fixed income: cfa level i fixed income iii - problem solving session harvard extension school mgmt...

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L I Fixed Income III -

Problem Solving Session

Harvard Extension SchoolMGMT E-2900b

CFA Exam Level IApril 6, 2010

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L I Fixed Income III:

Study Session 16Reading 64 & 65

Valuation of Debt SecuritiesYield Measures, Spot Rates & Forward

Rates

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L I Valuation, Yield Measures,

Spots & Forwards

Questions 1-3:Consider a 5-year, 8% semiannual

bond with a €1,000 face value. Current market rates 5.5%.

1. How much is each coupon payment?

A. €27.50B. €80.00C. €40.00

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Spots & Forwards

Questions 1-3:Consider a 5-year, 8% semiannual

bond with a €1,000 face value. Current market rates 5.5%.

1. How much is each coupon payment?

A. €27.50B. €80.00C. €40.00

€1,000 x (0.08/2) = €40

N=10, PV= -1,000, FV=1,000, I/Y=4CPT PMT = €40

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Spots & Forwards

Questions 1-3 (cont.):2. What would the bond trade for if it

were priced with YTM equal to current rates?

A. €1,107B. €1,108C. €899

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Spots & Forwards

Questions 1-3 (cont.):2. What would the bond trade for if it

were priced with YTM equal to current rates?

A. €1,107B. €1,108C. €899

N=10, I/Y=(5.5/2)=2.75, PMT=40, FV=1000CPT PV = 1,108

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Spots & ForwardsQuestions 1-3 (cont.):

3. Current market rates have moved. If the bond was quoted at €950, what would this infer about the new market rate and what would it be?

A. Market rates are lower than the bond’s rate, 7.15%

B. Market rates are higher than the bond’s rate, 9.27%

C. Market rates are equal to the bond’s rate, 8%

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Spots & Forwards

Questions 1-3 (cont.):3. Explained: Same as solving for YTM

€950 = ∑10t=1 40/(1+YTM/2)t +…+

1040/(1+YTM/2)10

or: N=10; PV=-950; PMT=40; FV=1,000 CPT I/Y = 4.636 x 2 = 9.27%

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Spots & Forwards4. Bond A is 10-year, 10% semiannual-pay

bond that is priced to yield 8% as an annual rate. Bond B is a 15-year, 8% semiannual-pay bond priced with a yield to maturity of 10%. If face value for each bond is $1,000, the prices of these two bonds would be?

Bond A Bond B

4. $1,136 $ 846– $ 875 $1,173A. $1,134 $ 848

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Spots & Forwards4. Explained:

Bond A: N=20; I/Y=8/2=4; PMT=50;

FV=1000 CPT PV = 1,136

Bond B: N=30; I/Y=10/2=5; PMT=40;

FV=1000 CPT PV = 846

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Spots & Forwards5. A 1-year, 5% Treasury bill is trading at

$950. Treasury spot rates (expressed as semiannual-pay yields to maturity) are: 6-months = 5%, 1-year = 6%. The arbitrage trade and profit are:

A. Sell the bond, buy the pieces, earn $40.55B. Buy the bond, sell the pieces, earn $50.00C. Buy the bond, sell the pieces, earn $40.55

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arbitrage free value: = 25 + 1025 = 1.025 1.032

24.39 + 966.16 = 990.55

bond price < discounted pricebuy the bond, sell the pieces for an

arbitrage profit of $40.55.

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Spots & Forwards

6. A $1,000, 10-year, 6% semiannual coupon bond is priced to yield 4.5%. How much will the bond value decrease in 4 years if the yield remains the same?

A. 3.694%B. -3.717%C. -3.694%

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Spots & Forwards

6. Explained:a) Calculate PV: N=20; I/Y=4.5/2;

PMT=30; FV=1,000 CPT PV = 1,119.73

b) Calculate PV in 4 years: N=12; I/Y=4.5/2; PMT=30; FV=1,000 CPT PV = 1,078.11

c) % ∆ = (1,078.11/1,119.73)-1 = -3.717%

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Spots & Forwards7. A 10-year, 5% option-free bond is issued

at the require yield to maturity. A year later the required rate increases. At what price is the bond issued, and what happens to the bond’s price as a result of the rise in yield?

A. Issued at par, bond price fallsB. Issued below par, bond price fallsC. Issued at par, bond price increases

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Spots & Forwards

7. Explained:

If the stated coupon rate is equal to the required rate (YTM), then the bond is priced at par.

There is an inverse relationship between price and yield. Thus, if the required yield increases (decreases), the bond’s price will fall (rise).

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Spots & ForwardsQuestions 8-11:Observe a $1,000 par, 3%, 5-year

semiannual-pay bond trading at $1,015 that is callable after one year at 103 (as a % of par) and putable at 101 in two years.

8. What is the current yield of the bond?

A. 3.000%B. 2.677%C. 2.956%

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8. What is the current yield of the bond?

A. 3.000%B. 2.677%C. 2.956%

Current Yield = CPN/PV = 30/1,015 = 2.956%

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9. What is the bond’s yield to maturity?

A. 1.339%B. 2.677%C. 3.000%

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9. What is the bond’s yield to maturity?

A. 1.339%B. 2.677%C. 3.000%

YTM: N=10; PV=-1,015; PMT=15; FV=1,000CPT I/Y = 1.3387 x 2 =2.677%

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10.What is the bond’s yield to call?

A. 4.417%B. 2.209%C. 2.466%

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10.What is the bond’s yield to call?

A. 4.417%B. 2.209%C. 2.466%

YTM: N=2; PV=-1,015; PMT=15; FV=1,030CPT I/Y = 2.209 x 2 = 4.417%

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11.What is the bond’s yield to put?

A. 4.417%B. 1.357%C. 2.714%

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11.What is the bond’s yield to put?

A. 4.417%B. 1.357%C. 2.714%

YTM: N=4; PV=-1,015; PMT=15; FV=1,010CPT I/Y = 1.357 x 2 = 2.714%

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Spots & Forwards

12. What is the bond equivalent yield for a bond with annual coupons that is priced to yield 7%?

A. 7.000%B. 6.881%C. 3.441%

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Spots & Forwards

12. What is the bond equivalent yield for a bond with annual coupons that is priced to yield 7%?

A. 7.000%B. 6.881%C. 3.441%

BEY = [(1+EAY)(1/2)-1] x 2BEY = [(1.07 )(1/2)-1] x 2 = 6.881%

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Spots & Forwards

12. What is the bond equivalent yield for a CDO paying 40bps per month?

A. 2.424%B. 4.800%C. 4.848%

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Spots & Forwards

12. What is the bond equivalent yield for a CDO paying 40bps per month?

A. 2.424%B. 4.800%C. 4.848%

BEY = [(1+CFY)6-1] x 2BEY = [(1.004 )6-1] x 2 = 4.848%

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Spots & ForwardsQuestions 13-16:Consider a 10-year, $1,000 semiannual

par value bond with prevailing market rates of 4%.

13.If the bond were a zero-coupon bond issued at $672.97, what is its YTM?

A. 4.000%B. 2.000%C. 4.200%

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Spots & ForwardsQuestions 13-16:Consider a 10-year, $1,000 semiannual

par value bond with prevailing market rates of 4%.

13.If they bond were a zero-coupon bond issued at $672.97, what is its YTM?

A. 4.000%B. 2.000%C. 4.200%

YTM: N=20; PV=-672.97; PMT=0; FV=1,000CPT I/Y = 2.000 x 2 = 4%

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Spots & ForwardsQuestions 13-16:Consider a 10-year, $1,000 semiannual par value

bond with prevailing market rates of 4%.

14.At what price would the bond sell for if it were issued with a 6% coupon rate, and which of the three sources of return is it most susceptible?

A. $851.23, principal lossB. $1,163.51, reinvestment of couponsC. $1,000.00, interest payments

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Spots & ForwardsQuestions 13-16:Consider a 10-year, $1,000 semiannual par

value bond with prevailing market rates of 4%.

14.At what price would the bond sell for if it were issued with a 6% coupon rate, and which of the three sources of return is it most susceptible?

A. $851.23, principal lossB. $1,163.51, reinvestment of couponsC. $1,000.00, interest paymentsN=20; I/Y=4/2; PMT=30;

FV=1,000CPT PV = $1,163.51

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15.At what price would the bond sell for if it were issued with a 6% coupon rate and prevailing rates increased to 6%?

A. $851.23B. $1,163.51C. $1,000.00

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15.At what price would the bond sell for if it were issued with a 6% coupon rate, and prevailing rates increased to 6%?

A. $851.23B. $1,163.51C. $1,000.00

N=20; I/Y=6/2; PMT=30; FV=1,000CPT PV = $1,000

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Spots & ForwardsQuestions 13-16:Consider a 10-year, $1,000 semiannual par value

bond with prevailing market rates of 4%.

16.Was the reinvestment risk from the bond in #14, higher, lower, or the same as the bond in #15?

A. HigherB. LowerC. Same

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Spots & Forwards

16. Explained: Reinvestment risk will increase with:

Higher Coupons Longer Maturities

Because both bonds paid the same coupon and had the same maturity, reinvestment risk was the same.

However, their reinvestment outcome varied due to differing reinvestment rates.

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Spots & Forwards

17.The 2-year spot rate is 6% and the 3-year spot rate is 7%. What is the 1-year forward rate two years from today?

A. 0.943%B. 7.000%C. 9.028%

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Spots & Forwards

17.The 2-year spot rate is 6% and the 3-year spot rate is 7%. What is the 1-year forward rate two years from today?

A. 0.943%B. 7.000%C. 9.028%

(1+S3)3 = (1+S2)2 x (1+1f2)

(1.07)3 = (1.06)2 x (1+1f2)

(1.07)3 – 1 = 1f2 = 9.028%(1.06)2

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Spots & Forwards

18.Consider a callable bond. If the Z-spread is 300 bps, the option-adjusted spread (OAS) will be:

A. equal to 300 bpsB. less than 300 bpsC. greater than 300 bps

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Option cost > 0; The investor receives compensation for writing the option to the issuer OAS < Z-spread. That is, the investor requires more yield on the callable bond than for an option-free bond. The opposite is true for putable bonds.

The OAS is the comparable spread for non-option bond characteristics like credit risk, interest rate risk, and liquidity risk.

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Spots & Forwards

19.A coupon bond’s nominal spread, Z-spread, and OAS spread would be equal if:

A. the bond has no embedded optionB. the bond is option free, the yield curve is

flat, and the coupons are relatively highC. the bond is not putable and the yield

curve is steep

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Spots & Forwards

19. Explained: Zero-volatility spread is the equal amount

that must be added to each rate on the Treasury spot curve in order the make the present value of the risky bond’s cash flow equal to its price.

Thus, a flat yield curve will make nominal and zero-volatility spreads equal.

The higher the coupon payment, the earlier principle is received and discounted with each periodic Z-spread.

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Spots & ForwardsQuestions 20 – 22:Consider the following: Current 1-year spot rate = 5%

1f1 = 6%

1f2 = 7%

1f3 = 8%

• What is the price of a 3-year, 8% annual-pay, $1,000 par value bond?

– $ 1,054.94– $ 863.84– $ 1,000.00

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Spots & ForwardsQuestions 20 – 22:20. Explained: S1 = 5% S2 = [(1.05)(1.06)]1/2 – 1 = 5.499%

20. S3 = [(1.05)(1.06)(1.07)]1/3 – 1 = 5.997% Bond Value:

N=1; PMT=80; FV=1,000; I/Y=5; CPT PV = 76.19 N=2; PMT=80; FV=1,000; I/Y=5.499; CPT PV = 71.88 N=3; PMT=80; FV=1,000; I/Y=5.997; CPT PV =

906.87 Total: $

1,054.94

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Spots & ForwardsQuestions 20 – 22:Consider the following: Current 1-year spot rate = 5%

1f1 = 6%

1f2 = 7%

1f3 = 8%

• Using annual compounding, what is the price of a 4-year, zero-coupon, $1,000 par value bond?

– $792.18– $822.70– $997.41

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Spots & Forwards

Questions 20 – 21:21. Explained:

S4 = [(1.05)(1.06)(1.07)(1.08)]1/4 – 1

= 6.494%N=4; FV=1,000; I/Y=6.494; CPT PV

= $997.41

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Spots & Forwards

Consider the following: Current 1-year spot rate = 5% Current 2-year spot rate = 6%

22.Which of the following is closest to the 1-year forward rate, one year from now?

A. 5%B. 6%C. 7%

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Spots & Forwards

22. Explained: Find 1f1 (1+S2)2 = (1+S1)(1+1f1)

1f1 = [(1+S2)2 / (1+S1)] - 1 1f1 = [(1.06)2 / (1.05)] - 1 = 7.01%

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L I

Ethics & Professional Standards

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L I Ethics Item Set

CFA Sample QuestionsJason Borneo, CFA, works for Moorea Capital Advisors (MCA) and serves as the lead investment advisors for Papeete Industries’ employee pension program. The CEO of Papeete, Mitchel Buillard, asks Jason to purchase Papeete’s stock in the open market for the employee plan in effort to dissuade Windward Enterprise’s attempted hostile takeover of Papeete. While Jason believes the stock to be overvalued, he does so to maintain the company’s good favor and to maintain a soft-dollar research arrangement with Auckland Securities, a subsidiary of Papeete. Are Jason and Mitchel in violation of the Standards of Practice?A.Jason is and violated Standard III (A) Loyalty, Prudence, and Care, and Mitchel is and violated Standard II(B) Market ManipulationB.Jason is and violated Standard III (A) Loyalty, Prudence, and Care, and Mitchel is not C.Jason is and violated Standard V(A) Diligence and Reasonable Basis, and Mitchel is and violated Standard III (A) Loyalty, Prudence, and Care

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L I Ethics Item Set

CFA Sample Questions Jason has a responsibility to the employees and

retirees of the pension program, not Papeete management. Duties to Clients - Loyalty, Prudence, Care: “...When

the manager is responsible for the portfolios of pension plans or trusts, however, the client is not the person or entity who hires the manager but, rather, the beneficiaries of the plan or trust. They duty of loyalty is owed to the ultimate beneficiaries and not just the client.”- Standards of Practice Handbook, 9th Ed., Pg. 53

Mitchel is not a CFA charterholder and Standards are not applicable

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L I Ethics Item Set

CFA Sample QuestionsReferring to the above vignette, is Jason in violation of any other Standards? If Mitchel were a CFA charter holder would he be in violation of the Standards of Practice?A.Jason is not in violation of further Standards, and Mitchel is in violation of Standard II(B) Market ManipulationB.Jason is in violation of Standard V(A) Diligence and Reasonable Basis, and Mitchel is not in violation of the Standards. C.Jason is in violation of Standard V(A) Diligence and Reasonable Basis, Standard III(C) Suitability, and two more instances of Standard III(A) Loyalty, Prudence, and Care, and Mitchel is in violation of Standard II(B) Market Manipulation

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L I Ethics Item Set

CFA Sample QuestionsStandard V(A) Diligence and Reasonable Basis: “Members and Candidates must: (1)Exercise diligence, independence, and thoroughness in analyzing investments, making investment recommend-ations, and taking investment actions. (2)Have a reasonable and adequate basis, supported by appropriate research and investigation, for any investment analysis, recommendation, or action.”

- Standards of Practice Handbook, 9th Ed., Pg. 99

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L I Ethics Item Set

CFA Sample QuestionsStandard III(C) Suitability: “…Determine that an investment is suitable to the client’s financial situation and consistent with the client’s written objectives, mandates, and constraints before making an investment recommendation or taking investment action.”


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L I Ethics Item Set

CFA Sample QuestionsStandard III(A) Loyalty, Prudence, Care: “…Conflicts arise when an investment manager uses client brokerage to purchase research services that benefit the investment manger, a practice commonly called ‘soft dollars’ or ‘soft commissions.’ Whenever a manager uses client brokerage to purchase goods or services that do not benefit the client, the manager should disclose to clients the method or policies followed by the manager in addressing the potential conflict. A manager who pays a higher commission than he or she would normally pay to purchase goods or services without corresponding benefit to the client, violates the duty of loyalty to the client.”


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L I Ethics Item Set

CFA Sample QuestionsStandard III(A) Loyalty, Prudence, Care: the standard “requires that a member or candidate, in evaluating a takeover bid, act prudently and solely in the interests of plan participants and beneficiaries. To meet this requirement, a member or candidate must carefully evaluate the long-term prospects of the company against the short-term prospects presented by the takeover offer and by the ability to invest elsewhere.”In this instance, Jason clearly violated Standard III(A) by using the employee pension program to “perpetuate existing management, perhaps to the detriment of plan participants and the company's shareholders, and to benefit himself.”


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L I Ethics Item Set

CFA Sample QuestionsStandard II(B) Market Manipulation: “Members and Candidates must not engage in practices that distort prices or artificially inflate trading volume with the intent to mislead market participants.”


fixed income: cfa level i fixed income iii - problem solving session harvard extension school mgmt...

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