READING 55 THE TERM STRUCTURE OF INTEREST RATES: SPOT, PAR, AND FORWARD CURVES Flashcards
(15 cards)
Which of the following best explains why par yields are usually slightly lower than spot rates in an upward-sloping yield curve environment?
A. Because par bonds are illiquid compared to zero-coupon bonds
B. Because spot rates average all forward rates over the bond’s life
C. Because early cash flows are discounted at lower rates than later ones
Correct Answer: C
Explanation:
In an upward-sloping yield curve, the earlier payments are discounted at lower spot rates, pulling the required par yield slightly below the final spot rate.
A is incorrect; this is irrelevant to how par yields are calculated.
B is true for spot rates, but the question is asking why par yields are slightly below spot rates.
Which of the following best describes the spot rate curve?
A. It shows the yield to maturities of recently issued U.S. Treasury bonds at various maturities.
B. It plots yields of coupon-paying bonds relative to their time to maturity.
C. It plots yields of zero-coupon U.S. Treasury securities for various maturities.
Correct Answer: C
Explanation:
The spot rate curve, also known as the zero curve or strip curve, shows the yields (spot rates) for zero-coupon U.S. Treasury securities across different maturities.
A is incorrect because YTMs of recently issued bonds refer to the on-the-run yield curve, not the spot curve.
B is incorrect because this describes the par yield curve, not the spot curve
Which yield curve is most commonly used as the benchmark for fixed-income pricing?
A. Spot rate curve
B. Par yield curve
C. On-the-run yield curve
Correct Answer: A
Explanation:
The spot rate curve provides the most accurate pricing of bonds because it reflects the appropriate discount rate for each individual cash flow.
B is incorrect because par curves are derived from spot curves and do not price cash flows precisely.
C is incorrect because the on-the-run curve is affected by liquidity and taxation biases.
Which statement best explains the shape of the spot curve when forward rates are declining?
A. The spot curve will be steeper than the forward curve.
B. The spot curve will also slope downward but less steeply.
C. The spot curve will become flat.
Correct Answer: B
Explanation:
The spot curve is the average of forward rates, so when forward rates decline, the spot curve also declines but more slowly.
A is incorrect; the spot curve is always less steep than the forward curve when direction is consistent.
C is incorrect; a flat spot curve would imply constant forward rates, not declining ones.
A flat yield curve most likely indicates:
A. Investors expect future interest rates to rise
B. All spot and forward rates are equal across maturities
C. Long-term bonds are trading at a premium
Correct Answer: B
Explanation:
A flat yield curve implies that forward rates = spot rates = par yields across all maturities.
A is incorrect because rising rate expectations would result in an upward-sloping curve.
C is irrelevant to yield curve shape.
Why might an inverted yield curve occur?
A. Investors expect interest rates to rise.
B. Bonds are trading at par.
C. Investors expect interest rates to fall.
Correct Answer: C
Explanation:
An inverted yield curve is typically due to market expectations of falling interest rates, often tied to a weakening economy.
A is incorrect; rising expectations lead to an upward curve.
B is unrelated to the curve’s slope.
Which of the following most accurately defines the par yield?
A. The coupon rate that sets a bond’s price above par
B. The yield at which a bond is expected to trade given spot rates
C. The coupon rate that causes a bond to trade at par value
Correct Answer: C
Explanation:
The par yield is the coupon rate that would make the bond’s price exactly equal to its face value.
A is incorrect; it describes a premium bond.
B is vague and incorrect; the par yield is not a market forecast, it’s a derived rate.
A par yield curve is constructed primarily using:
A. Spot rates
B. Coupon bond YTMs
C. Forward rates
Correct Answer: A
Explanation:
The par curve is derived from spot rates, by determining the coupon that makes a bond price equal to face value.
B is incorrect; coupon bond YTMs can be distorted by illiquidity and taxation.
C is also incorrect; forward rates are not directly used in par curve construction.
What is a major limitation of using traded coupon bond yields to build a yield curve?
A. There are too many available bonds.
B. Prices are often distorted by liquidity and tax issues.
C. They always trade at par, making yield estimation difficult.
Correct Answer: B
Explanation:
Using market bond prices can introduce bias because liquidity differences and tax treatment can distort observed yields.
A is false; the problem is too few reliable bonds, not too many.
C is false; most bonds trade at a discount or premium, not par.
Why are “on-the-run” Treasury bonds often used in yield curve estimation?
A. They offer higher yields than off-the-run bonds.
B. They are less affected by interest rate changes.
C. They are more liquid and frequently traded.
Correct Answer: C
Explanation:
“On-the-run” bonds are the most recently issued, hence more liquid and have less pricing noise.
A is incorrect; they often trade at a premium, not with higher yields.
B is incorrect; they are just as sensitive to rates, but more liquid.
Which of the following is most likely true when forward rates are rising?
A. Spot rates are constant.
B. Spot rates increase, but more gradually.
C. Spot rates fall more steeply than forward rates.
Correct Answer: B
Explanation:
Spot rates are averages of forward rates, so if forward rates rise, spot rates also rise, but less steeply.
A is false; rising forwards cause rising spots.
C is false; spot rates do not fall in this scenario.
If the spot curve is flat, which of the following must be true?
A. All future forward rates are zero.
B. Spot, forward, and par yields are equal.
C. Short-term bonds have higher yields than long-term bonds.
Correct Answer: B
Explanation:
A flat curve means all rates (spot, forward, and par) are equal across maturities.
A is incorrect; forward rates are not zero, they’re constant.
C is incorrect; that describes an inverted curve.
Which of the following yield curves is not directly observable in the market and must be derived from other data?
A. On-the-run yield curve
B. Spot rate curve
C. Treasury yield curve
Correct Answer: B
Explanation:
The spot curve is constructed from zero-coupon prices or stripped securities—it’s not directly observable.
A and C both refer to market yields based on traded securities.
The main reason par yields are close to but typically lower than spot rates is:
A. Par bonds are assumed to be riskier.
B. Par bonds are less sensitive to changes in interest rates.
C. Early cash flows are discounted at lower spot rates.
Correct Answer: C
Explanation:
Since early payments are discounted using lower spot rates, the weighted average (par yield) ends up slightly below the longest spot rate.
A and B are both unrelated or incorrect.
When forward rates are equal to current spot rates at all maturities, the yield curve is:
A. Inverted
B. Flat
C. Upward sloping
Correct Answer: B
Explanation:
If all forward rates = spot rates, and this is true across all periods, then the curve is flat — no change in interest rates is expected.
A and C describe changing rate environments.
