MCQ Quiz

Question 1 of 77

A spot rate is best described as the discount rate applicable to:

A single cash flow to be received in the future.
A series of equal coupon payments.
The yield-to-maturity of a coupon-paying bond.

Question 2 of 77

Given 1-year and 2-year spot rates of 4% and 5%, a 2-year bond with 6% annual coupons will trade at approximately:

Par
A premium
A discount

Question 3 of 77

An upward-sloping spot curve indicates that:

Longer-maturity spot rates exceed shorter-maturity spot rates
Shorter-maturity spot rates exceed longer-maturity spot rates
All spot rates are equal across maturities

Question 4 of 77

Pricing bonds using spot rates establishes no-arbitrage prices because:

The bond cannot be replicated more cheaply using zero-coupon bonds
All bonds must trade at par value
Forward rates are guaranteed to be realized

Question 5 of 77

A zero-coupon bond pays USD 121 in two years. If the 2-year spot rate is 10%, the current price of the bond is:

USD 110.00
USD 100.00
USD 105.00

Question 6 of 77

Given a 2-year spot rate of 4%, the price of a 2-year zero-coupon bond with face value of 100 is closest to:

92.46
96.00
98.00

Question 7 of 77

If $(1+Z_3)^3 = (1+Z_2)^2 \times (1+IFR_{2,1})$, which rearrangement correctly solves for $IFR_{2,1}$?

$IFR_{2,1} = \dfrac{(1+Z_3)^3}{(1+Z_2)^2} - 1$
$IFR_{2,1} = (1+Z_3)^3 - (1+Z_2)^2$
$IFR_{2,1} = \dfrac{1+Z_2}{1+Z_3} - 1$

Question 8 of 77

The par rate for a specific maturity is best defined as the:

Coupon rate that causes the bond's price to equal its face value.
Yield to maturity of a zero-coupon bond.
Forward rate for the final year of the bond's life.

Question 9 of 77

A three-year bond has annual coupon $PMT = 5$, face value $FV = 100$, and spot rates $Z_1 = 2\%$, $Z_2 = 3\%$, and $Z_3 = 4\%$. Its price is closest to:

102.96
100.00
104.50

Question 10 of 77

A bond priced at 100 falls to 96 when yields rise by 100 bps. Its approximate modified duration is:

2
4
8

Question 11 of 77

Given a 1-year spot rate of 3% and a 2-year spot rate of 5%, the 1-year forward rate one year from now (1y1y) is closest to:

4.00%
5.00%
7.04%

Question 12 of 77

Which equation is the CFA Curriculum pricing relation used to solve for a par-rate coupon payment $PMT$ on a bond priced at par?

$100 = \dfrac{PMT}{(1+z_1)^1} + \dfrac{PMT}{(1+z_2)^2} + \cdots + \dfrac{PMT+100}{(1+z_N)^N}$
$PV = \dfrac{PMT}{(1+r)^1} + \dfrac{PMT+100}{(1+r)^N}$
$100 = PMT + 100$

Question 13 of 77

A zero-coupon bond matures in 1 year and is currently trading at USD 90 with a face value of 100. The 1-year spot rate is closest to:

11.1%
10.0%
9.0%

Question 14 of 77

A par rate is best defined as the coupon rate that:

Makes a bond's price equal to its par value
Equals the longest-maturity spot rate
Represents the average of all spot rates

Question 15 of 77

The 1-year spot rate is 4% and the 1-year forward rate one year from now (1y1y) is 6%. The approximate 2-year spot rate is closest to:

5%
10%
2%

Question 16 of 77

A risk-free bond has a single payment of USD 105 due in one year. If the 1-year spot rate is 5%, the price of the bond is:

USD 100.00
USD 105.00
USD 99.50

Question 17 of 77

For a forward rate denoted as '3y2y', the loan period ends:

5 years from today.
3 years from today.
2 years from today.

Question 18 of 77

A buy-and-hold investor purchases a bond at par. If interest rates immediately rise and remain elevated, the investor's horizon yield will most likely be:

Lower than the original YTM
Equal to the original YTM
Higher than the original YTM

Question 19 of 77

The three sources of return from investing in a fixed-rate bond are:

Coupon income, reinvestment income, capital gain/loss
Coupon income, price appreciation, credit spread
Interest income, dividend income, capital gain/loss

Question 20 of 77

An investor buys a 5-year bond at par (100) with 6% annual coupons. If the bond is sold after 2 years at 102, and coupons are reinvested at 6%, the investor's horizon yield is closest to:

6%
7%
8%

Question 21 of 77

The 2-year spot rate is 4% and the 3-year spot rate is 5%. The approximate 1-year forward rate two years from now ($2y1y$) is:

7%
1%
4.5%

Question 22 of 77

A bond has modified duration of 6 and yield-to-maturity of 5%. If yields increase to 6%, the bond's approximate percentage price change is:

+6%
-6%
-12%

Question 23 of 77

If a 1-year zero-coupon bond trades at 96, the 1-year spot rate is closest to:

4.00%
4.17%
96.00%

Question 24 of 77

If all spot rates in the economy increase by 1%, the price of a standard fixed-coupon bond will:

Decrease.
Increase.
Remain unchanged.

Question 25 of 77

For a zero-coupon bond, Macaulay duration is equal to:

Its time-to-maturity
Half its time-to-maturity
Zero

Question 26 of 77

A 2-year forward rate starting in 1 year (1y2y) of 6% can be interpreted as the rate that makes an investor indifferent between:

Investing for 3 years versus investing for 1 year then reinvesting for 2 years
Investing for 2 years versus investing for 1 year then reinvesting for 1 year
Investing for 1 year versus investing for 2 years

Question 27 of 77

Which formula most accurately gives a bond's price using a sequence of spot rates?

$PV = \dfrac{PMT}{(1+Z_1)^1} + \dfrac{PMT}{(1+Z_2)^2} + \cdots + \dfrac{PMT+FV}{(1+Z_N)^N}$
$PV = \dfrac{PMT+FV}{(1+Z_1)^1} + \dfrac{PMT}{(1+Z_1)^2}$
$PV = \dfrac{PMT}{1+Z_N} + \dfrac{FV}{1+Z_N}$

Question 28 of 77

Given 1-year and 2-year spot rates of 2% and 4% respectively, the 2-year par rate is closest to:

3.00%
3.96%
4.00%

Question 29 of 77

A bond with modified duration of 5, priced at 98 per 100 face value, and a position size of USD 10 million face value has money duration closest to:

USD 490,000
USD 500,000
USD 5,000,000

Question 30 of 77

Using annual compounding, if $(1+0.03)^3(1+IFR_{3,2})^2 = (1+0.04)^5$, the implied two-year forward rate in three years is closest to:

5.52%
4.00%
1.00%

Question 31 of 77

If the price of a bond equals 100 and its coupon payment per 100 of par also equals the yield-to-maturity per 100 of par, the bond is most accurately described as trading at:

Par
A discount
A premium

Question 32 of 77

If the one-year forward rates are $0y1y = 1.88\%$ and $1y1y = 2.77\%$, the two-year spot rate is closest to:

2.324%
4.650%
1.880%

Question 33 of 77

A portfolio manager wants to reduce interest rate risk by USD 500,000 per 1% yield change. This requires adjusting:

Modified duration by 5
Money duration by USD 500,000
Macaulay duration by 500,000 years

Question 34 of 77

The forward rate notation '2y1y' refers to a rate for a:

1-year loan beginning 2 years from today.
2-year loan beginning 1 year from today.
1-year loan beginning 1 year from today.

Question 35 of 77

If an investor's horizon equals the bond's Macaulay duration, the investor is most hedged against:

Interest rate risk
Credit risk
Liquidity risk

Question 36 of 77

For a zero-coupon bond, the Yield to Maturity (YTM) is always equal to:

The spot rate for that maturity.
The par rate for that maturity.
The coupon rate.

Question 37 of 77

Positive convexity is most beneficial to bond investors when:

Yields are stable
Yields are volatile
Credit spreads widen

Question 38 of 77

A spot rate is best described as the:

Yield-to-maturity on a zero-coupon bond
Current yield on a coupon-paying bond
Forward rate starting today

Question 39 of 77

If a bond is trading at USD 98 in the market, but its value calculated using spot rates is 99, an arbitrageur would profit by:

Buying the bond and stripping it (selling the individual cash flows).
Selling the bond and buying the individual strips.
Doing nothing; the difference is transaction costs.

Question 40 of 77

Which expression most accurately prices a bond using one-year forward rates?

$PV = \dfrac{CF_1}{1+f_1} + \dfrac{CF_2}{(1+f_1)(1+f_2)} + \cdots + \dfrac{CF_N}{(1+f_1)(1+f_2)\cdots(1+f_N)}$
$PV = \dfrac{CF_1+CF_2+\cdots+CF_N}{1+f_N}$
$PV = CF_1(1+f_1) + CF_2(1+f_2)$

Question 41 of 77

If spot rates are flat across maturities, the formula relationships in the CFA Curriculum imply that forward rates and par rates are most likely:

Equal to the spot rates
Always above the spot rates
Always below the spot rates

Question 42 of 77

For an option-free bond, the convexity adjustment to the duration-based price estimate is always:

Positive
Negative
Zero

Question 43 of 77

If you can earn 3% for one year or 5% annually for two years, the market is effectively implying that rates next year will be:

Higher than 5%.
Exactly 5%.
Lower than 3%.

Question 44 of 77

If the spot curve is upward sloping, implied forward rates will most likely be:

Lower than corresponding spot rates
Equal to corresponding spot rates
Higher than corresponding spot rates

Question 45 of 77

Using forward rates $0y1y = 1.5\%$, $1y1y = 2.5\%$, and $2y1y = 3.5\%$, the price of a three-year 2% coupon bond with par value 100 is closest to:

98.619
100.000
102.500

Question 46 of 77

In a flat yield curve environment where all spot rates are 6%, the par rate for a 3-year bond is:

6%
Less than 6%
More than 6%

Question 47 of 77

A bond has Macaulay duration of 8 years. An investor with a 5-year investment horizon has a duration gap of:

-3 years
+3 years
+13 years

Question 48 of 77

Given $(1+S_3)^3 = 1.331USD and (1+S_2)^2 = 1.21$, the 1-year forward rate two years from now ($1+2y1y$) is:

1.10
1.121
0.121

Question 49 of 77

A bond has Macaulay duration of 5 years and yield-to-maturity of 4%. Its modified duration is closest to:

4.81
5.00
5.20

Question 50 of 77

A bond is purchased at par and held to maturity. If interest rates fall immediately after purchase, the investor's realized return will most likely be:

Lower than the original YTM
Equal to the original YTM
Higher than the original YTM

Question 51 of 77

The ideal dataset for constructing a government bond spot curve consists of:

Zero-coupon bonds across various maturities
High-coupon bonds priced at a premium
Corporate bonds with similar ratings

Question 52 of 77

Which formula most accurately gives a three-year spot rate from one-year forward rates $0y1y$, $1y1y$, and $2y1y$?

$(1+Z_3)^3 = (1+0y1y)(1+1y1y)(1+2y1y)$
$Z_3 = 0y1y + 1y1y + 2y1y$
$(1+Z_3) = (1+0y1y)(1+1y1y)(1+2y1y)$

Question 53 of 77

Convexity measures the:

First-order linear price change from yield changes
Second-order non-linear price change from yield changes
Average maturity of bond cash flows

Question 54 of 77

Which equation correctly links the 2-year spot rate ($S_2$), the 1-year spot rate ($S_1$), and the 1-year forward rate one year from now ($1y1y$)?

$(1+S_2)^2 = (1+S_1) \times (1+1y1y)$
$(1+S_2) = (1+S_1) + (1+1y1y)$
$2 \times S_2 = S_1 + 1y1y$

Question 55 of 77

Which formula most accurately gives the implied forward rate from spot rates in the CFA Curriculum?

$(1+Z_A)^A \times (1+IFR_{A,B-A})^{B-A} = (1+Z_B)^B$
$(1+Z_A)^B \times (1+IFR_{A,B-A})^A = (1+Z_B)^{B-A}$
$Z_A + IFR_{A,B-A} = Z_B$

Question 56 of 77

For coupon-paying bonds, Macaulay duration is always:

Equal to time-to-maturity
Greater than time-to-maturity
Less than time-to-maturity

Question 57 of 77

In a downward-sloping (inverted) yield curve, forward rates will most likely be:

Lower than spot rates
Equal to spot rates
Higher than spot rates

Question 58 of 77

A 2-year bond with a USD 100 par value pays an annual coupon of 5. The 1-year spot rate is 5% and the 2-year spot rate is 6%. To calculate the price, you sum:

PV of USD 5 at 5% and PV of 105 at 6%.
PV of USD 5 at 5% and PV of 105 at 5%.
PV of USD 5 at 6% and PV of 105 at 6%.

Question 59 of 77

Using annual compounding, if $Z_2 = 1.5\%$ and $Z_3 = 2.0\%$, the implied one-year forward rate two years from now is closest to:

3.01%
2.00%
0.50%

Question 60 of 77

If all spot rates equal 5% regardless of maturity, all implied forward rates will be:

Less than 5%
Equal to 5%
Greater than 5%

Question 61 of 77

Which bond characteristic will increase a bond's duration, all else equal?

Higher coupon rate
Higher yield-to-maturity
Longer time-to-maturity

Question 62 of 77

Given spot rates of 2% (1-year), 3% (2-year), and 4% (3-year), the price of a 3-year bond with 5% annual coupons and face value 100 is closest to:

102.78
100.00
97.45

Question 63 of 77

An investor with an investment horizon longer than a bond's Macaulay duration is most concerned about:

Reinvestment risk
Price risk
Neither risk

Question 64 of 77

In an upward-sloping yield curve environment, the par rate will most likely be:

Lower than the corresponding spot rate at the same maturity
Equal to the corresponding spot rate at the same maturity
Higher than the corresponding spot rate at the same maturity

Question 65 of 77

If a 1-year zero-coupon bond trades at 98 and a 2-year zero-coupon bond trades at 94, the 2-year spot rate is closest to:

2.04%
3.00%
3.19%

Question 66 of 77

An investor sells a bond before maturity. If interest rates rise after purchase, the investor will most likely experience:

A capital gain
A capital loss
No capital gain or loss

Question 67 of 77

If the coupon payment that solves the par-rate equation is $PMT = 2.607$ per 100 of par value, the par rate per period is closest to:

2.607%
0.02607%
26.07%

Question 68 of 77

An implied forward rate is best described as a:

Breakeven reinvestment rate linking two spot rates
Historical interest rate from a prior period
Current spot rate adjusted for inflation

Question 69 of 77

The 1-year spot rate is 3% and the 2-year spot rate is 5%. The implied 1-year forward rate one year from now (1y1y) is closest to:

7%
4%
2%

Question 70 of 77

A portfolio consists of 50% Bond A (duration 3) and 50% Bond B (duration 7). The portfolio duration is:

3.5
5.0
10.0

Question 71 of 77

If the spot rate curve is upward sloping (normal), which of the following relationships is true?

Forward Rate > Spot Rate > Par Rate
Spot Rate > Forward Rate > Par Rate
Par Rate > Spot Rate > Forward Rate

Question 72 of 77

A 3-year zero-coupon bond is priced at 90 per 100 face value. The 3-year spot rate is closest to:

3.33%
3.57%
10.00%

Question 73 of 77

A bond has modified duration of 4 and convexity of 20. If yields fall by 2%, the estimated percentage price change is closest to:

+8.0%
+8.4%
+7.6%

Question 74 of 77

If the 1-year spot rate is 25%, the 1-year discount factor is:

0.80
1.25
0.75

Question 75 of 77

Calculating the realized return of a bond to match its calculated YTM requires that all coupons are reinvested at:

The Yield to Maturity (YTM).
The spot rate corresponding to each coupon date.
The risk-free rate.

Question 76 of 77

The primary advantage of using spot rates rather than a single yield-to-maturity for bond pricing is that spot rates:

Eliminate the assumption of constant reinvestment rates across all cash flows
Always result in higher bond prices
Require less calculation than yield-to-maturity

Question 77 of 77

Given a 1-year spot rate of 2% and a 2-year spot rate of 4%, the 1-year forward rate starting in 1 year (1y1y) is closest to:

3.00%
6.00%
6.04%

First Principles Thinking: Spot Rates

First Principles Thinking: Premium/Discount Determination

First Principles Thinking: Yield Curve Shape

First Principles Thinking: No-Arbitrage Principle

First Principles Thinking: Discounting

First Principles Thinking: Zero-Coupon Bond Valuation

First Principles Thinking: core idea

First Principles Thinking: Definition of Par

First Principles Thinking: core idea

First Principles Thinking: Duration from Price Change

First Principles Thinking: Forward Rate Mechanics

First Principles Thinking: core idea

First Principles Thinking: Yield Calculation

First Principles Thinking: Par Rate Concept

First Principles Thinking: Arithmetic Average Approximation

First Principles Thinking: PV Calculation

First Principles Thinking: Timeline Addition

First Principles Thinking: Buy-and-Hold Return Dynamics

First Principles Thinking: Bond Return Components

First Principles Thinking: Horizon Yield Computation

First Principles Thinking: Weighted Averages

First Principles Thinking: Duration Price Sensitivity

First Principles Thinking: Single-Period Spot Rate

First Principles Thinking: Denominator Effect

First Principles Thinking: Zero-Coupon Bond Duration

First Principles Thinking: Forward Rate Breakeven

First Principles Thinking: core idea

First Principles Thinking: Par Rate Computation

First Principles Thinking: Money Duration Formula

First Principles Thinking: core idea

First Principles Thinking: core idea

First Principles Thinking: core idea

First Principles Thinking: Money Duration Application

First Principles Thinking: Forward Notation

First Principles Thinking: Duration Matching

First Principles Thinking: Single Cash Flow Discounting

First Principles Thinking: Convexity Value

First Principles Thinking: Defining Spot Rates

First Principles Thinking: Buy Low, Sell High

First Principles Thinking: core idea

First Principles Thinking: core idea

First Principles Thinking: Convexity Sign Property

First Principles Thinking: Break-Even Rates

First Principles Thinking: Yield Curve Relationships

First Principles Thinking: core idea

First Principles Thinking: Flat Curve Equality

First Principles Thinking: Duration Gap Formula

First Principles Thinking: Division of Growth Factors

First Principles Thinking: Modified Duration Formula

First Principles Thinking: Reinvestment Risk for Buy-and-Hold

First Principles Thinking: Spot Curve Data Requirements

First Principles Thinking: core idea

First Principles Thinking: Convexity Concept

First Principles Thinking: Geometric Compounding

First Principles Thinking: core idea

First Principles Thinking: Duration-Maturity Relationship

First Principles Thinking: Inverted Curve Dynamics

First Principles Thinking: No-Arbitrage Valuation

First Principles Thinking: core idea

First Principles Thinking: Flat Curve Properties

First Principles Thinking: Duration Determinants

First Principles Thinking: Multi-Period Cash Flow Valuation

First Principles Thinking: Duration Gap and Risk Exposure

First Principles Thinking: Par-Spot Relationship

First Principles Thinking: Multi-Period Spot Rate

First Principles Thinking: Price-Yield Relationship

First Principles Thinking: core idea

First Principles Thinking: Forward Rate Concept

First Principles Thinking: Bootstrapping Forwards

First Principles Thinking: Weighted-Average Duration

First Principles Thinking: Marginal Rates

First Principles Thinking: Extracting Spot Rates

First Principles Thinking: Combined Duration-Convexity Formula

First Principles Thinking: Discount Factors

First Principles Thinking: Internal Rate of Return

First Principles Thinking: Spot Rate Advantages

First Principles Thinking: Forward Rate Derivation