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Describe the 3 types of bonds where estimating cash flow is difficult?
- 1. Principal payments are not known with certainty
- 2. Interest Payments not known with certainty
- 3.Bond is convertible or exchangeable into another security
What are steps in bond valuation process?
- 1.Calculate cash flows
- 2. Calculate discount rate
- 3.Calculate present value of estimated cash flows
How is a Bond's price yield curve shaped?
Convex toward the origin. Looks like half smiley face. Price (Y-Axis) and Yield (X-axis)
What is arbitrage free valuation approach?Spot Rates?
Arbitage free valuation approach discounts each cash flow using a discount rate that is specific to the maturity of each cash flow. These discount rates are called spot rates and can be thought of as the required rate of returns on zero-coupon bonds maturing at various times in the future.
It says that if a T-bond based on spot rates must be equal to the value of the parts (sum of present values of all expected cahs flows) otherwise there is an arbitage opportunity. If bond selling for less than sum of present value of expected cash flows, arbitrageru will buy the bond and sell the pieces.
Assumes that there is a zero coupon priced alternative that can be bought.
Current Yield? Yield to Maturity?
Current Yield is simples of all return measures. Just the annual cash coupon payment over bond price. Even if the qeustion asks a 6% semiannual pay bond, you still use 6% over the current price.
Yield to maturity is an annualized interal rate of return based on a bond's price and it's promised cash flow.
Cash Flow Yield?
Yield on an amortizing loan. Use CF Keys for this, and solve for IRR. Limitation is that prepayment rates may differ fromt hose assumed in the calculation.
Limitation of YTM?
Limitation is that it does not factor in reinvestment income. Assumes income will be reinvested at YTM Rate.
If you purchased a 6% 10 year treasury bond at par how much reinvestment income must be generated over its life to provide the investor with a compuond return of 6% on a semiannual basis
FIrst determine value that must be generated: 100(1.03)^20 = 180.61. You must have the 100 be the purchase price, and if discounted or premium must replace 100. Then take 100 Par value and 20 payments of 3%, which is 3$ each and 60 dollars. 180.61-100-60= 20/.61
Higher or lower of these factors increase reinvestment risk? Coupon Payments? Long Maturities?
Higher coupon payments bc more cash flow to reinvest.
Longer maturities because more of the total value of the n invesmtne is in the coupon cash flow.
take a YTM bond with annual coupon of 6.25 % and YTM Semiannual coupon bond of 6.3% and compare. Do both ways.
((1.063)^1/2)*2=6.2% You do 1/2 first bc it gets the annualized semiannual rate into a annualized rate for 6 months
What is bootstrapping?
Solve for spot rates by knowing the prices of coupon bonds. We always know one spot rate to begin with and then calculate the spot rate for next period using the yields of the next period. Check page 112 for directions but you pretty much solve for 6 month spot rates going forward.
Say for example price is 1000. Coupon and yield are both 3% for 1 yr bond and 4% for 2 year bond.
To find spot rate of 2 year bond= 40/1.03+1040/(1+2 year spot rate)^2 = 1000$.
What is the Nominal Spread? What is Zero volatility spread?
Nominal spread is the spread measure which is YTM minus the YTM of a treasury secutiy of simliar maturity. Is only correct for a spot rate curve that is flat.
Zero volatility spread is the equal amount that we must add to each rate on the Treasury spot yield curve in order to make the presen value of the risky bond's cash flow equal to it's market price.
No difference between nominal and zero spread if curve is flate. Bigger the slope of benchmark, the larger the z-aspread. If spot yield is upward sloping, z-spread is larger than nominal spread. If z-spread is less than nominal spread when spot yield curve is negativley sloped..
When Principal is paid, the greater the difference between the wtwo spread measures. For postiviley sloped yield curve, amortizing will have a greater difference between its Z-spread and nominal spread than a coupon bond will.
Option adjusted Spread?
Measure is used when a bond has an embedded option. Callable bond must have a greter yield than identical option free bond, and a greater nominal spread or z-spread. For embedded callable bonds - OAS<Z-spread. In other words you require more yield on the callable bond than for an option free bond.
For put option, you must pay for option meaning higher price, and OAS>Z-spread. Require less yield on the putable bond.
Easy way to remember- Zspread-OAS=Option cost in percent.
If put option you pay for option, Option Cost<0, meaning OAS is greater.
If call Option, you get paid meaning positive option cost, and greater z-spread.
- si ab orrowing/lending rate for a loan to be made at some future date. Notation used must identify both the length of the lending/borrowing period . Note, by simple averaging the them, you can get a very good clue as to the the right price. 1f2 is one year spot rate in 2 years.
- Note, geometric mean must always be less than arithmetic.
What is the difference between full valuation approach and duration/convexity approach and what is advanatge of full valuation.
full valuation is measuring interes risk based on applying valuation techniques. Plug in rates described in interest rate scenarios and see what happens to value of the bond. Using this approach with extreme changes in interst rates is called stress testing.
Duration/convesity approachy provides approximation of the ac utal interest rate sensitivy of a buond or portfolio. It is much mores imple than full valuation.
Higher Coupon means lower duration
Longer Maturity means higher duration
Higher market yield means lower duration
Postive and Negative Convexity
Postive convexity works in your favor, that bonds price falls at a decreasing rate as yields rise. Is half smiley face
Negative convexity means it rises at a decreasing rate.Curve flips around.
Price change is smaller in rising rates than price change in falling rate for option free bonds. Effective duration uses the average price changes.
Formula is bond price when yields fall-bond price when yields rise/(2xinitial pricexchange in yield in decimal form)
Distinguish among the alternative defniitons of duariton and explain why effective duration is most appropriat measure for bonds with embedded options?
Macaulay duration is estimate of bonds interest rate senstivity based on the time in yeas until promied cash flow will arrive. Macauslay duration based on expected cash flow for option free bond, not appropriate for options.
Modified duration takes the current YTM into account
Limitations of portfolio duration
Limitations stem from fact that yields may not change equally on all bonds in porfolio. With a porftolio with different maturities, credit risks, etc, no reason to suspect that yields on indicvidual bonds will change by equal amounts when yield curve changes.
Duration is a good measure of the sensitivity of profolio value to PARALLEL changes in yield curve
Conexity, does what do the Duration based estimates?
- It throws it off bc duration assumes straight line, not curved. The curvature accounts for a higher price. Price changes based solely on duration are innacurate.
- Greater convexity is greater error.
What is the price change with duration and convexity?
Take modified duration + (convexity*(change in Y decimal)^2)= Percent change in price
Convexity it always positive, and if interest rates rise, price decrease is a negative then add convexity. Only change is when Callabla bond has negative convexity, the Convexity will be negative.
What do you use for convexity calcualtion on option bonds?
Use effective convexity
What is price value of a basis point?
Dollar change in price/ value or bond when the yield changes by one basis point or .01%.
Price value of a basis point = duration x .0001x bond value
1 percent change in yield is percent change in price. Basis point is .01 of 1 percent.