Properties concerning the price volatility of an option free bond:
· Price is inversely related to yield.
· Price sensitivity depends on maturity and coupon.
· For small changes in yield, the price change is same whether yield moves up or down.
· For large changes in yield, the price increase for a fall in yield is greater than the price decrease for a similar rise in yield, i.e. the price yield curve is convex.
· The lower the coupon, the longer the term to maturity, the lower the initial yield -> the greater the bond price volatility
· Yield/price relationship for option free bonds is not linear but convex, referred to as positive Convexity.
Positive convexity:
· The decrease in an option-free bond’s price due to a rise in yield is lower than the increase for an equal fall in yield. This results a positive adjustment to the duration-based estimate of price change whether yield goes up or down.
Price-Volatility Characteristics of Callable and Prepayable Securities
· Embedded options can dramatically change the price-yield profile.
· At high yields the profiles of these bonds are similar, but at low yields price of callable/prepayable securities grows slower with a fall in yield than the price of option-free bonds {price compression}.
Negative convexity:
· For callable and prepayable securities, at low levels of yield, the price increase for a given fall in yield is less than the price decrease for an equal rise in yield. ie, Prices rise at a decreasing rate. The point where the curve starts to flatten is at ( or near a yield level of y’
Price Volatility Characteristics of Putable Bonds
· The advantage of these bonds to an investor is that if market yields rise and the value of the bond falls below the put price, the investor can exercise the put option and stem his losses to the put price.
· The price of a puttable bond will react same way as an option-free bond at low yield levels. As rates rise, the puttable bond’s price will decrease at the same rate as an option-free bond, but the decline will be lessened because of the value of the put option.
Value of puttable bond = value of option free bond + the option.
Showing posts with label Debt Securities. Show all posts
Showing posts with label Debt Securities. Show all posts
Thursday, January 1
Convexity
Convexity is a measure of the degree of curvature of the price/yield relationship, to indicate the error in the estimated change in bond's price based on duration.
Effective convexity = (V_ + V+ - 2 x Vo) / (2 x Vo x dy2).
It is the 2nd derivative of price function wrt yield. For callable bond, V is capped at call price.
Contribution of convexity = Convexity x dy2.
For noncallable bond, convexity effect is always +ve no matter which direction interest rate move but it can be –ve if the bond has embedded options.
Thus, approximate bond price change (using duration and convexity), i.e.
Approx. price change = -1 x Duration x dy + Convexity x dy2
Modified Convexity vs. Effective Convexity
With modified convexity the cash flows do not change due to a change in interest rates.
Effective Convexity, on the other hand, assumes that cash flow does change due to a change in interest rates.
When bonds have options, it is best to use effective convexity just like you should use effective duration. For option-free bonds, either convexity measure will be a positive value, whereas when it comes to bonds with options, the effective convexity could be negative even if the modified convexity is positive.
Effective convexity = (V_ + V+ - 2 x Vo) / (2 x Vo x dy2).
It is the 2nd derivative of price function wrt yield. For callable bond, V is capped at call price.
Contribution of convexity = Convexity x dy2.
For noncallable bond, convexity effect is always +ve no matter which direction interest rate move but it can be –ve if the bond has embedded options.
Thus, approximate bond price change (using duration and convexity), i.e.
Approx. price change = -1 x Duration x dy + Convexity x dy2
Modified Convexity vs. Effective Convexity
With modified convexity the cash flows do not change due to a change in interest rates.
Effective Convexity, on the other hand, assumes that cash flow does change due to a change in interest rates.
When bonds have options, it is best to use effective convexity just like you should use effective duration. For option-free bonds, either convexity measure will be a positive value, whereas when it comes to bonds with options, the effective convexity could be negative even if the modified convexity is positive.
Price value of a basis point (PVBP)
A measure of bond price volatility that shows the extent to which the price of a bond will change when the required yield changes by one basis point. That is, the difference between the initial price and the price if yield is changed by 1bp, a variation of dollar duration.
PVBP = Duration x Price / 10,000
PVBP = Duration x Price / 10,000
Approximate % change in bond price
Approximate % change in bond price = (-) (duration)(dy)
Duration tends to:
· underestimate the increase in price that occurs with a drecrease in yield; overestimate the decrease in price that comes with an increse in yield.
· The difference is due to the curvature of the actual price path.
· The larger the change in yield, the larger the error.
· For small changes, estimated and actual price changes are equal or very close.
Duration
Duration is a measure of the slope of the price-yield function, steeper at low interest rate and flatter at high interest rate for non-callable bonds. It represents the percentage change in price for a 100 basis point change in yield.
Effective Duration
Duration is the approximate percentage change in price for a 100 basis point change in rates.
Effective Duration = (V_- V+) / (2 x Vo x dy in decimal).
Note:
· go down or up by same no. of basis points
Modified Duration
Modified duration is the approximate percentage change in a bond’s price for a 100 basis points change in yield, assuming that the bond’s expected cash flow does not change when the yield changes. This works for option-free bonds such as Treasuries but not with option-embedded bonds because the cash flows may change due to a call or prepayment.
Macaulay duration
Macaulay’s duration is the weighted average number of years remaining to receive the present value of a bond.
It gives the analysis a short cut to measure modified duration. But because modified duration is flawed by not incorporating the change in cash flows due to an embedded option, so are Macaulay durations.
Modified duration = Macaulay’s Duration/ (1 + yield/k)
Macaulay duration = Modified duration x (1 + BEY/2).
Notes:
· The duration of zero coupon bond = its maturity;
· Duration of a floater coupon bond = the time to the next reset date
When is Effective Duration a Better Measure?
When a bond has an embedded option, the cash flows can change when interest rates change because of prepayments and the exercise of calls and puts. Effective duration takes into consideration the changes in cash flows and values that can occur from these embedded options.
Duration of a portfolio
Duration of a portfolio equals the weighted average of the durations of the bonds in the portfolio.
Effective Duration
Duration is the approximate percentage change in price for a 100 basis point change in rates.
Effective Duration = (V_- V+) / (2 x Vo x dy in decimal).
Note:
· go down or up by same no. of basis points
Modified Duration
Modified duration is the approximate percentage change in a bond’s price for a 100 basis points change in yield, assuming that the bond’s expected cash flow does not change when the yield changes. This works for option-free bonds such as Treasuries but not with option-embedded bonds because the cash flows may change due to a call or prepayment.
Macaulay duration
Macaulay’s duration is the weighted average number of years remaining to receive the present value of a bond.
It gives the analysis a short cut to measure modified duration. But because modified duration is flawed by not incorporating the change in cash flows due to an embedded option, so are Macaulay durations.
Modified duration = Macaulay’s Duration/ (1 + yield/k)
Macaulay duration = Modified duration x (1 + BEY/2).
Notes:
· The duration of zero coupon bond = its maturity;
· Duration of a floater coupon bond = the time to the next reset date
When is Effective Duration a Better Measure?
When a bond has an embedded option, the cash flows can change when interest rates change because of prepayments and the exercise of calls and puts. Effective duration takes into consideration the changes in cash flows and values that can occur from these embedded options.
Duration of a portfolio
Duration of a portfolio equals the weighted average of the durations of the bonds in the portfolio.
Duration/convexity approach
To provide an approximation of the actual interest rate sensitivity of a bond or bond portfolio, simplier than full valuation approach.
Full Valuation Approach
To measure the interest rate risk by re-valuing the bond or portfolio for a given interest-rate change scenario, referred to as a scenario analysis. Work well for periodic reports but impractical for managing risk of large portfolio.
Steps:
1. Start with current market yield and price
2. Estimate chagnes in yields
3. Revalue bonds
4. Compare new value to current value
It take the changes in cash flows into account.
Steps:
1. Start with current market yield and price
2. Estimate chagnes in yields
3. Revalue bonds
4. Compare new value to current value
It take the changes in cash flows into account.
Tuesday, December 30
Nominal spread, Static spread, Zero-volatility spread, Option-adjusted spread
Nominal spread – simpliest
Nominal spread = (YTM of the bond – YTM of a Treasury security of similar maturity)
Limitations of nominal spread:
· Does not account for term structure of interest rates (no arbitrage pricing).
· Ignores affect of embedded options.
Static spread (Z-spread)
· Spread not over the treasury’s YTM but over each of the spot rates in a given treasury term structure, ie. same spread is added to all risk-free spot rates.
· more accurate than nominal spread as it is based upon the arbitrage free spot rates.
· Equal to nominal spread if yield curve is perfectly flat.
PV = CF1/(1+Z1 +SS) +CF2/(1+Z2 +SS)3+ CF3/(1+Z3+SS)3 , by trial & error to find SS (Z-spread)
Zero-volatility spread (Z-spread):
· Spread over the entire Treasury spot rate curve.
· Accounts for the term structure of interest rates, but ignores the affect of embedded options.
· Difference between Z-spread and nominal spread is greatest for amortizing bonds, for longterm high-coupon bonds, and for steep yield curves.
Option-adjusted spread (OAS):
· Spread over entire Treasury spot rate curve after accounting for embedded options.
· OAS is highly dependent on the model used to calculate the spread and the assumption for interest rate volatility.
· Higher interest rate volatility assumed » Lower OAS.
Option cost = Z-spread - OAS.
For option-free bonds OAS = Z-spread.
For option value greater than 0( call), OAS smaller than Z-spread;
For option value smaller than 0 (put), OAS greater than Z-spreadNominal spread may be misleading in the case of securities with embedded options. Buy securities with largest OAS for a given duration.
Nominal spread = (YTM of the bond – YTM of a Treasury security of similar maturity)
Limitations of nominal spread:
· Does not account for term structure of interest rates (no arbitrage pricing).
· Ignores affect of embedded options.
Static spread (Z-spread)
· Spread not over the treasury’s YTM but over each of the spot rates in a given treasury term structure, ie. same spread is added to all risk-free spot rates.
· more accurate than nominal spread as it is based upon the arbitrage free spot rates.
· Equal to nominal spread if yield curve is perfectly flat.
PV = CF1/(1+Z1 +SS) +CF2/(1+Z2 +SS)3+ CF3/(1+Z3+SS)3 , by trial & error to find SS (Z-spread)
Zero-volatility spread (Z-spread):
· Spread over the entire Treasury spot rate curve.
· Accounts for the term structure of interest rates, but ignores the affect of embedded options.
· Difference between Z-spread and nominal spread is greatest for amortizing bonds, for longterm high-coupon bonds, and for steep yield curves.
Option-adjusted spread (OAS):
· Spread over entire Treasury spot rate curve after accounting for embedded options.
· OAS is highly dependent on the model used to calculate the spread and the assumption for interest rate volatility.
· Higher interest rate volatility assumed » Lower OAS.
Option cost = Z-spread - OAS.
For option-free bonds OAS = Z-spread.
For option value greater than 0( call), OAS smaller than Z-spread;
For option value smaller than 0 (put), OAS greater than Z-spreadNominal spread may be misleading in the case of securities with embedded options. Buy securities with largest OAS for a given duration.
Forward Rate
A forward rate is the borrowing / lending rate in the future. The logic is that the return from investing in a 2-year bond is the same as that from investing in a 1-year bond and then rolling the proceeds into a second 1-year bond one year from now.
Forward rate from period 1 to period 2 = (1 +Z2)2 / (1 + Z1) – 1
Where:
Z1 is the spot rate for 1-year
Z2 is the spot rate for 2-year.
Given the forward rates, calculate spot rate
(1+Z3)3 = (1+ f1)(1+f2)(1+f3)
Calculate N-period spot rate (SN)
ZN)3 = [(1+ f1)(1+f2)…..(1+fN)]1/(N+1) –1
Forward rate from period 1 to period 2 = (1 +Z2)2 / (1 + Z1) – 1
Where:
Z1 is the spot rate for 1-year
Z2 is the spot rate for 2-year.
Given the forward rates, calculate spot rate
(1+Z3)3 = (1+ f1)(1+f2)(1+f3)
Calculate N-period spot rate (SN)
ZN)3 = [(1+ f1)(1+f2)…..(1+fN)]1/(N+1) –1
Bootstrapping Spot Rate
Bootstrapping is the process of calculating spot rates from coupon bond yields.
Example:
Given a 2-year bond price (P) with annual coupon (C) and 1-year spot rate Z1,
You can calculate 2-year spot rate in the following formula:
P = C/(1+Z1) + (C+PAR)/ (1+Z2)2
Given Z1,Z2 and the price of a 3-year bond, you can calculate Z3 in the same manner.
Example:
Given a 2-year bond price (P) with annual coupon (C) and 1-year spot rate Z1,
You can calculate 2-year spot rate in the following formula:
P = C/(1+Z1) + (C+PAR)/ (1+Z2)2
Given Z1,Z2 and the price of a 3-year bond, you can calculate Z3 in the same manner.
Annual pay, semi-annual pay, Reinvestment income
Annual pay versus semi-annual pay:
Many non-US governments and corporate bonds that pay annual coupons.
Annual pay yield = (1 + BEY/2)2 - 1.
BEY = [(1 + Annual-pay yield)1/2 - 1] x 2.
Total Dollar Return = coupons + principal + reinvestment income, i.e. to calculate the FV of the reinvestment coupon + principal at maturity
Reinvestment income
Reinvestment income can make up a large portion of the return for a bond due to its compounding effect.
Factors That Affect Reinvestment Risk
There are two characteristics that affect reinvestment risk:
· The longer the maturity, the more the total dollar return depends on reinvestment income to realize the yield to maturity at the purchase time. Longer maturity = greater reinvestment risk.
· The higher the coupon rate, the more the total dollar return depends on the reinvestment of the coupon payments. Higher coupon rate = greater reinvestment risk
Many non-US governments and corporate bonds that pay annual coupons.
Annual pay yield = (1 + BEY/2)2 - 1.
BEY = [(1 + Annual-pay yield)1/2 - 1] x 2.
Total Dollar Return = coupons + principal + reinvestment income, i.e. to calculate the FV of the reinvestment coupon + principal at maturity
Reinvestment income
Reinvestment income can make up a large portion of the return for a bond due to its compounding effect.
Factors That Affect Reinvestment Risk
There are two characteristics that affect reinvestment risk:
· The longer the maturity, the more the total dollar return depends on reinvestment income to realize the yield to maturity at the purchase time. Longer maturity = greater reinvestment risk.
· The higher the coupon rate, the more the total dollar return depends on the reinvestment of the coupon payments. Higher coupon rate = greater reinvestment risk
Yield Measurements
Current yield
= Annual coupon / Price
Problem: do NOT consider capital gain/ loss or reinvestment income
Yield to maturity (YTM)
IRR of an investment in the bond that equates the PV of all expected cash flows from bond to its full price.
At par, nominal yield(coupon) = current yield = YTM
At discount, nominal yield(coupon) smaller than current yield smaller than YTM
At premium, nominal yield(coupon) greater than current yield greater than YTM
Note:
· for semiannual bond, IRR is not YTM which is equal to BEY
Assumptions and limitations of YTM:
· Security will be held to maturity
· All intermediate cash flows will be reinvested at the same rate as yield. Higher term to maturity leads to higher reinvestment risk. Higher coupon rate implies higher reinvestment risk.
· All coupon payment are received promptly & timely fashion, ie no credit risk. So YTM is also referred to as promise yield.
· A flat yield curve (rarely exist)
Bond-equivalent yield (BEY)
· Discount rate calculated using six-monthly periods and annualized by multiplying by two.
Realized return (annualized basis) = YTM =BEY
Equivalent annual yield (EAY) = (1+YTM/2) 2 for semiannually paid bond
Yield to call
Value bond on the basis that it will be called on first call date. Market conversion is to use the lower /more convervative measure of yield (YTM or YTC) as the appropariate indicator of value.
For premium bond, YTC smaller than YTM
For discount bond, YTM smaller than YTC
Yield to put
Yield to worst(YTW)
The lowest expected return among YTC, YTP, YTM etc.
Cash flow yield (CFY)
Based on the cash flows that include an assumption regarding prepayment rate. Useful for MBS that have monthly payments. The estimated rate of principal repayment may be different from the actual rate of prepayment.
EAY= (1 + Monthly CFY)12 - 1
= Annual coupon / Price
Problem: do NOT consider capital gain/ loss or reinvestment income
Yield to maturity (YTM)
IRR of an investment in the bond that equates the PV of all expected cash flows from bond to its full price.
At par, nominal yield(coupon) = current yield = YTM
At discount, nominal yield(coupon) smaller than current yield smaller than YTM
At premium, nominal yield(coupon) greater than current yield greater than YTM
Note:
· for semiannual bond, IRR is not YTM which is equal to BEY
Assumptions and limitations of YTM:
· Security will be held to maturity
· All intermediate cash flows will be reinvested at the same rate as yield. Higher term to maturity leads to higher reinvestment risk. Higher coupon rate implies higher reinvestment risk.
· All coupon payment are received promptly & timely fashion, ie no credit risk. So YTM is also referred to as promise yield.
· A flat yield curve (rarely exist)
Bond-equivalent yield (BEY)
· Discount rate calculated using six-monthly periods and annualized by multiplying by two.
Realized return (annualized basis) = YTM =BEY
Equivalent annual yield (EAY) = (1+YTM/2) 2 for semiannually paid bond
Yield to call
Value bond on the basis that it will be called on first call date. Market conversion is to use the lower /more convervative measure of yield (YTM or YTC) as the appropariate indicator of value.
For premium bond, YTC smaller than YTM
For discount bond, YTM smaller than YTC
Yield to put
Yield to worst(YTW)
The lowest expected return among YTC, YTP, YTM etc.
Cash flow yield (CFY)
Based on the cash flows that include an assumption regarding prepayment rate. Useful for MBS that have monthly payments. The estimated rate of principal repayment may be different from the actual rate of prepayment.
EAY= (1 + Monthly CFY)12 - 1
Sources of return for a bond
Sources of return includes:
· Coupon
· Capital gain or loss
· Income from reinvestment of interim cash flows
Total return = Coupon interest payments + Reinvestment income + Capital gain/loss.
· Coupon
· Capital gain or loss
· Income from reinvestment of interim cash flows
Total return = Coupon interest payments + Reinvestment income + Capital gain/loss.
Stripping, Reconstitution
Stripping
If a dealer finds Treasury coupon bonds trading at a lower price than Treasury strips, he can make a riskless (arbitrage) profit by buying coupon bond and selling strips.
Reconstitution
If a dealer finds Treasury coupon bonds trading at a higher price than Treasury strips, he can make an arbitrage profit by buying strips and selling coupon bonds.
If a dealer finds Treasury coupon bonds trading at a lower price than Treasury strips, he can make a riskless (arbitrage) profit by buying coupon bond and selling strips.
Reconstitution
If a dealer finds Treasury coupon bonds trading at a higher price than Treasury strips, he can make an arbitrage profit by buying strips and selling coupon bonds.
Appropriate discount rate
· The minimum interest rate that an investor should accept is the yield that is available in the market place for a risk-free bond.
· The on-the-run Treasury security is most often used as they reflect the latest yields and are the most liquid securities.
· For corporate bonds, a risk premium can be added to the risk free rate.
Ideally, each cash flow should be valued using the spot rate corresponding to its maturity. Bond price is inversely related to discount rate. Can add risk premium to the risk free rate or series of risk free sport rates
· The on-the-run Treasury security is most often used as they reflect the latest yields and are the most liquid securities.
· For corporate bonds, a risk premium can be added to the risk free rate.
Ideally, each cash flow should be valued using the spot rate corresponding to its maturity. Bond price is inversely related to discount rate. Can add risk premium to the risk free rate or series of risk free sport rates
Computation of Bond Price
Bond prices can be expressed as a percentage of par value or as a yield.
Yield to Maturity (YTM)
· A single discount rate that makes the present value of a bond’s cash flows equal to the market price.
· YTM for a semiannual-pay bond is twice the semiannual discount rate and so called as bond equivalent yield.
YTMannual-pay = (1+YTM semianual-pay/2)2-1
YTMsemiannual-pay = [(1+YTMannual-pay)1/2-1]x2 = BEY
Bond price of a bond with semi-annual coupon payment:
P = CPN1 / (1-YTM/2) + CPN2 / (1-YTM/2)2 +.+ (CPN2N + PAR) / (1-YTM/2)2N
Where: YTM is BEY
Bond price for a zero-coupon bond
P = Par / (1 + YTM/2)2 N
Where: YTM is BEY
Full price of a bond between coupon payments
P= Σ[Cash flow in period t/(1 + Discount rate)(t-1+w)]
Where:
w is the no. of days remaining until next coupon (i.e. between settlement date (exclusive) and next copon date(inclusive)/ Total days in coupon period)
Accrued interest = Coupon x (1 - w)
Clean price = Full price - Accrued coupon.
Day count conventions:
· Actual/Actual (US governmentt bond);
· Actual/365 (Bristish government bond),
· 30E/360 (German government bond, Eurobond, most corporate bond, most munis)
Price-Yield Relationship
Inversely related, convex ( bond prices go up faster than they go down)
Pull to par
As time passes, the price of a bond trading at a premium will fall back to par and the price of a bond trading at a discount will rise to par.
Deficiency of traditional approach to valuation:
Each cash flow is unique. Valuing all cash flows of a security using a single discount rate is incorrect unless for a flat term structure. YTM is only a an approximate or weighted average of a set of spot rates.
Arbitrage-free valuation
Each individual cash flow is valued by discounting it at a spot rate corresponding to its maturity.
P = CPN1 / (1-S1) + CPN2 / (1-S2)2 +.+ (CPNN + PAR) / (1-SN)N
Where Si is the corresponding spot rate.
Arbitrage: If the sum of the PVs of cash flows is more than the price of the security, then buy the security and sell the cash flows individually, and vice versa.
Cash flows are valued using the spot rate corresponding to their maturity. It is more accurate than the traditional approach.
Yield to Maturity (YTM)
· A single discount rate that makes the present value of a bond’s cash flows equal to the market price.
· YTM for a semiannual-pay bond is twice the semiannual discount rate and so called as bond equivalent yield.
YTMannual-pay = (1+YTM semianual-pay/2)2-1
YTMsemiannual-pay = [(1+YTMannual-pay)1/2-1]x2 = BEY
Bond price of a bond with semi-annual coupon payment:
P = CPN1 / (1-YTM/2) + CPN2 / (1-YTM/2)2 +.+ (CPN2N + PAR) / (1-YTM/2)2N
Where: YTM is BEY
Bond price for a zero-coupon bond
P = Par / (1 + YTM/2)2 N
Where: YTM is BEY
Full price of a bond between coupon payments
P= Σ[Cash flow in period t/(1 + Discount rate)(t-1+w)]
Where:
w is the no. of days remaining until next coupon (i.e. between settlement date (exclusive) and next copon date(inclusive)/ Total days in coupon period)
Accrued interest = Coupon x (1 - w)
Clean price = Full price - Accrued coupon.
Day count conventions:
· Actual/Actual (US governmentt bond);
· Actual/365 (Bristish government bond),
· 30E/360 (German government bond, Eurobond, most corporate bond, most munis)
Price-Yield Relationship
Inversely related, convex ( bond prices go up faster than they go down)
Pull to par
As time passes, the price of a bond trading at a premium will fall back to par and the price of a bond trading at a discount will rise to par.
Deficiency of traditional approach to valuation:
Each cash flow is unique. Valuing all cash flows of a security using a single discount rate is incorrect unless for a flat term structure. YTM is only a an approximate or weighted average of a set of spot rates.
Arbitrage-free valuation
Each individual cash flow is valued by discounting it at a spot rate corresponding to its maturity.
P = CPN1 / (1-S1) + CPN2 / (1-S2)2 +.+ (CPNN + PAR) / (1-SN)N
Where Si is the corresponding spot rate.
Arbitrage: If the sum of the PVs of cash flows is more than the price of the security, then buy the security and sell the cash flows individually, and vice versa.
Cash flows are valued using the spot rate corresponding to their maturity. It is more accurate than the traditional approach.
Difficulty in estimating expected cash flow
· Bonds with embedded option - uncertain timing of principal repayment
· Bonds with variable coupon - uncertain coupon payment rate as it will be reset occasionally
· Bonds with conversion or exchange privilege
· Bonds with variable coupon - uncertain coupon payment rate as it will be reset occasionally
· Bonds with conversion or exchange privilege
Bond Valuation Process
1. Estimate the expected cash flows
2. Determine the appropriate discount rates.(either the bond’s yield to maturity or a series of spot rates
3. Calculate sum of present values {= ΣCash Flowt/(1 +Discount rate)t}
2. Determine the appropriate discount rates.(either the bond’s yield to maturity or a series of spot rates
3. Calculate sum of present values {= ΣCash Flowt/(1 +Discount rate)t}
LIBOR
LIBOR is:
· the interest rate at which banks can borrow funds from other banks in the London interbank market.
· fixed on a daily basis and derived from a filtered average of the world's most creditworthy banks' interbank deposit rates for larger loans with maturities between overnight and one full year.
· the world's most widely used benchmark for short-term interest rates.
· the interest rate at which banks can borrow funds from other banks in the London interbank market.
· fixed on a daily basis and derived from a filtered average of the world's most creditworthy banks' interbank deposit rates for larger loans with maturities between overnight and one full year.
· the world's most widely used benchmark for short-term interest rates.
Factors that affect the yield spreads
Impact of embedded options
Call option increases reinvestment risk and yield spread must be higher to compensate.
Option adjusted spread < nominal spread
Put option is favorable towards investors and thus reduces yield spread
Option adjusted spread > nominal spread
The yield spread of Agency MBS is primarily due to prepayment risk. Option-adjusted spread excludes the risk due to the embedded option, while the nominal spread does not, making an option-adjusted spread a superior measure to compare returns.
Impact of Liquidity
Lack of liquidity can increase yield spread, even of off-the-run Treasuries.
Impact of tax-exemption:
Munis trade at low yields (even negative yield spread) because their income is tax exempt.
After-tax yield = Pre-tax yield x (1 - Marginal tax rate of investor)
Impact of technical factors:
Imbalance between supply and demand for securities drives temporarily distorted. Yield spreads rise if there is a glut in supply of bonds. The yields spreads of sovereign bonds over US Treasuries are “nominal” since the currencies may be different and the spreads are simply differences in two yields.
Call option increases reinvestment risk and yield spread must be higher to compensate.
Option adjusted spread < nominal spread
Put option is favorable towards investors and thus reduces yield spread
Option adjusted spread > nominal spread
The yield spread of Agency MBS is primarily due to prepayment risk. Option-adjusted spread excludes the risk due to the embedded option, while the nominal spread does not, making an option-adjusted spread a superior measure to compare returns.
Impact of Liquidity
Lack of liquidity can increase yield spread, even of off-the-run Treasuries.
Impact of tax-exemption:
Munis trade at low yields (even negative yield spread) because their income is tax exempt.
After-tax yield = Pre-tax yield x (1 - Marginal tax rate of investor)
Impact of technical factors:
Imbalance between supply and demand for securities drives temporarily distorted. Yield spreads rise if there is a glut in supply of bonds. The yields spreads of sovereign bonds over US Treasuries are “nominal” since the currencies may be different and the spreads are simply differences in two yields.
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