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Transcript of Lecture Note 05_Bonds With Other Features (1)
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Lecture Note Five:
Bonds with Other Features
FINA0804/3323 Fixed Income Securities
Faculty of Business and Economics University of Hong Kong
Dr. Huiyan Qiu
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Outline
Callable bond
What is a callable bond? Why callable bond?
Pros and cons of calling a bond
Valuing a callable bond
Convertible bond: Basics
Floaters and inverse floaters
Repurchase agreement
Reference: Fabozzi’s chapter 17, 19
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What is a Callable Bond?
Acallable bondallows the issuer to buy back
the whole issue at a pre-specified price at some
point in the future.
Some terms• Thestrike price (or exercise price or call price):the price at which the issuer can buy back thebonds (typically par value plus one year’s
interest).• Call protection period:the period during whichthe issuer cannot call the bonds.
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Why Callable Bond?
Callable bonds give borrowers the option to
refinance when interest rates are low. In other
words, it is one way companies hedge against
possible decreases in future interest rates.• Before 1970 almost all corporate bonds wereissued with call features.
• Between 1970 and 1990, about 80% of fixed rate
corporate bonds were callable.• Now, less than 30% of corporate bonds are callabledue to the development of the interest ratederivatives markets.
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Why Callable Bond? (cont’d)
Some firms may still find callable bonds
desirable because by issuing callable bonds they
can send a strong positive signal to the markets
about the quality of their business.• If a firm is confident about their business andbelieves that their credit quality will improve inthe future (which will lower their borrowing costs),
it makes sense for them to issue a callable bond.• As soon as the market realizes their better values,they can simply call the old expensive bond andreplace it with a bond which pays lower coupons.
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Callable Bondholders
The presence of a call option results in two
disadvantages to the bondholder.
Disadvantage 1:Callable bonds expose
bondholders toreinvestment risk:• Investors are exposed to additional reinvestmentrisk due to the call option.
• Issuers will call the bonds when the price of the
bond is higher than the strike price, whichhappens when the interest rate is low enough.
• Bondholders are forced to reinvest the proceedsreceived in redemption at a lower interest rate.
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Callable Bondholders (cont’d)
Disadvantage 2:The price appreciation
potential for a callable bond in a declining
interest-rate environment is limited:
•
As interest rate drops, the price of a straight debtwill increase (in theory, no limit). However, in thecase of callable bonds, bonds are expected to beredeemed when interest rate drops, therefore wehave a limit on the price appreciation. This iscalled “price compression”.
Investors are willing to accept the call risk if
higher yield is offered.
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Issuers: Reasons for Calling a Bond
There can be different reasons for a bond issuer
to call a bond.
1.To remove an undesirable protectivecovenant in the bond indenture
2. An improved credit rating
3.Drop in the market-wide interest rate
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To Remove an Undesirable Covenant
An old debt indenture requires the firm to have
an interest coverage ratio of at least 2
• Interest coverage ratio= Earnings before
interest and taxes divided by Interest expenseThe firm wants to lower this requirement to 1.5
but has failed to negotiate with old bond holders
The firm can “call” the old bond (if the old bond is
callable) and issue new ones where the newrequired interest coverage ratio is 1.5
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An Improved Credit Rating
If the rating of a firm has improved, for example,
from junk (below BBB) to investment grade
(BBB and above), the firm may consider “calling”
the old bond• The firm can now issue debt at a more favorablerate
• Investors are willing to accept a lower yield to
maturity or lower coupon rate because the firmhas become less risky
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Drop in the Interest Rate
If the market-wide interest rates drop, the firm
may want to “call” the old bond (with a higher
coupon rate) and replace it by a lower-coupon
bond• The firm gains the present value of the couponssaved
• The new bond may or may not have a longer
maturity than the old bond
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Pros and Cons of Calling a Bond
By calling a bond and refunding by issuing a new
bond, the firm usually benefits from a lower
coupon rate – the firm gains the present value of
the coupons saved.This saving has to be balanced against the costs
of calling a bond, which include:
• Paying the call premium.
• Flotation costs for the replacement bond issue• The loss of the opportunity to call the bond in thefuture if interest rates were to drop even further.The timing of calling is very crucial.
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Refunding Benefit: Example 1
Suppose there is a $100-par perpetual callable
bond with the following characteristics:
• Coupon rate = 10%
•
Strike price = $100• No call protection
Suppose all interest rates drop to 7%. Then
• Calling the old debt
• Issuing new debt at 7%
If the costs of refinancing are 1.25% of par, what
is the refunding benefit?
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Refunding Benefit: Example 1
Refunding benefit
= ($3/0.07) – ($100 × 1.25%)
= $42.86 – $1.25 = $41.61
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Refunding Benefit: Example 2
Suppose a firm issued a semi-annual par coupon
bond with the following characteristics:
• Maturity = 30 years
•
Par = $100• Coupon rate = 12%
• Strike price = $105
• Call protection for the first 5 years
At the end of the 5th year, rates are 9%.
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Refunding Benefit: Example 2
There are 25 years remaining. The present value
of the firm’s liabilityif the debt is not calledis
$129.64.
•
N = 50, PMT = 6, Rate = 4.5%, FV = $100.Ifthe bond is called at the strike price and a
new bond is issued with a 9% coupon rate.
• The coupon rate is reduced by 3% for 25 years.
Present value of coupon saving is $29.64. (N = 50,PMT = 1.5, Rate = 4.5%, FV = $0).
• The call premium is $105 – $100 = $5.
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Refunding Benefit: Example 2
Suppose the flotation costs are 2% of par. The
overall refinancing costs is
• Refinancing costs = Flotation costs + Call
premium = (2% × $100) + ($105 – $100) = $7
Refinancing benefit= PV of savings –
Refinancing costs = $29.64 – $7.00 = $22.64
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Valuing a Callable Bond
Callable bond can be considered as having two
components:a non-callable bondanda call
option.
A valuation model must produce arbitrage-free
values; that is, a valuation model must produce avalue for each on-the-run issue that is equal toits observed market price. To price the bond wewill use abinomial interest rate tree model.
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Valuing a Callable Bond (cont’d)
The construction of binomial interest rate tree will becovered in later lecture. We take the following tree as
given.
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Valuing a Callable Bond: Example
Consider a three-year bond with 5.25% annual
coupon payment. We employ thebackward
induction methodology to compute the price of
bond (non-callable or callable at par in one year.)
Following figure shows the calculation of theprice of the bond that iscallable at parin one
year. The slides followed provide the detail of thecalculation.
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Valuing a Callable Bond
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Calculation
If the bond is not called in year 2, the price of the
bond then is
• At nodeNHH, $105.25/1.067573 = $98.5881
• At nodeNHL, $105.25/1.055324 = $99.7324• At nodeNLL, $105.25/1.045296 = $100.6892
At nodeNLL, the bond will be called since the
bond price is higher than the strike price $100.There are $5.25 coupon payment at the end of
year 2.
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Calculation (cont’d)
If the bond is not called in year 1, the price of the
bond then is
• At nodeNH,
• At nodeNL,
At nodeNL, the bond will be called since the bond
price is higher than the strike price $100.
There are $5.25 coupon payment at the end ofyear 1.
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Calculation (cont’d)
At node N, now, the bond price is
The price of the callable bond is$101.4307.
For thenon-callable bond, the price of the
bond at nodeNL is
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Calculation (cont’d)
The price of the non-callable bond at node N,now, is
Therefore, the value of the option embedded inthe callable bond is
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Option-Adjusted Spread
Option-adjusted spread (OAS)
• OAS is the spread such that the market price of asecurity equals its model price when discountedvalues are computed at risk-neutral rates plusthat spread.
• Assume the 5.25% callable three-year coupon bondin our example is currently selling for $100.7874(versus $101.4307 previously calculated). The OAS
of the callable bond is then 45 basis points.• Note:the computation can be done using trial anderror method or solver in excel.
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What is a Convertible Bond?
Aconvertible bondis a bond with a call option
to buy the common stock of the issuer.
• At the discretion of the bondholder, the convertible
bond can be converted into a predeterminedamount of the company’s equity at certain timesduring its life.
Exchangeable bondsgrant the bondholder the
right to exchange the bonds for the common stockof a firm other than the issuer of the bond.
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Convertible Bond: Basics
The number of shares of common stock that the
bondholder will receive from exercising the call
option of a convertible bond or an exchangeable
bond is called theconversion ratio.• Upon conversion, the bondholder typically receivesfrom the issuer the underlying shares. This isreferred to as aphysical settle.
•
There are issues where the issuer may have thechoice of paying the bondholder the cash value ofthe underlying shares. This is referred to as acash settle.
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Conversion Value and Minimum Value
Theconversion valueof a convertible bond is
the value of the bond if it is converted
immediately
Theminimum valueof a convertible bond is the
greater of
• its conversion value, and• its straight value (the value without theconversion option)
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Market Conversion Price
Themarket conversion priceis the price thatan investor effectively pays for the common stockif the convertible bond is purchased and thenconverted into the common stock
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Why Pay a Premium?
An investor who purchases a convertible bond
rather than the underlying stock typically pays a
premium over the current market price of the
stock.• As the stock price declines, the price of theconvertible bond will not fall below its straightvalue. The straight value acts as a floor for theconvertible bond price.
• The investor realizes higher current income fromthe coupon interest paid on the convertible bondthan would be received as dividends paid on thenumber of shares equal to the conversion ratio.
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Investment Characteristics
The investment characteristics of a convertible
bond depend on the stock price
• If the stock price is low the straight value isconsiderably higher than the conversion value no conversion
• Bond equivalent or busted convertible
• If the stock price is high
•
Equity equivalent• Between the two cases
• Hybrid security
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Convertible Bond: Example
XYZ convertible bond:
• Maturity = 10 years
• Coupon rate = 10%
•
Conversion ratio = 50• Par value = $1,000
• Current market price of the bond = $950
• Straight value (the value of the non-convertible
bond) = $788Current market price of XYZ common stock =
$17; Dividends per share = $1 per year
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Convertible Bond: Example (cont’d)
Conversion value = $17 × 50 = $850
Market conversion price = $950 / 50 = $19
Market conversion premium per share
= $19 – $17 = $2Market conversion premium ratio = 2/17 ≈ 11.8%
The bondholder receives $100 annual coupon
payment versus $50 dividend if the bond isconverted into 50 shares. ($2 per share versus $1
per share.)
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Downside Risk with a Convertible Bond
The downside risk of convertible bond is often
estimated by comparing the market price of the
bond with the straight value since the price of
the bond cannot fall below its straight valueThe downside risk is measured as a percentageof the straight value
The higher the premium over straight value, allother factors constant, the less attractive theconvertible bond.
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Downside Risk with a Convertible Bond
Despite its use in practice, the measure of
downside risk is flawed because the straight
value (floor) changes as interest rates change.
Anadvantage of buying the convertible ratherthan the common stock is the reduction in
downside risk.
Thedisadvantageof a convertible relative to
the straight purchase of the common stock is theupside potential give-up because a premium pershare must be paid.
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Pros and Cons of Investing in a Convertible Bond
Suppose that an investor is considering purchase
of the XYZ stock or the XYZ convertible bond.
• The stock can be purchased in the market for $17
•
By buying the convertible bond, the investor iseffectively purchasing the stock for $19
One month later, XYZ stock rises to $34, with
everything else remaining the same
• The stock investor would realize a gain of $17 anda return of 100%.
• The bond holder would realize a gain of $1,700 –$950 = $750 and a return of 79%.
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Pros and Cons of Investing in a Convertible Bond
One month later, XYZ stock falls to $7, with
everything else remaining the same.
• The stock investor buying the stock would realizea loss of $10 and a return of – 59%.
• The bond holder would realize a loss of $950 –$788 = $162 and a return of – 17%.
Downside riskis reduced as the bondholder
has the opportunity to recoup the premium pershare through the higher current income from
owning the convertible bond.
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Pros and Cons of Investing in a Convertible Bond
Call risk: convertible issues are callable by the
issuer.
• Most convertible bonds are callable (for the issuer)and some are puttable (for the bondholder).
Takeover Risk
• Corporate takeovers represent another risk toinvesting in convertible bonds.
•
As the stock of the acquired company may nolonger trade after a takeover, the investor can beleft with a bond that pays a lower coupon ratethan comparable-risk corporate bonds.
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Options Approach to Valuation
An investor who purchases a non-callable /non-
puttable convertible bond would be entering into
two separate transactions:
•
buying a non-callable/non-puttable straight bond• buying a call option on the stock, where thenumber of shares that can be purchased with thecall option is equal to the conversion ratio
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Options Approach to Valuation
Consider a common feature of a convertible bond:
the issuer’s right to call the bond.
• If called, the investor can lose any premium overthe conversion value that is reflected in themarket price.
• Therefore, the analysis of convertible bonds musttake into account the value of the issuer’s right tocall the bond.
• This depends, in turn, future interest ratevolatility, and economic factors that determinewhether it is optimal for the issuer to call the bond
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Options Approach to Valuation
The Black-Scholes option pricing model cannot
handle this situation.
• Instead, the binomial option pricing model can beused simultaneously to value the bondholder’s calloption on the stock and the issuer’s right to callthe bonds.
• The bondholder’s put option can also beaccommodated.
• To link interest rates and stock prices together,statistical analysis of historical movements ofthese two variables must be estimated andincorporated into the model.
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Floating Rate Note: Introduction
A floating rate note (FRN) is a bond with coupon
rate reset periodically accordingly to a
benchmark interest rate, or indexed to this rate.
Possible benchmark rates:• US Treasury rates, LIBOR, prime rate, ....
The coupon rate on a floating rate note is often
equal to the benchmark interest rate plus apremium (called spread).
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Floating Rate Jargon
Other terms commonly used for floating-rate
notes are
• FRNs
•
Floaters and Inverse Floaters• Variable-rate notes (VRNs)
• Adjustable-rate notes
FRN usually refers to an instrument whose
coupon is based on a short term rate (3-month T-bill, 6-month LIBOR), while VRNs are based on
longer-term rates (1-year T-bill, 2-year LIBOR)
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Cash Flow Rule for Floater
Consider a semi-annual coupon floating rate
note, with the coupon indexed to the 6-month
interest rate.
•
On each coupon date, the coupon paid is based onthe previous 6-month rate.
• The note pays par value at maturity.
•Only the next coupon is known at the currentdate. The later ones are random.
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Example: Two-Year Floater
Consider a two-year floater with coupon rate set
to equal the six-month T-bill rate. The current
six-month T-bill rate is 5.54%. Suppose the
future six-month T-bill rates turn out as follows.
Find the cash flows from $100 par of the note.
5.54% 6.00% 5.44% 6.18%
Floater Cash Flows:
2.77 3.00 2.72 103.09
0 0.5 1 1.5 2
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Valuation of Floater
Consider a $100 par of a floater with coupon rate
set to equal the six-month rate and maturing at
timeT. What is the price of the floater on the
coupon date before the maturity date, that is,
timeT – 0.5?
where is the annualized six-month rate fromt–0.5 tot.
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Valuation of Floater (cont’d)
What is the price of the floater two coupon dates
before the maturity date, that is, timeT – 1?
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Valuation of Floater (cont’d)
Working backwards to the present, repeatedly
using this valuation method, proves that the
price of a floater is always equal to par on a
coupon date.
• The coupon (the numerator) and interest rate (thedenominator) move together over time to make theprice (the ratio) stay constant.
A floater can be replicated by a dynamic strategyof rolling six-month par bonds until floatermaturity, collecting the coupons along the way.
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Valuation of Floater: Complications
The valuation of floater is more complicated than
presented.
• If the spread is not equal to zero, the coupon rateand the discount rate are different.
• There might be restrictions imposed on theresetting of the coupon rate.
• For example, a floater may have a maximum couponrate called a cap or a minimum coupon rate called a
floor.
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Inverse Floating Rate Notes
Unlike a floating rate note, aninverse floater is
a bond with a coupon that variesinverselywith a
benchmark interest rate.
Inverse floaters come about through theseparation of fixed-rate bonds into two classes:
• a floater, which moves directly with some interestrate index, and
•
an inverse floater, which represents the residualinterest of the fixed-rate bond, net of the floating-rate.
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Fixed/Floater/Inverse Floaters
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Fixed/Floater/Inverse Floaters
FIXED RATE BOND
The fixed rate bond can be split into a floater and an inversefloater unevenly.50/50 is the most popular split.
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Fixed/Floater/Inverse Floaters
The sum of the face value of the floater and
inverse floater must equal the face value of the
fixed-rate bond.
The sum of the interest paid on the floater and
inverse floater must always equal the interestpaid on the fixed-rate bond.
• Therefor a maximum/minimum interest rate(cap/floor) is implicitly imposed on floater/inversefloater.
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Floater and Inverse Floater: Example
An investment banking firm purchases $100million of a two-year 5.5% coupon bond in the
secondary market. Coupon is paid semi-annually.
The firm issues $50 million of floaters and $50million of inverse floaters. The coupon rate on
the floater is set to equal the six-month T-bill
rate. Suppose the future six-month T-bill rates
turn out as follows.
5.54% 6.00% 5.44% 6.18%
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Floater and Inverse Floater: Example
What is the cash flows to the floater and theinverse floater?
What is the coupon rate for the inverse floater?
Answer:for the first period, the coupon rate onthe floater is 5.54%. The coupon payment is
The coupon payment from the fixed rate bond is
Therefore, the coupon payment on the inverse
floater is .
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Floater and Inverse Floater: Example
(cont’d) The coupon rate on the inverse floater isthus
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Repurchase Agreement (Repo)
An agreement between two parties whereby oneparty sells securities to another party in return
for cash and agrees to repurchase equivalent
securities at an agreed price and on an agreed
future date.
• Repos may be seen as being akin tocollateralizedborrowing and lending.
•
Legally, however, the transaction under a repoinvolves an outright sale of the securities thatpasses full ownership of the securities to thepurchaser.
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Use of Repo: An Example
On August 31, 2007, the 30-year T-bond with acoupon of 5.00% and maturing on May 15, 2037,
was quoted at a clean price of 102.50. The
general collateral repo rate for a term of one
month was 4.775%.
A bond dealer receives an order from a client to
buy this bond forward in one month’s time. What
is the forward price that dealer should quote?Why? How should the dealer hedge the exposure,
assuming that the deal is done on August 31,
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Use of Repo: An Example
The dealer will first compute the forward price asfollows:
• Borrow cash in the repo markets for a one-monthterm on August 31, 2007. (Cash borrowed is usedto buy the bond used in repo as collateral.)
• Figure out how much has to be paid in the repomarkets on September 30, 2007, to retrieve thecollateral.
• This is the forward price at which the dealers willbreak even. Any additional profit margin woulddepend on the extent of competition.
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Use of Repo: An Example
August 31, 2007:Using repo to finance thepurchase of the bond.
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Use of Repo: An Example
September 30, 2007:close the repo position.Buy back the bond and deliver to the client.
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Use of Repo: An Example
Calculation:
Break-even forward price =
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End of the Notes!