FIXED INCOME: CFA LEVEL I Fixed Income IV Problem Solving Session Harvard Extension School MGMT E-2900b CFA Exam Level I April 13, 2010

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L I Fixed Income IV

Problem Solving Session

Harvard Extension SchoolMGMT E-2900b

CFA Exam Level IApril 13, 2010

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L I Fixed Income IV:

Duration and ConvexityStudy Session 16: Reading 66

Term Structure of Interest Rates: Alternative Theories

Study Session 15: Reading 63

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Duration, Convexity & the Term Structure of Interest

Rates1. Using the full valuation approach and

given a 50 bps decrease in required yield, what is the interest rate sensitivity of a portfolio of $17,000 face value 5-year bonds, with 4% semiannual-pay coupons priced to yield 5%.

A. -2.285%B. 2.285%C. -2.200%

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Rates1. Using the full valuation approach and

given a 50 bps decrease in required yield, what is the interest rate sensitivity of a portfolio of $17,000 face value 5-year bonds, with 4% semiannual-pay coupons priced to yield 5%.

A. -2.285%B. 2.285%C. -2.200%

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Rates1. Explained: Find PV2/PV1 – 1

1. PV1: N=10; I/Y=5/2; PMT=17,000(.04/2) = 340; FV=17,000; CPT PV1 = –16,256.07

PV2: N=10; I/Y=4.5/2; PMT=17,000(.04/2) = 340; FV=17,000; CPT PV2 = –16,623.19

1. PV2/PV1 – 1 = (16,623.19/16,256.07) – 1 = 2.258%

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RatesQuestions 2-3:2. Given a 75 bps change in yield,

which of the following is the closest to the effective duration of a 7% semiannual-pay bond with 5-years to maturity trading at par:

A. 4.102.B. 4.158.C. 0.416.

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RatesQuestions 2-3:2. Given a 75 bps change in yield,

which of the following is the closest to the effective duration of a 7% semiannual-pay bond with 5-years to maturity trading at par:

A. 4.102.B. 4.158.C. 0.416.

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RatesQuestions 2-3:2. Explained:

ED = V- – V+ ;

2V0(∆y)

where: V- = bond value if yield ↓ by ∆y

V+ = bond value if yield ↑ by ∆y

V0 = initial bond price

∆y = change in yield

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RatesQuestions 2-3:2. Explained:

V- = 103.18: N=10; I/Y=6.25/2=3.125; PMT=3.5; FV=100; CPT PV = 103.18V+ = 96.94: N=10; I/Y=7.75/2=3.875; PMT=3.5; FV=100; CPT PV = 96.94ED = (103.18 – 96.94)/2(100)(.0075)

= 6.24/1.5 = 4.158

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RatesQuestions 2-3:3. Assume the bond is callable today

at 102 and the change in yield remains 75 bps. The effective duration would be closest to:

A. 3.373B. 4.158C. 0.337

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RatesQuestions 2-3:3. Assume the bond is callable today

at 102 and the change in yield remains 75 bps. The effective duration would be closest to:

A. 3.373B. 4.158C. 0.337

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RatesQuestions 2-3:

3. Explained:

V- = 102: N=10; I/Y=6.25/2=3.125; PMT=3.5; FV=100; CPT PV = 103.18 102 (call price)

V+ = 96.94: N=10; I/Y=7.75/2=3.875; PMT=3.5; FV=100; CPT PV = 96.94

ED = (102 – 96.94)/2(100)(.0075)

= 5.06/1.5 = 3.37

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Rates4. Given a modified duration of 5.21

and a convexity of 52.1 which of the following is closest to the % price change for an increase in yield of 1.21%?

A. 0.7627%B. -6.3041%C. -5.5414%

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Rates4. Given a modified duration of 5.21

and a convexity of 52.1 which of the following is closest to the % price change for an increase in yield of 1.21%?

A. 0.7627%B. -6.3041%C. -5.5414%

% ∆ price = -(MD)(∆y) = -(5.21)(.0121) = -0.06304 = -

6.3041%Conv. Effect = (convexity)(∆y)2

= 52.1(.0121)2

= 0.007627 = 0.7627%Sum: -6.3041% + 0.7627% = -5.5414%

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Rates5. Which of the following is closest to a

bond’s duration, given a total % price change of 8% when yields fall 2% and a convexity of 45?

A. -3.1 B. 4.5C. 3.1

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Rates5. Which of the following is closest to a

bond’s duration, given a total % price change of 8% when yields fall 2% and a convexity of 45?

A. -3.1 B. 4.5C. 3.1

% ∆ price = duration effect + convexity effect

0.08 = [-(D)(-0.02)] + [45(-0.02)2]0.08 = 0.02D + 0.018D = 3.1

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Rates6. Consider a 5-year, 6% semiannual-

pay bond priced at 99.5. The price value of a basis point for this bond is closest to:

A. $0.04B. $0.05C. $0.06

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Rates6. Consider a 5-year, 6% semiannual-

pay bond priced at 99.5. The price value of a basis point for this bond is closest to:

A. $0.04B. $0.05C. $0.06

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Rates6. Explained:

Find I/Y: N=10; PV=-99.5; PMT=3; FV=100 CPT I/Y = 3.0588 x 2 = 6.1176%

Find PV w/ +0.01%: N=10; I/Y=6.1276/2= 3.0638; PMT=3; FV=100 CPT PV = 99.4575

6. PVBP = 99.50 – 99.4575 = $0.0425 ≈ $0.04

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Rates7. Which of the following combinations of

convexity and duration measures will provide the most accurate forecast of a price change for a callable bond?

A. Modified Duration and Modified Convexity.B. Effective Duration and Effective Convexity.C. Macaulay Duration and Modified Convexity.

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Rates7. Which of the following combinations of

convexity and duration measures will provide the most accurate forecast of a price change for a callable bond?

A. Modified Duration and Modified Convexity.B. Effective Duration and Effective Convexity.C. Macaulay Duration and Modified Convexity.

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Rates7. Explained:

Both effective duration and effective convexity takes into account changes in cash flow due to embedded options.

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Rates8. A bond whose price changes by a

larger magnitude with a 1bp increase in yield versus a 1bp decrease in yield, is what type of bond?

A. A putable bondB. A bond with negative convexityC. A zero-coupon bond

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Rates8. A bond whose price changes by a

larger magnitude with a 1bp increase in yield versus a 1bp decrease in yield, is what type of bond?

A. A putable bondB. A bond with negative convexityC. A zero-coupon bond

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L I Duration, Convexity & the Term

Structure of Interest RatesPrice-Yield Curve for a Callable Bond

Y1 Y2

Ps1Ps2

Pc1Pc2

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Rates9. The Fed’s most commonly used

method to manage interest rates is:

A. bank reserve requirementsB. the discount rateC. open market operations

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Rates9. The Fed’s most commonly used

method to manage interest rates is:

A. bank reserve requirementsB. the discount rateC. open market operations

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Rates9. Explained: Open Market Operations: buying and selling of

Treasury securities by the Fed in the open market. Sell MS↓ interest rates ↑9. Buy MS↑ interest rates ↓

Discount Rate: rate at which banks can borrow from the Fed; low rate encourages lending.

Bank Reserve Requirements: % of deposits that banks must retain; lower % encourage more loans.

Persuading banks to tighten/loosen credit policies: encouraging lending interest rates ↓

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Rates10.According to pure expectations

theory, a normal yield curve indicates that investors expect:

A. short-term rates will increase in the future

B. higher return for illiquidityC. inflation to remain flat

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Rates10.According to pure expectations

theory, a normal yield curve indicates that investors expect:

A. short-term rates will increase in the future

B. higher return for illiquidityC. inflation to remain flat

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Rates10.Pure Expectations Theory: Average of short-term rates that are

expected in the future. If short-term rates are expected to rise in the future, then rates on longer maturities will be higher in the future.

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Rates11.According to liquidity preference

theory, which of the following would investors not expect?

A. An illiquidity premiumB. Little risk differential between short-

term and long-term securitiesC. A flat yield curve

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Rates11.According to liquidity preference

theory, which of the following would investors not expect?

A. An illiquidity premiumB. Little risk differential between short-

term and long-term securitiesC. A flat yield curve

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Rates11.Liquidity Preference Theory: In addition to expectations about

the future of short term rates (pure expectations), investors demand a risk premium for holding longer dates securities.

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Rates12.According to market segmentation

theory, the structure of interest rates is most likely determined by:

A. An increase in demand for short-term bonds

B. The relationship between short-term and long-term securities

C. The demand for various maturities by investors

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Rates12.According to market segmentation

theory, the structure of interest rates is most likely determined by:

A. An increase in demand for short-term bonds

B. The relationship between short-term and long-term securities

C. The demand for various maturities by investors

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Rates11.Market Segmentation Theory: The supply (desire to borrow) and

demand (desire to lend) for bonds determines the equilibrium rate for various maturity ranges.

Based on the idea that investors have a preference for different maturities.

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Rates12. Consider a corporate bond structure

with three-year bonds yielding 6%, four-year bonds yielding 7%, and five-year bond yielding 8%. What is the absolute and relative yield spread on the five-year corporate issue if a similar dated Treasury is yielding 6%.

A. 0, 0%B. 100bps, 14.28% C. 200bps, 33.33%

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Rates12. Consider a corporate bond structure

with three-year bonds yielding 6%, four-year bonds yielding 7%, and five-year bond yielding 8%. What is the absolute and relative yield spread on the five-year corporate issue if a similar dated Treasury is yielding 6%.

A. 0, 0%B. 100bps, 14.28% C. 200bps, 33.33%

Absolute yld spread = corp – trsy

= 8% - 6% = 200 bps

Relative yld spread = absolute/trsy

= .02/.06 = 33.33%

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Rates13.Consider two bonds similar in all

respects except duration who exhibit a yield ratio of 1.0825. The relative yield is closest to:

A. 8.25%B. 108.25C. 0.825

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Rates13.Consider two bonds similar in all

respects except duration who exhibit a yield ratio of 1.0825. The relative yield is closest to:

A. 8.25%B. 108.25C. 0.825

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Rates13.Explained:

Relative Yld Spread = absolute yld spread / lower yld = higher yld/lower yld - 1

Yield Ratio = higher yld/lower yldrelative yld spread = yield ratio – 1relative yld spread = 1.0825 – 18.25%

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Rates14.An economist is projecting a

tightening in the yield spread between corporate bonds and U.S. Treasury. The economist most likely expects:A. the economy to expand.B. the economy to contract.C. the economy to remain the same.

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Rates14.An economist is projecting a

tightening in the yield spread between corporate bonds and U.S. Treasury. The economist most likely expects:A. the economy to expand.B. the economy to contract.C. the economy to remain the same.

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Rates14.Explained:

Credit spreads shrink during an expanding economy as corporations are expected to have increasing cash flows to service outstanding debt.

Conversely, credit spreads widen during a slowing economy as corporations are expected to experience shrinking cash flows and become more susceptible to default.

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Rates15.Investors will demand a higher

yield for which of the following bond types:A. a putable bond.B. a convertible bond. C. a callable bond.

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Rates15.Investors will demand a higher

yield for which of the following bond types:A. a putable bond.B. a convertible bond. C. a callable bond.A call feature is beneficial to the issuer and will be exercised when it’s advantageous for the issuer to do so. As such, an investor would prefer a straight bond to a callable bond and will demand additional compensation in the form of higher yields for a callable bond.

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Rates16.Consider two equivalent bonds that

are the same except for tax status. What is the marginal tax rate that would make an investors indifferent between a 4.5% tax-exempt bond and a 6.5% taxable bond?A. 30.77%B. 44.44%C. 69.23%

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Rates16.Consider two equivalent bonds that

are the same except for tax status. What is the marginal tax rate that would make an investors indifferent between a 4.5% tax-exempt bond and a 6.5% taxable bond?A. 30.77%B. 44.44%C. 69.23%

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Rates16.Explained:

Taxable-equivalent yield = (tax-free yield)/(1 – marginal tax rate)6.5% = 4.5%/(1 – MTR)MTR = - (4.5%/6.5% - 1) = 30.77%

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Rates17. Consider an investor in the 39% marginal

tax bracket who is deciding between purchasing a 7.25% taxable corporate bond or a 5% tax-exempt municipal bond. If both bonds are selling at par and are the same in all other respects, which bond should the investor purchase?

A. Corporate bond, since it has a higher yield of 7.25%

B. Municipal bond, since its taxable equivalent yield is 12.82%

C. Municipal bond, since its taxable equivalent yield is 8.2%

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Rates17. Consider an investor in the 39% marginal

tax bracket who is deciding between purchasing a 7.25% taxable corporate bond or a 5% tax-exempt municipal bond. If both bonds are selling at par and are the name in all other respects, which bond should the investor purchase?

A. Corporate bond, since it has a higher yield of 7.25%

B. Municipal bond, since its taxable equivalent yield is 12.82%

C. Municipal bond, since its taxable equivalent yield is 8.2%

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Rates17.Explained:

Taxable-equivalent yield = (tax-free yield)/(1 – marginal tax rate)TEY = 5%/(1 – .39) = 8.2%

The investor would prefer the tax-exempt municipal bond with a TEY of 8.2% versus a taxable bond yielding 7.25%

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Rates18.A funded investor is most

concerned with movements in:

A. rates on Certificates of Deposits (CDs).

B. the risk-free rate.C. published LIBOR.

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Rates18.A funded investor is most

concerned with movements in:

A. rates on Certificates of Deposits (CDs).

B. the risk-free rate.C. published LIBOR.

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Rates18.Explained: LIBOR: London Interbank Offered Rate, is published

daily by the British Banker’s Association (BBA) and is in reference to the rates paid on negotiable CDs by banks and bank branches in London. It is the most important reference rate for floating rate debt and short-term lending, and largely for maturities of less than one year.

Funded Investor: Someone who borrows to finance an investment and whose borrowing rate is determined by LIBOR plus a spread. The higher LIBOR is, the lower the funded investors profits.

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Ethics & Professional Standards

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L I Ethics Item Set

CFA Sample QuestionsSmith, a research analyst with a brokerage firm, decides to change his recommendation on the common stock of Green Company, Inc., from a buy to a sell. He mails this change in investment advice to all the firm’s clients on Wednesday, the day after the mailing, a client calls with a buy order for 500 shares of Green Company. In this circumstance, Smith should:A.accept the order.B.advise the customer of the change in recommendation before accepting the order.C.not accept the order because it is contrary to the firm’s recommendation.

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L I Ethics Item Set

CFA Sample QuestionsSmith, a research analyst with a brokerage firm, decides to change his recommendation on the common stock of Green Company, Inc., from a buy to a sell. He mails this change in investment advice to all the firm’s clients on Wednesday, the day after the mailing, a client calls with a buy order for 500 shares of Green Company. In this circumstance, Smith should:A.accept the order.B.advise the customer of the change in recommendation before accepting the order.C.not accept the order because it is contrary to the firm’s recommendation.

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L I Ethics Item Set

CFA Sample QuestionsStandard III(B) Fair Dealing: Prior to executing the order, Smith should take additional steps to ensure that the customer has received the change of recommendation. The client does not have the benefit of Smith’s most recent recommendation, so by fulfilling the order without notifying them of the change would be a disservice. If the client still wants to place the order, smith is obligated to comply with the client’s directive, irrespective of his recommendation

- Standards of Practice Handbook, 9th Ed., Pg. 152

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L I Ethics Item Set

CFA Sample QuestionsJamison is a junior research analyst with Howard & Howard, a brokerage and investment banking firm. Howard & Howard’s mergers and acquisitions department has represented the Britland Company in all of its acquisitions for the past 20 years. Two of Howard & Howard’s senior officers are directors of various Britland subsidiaries. Jamison has been asked to write a research report on Britland. What is the best course of action for her to follow?A.Jamison may write the report but must refrain from expressing any opinions because of the special relationships between the two companies.B.Jamison may write the report if she discloses the special relationships with the company in the report.C.Jamison should not write the report because the two Howard officers are constructive insiders.

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L I Ethics Item Set

CFA Sample QuestionsJamison is a junior research analyst with Howard & Howard, a brokerage and investment banking firm. Howard & Howard’s mergers and acquisitions department has represented the Britland Company in all of its acquisitions for the past 20 years. Two of Howard & Howard’s senior officers are directors of various Britland subsidiaries. Jamison has been asked to write a research report on Britland. What is the best course of action for her to follow?A.Jamison may write the report but must refrain from expressing any opinions because of the special relationships between the two companies.B.Jamison may write the report if she discloses the special relationships with the company in the report.C.Jamison should not write the report because the two Howard officers are constructive insiders.

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L I Ethics Item Set

CFA Sample QuestionsStandard VI(A) Disclosure of Conflicts: There are two conflicts: (1) Jamison is asked to write a research report on a company that is a client of Jamison’s employer, and (2) two directors of the company are senior officers at Jamison’s employer.Both facts must be disclosed: “…Requiring members and candidates to disclose all matters that reasonably could be expected to impair the member or candidate's objectivity allows clients and prospects to judge motives and possible biases for themselves.” - Standards of Practice Handbook, 9th Ed., Pg. 113 & 152

Documents

FIXED INCOME: CFA LEVEL I Fixed Income IV Problem Solving Session Harvard Extension School MGMT E-2900b CFA Exam Level I April 13, 2010