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CFA® Exam Sample Questions

By: Kaplan Schweser
January 15, 2021
Graphic representing CFA Exam Sample Questions

CFA® exam sample questions might be just what you need if you are trying to get a sense of what the exam is like. In this article, we explain the question formats for each level and provide examples (and answers!) from past exams. For the sake of continuity, and to give you an idea of how the questions change at each level, all of them relate to the fixed income exam topic.

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Level I CFA® Exam Questions

The Level I exam consists of multiple-choice questions with three answers to choose from. The questions vary from open-ended statements to evaluating data and information. CFA Institute provides more details about the format on its website. You can also learn more about the CFA Level I exam in this article. Here are some fixed-income Level I question examples.

Question Examples

Question 1: If the market yield does not change, the price of a Treasury bill:

A. Will increase as the bill approaches maturity.
B. Will decrease as the bill approaches maturity.
C. Stay the same as the bill approaches maturity.

Question 2: Which of the following is closest to the percentage price change of a bond for a 20 basis point increase in the yield if the bond’s duration is 8.54 and the convexity is 58.66?
A. –1.696%.
B. –1.708%.
C. –1.720%.

Question 3: The following details are gathered from Treasury securities:

Which of the following is the best estimate of the one-year implied forward rate three years from now?

A. 2.91%
B. 3.12%
C. 3.20%

Question 4: Evaluate the following statements.
Statement 1: “A putable bond exhibits negative convexity at low yields and positive convexity at high yields.”
Statement 2: “Effective duration measures the sensitivity of a bond’s price to changes in its yield to maturity.”

A. Both statements are correct.
B. Exactly one statement is correct.
C. None of the statements are correct.

Level I Answers

The answer to question 1 is A, the answer to question 2 is A, the answer to question 3 is A, and the answer to question 4 is C.

Level I Answer Explanations

Question 1

Treasury bills are discount instruments. As the bond approaches maturity, the price would increase.


For all bonds, the present value of the redemption value will begin to dominate price as the bond gets closer to maturity. For bonds issued at a discount, this means their price will increase to par over their life. For bonds issued at a premium, the price will decline to par value. This is known as the bond’s price on a constant yield trajectory. In FRA the impact on a bond’s price due to the passage of time, keeping yield constant, is known as amortized cost.

Question 2

Percentage price change in the bond price:

= (- Duration x change in yield) + (½ x Convexity x change in yield2)
= – 8.54 x 0.002 + ½ x 58.66 x 0.0022 = –0.01696 x 100 = –1.696%

Question 3

The one year rate three years from now

= [(1 + spot 4)4/(1 + spot 3)3] – 1 = [1.0384/1.0413] – 1 = 0.0291 or 2.91%

Question 4

Statement 1 is incorrect. The statement is describing a callable bond not a putable bond. Statement 2 is incorrect. Effective duration measures the sensitivity of a bond’s price to changes in the benchmark yield curve, not its yield to maturity.

Level II CFA Exam Questions

Level II of the CFA exam introduces vignettes. A vignette describes a business scenario in several paragraphs using a mix of text, tables, financial statements, and so on. (You can get more information about the Level II exam here.) As part of preparing for Level II, you must develop the ability to quickly scan through a vignette and pick out the pieces of data needed to answer a particular question. Let’s look at a sample vignette and its questions.

Level II Vignette: Holly Jameson, CFA

Holly Jameson has recently started a new role as a bond analyst at Holt Investment Management, LLC, based in Farland. Her team leader has provided her with up-to-date but incomplete data on the term structure of interest rates, summarized in Exhibit 1.

Exhibit 1: Farland Treasury Bond Rates

Holly has been asked to assess whether a specific treasury bond that Holt is considering recommending to its clients is fairly priced. The bond pays a 6% annual coupon, matures in three years’ time, and is trading at $108.30.

In a discussion in the staff dining room shortly after she joined the firm, Holly’s colleague, Doug Ross, made a confident assertion, “I really don’t know how some people find bond trading difficult. For each specific maturity, spot rates are always lower than forward rates, and forward rates are always lower than YTM. So, you can always achieve a higher return by riding the yield curve. I’ve been doing that since my first day on the job.”

Holt offers both domestic and international bonds to its clients to enable them to benefit from risk reduction through diversification. Holly has carried out some preliminary research on the Farland bond market and has found that the yield curve has an unexpected shape and does not seem to be driven by interest rate expectations.

She asks her team leader for advice, who tells her, “Things are strange in Farland. Rates are influenced simply by the supply and demand of bonds of specific maturities. Different types of investors want particular maturity bonds, and they never seem to deviate from their preferences. High demand for 5-year bonds has pushed prices up and yields down.”

Alex Allan, a bond analyst colleague of Holly, started another discussion with the group by stating, “I’m more interested in what happens to bond prices when the yield curve changes. I need to estimate how much prices will change when short-term yields increase but long-term yields stay constant.”

Question 1: The BBB-rated corporate bond being assessed by Holly is most likely:

A. Undervalued by $2.34.
B. Overvalued by $3.75.
C. Overvalued by $3.70.

Question 2: The comments made by Doug Ross are most likely:
A. Inaccurate in respect to the statement about spot rates, forward rates, and yields-to-maturity.
B. Inaccurate in respect to the statement about riding the yield curve.
C. Inaccurate in both respects.

Question 3: Holly’s team leader’s comments about interest rates in Farland most likely supports which theory of the term structure of interest rates?

A. Liquidity preference theory.
B. Segmented markets theory.
C. Local expectations theory.

Question 4: The most appropriate measure for Alex Allan to assess bond price sensitivity is:

A. Key rate duration.
B. Effective duration.
C. Macaulay duration.

 

Level II Answers

The answer to question 1 is C, the answer to question 2 is C, the answer to question 3 is B, and the answer to question 4 is A.

Question 1

Holly must first bootstrap spot rates for years 2 and 3 from the given par yields-to-maturity. A bond trading at par must have the same coupon rate as the yield-to-maturity. Using a hypothetical 2-year par bond, the 2-year spot rate can be derived as follows:

CFA Level 2 Answer Explanation Equations Part 1

 

Likewise, the 3-year spot rate:

CFA Level 2 Answer Explanation Equations Part 2

 

Having derived the relevant spot rates, Holly can now value the BBB-rated corporate bond, discounting the future cash flows using the spot rates:

CFA Level 2 Answer Explanation Equations Part 3

 

The bond is trading at $108.30 and is therefore overvalued by $3.70.

 

Question 2

Doug’s comments about the relative values of spots, forwards, and yields-to-maturity apply only when the yield curve is upward-sloping. If the yield curve is downward-sloping, spots will be higher than forwards, and forwards will be higher than yields.

Riding the yield curve describes a strategy whereby an investor will buy a bond with a maturity greater than his investment horizon and sell it before maturity. This strategy will provide higher returns than buying a bond and holding it to maturity over the same period only if the yield curve is upward sloping and its shape remains stable over the investment period. If the yield curve steepens sufficiently, then the strategy may produce losses.

 

Question 3

The segmented markets theory states that the shape of the yield curve is determined by varying levels of supply and demand for bonds of specific maturities, and investors only deal in bonds with their preferred maturities, regardless of yields on bonds of different maturity.

The preferred habitat theory has similar principles, but investors may be tempted to invest in bonds that are not of their preferred maturity if expected returns are attractive enough, with low prices and high yields.

 

Question 4

Assuming an upward-sloping yield curve as a starting point, if short-term yields increase, but long-term yields remain constant, then the yield curve will flatten. This is a non-parallel shift in the yield curve, which makes effective duration an inappropriate measure of bond price sensitivity. Key rate duration is the preferred measure for non-parallel shifts in the yield curve.

Effective duration is only suitable for measuring the sensitivity of a bond’s price to parallel shifts in the yield curve. Macaulay duration measures the weighted average length of time to receive the present value of a bond’s cash flows and is inappropriate in this instance.

 

Level III Exam Questions

The morning session of the CFA Level III exam introduces a type of essay question called constructed response to test your ability to apply judgment (the afternoon session of the exam has more vignettes, and you can learn more about the exam format and more here). These constructed response questions are open-ended. You must write your own answer; there are no options to choose from. Here is an example of a constructed response question related to fixed income.

Level III Constructed Response

Algonquin Enterprises is a US company that recently raised a substantial quantity of cash from the sale of a redundant factory site and would like to use this cash to retire a set of debt liabilities. Summary statistics for the liabilities, which range in maturity from five to eight years, are given in Exhibit 1-1:

Exhibit 1-1: Debt liabilities to be retired

Algonquin’s treasury department is considering three possible methods that could be used: a bond tender offer, whereby the liabilities are repurchased on the open market, which they hope will lead to an upgrade from the company’s current A- rating to AA. However, the tender offer would need to be at a price reflecting the improvement in rating; cash flow matching using government bonds, which would allow for defeasement of the assets and liabilities; or duration matching using high-quality corporate bonds.

A. Identify and explain one advantage and one disadvantage of the duration matching approach compared to the cash flow matching approach.

Three different portfolios of investment-grade corporate bonds, ranging in maturity from 3 years to 10 years, have been proposed for the duration matching approach. Each portfolio has a market value of $650 million, which will be adequate for the funding of the liabilities. Exhibit 1-2 shows relevant information for these portfolios:

Exhibit 1-2: Portfolios for Duration Matching Strategy

B. Identify and justify with two reasons which of the three portfolios (P, Q, or R) should be chosen if the duration matching strategy is adopted.

Algonquin is currently pursuing a contingent immunization strategy with another set of liabilities. These liabilities have a current market value of $78.96 million and a BPV of $36,374. The associated T-Note portfolio has a market value of $83.15 million and a BPV of $41,458. Additionally, 140 contracts of the five-year T-Note futures have been sold. The futures have a par value of $100,000 and an estimated BPV of $51.0745.

C. Assuming that any remaining duration gap is intentional, state with justification the likely view held by Algonquin’s treasury department on the future five-year T-Note interest rate.

 

Level III Answers

A: The duration-matching approach is likely to be cheaper than the cash flow matching approach, partly because it will use corporate bonds, which are likely to pay higher yields than the government bonds used in the cash flow matching strategy. Also, the duration matching approach only hedges against a small parallel change in the yield curve and is thus less exact, hence riskier, than the cash flow matching approach, so should be cheaper. The extra risk is the main disadvantage of the duration matching approach.


B:
Portfolio Q has the nearest duration to the liability, but we have to take account of the different values of assets and liabilities, so the correct target is to match BPVs.

The BPV of the liabilities is $624 million × 6.35 × 0.0001 = $396,240

For the portfolios:
BPVP = $650 million × 6.09 × 0.0001 = $395,850
BPVQ = $650 million × 6.37 × 0.0001 = $414,050
BPVR = $650 million × 6.11 × 0.0001 = $397,150

On the basis of duration matching, P and R would both be acceptable.

We also require that the convexity of the assets be no less than that of the liabilities (53.56). P has too low a level of convexity, meaning that portfolio R should be recommended.


C:
The duration gap is the difference between the asset and liability BPVs.

Duration gap = $41,458 - $36,374 = +$5,084.

To close the duration gap, 5,084 ÷ 51.0745 = 100 (rounded) futures should be sold. Algonquin has sold 140 futures, thus has over-hedged the gap so that factoring in the futures:

Asset (net of futures) BPV < Liability BPV.

This is a position that will benefit from a rise in the five-year interest rate (assets will fall by less than liabilities, and the surplus will increase).


What’s Next?

Now that you have insight into the kinds of questions that are on the three levels of the CFA exam, you might be wondering how you can learn to answer them. Signing up for an exam preparation package is a great place to start.

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