Print › Fixed Income Concepts | Quizlet

Print › Fixed Income Concepts | Quizlet

Fixed Income Concepts Study online at quizlet.com/_2b284 1. Duration Definition A measure of the sensitivity of an asset's value to interest rate movements (% change in price corresponding to a parallel shift in yields or YTM) ex - a 5yr duration means the bond will decrease in val by 5% if int rates rise 1% and increase in val by 5% if interest rates fall 1% 2. Duration Characteristics * tends to increase w/ maturity but at a decreasing rate * if an investor expects IR to fall, a bond with long duration would be appealing if expected to fall, chose a shorter dur * all else equal, higher rates=lower dur 3. Yield to Maturity * the one discount rate that equilibrates PV of cash flows to the market price * the IRR that a buyer would receive if they purchased the bond at market price 4. What are the key 1) assumes that the bond is held to maturity assumptions of YTM and that 2) the interim cash flows are reinvested at the same YTM 5. Macaulay Duration *Defined as the present-value wgted Definition avg time to receipt of cash flows, units=years 6. Problems with 1) assume that prices are a function of one-factor: YTM Macaulay/Modified 2) do not work for large IR changes (only the Duration linear component of the price/yield relationship) 3) not appropriate for sec with embedded options or where CF will be affected by IR changes 7. Analytic vs. numerical We say we have an analytic solution if we can actually solve the equation explicitly for the unknown solutions variable. In this case, it is easy to see that the explicit analytic solution is x = 5, and that this is the exact solution. If we were not so smart, we might develop an "algorithm" on a computer to solve this equation numerically. 8. Macaulay Duration Formula D = -(∂P/∂Y) 1/P (1+Y) (using partials) where P = Price Y=YTM 9. Macaulay Duration Analytic for fixed cash flow securities: Formula D = SIGMA (Pi*ti / V ) where Pi=PV of Cashflow i ti= time i V = PV of security (dirty price) 10. Modified Duration % change in price wrt a 1% change in YTM Definition 11. Modified Duration Formula MD = -∂P/∂Y * 1/P where P = dirty price, Y = YTM 12. Modified Duration - Modified Dur = Macaulay Duration / (1+YTM/n) Macaulay Duration Relationship 13. How can Modified Duration delta P = -modified duration * yield change be used to estimate the ex: MD=7, YTM change =+1%, P* = -7% change in price given a change in Yield? 14. Define Dollar Duration $ duration shows the effect of a change in yield (YTM) on the dollar value of a bond $D = -∂V/∂Y or Modified duration * price 15. Define PV01 and DV01 DV01 = $ val of a basis point = $D / 10,000 if currency is USD, DV01 = PV01 DV01 = DVBP, PV01 = PVBP 16. Define the Effective Duration ED = Option Adjusted Duration OAD = - (1/p) * (∂p/∂r) where r = parallel spot curve shock (one factor model) allows for CF to change as Yield changes as will happen with securities with embedded options 17. How is Effective Duration One method using a binomial tree: Calculated 1) Move the current YC up and down by a spec amt 2) recalculate the IR tree for each path 3) Re-estimate the CF along each path, holding OAS constant at current value 4) recalculate the avg price for the up and down trees Calc ED = {(Value IR down) - (Value IR up) } / (2V0deltaY) 18. Define Convexity Convexity measures the sensitivity of bond duration to changes in interest rates. It is the second order taylor expansion and accounts for the nonlinearity in the price/ytm relationship 19. Describe the effects of Assuming duration is negative: positive/negative convexity If pos convex = yields decr -> Slope (dp/dr) decreases -> Dur (-1/p*dp/dr) increases yields increase -> slope decreases -> Dur decreases higher convex = less affected by rise in IR, more affected by fall & higher price regardless of whether rates rise or fall 20. Explain the parametric approach assume Price is a function of N factors: P=P(F1,...FN) to risk mgmt *Param app investigates the price sensitivity of securities and ports to each risk factor in isolation, others fixed *Assume price is a function of a single factor, x: P = P (x) *Use a TS to estimate the behavior of percent changes around an arbitrary point x0 The first order expressions: -1/P (∂P/∂x) are partial dur (OAD, Key rate dur, spread dur, vol dur, prepay dur, etc.) * second order=convexities 21. Spread Duration The Approximate percentage change in a bond's price for a 100 basis point change in the credit spread assuming that the Treasury rate is unch Also can measures a bond's market price to a change in Option Adjusted Spread Does not account for prepayments 22. OAD/OAC drift drift = -∂OAD/∂r, OAC drift = -∂OAC/∂r 23. MBS Duration measures • Volatility duration - measures the % change in the price of an MBS that results from a 1% change in vol • Prepayment duration - % change in price resulting from a 1% change in the prepayment model • Current Coupon Spread Duration - % change in the price resulting from a 10bps change in cc spread • Refi Duration / Turnover Duration / Elbow duration - changes in refi dial, turnover dial, and elbow effect (lower costs=more refi) • Coupon Curve Duration measures the price sensitivity of MBS to changes in IR using the prices of MBS with the same agency and term. 24. Define a Bullet Bond Non-callable, coupon paying bond that pays principal at maturity (no amortization payments) amortizing bond - bond that repays part of principal along w/ coupon (mbs, abs) 25. Define Swap Spread Swap Spread = Swap Yield - Tsy Yield w/ same maturity regarded as a systematic credit premium spread over swap = specific credit risk 26. Define Nominal Nominal Yield spread: diff in YTM of a bond and YTM of benchmark Yield Spread 27. Define Zero Zero Volatility Spread (zspread) - The constant spread that, when added to the yield at each point on the spot Volatility Spread rate Treasury curve where a bond's cash flow is received, will make the price of a security equal to the present value of its cash flows. for option-free bonds, zspread=oas 28. Define OAS the flat spread which has to be added to the treasury yield curve in a pricing model (that accounts for embedded options) to discount a security payment to match its market price. OAS is hence model dependent. to calculate the OAS, the spot rate curve is given multiple interest rate paths. In other words, many different spot rate curves are calculated and the different interest rate paths are averaged An OAS accounts for interest rate vol and the prob of the prepayment of principal of the bond. 29. Define Discount Discount Margin (DM) - Bonds with var int rates are usually priced close to their par value. because the interest Margin rate (coupon) on a var rate bond adjusts to current IR based on changes in the bond's ref rate. The DM is the spread that, when added to the bond's current reference rate, will equate the bond's CF to its current P. 30. How is OAS 1) Estimate a series of IR paths representative of possible future rates so that no arbitrage exists calculated? 2) Project cash flows of the security along each of the paths 3) Estimate the OAS as the spread that when added to the yields used to discount cash flows, makes the avg of discounted cash flows equal to the price 31. How is Price • Using only duration: ∂ Price = (∂P * Duration) Approximation • Using duration + convexity: ∂ price = (∂yduration) + (0.5 Conv * (∂y)^2) done using duration/convexity? 32. Describe the YB 1) Determine which sector each position is in method for 2) For each position, assemble Risk Factors: Level of IR, vol of rates, credit spread, liquidity spread, hedging estimating TE risk, exchange rate risk, etc. 3) Decompose the covariance matrix for each sector risk factor set into principal components 4) Based on a multivariate normal distribution, the principal components cov matrix, and the initial values, sample a draw from the set of risk factors 5) Estimate the return of each position in the portfolio and benchmark (do this by estimating the change in return do to the change in each risk factor from its initial state and summing the differences) 6) repeat 4 and 5 10,000 times Rather than estimate the entire covariance matrix that would incorporate all relationships of risk factors and positions, YB uses principal components which can explain 90% of the total variance of each subsector 33. Define OAC/OAD describes how OAC and OAD change as rates change: drift OAD Drift = - dOAD/dr OAC drift = -dOAC/Dr 34. Define Constant measures empirical duration for securities in particular price ranges Dollar Duration 35. List some MBS All measure price sensitivity Duration Measures Volatility Duration - to volatility Prepayment Duration - to prepayments Current Coupon Spread Duration - to cc spread Refi Duration - to refinancing dial Coupon Curve Duration - to changes in IR using prices of mbs w/ same agency and term 36. Describe the Monte Delta normal = dur and conv are calculated at the current price and scenarios with IR changes use that duration Carlo Method of est and convexity estimate which will lead to false results for path-dependent securities where the cash flow is TE dependent upon the IR. Return dist of each security is assumed to be a linear function of the underlying risk factors and risk factors are assumed to be normally distributed.

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