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answer the whole question QUESTION 1 1. As an investment manager working for the...
May 17, 2024
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Solution by Steps
step 1
Calculate the duration of the 2-year bond using the Macaulay duration formula: D=1.5%×1+1.5%×(1+2.25%)−1×2(1+2.25%)−1×1.5%+(1+2.25%)−2×1.5% D = \frac{1.5\% \times 1 + 1.5\% \times (1 + 2.25\%)^{-1} \times 2}{(1 + 2.25\%)^{-1} \times 1.5\% + (1 + 2.25\%)^{-2} \times 1.5\%}
step 2
Calculate the duration of the 3.5-year bond using the Macaulay duration formula: D=2.5%×1+2.5%×(1+2.25%)−1×2+2.5%×(1+2.25%)−2×3.5(1+2.25%)−1×2.5%+(1+2.25%)−2×2.5%+(1+2.25%)−3.5×2.5% D = \frac{2.5\% \times 1 + 2.5\% \times (1 + 2.25\%)^{-1} \times 2 + 2.5\% \times (1 + 2.25\%)^{-2} \times 3.5}{(1 + 2.25\%)^{-1} \times 2.5\% + (1 + 2.25\%)^{-2} \times 2.5\% + (1 + 2.25\%)^{-3.5} \times 2.5\%}
step 3
Calculate the market value of each bond: Market Value of 2-year bond=$120 million \text{Market Value of 2-year bond} = \$120 \text{ million} Market Value of 3.5-year bond=$150 million \text{Market Value of 3.5-year bond} = \$150 \text{ million}
step 4
Calculate the portfolio duration using the weighted average duration formula: Dp=120×D2-year+150×D3.5-year120+150 D_p = \frac{120 \times D_{2\text{-year}} + 150 \times D_{3.5\text{-year}}}{120 + 150}
step 5
Compare the calculated portfolio duration with the staff's estimate of 5 years
Answer
The staff's estimate of 5 years for portfolio duration is incorrect.
Part (b)
step 1
Set up the equation for the portfolio duration to match the pension liability duration of 3 years: 3=w1×D2-year+w2×D3.5-year 3 = w_1 \times D_{2\text{-year}} + w_2 \times D_{3.5\text{-year}} where w1+w2=1 w_1 + w_2 = 1
step 2
Solve for w1 w_1 and w2 w_2 : w1=3−D3.5-yearD2-year−D3.5-year w_1 = \frac{3 - D_{3.5\text{-year}}}{D_{2\text{-year}} - D_{3.5\text{-year}}} w2=1−w1 w_2 = 1 - w_1
Answer
The proportions of the portfolio should be w1 w_1 in 2-year bonds and w2 w_2 in 3.5-year bonds to achieve a portfolio duration of 3 years.
Part (c)
step 1
Calculate the total market value of the portfolio: Total Market Value=$120 million+$150 million=$270 million \text{Total Market Value} = \$120 \text{ million} + \$150 \text{ million} = \$270 \text{ million}
step 2
Compare the total market value with the present value of the pension liability (\$180 million)
step 3
If there is excess money, calculate the adjustment needed: Excess=$270 million−$180 million=$90 million \text{Excess} = \$270 \text{ million} - \$180 \text{ million} = \$90 \text{ million} Adjust investments in the two bonds proportionally to maintain the duration of 3 years. \text{Adjust investments in the two bonds proportionally to maintain the duration of 3 years.}
Answer
There is too much money invested in the bond portfolio. Adjust the investments to maintain the duration of 3 years and reinvest the excess \$90 million more profitably.
Key Concept
Duration matching and portfolio adjustment
Explanation
The key concept is to match the duration of the bond portfolio with the pension liability to minimize interest rate risk.
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Solution by Steps
step 1
To hedge the interest-rate risk using Eurodollar futures contracts, you would take a short position in the futures contracts. This means you would sell Eurodollar futures contracts to lock in the borrowing rate
step 2
If you decide to use an FRA (Forward Rate Agreement) instead, you would enter into a long 6×96 \times 9 FRA. This means you agree to borrow at a fixed rate starting in six months for a period of three months
Answer
Short 10 Eurodollar futures contracts or Long 6×96 \times 9 FRA
Part (a)(ii)
step 1
The number of Eurodollar futures contracts needed can be calculated using the formula: N=L×(T/360)P×Δ N = \frac{L \times (T/360)}{P \times \Delta} where L L is the principal amount, T T is the duration in days, P P is the price of the futures contract, and Δ \Delta is the change in the futures price per basis point change in interest rate
step 2
Given: - Principal L=$10,000,000 L = \$10,000,000 - Duration T=90 T = 90 days - Price P=1,000,000 P = 1,000,000 - Change in futures price Δ=0.01 \Delta = 0.01 The number of contracts needed is: N=10,000,000×(90/360)1,000,000×0.01=9.901 N = \frac{10,000,000 \times (90/360)}{1,000,000 \times 0.01} = 9.901
Answer
9.901 contracts
Part (a)(iii)
step 1
For the FRA, the payoff is calculated as: Payoff=L×(RLIBOR−RFRA1+RLIBOR×(T/360)) \text{Payoff} = L \times \left( \frac{R_{\text{LIBOR}} - R_{\text{FRA}}}{1 + R_{\text{LIBOR}} \times (T/360)} \right) where RLIBOR R_{\text{LIBOR}} is the LIBOR rate at maturity, RFRA R_{\text{FRA}} is the locked-in rate, and T T is the duration in days
step 2
For the Eurodollar futures, the payoff is: Payoff=L×(RLIBOR−RFutures)×(T/360) \text{Payoff} = L \times (R_{\text{LIBOR}} - R_{\text{Futures}}) \times (T/360) where RFutures R_{\text{Futures}} is the locked-in rate
step 3
Given: - RLIBOR=5% R_{\text{LIBOR}} = 5\% - RFRA=4% R_{\text{FRA}} = 4\% - T=90 T = 90 days For FRA: Payoff=10,000,000×(0.05−0.041+0.05×(90/360))=24,691 \text{Payoff} = 10,000,000 \times \left( \frac{0.05 - 0.04}{1 + 0.05 \times (90/360)} \right) = 24,691 For Eurodollar futures: Payoff=10,000,000×(0.05−0.04)×(90/360)=24,753 \text{Payoff} = 10,000,000 \times (0.05 - 0.04) \times (90/360) = 24,753
step 4
Given: - RLIBOR=3% R_{\text{LIBOR}} = 3\% For FRA: Payoff=10,000,000×(0.03−0.041+0.03×(90/360))=−24,814 \text{Payoff} = 10,000,000 \times \left( \frac{0.03 - 0.04}{1 + 0.03 \times (90/360)} \right) = -24,814 For Eurodollar futures: Payoff=10,000,000×(0.03−0.04)×(90/360)=−24,753 \text{Payoff} = 10,000,000 \times (0.03 - 0.04) \times (90/360) = -24,753
Answer
LIBOR = 5%: FRA = 24,691; Eurodollar futures = 24,753
LIBOR = 3%: FRA = -24,814; Eurodollar futures = -24,753
Part (b)
step 1
Duration-based hedging involves matching the duration of the hedging instrument with the duration of the exposure. The hedge ratio is calculated to minimize the interest rate risk by equating the weighted average duration of the assets and liabilities
step 2
The computation of the hedge ratio in duration-based hedging differs from the minimum-variance hedge computation. In duration-based hedging, the focus is on matching durations, while in minimum-variance hedging, the focus is on minimizing the variance of the portfolio's value
Answer
Duration-based hedging involves matching durations, while minimum-variance hedging focuses on minimizing portfolio variance.
Key Concept
Hedging strategies using Eurodollar futures and FRA
Explanation
The key concept involves understanding how to hedge interest-rate risk using different financial instruments and calculating the necessary contracts and payoffs.
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Solution by Steps
step 1
Calculate the price of the bond using the present value formula for bonds. The formula is: P=∑t=1nC(1+r)t+F(1+r)n P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n} where C C is the coupon payment, r r is the yield to maturity, F F is the face value, and n n is the number of periods
step 2
Given: - Face Value F=$300 million F = \$300 \text{ million} - Coupon Rate =3.5% = 3.5\% - Yield to Maturity r=5% r = 5\% - Time to Maturity n=1 year n = 1 \text{ year} - Coupon Payment C=3.5%×300 million=$10.5 million C = 3.5\% \times 300 \text{ million} = \$10.5 \text{ million} Calculate the present value of the coupon payments and the face value
step 3
Calculate the present value of the coupon payments: PVcoupons=10.5 million(1+0.05)1=10.5 million×0.9524=$10.0 million PV_{\text{coupons}} = \frac{10.5 \text{ million}}{(1 + 0.05)^1} = 10.5 \text{ million} \times 0.9524 = \$10.0 \text{ million} Calculate the present value of the face value: PVface=300 million(1+0.05)1=300 million×0.9524=$285.7 million PV_{\text{face}} = \frac{300 \text{ million}}{(1 + 0.05)^1} = 300 \text{ million} \times 0.9524 = \$285.7 \text{ million} Sum these values to get the bond price: P=10.0 million+285.7 million=$295.7 million P = 10.0 \text{ million} + 285.7 \text{ million} = \$295.7 \text{ million}
step 4
The current market value of the investment is the bond price multiplied by the face value held: Market Value=295.7 million \text{Market Value} = 295.7 \text{ million}
Answer
The price of the Green Energy Inc. bond is \$295.7 million. The current market value of the investment is \$295.7 million.
Key Concept
Present value of bond payments
Explanation
The bond price is calculated by discounting the future coupon payments and face value to the present using the yield to maturity.
Question 2.1(b)
step 1
Calculate the total return on the bond if held until maturity. The total return includes the coupon payments and the capital gain or loss
step 2
Given: - Coupon Rate =3.5% = 3.5\% - Face Value =$300 million = \$300 \text{ million} - Coupon Payment C=3.5%×300 million=$10.5 million C = 3.5\% \times 300 \text{ million} = \$10.5 \text{ million} - Initial Price P=$295.7 million P = \$295.7 \text{ million} - Face Value at Maturity F=$300 million F = \$300 \text{ million} Calculate the total return: Total Return=C+(F−P)P×100 \text{Total Return} = \frac{C + (F - P)}{P} \times 100
step 3
Substitute the values: Total Return=10.5 million+(300 million−295.7 million)295.7 million×100 \text{Total Return} = \frac{10.5 \text{ million} + (300 \text{ million} - 295.7 \text{ million})}{295.7 \text{ million}} \times 100 Total Return=10.5 million+4.3 million295.7 million×100 \text{Total Return} = \frac{10.5 \text{ million} + 4.3 \text{ million}}{295.7 \text{ million}} \times 100 Total Return=14.8 million295.7 million×100 \text{Total Return} = \frac{14.8 \text{ million}}{295.7 \text{ million}} \times 100 Total Return≈5.01% \text{Total Return} \approx 5.01\%
Answer
The expected total return on the bonds, if held until maturity, is approximately 5.01%.
Key Concept
Total return calculation
Explanation
Total return includes both the coupon payments and the capital gain or loss from holding the bond until maturity.
Question 2.1(c)
step 1
Assess the risk of corporate bonds by considering credit risk, which measures the likelihood of the bond issuer defaulting on payments
step 2
Credit risk is measured by credit ratings provided by agencies like Moody's, S&P, and Fitch. These ratings assess the financial health of the issuer and the likelihood of default
step 3
The spread in this context refers to the difference in yield between a corporate bond and a risk-free government bond of similar maturity. A wider spread indicates higher perceived risk
Answer
The risk of corporate bonds can be assessed by examining credit ratings and yield spreads. Credit risk measures the likelihood of default, and the spread indicates the risk premium investors demand.
Key Concept
Credit risk and yield spread
Explanation
Credit risk is the probability of default, and the yield spread reflects the additional yield required by investors to compensate for this risk.
Question 2.2
step 1
Discuss the statement that buying a credit default swap (CDS) is comparable to being long on a risk-free bond and short on a corporate bond
step 2
A CDS is a financial derivative that provides protection against the default of a borrower. The buyer of a CDS pays a premium to the seller, who compensates the buyer if the borrower defaults
step 3
Being long on a risk-free bond means holding a bond with no default risk, such as a government bond. Being short on a corporate bond means selling a corporate bond, which involves taking on the risk of the bond issuer defaulting
step 4
By buying a CDS, the investor is protected against the default of the corporate bond, effectively removing the credit risk. This is similar to holding a risk-free bond. At the same time, the investor pays premiums, similar to the interest payments on a short position in a corporate bond
Answer
Buying a CDS is comparable to being long on a risk-free bond and short on a corporate bond because it provides protection against default (like a risk-free bond) while requiring premium payments (similar to interest on a short position).
Key Concept
Credit default swap (CDS)
Explanation
A CDS provides default protection, making it similar to holding a risk-free bond while requiring premium payments, akin to shorting a corporate bond.
Question 2.3
step 1
Calculate the payment under the cap. The cap limits the interest rate to 10%, so any rate above this results in a payment to the cap holder
step 2
Given: - Principal Amount =$50,000,000 = \$50,000,000 - Cap Rate =10% = 10\% - LIBOR Rate =13% = 13\% Calculate the payment: Payment=Principal×(LIBOR Rate−Cap Rate) \text{Payment} = \text{Principal} \times (\text{LIBOR Rate} - \text{Cap Rate}) Payment=50,000,000×(0.13−0.10) \text{Payment} = 50,000,000 \times (0.13 - 0.10) Payment=50,000,000×0.03 \text{Payment} = 50,000,000 \times 0.03 Payment=$1,500,000 \text{Payment} = \$1,500,000
step 3
The payment would be made at the end of the 6-month period when the LIBOR rate is reset
Answer
The payment under the cap is \$1,500,000, and it would be made at the end of the 6-month period.
Key Concept
Interest rate cap
Explanation
An interest rate cap limits the maximum interest rate, and payments are made when the actual rate exceeds the cap rate.
Question 2.4
step 1
Discuss how a Long Collar could be implemented by Adelco. A Long Collar involves buying a cap and selling a floor
step 2
By buying a cap, Adelco limits the maximum interest rate it will pay. By selling a floor, Adelco agrees to pay a minimum interest rate, receiving a premium for this agreement
step 3
If the yield on Treasury bonds becomes an inverted yield curve, short-term rates are higher than long-term rates. This could affect the cost of borrowing and the effectiveness of the collar strategy
Answer
Adelco can implement a Long Collar by buying a cap to limit maximum interest rates and selling a floor to receive premiums. An inverted yield curve could impact borrowing costs and the collar's effectiveness.
Key Concept
Long Collar strategy
Explanation
A Long Collar involves buying a cap and selling a floor to manage interest rate risk, with potential impacts from changes in the yield curve.
[question number] Answer
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Solution by Steps
step 1
Advantages of Index Tracking: - Lower Costs: Index funds typically have lower management fees compared to actively managed funds. - Diversification: By tracking an index, the fund automatically diversifies across all the securities in the index. - Performance Consistency: Index funds aim to replicate the performance of the index, providing more predictable returns. Disadvantages of Index Tracking: - Lack of Flexibility: Index funds cannot adjust their holdings in response to market conditions. - Limited Upside: Index funds will not outperform the market since they are designed to match the index. - Tracking Error: There can be slight deviations from the index performance due to fees and other factors
Answer
Index tracking offers lower costs and diversification but lacks flexibility and has limited upside potential.
Question 1(b)
step 1
Calculate Average Sub-Period Returns: - Fund Returns: - R1=10450−1040010400=0.0048 R_1 = \frac{10450 - 10400}{10400} = 0.0048 - R2=10477−1045010450=0.0026 R_2 = \frac{10477 - 10450}{10450} = 0.0026 - R3=10450−1047710477=−0.0026 R_3 = \frac{10450 - 10477}{10477} = -0.0026 - R4=10460−1045010450=0.0010 R_4 = \frac{10460 - 10450}{10450} = 0.0010 - Benchmark Returns: - R1=10012−1002410024=−0.0012 R_1 = \frac{10012 - 10024}{10024} = -0.0012 - R2=10048−1001210012=0.0036 R_2 = \frac{10048 - 10012}{10012} = 0.0036 - R3=10096−1004810048=0.0048 R_3 = \frac{10096 - 10048}{10048} = 0.0048 - R4=10076−1009610096=−0.0020 R_4 = \frac{10076 - 10096}{10096} = -0.0020
step 2 ⋮ Calculate Average Returns: - Fund Average Return: - Average Fund Return=0.0048+0.0026−0.0026+0.00104=0.00145 \text{Average Fund Return} = \frac{0.0048 + 0.0026 - 0.0026 + 0.0010}{4} = 0.00145 - Benchmark Average Return: - Average Benchmark Return=−0.0012+0.0036+0.0048−0.00204=0.0013 \text{Average Benchmark Return} = \frac{-0.0012 + 0.0036 + 0.0048 - 0.0020}{4} = 0.0013
step 3
Calculate Tracking Error: - Tracking Error Formula: - Tracking Error=1n−1∑i=1n(Rf,i−Rb,i)2 \text{Tracking Error} = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (R_{f,i} - R_{b,i})^2} - Tracking Error=13[(0.0048+0.0012)2+(0.0026−0.0036)2+(−0.0026−0.0048)2+(0.0010+0.0020)2] \text{Tracking Error} = \sqrt{\frac{1}{3} [(0.0048 + 0.0012)^2 + (0.0026 - 0.0036)^2 + (-0.0026 - 0.0048)^2 + (0.0010 + 0.0020)^2]} - Tracking Error=13[0.036+0.001+0.056+0.009]=0.004 \text{Tracking Error} = \sqrt{\frac{1}{3} [0.036 + 0.001 + 0.056 + 0.009]} = 0.004 ∻Answer∻ ⚹ The fund has an average return of 0.00145, the benchmark has an average return of 0.0013, and the tracking error is 0.004. ⚹ Question 1(c)
step 1 ⋮ Evaluating an Index Fund: - Performance Comparison: An index fund would closely match the benchmark returns with minimal tracking error. - Cost Efficiency: Lower management fees would result in slightly higher net returns. - Predictability: The returns would be more predictable and consistent with the benchmark.
Answer
An index fund would show minimal tracking error and more predictable returns compared to an actively managed fund.
Question 2
step 1
Calculate Loss to CIMB Bank: - Default on 4th Payment Date: - LIBOR Rate: 4.75% per annum with semi-annual compounding. - Semi-Annual Rate: 4.75%2=2.375% \frac{4.75\%}{2} = 2.375\% - Payment Due: 500,000,000×0.02375=11,875,000 500,000,000 \times 0.02375 = 11,875,000 - Loss: Since Maybank defaults, CIMB Bank loses the payment of RM 11,875,000. ∻Answer∻ ⚹ The loss to CIMB Bank is RM 11,875,000 due to Maybank's default. ⚹ Question 3
step 1 ⋮ Rationale for Discounting Cash Flows at Different Rates: - Credit Risk: Banks may use a discount rate higher than LIBOR to account for the credit risk of the counterparty. - Liquidity Premium: A higher discount rate may be used to reflect the liquidity premium required for less liquid currencies. - Market Conditions: Different discount rates can be used to reflect current market conditions and expectations.
Answer
Banks discount cash flows at different rates to account for credit risk, liquidity premium, and market conditions.
Key Concept
Index tracking vs. active management, performance evaluation, interest rate swap default, and discounting cash flows.
Explanation
Index tracking offers cost efficiency and predictability, while active management aims for higher returns. Performance evaluation involves calculating returns and tracking error. Interest rate swap default results in loss of expected payments. Discounting cash flows at different rates accounts for various financial risks.
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Solution by Steps
step 1
Identify the current interest rates and the terms of the swap. The fixed rate is 4.7%+1.2%=5.9%4.7\% + 1.2\% = 5.9\%. The floating rate is 6-month LIBOR
step 2
Calculate the net payment basis. The bank will pay the floating rate (LIBOR) and receive the fixed rate (5.9%)
step 3
Use interest rate futures to hedge against interest rate risk. The futures contract is quoted at 96.00, implying an interest rate of 100−96=4%100 - 96 = 4\%
step 4
Calculate the correlation coefficient between the futures and cash market, which is 96%. This high correlation suggests that futures contracts are an effective hedging tool
step 5
Determine the notional principal for the futures contracts. The minimum contract value is RM 1,000,000. For a notional principal of RM 100,000,000, the bank needs 100,000,0001,000,000=100 \frac{100,000,000}{1,000,000} = 100 contracts
step 6
Evaluate the effectiveness of the hedge by comparing the fixed rate payments with the floating rate receipts adjusted by the futures contracts
Answer
The bank should use interest rate futures contracts to hedge against interest rate risk, given the high correlation between futures and cash markets.
Key Concept
Interest rate futures as a hedging tool
Explanation
Interest rate futures can effectively hedge against interest rate risk due to their high correlation with the cash market.
# Part 2: Arbitrage Opportunity
step 1
Identify the yields and costs: MGB yield is 5%, Junk bond yield is 7.5%, and CDS cost is 130 basis points (1.3%)
step 2
Calculate the net yield from the arbitrage opportunity. The net yield is 7.5%−1.3%=6.2%7.5\% - 1.3\% = 6.2\%
step 3
Compare the net yield with the MGB yield. The arbitrage profit is 6.2%−5%=1.2%6.2\% - 5\% = 1.2\%
step 4
If the CDS cost increases to 260 basis points (2.6%), the net yield becomes 7.5%−2.6%=4.9%7.5\% - 2.6\% = 4.9\%
step 5
Compare the new net yield with the MGB yield. The arbitrage profit is 4.9%−5%=−0.1%4.9\% - 5\% = -0.1\%, indicating no arbitrage opportunity
Answer
There is an arbitrage opportunity when the CDS cost is 130 basis points, yielding a profit of 1.2%. If the CDS cost increases to 260 basis points, the arbitrage opportunity disappears.
Key Concept
Arbitrage opportunity in bond markets
Explanation
Arbitrage opportunities arise when the net yield from a higher-risk bond, adjusted for CDS costs, exceeds the yield from a lower-risk bond.
Question 5 # Part (a): Convertible Bond Calculations
step 1
Calculate the conversion value: Conversion value=Conversion ratio×Stock price=37.383×23=859.81 \text{Conversion value} = \text{Conversion ratio} \times \text{Stock price} = 37.383 \times 23 = 859.81
step 2
Calculate the market conversion price: Market conversion price=Market price of bondConversion ratio=100037.383=26.75 \text{Market conversion price} = \frac{\text{Market price of bond}}{\text{Conversion ratio}} = \frac{1000}{37.383} = 26.75
step 3
Calculate the conversion premium per share: Conversion premium per share=Market conversion price−Stock price=26.75−23=3.75 \text{Conversion premium per share} = \text{Market conversion price} - \text{Stock price} = 26.75 - 23 = 3.75
step 4
Calculate the conversion premium ratio: Conversion premium ratio=Conversion premium per shareStock price×100=3.7523×100=16.3% \text{Conversion premium ratio} = \frac{\text{Conversion premium per share}}{\text{Stock price}} \times 100 = \frac{3.75}{23} \times 100 = 16.3\%
step 5
Calculate the premium over straight value: Premium over straight value=Market price of bond−Straight valueStraight value×100=1000−510510×100=96.08% \text{Premium over straight value} = \frac{\text{Market price of bond} - \text{Straight value}}{\text{Straight value}} \times 100 = \frac{1000 - 510}{510} \times 100 = 96.08\%
step 6
Calculate the favorable income differential per share: Favorable income differential per share=Coupon rate×Par valueConversion ratio−Dividend per share=0.095×100037.383−0.75=1.80 \text{Favorable income differential per share} = \frac{\text{Coupon rate} \times \text{Par value}}{\text{Conversion ratio}} - \text{Dividend per share} = \frac{0.095 \times 1000}{37.383} - 0.75 = 1.80
step 7
Calculate the premium payback period: Premium payback period=Conversion premium per shareFavorable income differential per share=3.751.80=2.08 years \text{Premium payback period} = \frac{\text{Conversion premium per share}}{\text{Favorable income differential per share}} = \frac{3.75}{1.80} = 2.08 \text{ years}
Answer
Conversion value: 859.81, Market conversion price: 26.75, Conversion premium per share: 3.75, Conversion premium ratio: 16.3%, Premium over straight value: 96.08%, Favorable income differential per share: 1.80, Premium payback period: 2.08 years
Key Concept
Convertible bond valuation
Explanation
The calculations involve determining the value of converting the bond into stock and comparing it to the bond's market price and straight value.
# Part (b): Stock Price Increases to $46
step 1
Calculate the return from the convertible bond: Return=New conversion value−Market price of bondMarket price of bond×100=37.383×46−10001000×100=71.96% \text{Return} = \frac{\text{New conversion value} - \text{Market price of bond}}{\text{Market price of bond}} \times 100 = \frac{37.383 \times 46 - 1000}{1000} \times 100 = 71.96\%
step 2
Calculate the return from investing in the stock: Return=New stock price−Initial stock priceInitial stock price×100=46−2323×100=100% \text{Return} = \frac{\text{New stock price} - \text{Initial stock price}}{\text{Initial stock price}} \times 100 = \frac{46 - 23}{23} \times 100 = 100\%
step 3
Explain why the return on the stock is higher: The stock return is higher because the bond's return is capped by its conversion ratio, while the stock's return is directly proportional to its price increase
Answer
Return from convertible bond: 71.96%, Return from stock: 100%, Stock return is higher due to direct price proportionality.
Key Concept
Return comparison between convertible bonds and stocks
Explanation
Convertible bonds have capped returns due to conversion ratios, while stocks have unlimited upside potential.
# Part (c): Stock Price Declines to $8
step 1
Calculate the return from the convertible bond: The bond's value will be closer to its straight value. Return=Straight value−Market price of bondMarket price of bond×100=510−10001000×100=−49% \text{Return} = \frac{\text{Straight value} - \text{Market price of bond}}{\text{Market price of bond}} \times 100 = \frac{510 - 1000}{1000} \times 100 = -49\%
step 2
Calculate the return from investing in the stock: Return=New stock price−Initial stock priceInitial stock price×100=8−2323×100=−65.22% \text{Return} = \frac{\text{New stock price} - \text{Initial stock price}}{\text{Initial stock price}} \times 100 = \frac{8 - 23}{23} \times 100 = -65.22\%
step 3
Explain why the bond return is higher: The bond's return is higher because it has a floor value (straight value), while the stock can decline more significantly
Answer
Return from convertible bond: -49%, Return from stock: -65.22%, Bond return is higher due to its floor value.
Key Concept
Downside protection in convertible bonds
Explanation
Convertible bonds offer downside protection through their straight value, limiting losses compared to stocks.
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Solution by Steps
step 1
Identify the types of bonds in the portfolio: Junk Corporate Bonds, Principal Indexed Bonds, Convertible Bonds, and Zero-Coupon Bonds
step 2
For Junk Corporate Bonds, consider using credit default swaps (CDS) to hedge against default risk
step 3
For Principal Indexed Bonds, use inflation swaps to hedge against inflation risk
step 4
For Convertible Bonds, consider using options to hedge against equity risk
step 5
For Zero-Coupon Bonds, use interest rate swaps to hedge against interest rate risk
Answer
Use CDS for Junk Corporate Bonds, inflation swaps for Principal Indexed Bonds, options for Convertible Bonds, and interest rate swaps for Zero-Coupon Bonds.
Key Concept
Hedging strategies for different bond types
Explanation
Different types of bonds require different hedging strategies to mitigate specific risks associated with each type.
Question 1b
step 1
Consider the assumptions of bond valuation models such as the yield curve, interest rate movements, and market conditions
step 2
Assume that interest rates will continue to rise due to inflationary pressures and fiscal stimulus
step 3
Assume that the yield curve will remain upward sloping, indicating higher yields for longer maturities
step 4
Consider the impact of monetary policies on bond prices and yields
Answer
Assumptions include rising interest rates, an upward sloping yield curve, and the impact of monetary policies.
Key Concept
Assumptions in bond valuation models
Explanation
Assumptions about interest rates, yield curves, and monetary policies are crucial for accurate bond valuation.
Question 2a
step 1
Identify the risk of using a plain vanilla interest-rate swap, which is primarily interest rate risk
step 2
Consider the risk of changes in the floating rate, which can lead to higher payments
step 3
Evaluate the counterparty risk, where the other party may default on the swap agreement
Answer
Risks include interest rate risk, floating rate changes, and counterparty risk.
Key Concept
Risks of plain vanilla interest-rate swaps
Explanation
Interest rate swaps carry risks related to interest rate changes and counterparty defaults.
Question 2b
step 1
Consider the benefits of a declining notional principal amount, which reduces exposure over time
step 2
Evaluate how this can match the declining balance of the underlying mortgage portfolio
step 3
Assess the reduced risk of higher payments as the notional principal decreases
Answer
A declining notional principal amount reduces exposure and matches the declining balance of the mortgage portfolio.
Key Concept
Benefits of declining notional principal in swaps
Explanation
A declining notional principal amount reduces risk and aligns with the amortization of the underlying assets.
Question 2c
step 1
Define a swaption as an option to enter into a swap agreement in the future
step 2
Consider the flexibility it provides to hedge against future interest rate movements
step 3
Evaluate the potential cost savings if interest rates move favorably
Answer
A swaption provides flexibility and potential cost savings by allowing the manager to enter into a swap in the future.
Key Concept
Advantages of swaptions
Explanation
Swaptions offer flexibility and potential cost savings by allowing future entry into swap agreements.
Question 3
step 1
Identify the interest rate risk exposure for Presco and Osel due to borrowing in different currencies
step 2
Consider the impact of exchange rate fluctuations on the cost of borrowing
step 3
Evaluate the use of Euro Dollar or Euro Sterling Interest Rate Futures Options to hedge against interest rate risk
step 4
Propose a currency swap where Presco borrows in USD and Osel borrows in GBP, with the swap dealer earning 0.5% per year
Answer
Use Euro Dollar or Euro Sterling Interest Rate Futures Options to hedge interest rate risk and propose a currency swap with a 0.5% fee for the swap dealer.
Key Concept
Hedging interest rate and currency risk
Explanation
Interest rate futures options and currency swaps can effectively hedge against interest rate and currency risk.
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