows backed by the principal repayment component of property owner's mortgage payments.
Valuation
The weighted-average maturity (WAM) and weighted average coupon (WAC) are used for valuation of a passthrough MBS, and they form the basis for the computation of cash flows from that mortgage passthrough. Just as we describe a bond as a 30 year bond with 6% coupon rate, we describe a passthrough MBS as a $3 billion passthrough with 6% passthrough rate, 6.5% WAC, and 340 month WAM. The passthrough rate is different from the WAC; it is the rate that the investor would receive if he/she holds this passthrough MBS, and the passthrough rate is almost always less than the WAC. The difference goes to servicing costs (i.e. costs incurred in collecting the loan payments and transferring the payments to the investors.) To illustrate the concepts, consider a mortgage pool with just three mortgage loans that have the below mentioned outstanding mortgage balances, mortgage rates, and months remaining to maturity:
Loan
Outstanding Mortgage Balance
Mortgage Rate
Remaining Months to Maturity
% of pool's total $900,000 balance (aka the loan's "Weighting")
Loan 1
$200,000
6.00%
300
22.22%
Loan 2
$400,000
6.25%
260
44.44%
Loan 3
$300,000
6.50%
280
33.33%
Overall Pool $900,000
WAC: 6.277% WAM: 275.55
100%
Weighted-average maturity
The weighted-average maturity (WAM) of a passthrough MBS is the average of the maturities of the mortgages in the pool, weighted by their balances at the issue of the MBS. Note that this is an average across mortgages, as distinct from concepts such as weighted-average life and duration, which are averages across payments of a single loan. The weightings are computed by dividing each outstanding loan amount by total amount outstanding in the mortgage pool (i.e., $900,000). These amounts are the outstanding amounts at the issuance/initiation of the MBS. The WAM for the above example is computed as follows:
WAM = (22.22% × 300) + (44.44% × 260) + (33.33% × 280) = 66.66 + 115.55 + 93.33 = 275.55 month Weighted-average coupon
The weighted average coupon (WAC) of a passthrough MBS is the average of the coupons of the mortgages in the pool, weighted by their original balances at the issuance of the MBS. For the above example this is:
WAC = (22.22% × 6.00%) + (44.44% × 6.25%) + (33.33% × 6.50%) = 1.33% + 2.77% + 2.166% = 6.277%
FORWARD RATE
he forward rate is the future yield on a bond. It is calculated using the yield curve. For example, the yield on a threemonth Treasury bill six months from now is a forward rate. A forward discount is when the forward rate of one currency relative to another currency is higher than the spot rate. A forward premium is when the forward rate of one currency relative to another currency is lower than the spot rate.
SPOT RATE The spot price or spot rate of a commodity, a security or a currency is the price that is quoted for immediate (spot) settlement (payment and delivery). Spot settlement is normally one or two business days from trade date. This is in contrast with the forward price established in a forward contract or futures contract, where contract terms (price) are set now, but delivery and payment will occur at a future date. Spot rates are estimated via the bootstrapping method, which uses prices of the securities currently trading in market, that is, from the cash or coupon curve. The result is the spot curve, which exists for each of the various classes of securities. A simple example: even if you know tomatoes are cheap in July and will be expensive in January, you can't buy them in July and take delivery in January, since they will spoil before you can take advantage of January's high prices. The July price will reflect tomato supply and demand in July. The forward price for January will reflect the market's expectations of supply and demand in January. July tomatoes are effectively a different commodity from January tomatoes
YIELD CURVE
In finance, the yield curve is the relation between the (level of) interest rate (or cost of borrowing) and the time to maturity, known as the "term", of the debt for a given borrower in a given currency. YIELD TO MATURITY What Does Yield To Maturity - YTM Mean? The rate of return anticipated on a bond if it is held until the maturity date. YTM is considered a long-term bond yield expressed as an annual rate. The calculation of YTM takes into account the current market price, par value, coupon interest rate and time to maturity. It is also assumed that all coupons are reinvested at the same rate. Sometimes this is simply referred to as "yield" for short.
If the yield to maturity for a bond is less than the bond's coupon rate, then the (clean) market value of the bond is greater than the par value (and vice versa). 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.
Variants of yield to maturity
As some bonds have different characteristics, there are some variants of YTM:
Yield to call: when a bond is callable (can be repurchased by the issuer before the maturity), the market looks also to the Yield to call, which is the same calculation of the YTM, but assumes that the bond will be called, so the cashflow is shortened. The yield of a bond or note if you were to buy and hold the security until the call date. This yield is valid only if the security is called prior to maturity. The calculation of yield to call is based on the coupon rate, the length of time to the call date and the market price.
Yield to put: same as yield to call, but when the bond holder has the option to sell the bond back to the issuer at a fixed price on specified date. Yield to worst: when a bond is callable, puttable, exchangeable, or has other features, the yield to worst is the lowest yield of yield to maturity, yield to call, yield to put, and others. The lowest potential yield that can be received on a bond without the issuer actually defaulting. The yield to worst is calculated by making worst-case scenario assumptions on the issue by calculating the returns that would be received if provisions, including prepayment, call or sinking fund, are used by the issuer. This metric is used to evaluate the worst-case scenario for yield to help investors manage risks and ensure that specific income requirements will still be met even in the worst scenarios.
WHAT ARE INTEREST RATE FUTURES?
Buying an interest rate futures contract allows the buyer of the contract to lock in a future investment rate; not a borrowing rate as many believe. Interest rate futures are based off an underlying security which is a debt obligation and moves in value as interest rates change.
When interest rates move higher, the buyer of the futures contract will pay the seller in an amount equal to that of the benefit received by investing at a higher rate versus that of the rate specified in thefutures contract. Conversely, when interest rates move lower, the seller of the futures contract will compensate the buyer for the lower interest rate at the time of expiration. To accurately determine the gain or loss of an interest rate futures contract, an interest rate futures price index was created. When buying, the index can be calculated by subtracting the futures interest rate from 100, or (100 - Futures Interest Rate). As rates fluctuate, so does this price index. You can see that as rates increase, the index moves lower and vice versa.
How do you calculate the gain or loss on the futures contract?
Typically, the interest rate futures contract has a base price move (tick) of .01, or 1 basis point however, some contracts have a tick value of .005 or half of 1 basis point. For example, for Eurodollar contracts, a tick is worth $12.50 and a move from 94 to 94.50 would result in a $1250 gain per contract for someone who is long the futures.
HEDGING WITH FUTURES
Many participants in the interest rate futures market hedge their positions that have an interest rate risk with an offsetting futures contract. As the hedge becomes profitable and traders see less risk in the market, the hedge will be peeled off. Other participants will use interest rate futures to hedge forward borrowing rates. For example, it is currently March and I need to borrow money in June for 1 month at Libor plus 2. The current LIBOR rate is 2.75% and let's say the 3 month LIBOR futures are 3%. I will basically be locking in a 5% forward rate by shorting or selling the LIBOR June1 month LIBOR futures contracts.
CONVINIENCE YIELD A convenience yield is an adjustment to the cost of carry in the non-arbitrage pricing formula for forward prices in markets with trading constraints. Let Ft,T be the forward price of an asset with initial price St and maturity T. Suppose that r is the continuously compounded interest rate for one year. Then, the non-arbitrage pricing formula should be
However, this relationship does not hold in most commodity markets, partly because of the inability of investors and speculators to short the underlying asset, St. Instead, there is a correction to the forward pricing formula given by the convenience yield c. Hence
This makes it possible for backwardation to be observable. [edit]Example A trader has observed that the price of 6-month (T) gold futures price (F) is $1,300 per troy ounce, whereas the spot price (S) is $1,371 per troy ounce. The (not compounded) borrowing rate for a 6-month loan (r) is 3.5% per annum, and storage cost for gold is negligible (0%). Since we know we have the relation:
What is the convenience yield implied by the futures price? From the formula above, we isolate the convenience yield (c), and we obtain:
(per annum, not compounded)
For information, if we had a continuously compounded 6-month borrowing rate and if we were looking for the continuously compounded convenience yield, we would have the formula:
And the convenience yield would therefore be:
(per annum, continuously compounded)
Yield spread measures It is commonplace to refer to the additional yield over the benchmark Treasury issue of the same maturity as the yield spread. Since non-treasury bond sectors offer a yield over the Treasury securities, they are called spread sectors. Examples include the corporate sector, the agency sector, etc. Non-Treasury securities in a spread sector are called spread products. The yield spread can be computed in one of three ways:
• • •
Absolute yield spread, which is the difference between the yield on two bonds or bond sectors: yield spread = yield on bond A - yield on bond B. Relative yield spread, which is the percentage of one yield relative to another: relative yield spread = (yield on bond A - yield on bond B) / yield on bond B. Yield ratio, which is the ratio of one yield to another yield: yield ratio = yield on bond A / yield on bond B.
Typically when the various forms of yield spread are computed, bond B is the benchmark Treasury issue. For example, the yield on a 5-year corporate bond is 6.51%, and the yield on the on-the-run 5-year Treasury security is 5.83%:
• • •
absolute yield spread = 6.51% - 5.83% = 68 basis points. relative yield spread = (6.51% - 5.83%) / 5.83% = 11.7%. yield ratio = 6.51%/5.83% = 1.12.
Since the magnitude of the yield spread is affected by the level of interest rates, relative yield spread is a better measure of yield spread than the absolute yield spread. Continue with the above example, if the yield on a 5-year corporate bond is 8.51%, and the yield on the on-therun 5-year Treasury security is 7.83%, the absolute yield spread is still 68 basis points. However, the relative
yield spread is now (8.51% - 7.83%)/7.83% = 8.7%, instead of 11.7% as determined above. The absolute yield spread fails to reflect the change in the level of interest rate. However, the relative yield spread declines, reflecting the increase in the level of interest rates. SPREAD MEASURES FOR BONDS Three measures of spreads in Bond are: Nominal Yield Spread, Zero Volatility Spread, Option Adjusted Spread. Nominal Yield Spread: This is difference between the YIELD of a Corporate Bond vs the YIELD of a similar maturity Treasury Bond. The Yield mentioned here is the YTM (Yield to Maturity) for the bond. This is basically a measure of the distance between the YTM of the Corporate Bond and the Treasury Bond of the same maturity. As it uses a single discount rate to value the cash flows, it ignores the shape of the yield curve i.e. the Yields at other maturities (other than the maturity of the 2 bonds relevant) are ignored. The problem with this measure is that for example, in a positively sloped Yield Curve environment and comparing two bonds with the same cash flow dates and maturity – A higher coupon bond will offer a lower YTM than a low coupon bond. Thus two fairly and correctly priced corporate bonds from the same borrower and having the same cash flow dates and maturity may well have significantly different Yields to Maturity. It follows that when these Yields are compared to that of a same-maturity benchmark, the resulting spreads may be markedly different i.e the nominal spread. Zero Volatility Spread (Z-Spread): This is the parallel difference between the SPOT RATE curve of the Corporate Bond and the SPOT RATE curve of the Treasury Bond. Here a fixed value (in basis points) is added to all the Treasury Spot rates to measure the approx. parallel distance between the spot rate curves of the 2 bonds. Unlike the Nominal Yield Spread, this measure takes into account the rate of return for the entire maturity range. The idea is that the present value of the cash flows will equal to the price of the bond. The Zspread is calculated as the spread that will make the present value of cash flows from the non-benchmark security when they are discounted at the benchmark Zero rates (plus the Z-spread) equal to the non-benchmark security’s price. This is done by trial and error. This is different than the nominal spread because the nominal spread just uses one point on the curve. As the Z-Spread is not dependent upon only one point on the Yield Curve and takes account of all of the relevant term-structure, the distortions of Yield-to-Maturity spreads outlined above are eliminated. The Z-spread includes the higher spread due to Credit Risk, Interest Rate Risk, Liquidity Risk and Option Risk. The drawback of the Z-spread is that it does not take into account the change in the cash flows due to Option embedded in the Bond. OAS: This is similar to the Z-spread, but now the spread is calculated after adjusting for the cash flows for the option embedded in the bond. So the calculation of the Z-spread and the OAS is very similar, just with the difference being that the cash flows in the OAS are adjusted. Also note, that in calculating the OAS the parallel distance between the Spot Rate curves is being calculated. OAS adjusts the Option Risk from the bond and then measures the spread. Therefore, the OAS takes into account only the Credit Risk, Liquidity Risk and the Interest rate risk.
Types
The following descriptions are not mutually exclusive, and more than one of them may apply to a particular bond.
Fixed rate bonds have a coupon that remains constant throughout the life of the bond. Floating rate notes (FRNs) have a variable coupon that is linked to a reference rate of interest, such as LIBOR or Euribor. For example the coupon may be defined as three month USD LIBOR + 0.20%. The coupon rate is recalculated periodically, typically every one or three months.
Zero-coupon bonds pay no regular interest. They are issued at a substantial discount to par value, so that the interest is effectively rolled up to maturity (and usually taxed as such). The bondholder receives the full principal amount on the redemption date. An example of zero coupon bonds is Series E savings bonds issued by the U.S. government. 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. See IO (Interest Only) and PO (Principal Only).
Inflation linked bonds, in which the principal amount and the interest payments are indexed to inflation. The interest rate is normally lower than for fixed rate bonds with a comparable maturity (this position briefly reversed itself for short-term UK bonds in December 2008). However, as the principal amount grows, the payments increase with inflation. The United Kingdom was the first sovereign issuer to issue inflation linked Gilts in the 1980s. Treasury Inflation-Protected Securities (TIPS) and Ibonds are examples of inflation linked bonds issued by the U.S. government.
Asset-backed securities are bonds whose interest and principal payments are backed by underlying cash flows from other assets. Examples of asset-backed securities are mortgage-backed securities (MBS's), collateralized mortgage obligations (CMOs) and collateralized debt obligations (CDOs).
Subordinated bonds are those that have a lower priority than other bonds of the issuer in case of liquidation. In case of bankruptcy, there is a hierarchy of creditors. First the liquidator is paid, then government taxes, etc. The first bond holders in line to be paid are those holding what is called senior bonds. After they have been paid, the subordinated bond holders are paid. As a result, the risk is higher. Therefore, subordinated bonds usually have a lower credit rating than senior bonds. The main examples of subordinated bonds can be found in bonds issued by banks, and asset-backed securities. The latter are often issued in tranches. The senior tranches get paid back first, the subordinated tranches later.
Bearer bond is an official certificate issued without a named holder. In other words, the person who has the paper certificate can claim the value of the bond. Often they are registered by a number to prevent counterfeiting, but may be traded like cash. Bearer bonds are very risky because they can be lost or stolen. Especially after federal income tax began in the United States, bearer bonds were seen as an opportunity to conceal income or assets.[5] U.S. corporations stopped issuing bearer bonds in the 1960s, the U.S. Treasury stopped in 1982, and state and local tax-exempt bearer bonds were prohibited in 1983.[6]
Treasury bond, also called government bond, is issued by the Federal government and is not exposed to default risk. It is characterized as the safest bond, with the lowest interest rate. A treasury bond is backed by the “full faith and credit” of the federal government. For that reason, this type of bond is often referred to as risk-free. Municipal bond is a bond issued by a state, U.S. Territory, city, local government, or their agencies. Interest income received by holders of municipal bonds is often exempt from the federal income tax and from the income tax of the state in which they are issued, although municipal bonds issued for certain purposes may not be tax exempt.
A mortgage-backed security (MBS) is an asset-backed security that represents a claim on the cash flows from mortgage loans through a process known assecuritization. Types
A residential mortgage-backed security (RMBS) is a pass-through MBS backed by mortgages on residential property. A commercial mortgage-backed security (CMBS) is a pass-through MBS backed by mortgages on commercial property.
A stripped mortgage-backed security (SMBS) where each mortgage payment is partly used to pay down the loan's principal and partly used to pay the interest on it. An interest-only stripped mortgage-backed security (IO) is a bond with cash flows backed by the interest component of property owner's mortgage payments. A principal-only stripped mortgage-backed security (PO) is a bond with cash flows backed by the principal repayment component of property owner's mortgage payments.
Valuation
The weighted-average maturity (WAM) and weighted average coupon (WAC) are used for valuation of a passthrough MBS, and they form the basis for the computation of cash flows from that mortgage passthrough. Just as we describe a bond as a 30 year bond with 6% coupon rate, we describe a passthrough MBS as a $3 billion passthrough with 6% passthrough rate, 6.5% WAC, and 340 month WAM. The passthrough rate is different from the WAC; it is the rate that the investor would receive if he/she holds this passthrough MBS, and the passthrough rate is almost always less than the WAC. The difference goes to servicing costs (i.e. costs incurred in collecting the loan payments and transferring the payments to the investors.) To illustrate the concepts, consider a mortgage pool with just three mortgage loans that have the below mentioned outstanding mortgage balances, mortgage rates, and months remaining to maturity:
Loan
Outstanding Mortgage Balance
Mortgage Rate
Remaining Months to Maturity
% of pool's total $900,000 balance (aka the loan's "Weighting")
Loan 1
$200,000
6.00%
300
22.22%
Loan 2
$400,000
6.25%
260
44.44%
Loan 3
$300,000
6.50%
280
33.33%
Overall Pool $900,000
WAC: 6.277% WAM: 275.55
100%
Weighted-average maturity
The weighted-average maturity (WAM) of a passthrough MBS is the average of the maturities of the mortgages in the pool, weighted by their balances at the issue of the MBS. Note that this is an average across mortgages, as distinct from concepts such as weighted-average life and duration, which are averages across payments of a single loan. The weightings are computed by dividing each outstanding loan amount by total amount outstanding in the mortgage pool (i.e., $900,000). These amounts are the outstanding amounts at the issuance/initiation of the MBS. The WAM for the above example is computed as follows:
WAM = (22.22% × 300) + (44.44% × 260) + (33.33% × 280) = 66.66 + 115.55 + 93.33 = 275.55 month Weighted-average coupon
The weighted average coupon (WAC) of a passthrough MBS is the average of the coupons of the mortgages in the pool, weighted by their original balances at the issuance of the MBS. For the above example this is:
WAC = (22.22% × 6.00%) + (44.44% × 6.25%) + (33.33% × 6.50%) = 1.33% + 2.77% + 2.166% = 6.277%
FORWARD RATE
he forward rate is the future yield on a bond. It is calculated using the yield curve. For example, the yield on a threemonth Treasury bill six months from now is a forward rate. A forward discount is when the forward rate of one currency relative to another currency is higher than the spot rate. A forward premium is when the forward rate of one currency relative to another currency is lower than the spot rate.
SPOT RATE The spot price or spot rate of a commodity, a security or a currency is the price that is quoted for immediate (spot) settlement (payment and delivery). Spot settlement is normally one or two business days from trade date. This is in contrast with the forward price established in a forward contract or futures contract, where contract terms (price) are set now, but delivery and payment will occur at a future date. Spot rates are estimated via the bootstrapping method, which uses prices of the securities currently trading in market, that is, from the cash or coupon curve. The result is the spot curve, which exists for each of the various classes of securities. A simple example: even if you know tomatoes are cheap in July and will be expensive in January, you can't buy them in July and take delivery in January, since they will spoil before you can take advantage of January's high prices. The July price will reflect tomato supply and demand in July. The forward price for January will reflect the market's expectations of supply and demand in January. July tomatoes are effectively a different commodity from January tomatoes
YIELD CURVE
In finance, the yield curve is the relation between the (level of) interest rate (or cost of borrowing) and the time to maturity, known as the "term", of the debt for a given borrower in a given currency. YIELD TO MATURITY What Does Yield To Maturity - YTM Mean? The rate of return anticipated on a bond if it is held until the maturity date. YTM is considered a long-term bond yield expressed as an annual rate. The calculation of YTM takes into account the current market price, par value, coupon interest rate and time to maturity. It is also assumed that all coupons are reinvested at the same rate. Sometimes this is simply referred to as "yield" for short.
If the yield to maturity for a bond is less than the bond's coupon rate, then the (clean) market value of the bond is greater than the par value (and vice versa). 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.
Variants of yield to maturity
As some bonds have different characteristics, there are some variants of YTM:
Yield to call: when a bond is callable (can be repurchased by the issuer before the maturity), the market looks also to the Yield to call, which is the same calculation of the YTM, but assumes that the bond will be called, so the cashflow is shortened. The yield of a bond or note if you were to buy and hold the security until the call date. This yield is valid only if the security is called prior to maturity. The calculation of yield to call is based on the coupon rate, the length of time to the call date and the market price.
Yield to put: same as yield to call, but when the bond holder has the option to sell the bond back to the issuer at a fixed price on specified date. Yield to worst: when a bond is callable, puttable, exchangeable, or has other features, the yield to worst is the lowest yield of yield to maturity, yield to call, yield to put, and others. The lowest potential yield that can be received on a bond without the issuer actually defaulting. The yield to worst is calculated by making worst-case scenario assumptions on the issue by calculating the returns that would be received if provisions, including prepayment, call or sinking fund, are used by the issuer. This metric is used to evaluate the worst-case scenario for yield to help investors manage risks and ensure that specific income requirements will still be met even in the worst scenarios.
WHAT ARE INTEREST RATE FUTURES?
Buying an interest rate futures contract allows the buyer of the contract to lock in a future investment rate; not a borrowing rate as many believe. Interest rate futures are based off an underlying security which is a debt obligation and moves in value as interest rates change.
When interest rates move higher, the buyer of the futures contract will pay the seller in an amount equal to that of the benefit received by investing at a higher rate versus that of the rate specified in thefutures contract. Conversely, when interest rates move lower, the seller of the futures contract will compensate the buyer for the lower interest rate at the time of expiration. To accurately determine the gain or loss of an interest rate futures contract, an interest rate futures price index was created. When buying, the index can be calculated by subtracting the futures interest rate from 100, or (100 - Futures Interest Rate). As rates fluctuate, so does this price index. You can see that as rates increase, the index moves lower and vice versa.
How do you calculate the gain or loss on the futures contract?
Typically, the interest rate futures contract has a base price move (tick) of .01, or 1 basis point however, some contracts have a tick value of .005 or half of 1 basis point. For example, for Eurodollar contracts, a tick is worth $12.50 and a move from 94 to 94.50 would result in a $1250 gain per contract for someone who is long the futures.
HEDGING WITH FUTURES
Many participants in the interest rate futures market hedge their positions that have an interest rate risk with an offsetting futures contract. As the hedge becomes profitable and traders see less risk in the market, the hedge will be peeled off. Other participants will use interest rate futures to hedge forward borrowing rates. For example, it is currently March and I need to borrow money in June for 1 month at Libor plus 2. The current LIBOR rate is 2.75% and let's say the 3 month LIBOR futures are 3%. I will basically be locking in a 5% forward rate by shorting or selling the LIBOR June1 month LIBOR futures contracts.
CONVINIENCE YIELD A convenience yield is an adjustment to the cost of carry in the non-arbitrage pricing formula for forward prices in markets with trading constraints. Let Ft,T be the forward price of an asset with initial price St and maturity T. Suppose that r is the continuously compounded interest rate for one year. Then, the non-arbitrage pricing formula should be
However, this relationship does not hold in most commodity markets, partly because of the inability of investors and speculators to short the underlying asset, St. Instead, there is a correction to the forward pricing formula given by the convenience yield c. Hence
This makes it possible for backwardation to be observable. [edit]Example A trader has observed that the price of 6-month (T) gold futures price (F) is $1,300 per troy ounce, whereas the spot price (S) is $1,371 per troy ounce. The (not compounded) borrowing rate for a 6-month loan (r) is 3.5% per annum, and storage cost for gold is negligible (0%). Since we know we have the relation:
What is the convenience yield implied by the futures price? From the formula above, we isolate the convenience yield (c), and we obtain:
(per annum, not compounded)
For information, if we had a continuously compounded 6-month borrowing rate and if we were looking for the continuously compounded convenience yield, we would have the formula:
And the convenience yield would therefore be:
(per annum, continuously compounded)
Yield spread measures It is commonplace to refer to the additional yield over the benchmark Treasury issue of the same maturity as the yield spread. Since non-treasury bond sectors offer a yield over the Treasury securities, they are called spread sectors. Examples include the corporate sector, the agency sector, etc. Non-Treasury securities in a spread sector are called spread products. The yield spread can be computed in one of three ways:
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Absolute yield spread, which is the difference between the yield on two bonds or bond sectors: yield spread = yield on bond A - yield on bond B. Relative yield spread, which is the percentage of one yield relative to another: relative yield spread = (yield on bond A - yield on bond B) / yield on bond B. Yield ratio, which is the ratio of one yield to another yield: yield ratio = yield on bond A / yield on bond B.
Typically when the various forms of yield spread are computed, bond B is the benchmark Treasury issue. For example, the yield on a 5-year corporate bond is 6.51%, and the yield on the on-the-run 5-year Treasury security is 5.83%:
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absolute yield spread = 6.51% - 5.83% = 68 basis points. relative yield spread = (6.51% - 5.83%) / 5.83% = 11.7%. yield ratio = 6.51%/5.83% = 1.12.
Since the magnitude of the yield spread is affected by the level of interest rates, relative yield spread is a better measure of yield spread than the absolute yield spread. Continue with the above example, if the yield on a 5-year corporate bond is 8.51%, and the yield on the on-therun 5-year Treasury security is 7.83%, the absolute yield spread is still 68 basis points. However, the relative
yield spread is now (8.51% - 7.83%)/7.83% = 8.7%, instead of 11.7% as determined above. The absolute yield spread fails to reflect the change in the level of interest rate. However, the relative yield spread declines, reflecting the increase in the level of interest rates. SPREAD MEASURES FOR BONDS Three measures of spreads in Bond are: Nominal Yield Spread, Zero Volatility Spread, Option Adjusted Spread. Nominal Yield Spread: This is difference between the YIELD of a Corporate Bond vs the YIELD of a similar maturity Treasury Bond. The Yield mentioned here is the YTM (Yield to Maturity) for the bond. This is basically a measure of the distance between the YTM of the Corporate Bond and the Treasury Bond of the same maturity. As it uses a single discount rate to value the cash flows, it ignores the shape of the yield curve i.e. the Yields at other maturities (other than the maturity of the 2 bonds relevant) are ignored. The problem with this measure is that for example, in a positively sloped Yield Curve environment and comparing two bonds with the same cash flow dates and maturity – A higher coupon bond will offer a lower YTM than a low coupon bond. Thus two fairly and correctly priced corporate bonds from the same borrower and having the same cash flow dates and maturity may well have significantly different Yields to Maturity. It follows that when these Yields are compared to that of a same-maturity benchmark, the resulting spreads may be markedly different i.e the nominal spread. Zero Volatility Spread (Z-Spread): This is the parallel difference between the SPOT RATE curve of the Corporate Bond and the SPOT RATE curve of the Treasury Bond. Here a fixed value (in basis points) is added to all the Treasury Spot rates to measure the approx. parallel distance between the spot rate curves of the 2 bonds. Unlike the Nominal Yield Spread, this measure takes into account the rate of return for the entire maturity range. The idea is that the present value of the cash flows will equal to the price of the bond. The Zspread is calculated as the spread that will make the present value of cash flows from the non-benchmark security when they are discounted at the benchmark Zero rates (plus the Z-spread) equal to the non-benchmark security’s price. This is done by trial and error. This is different than the nominal spread because the nominal spread just uses one point on the curve. As the Z-Spread is not dependent upon only one point on the Yield Curve and takes account of all of the relevant term-structure, the distortions of Yield-to-Maturity spreads outlined above are eliminated. The Z-spread includes the higher spread due to Credit Risk, Interest Rate Risk, Liquidity Risk and Option Risk. The drawback of the Z-spread is that it does not take into account the change in the cash flows due to Option embedded in the Bond. OAS: This is similar to the Z-spread, but now the spread is calculated after adjusting for the cash flows for the option embedded in the bond. So the calculation of the Z-spread and the OAS is very similar, just with the difference being that the cash flows in the OAS are adjusted. Also note, that in calculating the OAS the parallel distance between the Spot Rate curves is being calculated. OAS adjusts the Option Risk from the bond and then measures the spread. Therefore, the OAS takes into account only the Credit Risk, Liquidity Risk and the Interest rate risk.
