The Term Structure of Interest Rates: Spot, Par, and Forward Curves
50 questions available
Key Points
- Yield curve relates yield to maturity for similar credit quality bonds.
- Normal curve: Upward sloping (Long-term rate > Short-term rate).
- Inverted curve: Downward sloping (Short-term rate > Long-term rate).
- Spot rates are zero-coupon rates used for specific cash flow discounting.
Key Points
- Bonds are priced as a package of zero-coupon instruments.
- Arbitrage-free price is the sum of PVs of cash flows using spot rates.
- Spot rates remove the reinvestment assumption inherent in YTM.
Key Points
- Par rate makes PV of cash flows equal to Par Value.
- Par curve is a sequence of yields-to-maturity for par bonds.
- Par rates are derived from spot rates via discount factors.
Key Points
- Forward rates are implied future rates derived from current spot rates.
- Notation 'AyBy': A = start time from today, B = tenor.
- Upward Curve: Forward > Spot > Par.
- Inverted Curve: Par > Spot > Forward.
Questions
What does an upward-sloping yield curve indicate regarding the relationship between short-term and long-term yields?
View answer and explanationWhich curve represents the yields of bonds trading at 100 percent of their face value?
View answer and explanationIn the context of forward rates, what does the notation '3y1y' typically represent?
View answer and explanationGiven the following spot rates: Year 1 = 4 percent, Year 2 = 5 percent. What is the value of a 2-year annual pay bond with a 6 percent coupon and a Face Value of 100?
View answer and explanationIf the spot curve is downward sloping (inverted), which of the following orderings is correct?
View answer and explanationCalculate the 1-year forward rate, 1 year from now (1y1y), given the following spot rates: 1-year spot = 5 percent, 2-year spot = 6 percent.
View answer and explanationWhat is the primary characteristic of a 'flat' yield curve regarding the relationship between Spot, Par, and Forward curves?
View answer and explanationSpot rates are also commonly referred to as:
View answer and explanationCalculate the price of a 3-year, 5% annual coupon bond (Face Value 100) using the following spot rates: Year 1 = 2%, Year 2 = 3%, Year 3 = 4%.
View answer and explanationWhich rate is considered a 'breakeven reinvestment rate'?
View answer and explanationGiven 1-year spot rate = 3% and 2-year spot rate = 4%. What is the implied 1-year forward rate 1 year from now?
View answer and explanationIf the yield curve is upward sloping, the forward curve will be:
View answer and explanationThe par rate is essentially a:
View answer and explanationWhich technique is used to derive zero-coupon rates from the prices of coupon-paying bonds?
View answer and explanationGiven: 1-year spot = 4%, 2-year spot = 5%, 3-year spot = 6%. Calculate the 3-year Par Rate.
View answer and explanationUsing the '2y1y' forward rate notation, how long is the forward period (tenor)?
View answer and explanationGiven 2-year spot rate = 8% and 5-year spot rate = 15%. What is the implied '2y3y' forward rate?
View answer and explanationIf the spot curve is inverted (downward sloping), which yield is the highest?
View answer and explanationWhy are par rates derived for hypothetical government bonds used for term structure analysis?
View answer and explanationCalculate the price of a Zero-Coupon bond with 5 years maturity and Face Value 100, if the 5-year spot rate is 10%.
View answer and explanationWhat is the relationship between the Spot Curve and the Par Curve when the yield curve is flat?
View answer and explanationThe 1y1y rate is 8% and the current 1-year spot rate is 4%. What is the approximate 2-year spot rate?
View answer and explanationWhich curve is typically constructed using on-the-run government bonds?
View answer and explanationCalculate the value of a bond with annual coupons of 10%, 2 years maturity, Face Value 1000, using Spot rates: 1yr = 5%, 2yr = 6%.
View answer and explanationIf 1-year spot = 5% and 1y1y forward = 5%, what is the 2-year spot rate?
View answer and explanationWhat is the discount factor for year 2 if the 2-year spot rate is 6%?
View answer and explanationWhich curve is typically 'below' the spot curve in an upward-sloping market?
View answer and explanationCalculate the 2-year spot rate given: 1-year spot = 3%, 2-year par rate = 4%.
View answer and explanationA '3y1y' forward rate refers to:
View answer and explanationIn a 'normal' market conditions scenario, the yield curve is:
View answer and explanationCalculate the 1-year discount factor given a 1-year spot rate of 5%.
View answer and explanationGiven 3-year spot rate = 7% and 4-year spot rate = 8%. What is the implied 1-year forward rate 3 years from now (3y1y)?
View answer and explanationInterpolation is used in yield curve construction to:
View answer and explanationIf the spot curve is flat at 5%, what is the 1-year Par Rate?
View answer and explanationWhich bond pricing method provides an arbitrage-free value?
View answer and explanationWhat is the 3-year Spot Rate if the 1-year rate is 2%, 2-year rate is 3%, and a 3-year annual par bond (coupon=4%) is priced at 100?
View answer and explanationIf a yield curve is downward sloping, what is likely true about future interest rate expectations?
View answer and explanationCalculate the implied 2-year forward rate 1 year from now (1y2y) given: 1-year spot = 3%, 3-year spot = 5%.
View answer and explanationThe term 'Maturity Effect' generally implies that for the same change in yield:
View answer and explanationIn the notation '0y1y', what does this rate essentially represent?
View answer and explanationWhich of the following describes the relationship between Spot (S) and Forward (F) rates when the yield curve is upward sloping?
View answer and explanationCalculate the 2-year Par Rate given: 1-year spot = 5%, 2-year spot = 6%.
View answer and explanationWhich rate is used to discount cash flows when valuing a bond using forward rates?
View answer and explanationGiven 1y1y = 8%, and 1-year spot = 4%. The 2-year spot rate is approximately:
View answer and explanationIn a 'humped' yield curve scenario, intermediate-term yields are:
View answer and explanationGiven: 2-year spot = 6%, 2y1y = 8%. What is the 3-year spot rate?
View answer and explanationWhy do on-the-run government bonds typically trade at lower yields than off-the-run bonds?
View answer and explanationIf the forward curve is below the spot curve, the spot curve must be:
View answer and explanationCalculate the 1-year spot rate if a 1-year par bond has a coupon of 5%.
View answer and explanationUsing spot rates 3% (1yr) and 4% (2yr), value a 2-year Zero Coupon Bond (FV 100).
View answer and explanation