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Bank Lending BFC5914

Monash Business School

Monash University

Week 12, 2021

General Exam Instructions Part 1 Part 2

1 General

2 Exam Instructions

3 Part 1

4 Part 2

General Exam Instructions Part 1 Part 2

Structure of The Course

• The principles and techniques of lending
– Topics 1 to 5.

• Making a decision : Credit risk measurement, Special
customers, loan pricing and ethics in lending

• Topics 6, 7 and 8.

• Regulate Banks, Important Issues and Prevent Defaults
– Topics 9 and 10.

General Exam Instructions Part 1 Part 2

Exam Instructions

• There are 3 compulsory questions in the whole exam paper.

• The duration of exam : 2 hours and 10 minutes.

• It is an Open-Book exam, only open to all the materials
provided on Moodle and textbooks.

• No formula sheet.

• Only HP 10bII+ or Casio FX82 (any suffix) calculator
permitted.

General Exam Instructions Part 1 Part 2

Exam Instructions

• The final exam will be run on the Moodle platform, similar to
the MST platform.

• Do not navigate between questions to avoid any system errors.

• The university will use similarity-detection software to
compare your works. Both of you will be graded 0, if your
answers bear a remarkable similarity or are the same. If it
happens, no negotiation will be applied.

• Do not input %, $ or million $ in your calculated solutions.
– E.g., obtain 11.5%, then input 0.12 in the solution box.

General Exam Instructions Part 1 Part 2

Exam Instructions

• Exam Time : 18th Nov 2021, 13 :00 – 15 :10. (Check your
timetable)

• Question 1 (20 marks) : Four Calculation Questions.

• Question 2 (20 marks) : A Lending Case Study.
– Punctuate properly and express clearly

– Three sub-questions

• Question 3 (20 marks) : Three Short-Answer Questions.

• Again : this is an individual assessment, cooperation is not
allowed.

General Exam Instructions Part 1 Part 2

Exam Instructions

• If you experience any issues during the exam :

1 Technical system issues, please contact +61 3 9903 2777

2 Clarifying questions, contact CE via email :
[email protected]

• Apply Special Considerations via the online process, not CE.
https://www.monash.edu/exams/changes/special-
consideration

General Exam Instructions Part 1 Part 2

Final Exam

• 60% of final grade.

• Hurdle requirement – must obtain 45% on the final exam.

• Based on material covered throughout the semester.

• Do not browse any other websites during the exam
– Especially, do not open Google translation during the exam.

General Exam Instructions Part 1 Part 2

Part 1 : Topic 1 – 5

• General Lending Principles

• Application of 5 Cs : Credit scoring system, personal loans,
corporate loans etc.

General Exam Instructions Part 1 Part 2

Topic 6 : Traditional Approaches to Credit Risk
Measurement

How to Measure Credit Risk ?

• Four Categories :

• Expert systems (human judgement)

• Risk premium analysis (market-based premium)

• Econometric based systems (statistical methods)

• Hybrid systems (financial theory)

General Exam Instructions Part 1 Part 2

Topic 6 : Traditional Approaches : Risk Premium Analysis

• Assuming a world with no arbitrages : the difference between
the risk free bond and the risky bond, should exactly
compensate the investor for the risk of default

• Case 1 : No recovery rate if firm defaults
Then we have : p(1 + r) = 1 + i

• Case 2 : With recovery rate, get back e(1+r) if firm defaults
Then we have : e × (1 −p) × (1 + r) + p(1 + r) = 1 + i

• Case 3 : Multi-periods loans
Cumulative Default Probability = 1 −p1 ×p2 ×p3…pn

– NO Arbitrage Condition (Geometric) : we have
(1 + i0,2)

2 = (1 + i0,1)(1 + i1,1)

– Then we have the expected forward rate : i1,1 =
(1+i0,2)

2

(1+i0,1)
− 1

– Similar computation applied to have r1, 1 ; then derive the
probability of repayment p2,p3, …pn

General Exam Instructions Part 1 Part 2

Topic 6 : Traditional Approaches :Marginal Mortality Rate

• Also using the information contained in the term structure of
interest rates, an alternative is to use the observed historical
default rates of bonds which have characteristics similar to
those of the loan we are evaluating

• Determine the marginal default rate (or called Marginal
Mortality Rate, MMR ) :

MMRit (R) =
mit (R)

Mit (R)
(1)

• Pricing risky debt using the info above and considering the
ratings migration.

General Exam Instructions Part 1 Part 2

Topic 6 : Traditional Approaches : Econometric Analysis

• Two main techniques are regression analysis and
discriminant analysis

• Regression Analysis : There are a large number of various
regression based approaches which relate default to observable
variables

• Discriminant Analysis
• The Z score model takes the form of

• Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5

• If the Z score is below 1.81 the loan is a bad risk, and above
2.99 the loan is a good risk ; a score between 1.81 and 2.99 is
indeterminate.

General Exam Instructions Part 1 Part 2

Topic 6 : Traditional Approaches : Hybrid Systems

• Advantages of this approach
• RAROC is the risk adjusted return on capital model

RAROC =
Risk Adjusted Return

Loan Risk

(or credit risk capital)

– Risk adjusted income
= (Spread + Fees −ExpectedLoss −OperatingCosts)(1 − τ)

– Denominator :

4L = −DL ×L×
4R

1 + RL

General Exam Instructions Part 1 Part 2

Topic 7 : Credit Risk Models Based on Stock Price

• Option Pricing Theory, the general form : Option Value
= fcn(S,X,r,σ,τ)

– S the price of underlying, X the strike price, r the interest rate,
τ the maturity, σ2 the volatility of the underlying

General Exam Instructions Part 1 Part 2

Topic 7 : Equity As a Call Option

• The equity holders have exactly the same payoff as a call
option as held by the firm with an exercise price of D

• The option would be exercised when the assets of the firm is
worth more than D ; and the payoff would be the difference
between the stock value and D and otherwise the option is
worthless

• The equity of the firm is a call option on the assets of the
firm where the exercise price and maturity are given by the
face value and the maturity of the debt.

General Exam Instructions Part 1 Part 2

Topic 7 :Debt As a Put Option

• At maturity :
• If the asset is worth < D, one sells the asset for D using the

put option and uses that to pay back the debt, with nothing
left over

• If the asset is worth > D, one sells it and uses the proceeds to
pay the debt, and does not use the put option

General Exam Instructions Part 1 Part 2

Topic 7 : Pricing Equity and Debt through Option Model

General Exam Instructions Part 1 Part 2

Topic 7 : KMV Model

• Expected default frequency (EDF) is a forward-looking
measure of actual probability of default ; EDF is firm specific

• KMV model is based on the structural approach to calculate
EDF (credit risk is driven by the firm value process)

• Three steps to derive the actual probabilities of default :
1. Estimation of the market value and volatility of the firm’s asset
2. Calculation of the distance to default, an index measure of

default risk
3. Scaling of the distance to default to actual probabilities of

default using a default database

General Exam Instructions Part 1 Part 2

Topic 7 : KMV Model Schematic

General Exam Instructions Part 1 Part 2

Topic 8 : Special Customers /Pricing Loan/ Ethics in Bank
Lending

• Advances to Special Customers
– Calculate the amount according to the builder’s contract

• The lender needs to look for clauses covering the following :
• Fluctuations in cost
• Penalties
• Extension of time to permit interim payments
• Retention fund

• Property investment

• Property development

General Exam Instructions Part 1 Part 2

Topic 8 : Pricing Loans

• Cost-Plus Pricing Models

• Price Leadership Pricing Models

• Below Prime Market Pricing

• Loans Bearing Maximum Interest Rates

• Customer Profitability Analysis

General Exam Instructions Part 1 Part 2

Topic 8 : Pricing Loans

• Contractually Promised Return on a Loan
• Gross return on loan (k) per dollar lent :

1 + k = 1 +
[f + (BR + m)]

[1 −b(1 −R)]

– Loan origination fee (f),
– Compensating balance requirements (b) : a fraction of the loan

principal required to be held in demand deposits at the bank
– Reserve requirement (R)
– Base Rate (BR)

General Exam Instructions Part 1 Part 2

Topic 8 : Ethics in Bank Lending

• Ethical dilemmas that a banker may face

• Effort made by banks : Equator Principles, BankTrack etc

• Conflicts of Interests

• Predatory Lending

• Responsible Lending

General Exam Instructions Part 1 Part 2

Topic 9 : Problem Loans/Regulations in Banking

• Loan Default : ‘a loan where repayments are overdue’

• Causes of Loan Default (not well-designed policies, Inadequate
controls, Over-concentration, Insufficient knowledge )

• Timing of Loan in the Business Cycle

• Provisions : If payment more than 90 days, loan is considered
an ‘impaired asset’

– Specific Provisions,
– General Provision,
– Bad-Debt Write-Offs
– Dynamic provisioning

General Exam Instructions Part 1 Part 2

Topic 9 : Problem Loans(Dealing With Defaults)

• If the loan is in default, the bank must act to minimise the
losses arising from defaulting clients and may reschedule
payments rather than liquidate loan

• Classify defaulting clients into three categories :
– Mild financial distress
– Moderate financial distress
– Severe financial distress

• Lender needs to very carefully evaluate whether it is better
to :

i Liquidate firms to recover greatest percentage of loan possible ;
or

ii Restructure debt (inclusive of debts to other lenders) to
maintain operations to allow firm to trade out of current crisis
or be sold as going concern

General Exam Instructions Part 1 Part 2

Topic 9 : Why Regulate Banks

• Financial system is among the most heavily regulated sectors
of the economy.

• Banks are among the most heavily regulated of financial
institutions. Why ?

• Regulations could sometimes impede development of banks.

• Regulations sometimes can’t prevent financial crisis.

• Are banking regulations beneficial ?

General Exam Instructions Part 1 Part 2

Topic 9 : Aim of Regulations

• Market confidence – to maintain confidence in the financial
system

• Financial stability – contributing to the protection and
enhancement of stability of the financial system

• Consumer protection – securing the appropriate degree of
protection for consumers.

• Reduction of financial crime – reducing the extent to which
it is possible for a regulated business to be used for a purpose
connected with financial crime.

• regulating foreign participation in the financial markets.

General Exam Instructions Part 1 Part 2

Topic 9 : How to Regulate Banks ?

• There are nine basic categories of bank regulation, which we
will examine from an asymmetric information perspective.

General Exam Instructions Part 1 Part 2

Topic 10 : Overview of Products

• Asset swaps
– Asset swaps, Callable and Puttable Asset Swaps and Asset

swap switches and asset swapoptions

• Credit default swaps (Company reference, index)

• Credit spread forwards

• Total return swaps

• Basket swaps

• Credit spread options

General Exam Instructions Part 1 Part 2

Topic 10 : Asset Swaps

a Synthetic FRN Investment Package

General Exam Instructions Part 1 Part 2

Topic 10 : Asset Swaps

b Synthetic Fixed Rate Investment Package

General Exam Instructions Part 1 Part 2

Topic 10 : Asset Swaps Arbitrage

• Option 1 : LIBOR +15bps on a 3-year FRN or + Bond
• Option 2 : Using Swap and receiving LIBOR +25bps or +

Bond

General Exam Instructions Part 1 Part 2

CDS on Tobacco Company Reference

General Exam Instructions Part 1 Part 2

Topic 10 : Factors Affecting The Price of a CDS

• Time To Maturity : The longer the maturity, the greater the
likelihood of default, the higher the premium

• Default Probability Reference Credit : The higher the
probability of default, the higher the premium

• Credit Rating of CDS Counterparty (as Seller) : The lower
credit rating of the CDS counterparty, the lower the premium

• Correlation between CDS Seller and Reference Credit :
The higher the correlation between the seller and reference,
the lower the premium

• Expected Recovery Rate : The higher the recovery rate, the
lower the premium

General Exam Instructions Part 1 Part 2

Total Return Swaps

– Total Return = Interest Flows + (Final Value – Original Value)
– Total return receiver is long both the price and default risk of

the reference asset
– Total return payer is the legal owner of the reference asset and

has changed to credit risk of the reference asset into credit risk
of the total return receiver

General Exam Instructions Part 1 Part 2

It never gets easier, you just get
better ! Work hard and have fun !

Wish you good luck for all the final exams !

  • General
  • Exam Instructions
  • Part 1
  • Part 2

Dear Students,

Your end of semester assessment of BFC5914 Bank Lending will be held during the official

examination period – please check your student timetable for the start time (this will be at

Australian Eastern Standard time AEST). The assessment duration will be 2 hours and 10

minutes and it will be run via the Moodle page of BFC5914.

Students need to apply Special Considerations via the online process

https://www.monash.edu/exams/changes/special-consideration

CEs are not in charge of special considerations approval.

Exam Instructions

Date of Final Exam: Check your timetable

The total grade is 60 marks.

It consists of Three compulsory questions.

The duration of the exam: 2 hours and 10 minutes.

The exam will be run on the Moodle platform.

It is an Open-Book exam, only open to all the materials provided on Moodle and textbooks.

Do not open any other websites during the exam.

No formula sheet provided.

Only HP 10bII+ or Casio FX82 (any suffix) calculator permitted.

The university will use similarity-detection software to compare your works. Both of you

will be graded 0 if your answers bear a remarkable similarity or are the same.

❖ Question 1 (20 marks): Four Calculation Questions.
❖ Question 2 (20 marks): A Lending Case Study.
❖ Question 3 (20 marks): Three Short-Answer Questions.

Again, this is an individual assessment and cooperation is not allowed.

You are highly suggested not to skip any questions.

You only have one attempt in the system.

When inputting the figures in the solution box of questions, please follow closly the

instructions on the exam paper.

In terms of rounding issues, we do not ask you to keep 2 decimal places in the middle of the

calculation steps. In the middle of the calculations, keep all the digitals.

If you experience any issues during the exam:

– Issues seeking clarity with a question, contact CE: [email protected]

– Technical system issues, please contact +61 3 9903 2777

Good luck with the exam.

Kind regards,

Ying

1

BFC 5914 Bank Lending: Tutorial of Topic 10

Q.1 Explain how the asset swap arbitrage works and provide an example using the

following instruments/rates:

5- year fixed bond rate of 6%

5-year FRN yield of LIBOR +35bps

5-year swap rate of LIBOR +50bps

Q.2 Describe how a bank or investor can obtain default protection by using as asset swap

switch.

Q.3 In what way is a CDS different to a conventional OTC swap contract? Describe a more

appropriate analogy from the financial markets.

Q.4 Name three factors that drive the price of a CDS and describe how each one

influences prices levels.

Q.5 Explain why an unfunded TRS is similar to a synthetic financing

2

Q.6 If an investor buys a 12-month credit spread call option on Company ABC’s bond

with a strike spread of 100bps for a premium of 35 bps, what is the appropriate course of

action if ABC’s spread tightens to 50bps? Widens to 150bps? What is the breakeven level of

the trade?

Q.7 Assume the following reference credit portfolio:

Credit 1: $10 million notional, post-default price 40

Credit 2: $10 million notional, post-default price 30

Credit 3: $10 million notional, post-default price 50

Given a $30 million structure, how much will an investor receive?

(a) If credit 2 defaults in a standard default?

(b) If credit 2 defaults in a first-to-default basket?

(c) If credit 1 and 2 default in a first-to-default basket (in that order)?

(d) If credit 3 defaults in a senior basket with a $5 mn first-loss limit?

(e) If credit 1 defaults in a senior basket with a $5 mn first-loss limit?

Bank Lending BFC5914

Monash Business School

Monash University

Week 11

Review of Last Lecture Introduction Products of Credit Derivatives

1 Review of Last Lecture

2 Introduction

3 Products of Credit Derivatives

Review of Last Lecture Introduction Products of Credit Derivatives

Problem Loans

• Loan Default

• Causes of Loan Default

• Business Cycle

• Provisions

• Dealing With Defaults

Review of Last Lecture Introduction Products of Credit Derivatives

Regulations in Bank Lending

• Aims of Regulations

• Causes of Banking Problems

• Possible Solutions of Regulations

Review of Last Lecture Introduction Products of Credit Derivatives

Topic 10 : Fundamental Credit
Derivative Products

Reading : Saunders and Allen, Chapter 12

Review of Last Lecture Introduction Products of Credit Derivatives

Credit Derivatives

• Credit derivative (CD) contracts are financial instruments
that transfer between two parties the risk and return
characteristics of a credit-risky reference asset

• The underlying assets may or may not be owned by either
party in the transaction

• Though CD are relatively new compared to other derivatives,
but now are already widespread and growth rates are
impressive

• Innovation and expansion show no signs of slowing, suggesting
that the sector should continue to remain vital and vibrant.

Review of Last Lecture Introduction Products of Credit Derivatives

Overview of Products

• Credit Derivatives are contracts that generate an economic
pay-off based on the credit performance of a reference credit
asset ; performance may be determined by whether or not the
reference credit defaults, and/or whether its credit spreads
improve or deteriorate

• Credit default contracts pay-off based on the occurrence of a
predefined credit event related to a specific reference obligor ;
the event may be related to failure to pay, bankruptcy,
restructuring, moratorium or repudiation

• If the event occurs, the credit guarantor (or protection seller,
who is effectively ’long’ the credit) makes a payment to the
beneficiary (protection buyer, who is ’short’ the credit) based
on physical or cash settlement procedures

Review of Last Lecture Introduction Products of Credit Derivatives

Overview of Products

• Credit spread contracts pay off based on the creditworthiness
of the reference asset ; default is thus just one state in a
continuum of creditworthiness

• Credit deterioration may occur as a result of weakness in the
obligor’s financial position

– This leads to credit rating downgrades and a widening of
the credit spread versus a risk-free benchmark

– Even if the obligor does not default on its obligations, the
holder of the derivative will receive a payment related to the
differential between the credit spread at trade date and
maturity date

Review of Last Lecture Introduction Products of Credit Derivatives

Overview of Products

• CD have evolved considerably over the past decade and the
market now features a range of core default and spread
products, along with certain ’second generation’ variations

• The most common structures are as follows :
• Asset swaps

– Asset swaps, Callable and Puttable Asset Swaps and Asset
swap switches and asset swaptions

• Credit default swaps (Company reference, index)
• Credit spread forwards
• Total return swaps
• Basket swaps
• Credit spread options

• These core products can be used to create other types of
structured credit instruments, which we classify broadly as :

• Credit linked notes
• Synthetic collateralized debt obligations

Review of Last Lecture Introduction Products of Credit Derivatives

An Important note

• It should be noted that GFC has taught us (yet again), that
Credit Derivatives are only as good as the credit worthiness of
the party writing the derivatives

• In effect one type of credit risk is changed into a different
type of credit risk ; in that the effectiveness of the credit
derivative depends on the ability of the writer of the derivative
to honour its part of the contract

• During the pre-GFC period many holders of risky securitised
housing loan portfolios thought that they had hedged their
credit risk via credit derivatives. Ultimately many of these
contracts were found to be with AIG which defaulted on its
obligations.

Review of Last Lecture Introduction Products of Credit Derivatives

The Response to the GFC

• Today the preferred counter-parties tend to be with major
banks, under the assumption that the national regulators will
not allow the banks to default on these obligations

– However, moves toward ringfencing are aimed at reducing the
obligations of regulators to bail out contracts of this type

• Credit risk management contracts such as Credit Default
Swaps are now required to be centrally cleared via an exchange
(even if OTC) to prevent a repeat of the AIG problems

• In the lead up to the GFC is was not well understood the AIG
had such a disproportionate exposure.

Review of Last Lecture Introduction Products of Credit Derivatives

Asset Swaps

• If an investor seeks to invest in Company XYZ’s bonds on a
floating-rate basis, but XYZ has only issued fixed-rate
liabilities, the intermediary can sell the investor fixed-rate
bonds and attach a swap that converts the fixed-rate coupons
into LIBOR.

• In practice the swap flows are adjusted to provide investors
with a synthetic investment trading at par with a stated
yield. Though no specific floating-rate XYZ asset actually
exists, the intermediary synthesizes one by combining the
fixed bond and the interest rate swap.

Review of Last Lecture Introduction Products of Credit Derivatives

Asset Swaps

a Synthetic FRN Investment Package

Review of Last Lecture Introduction Products of Credit Derivatives

Asset Swaps

• The reverse transaction is also possible :
if XYZ only features LIBOR-based liabilities and an investor
seeks a fixed-rate return, the investor can buy the FRN and
enter into an associated swap where it receives fixed and pays
LIBOR plus a spread

Review of Last Lecture Introduction Products of Credit Derivatives

Asset Swaps

b Synthetic Fixed Rate Investment Package

Review of Last Lecture Introduction Products of Credit Derivatives

Asset Swaps

• The same concept applies to asset swaps created with
currency, rather than interest rate swaps ; in such cases the
transaction also involves initial and final exchange of
principal, as in any conventional currency swap

• Regardless of the specific structural details, the intent is to
provide the investor with an opportunity to benefit from
XYZ’s credit spread levels and movements

• Asset swaps are typically arranged on notional amounts
ranging from $5 million to several hundred million, with
maturities extending from approximately 1 year up to 10 years.

Review of Last Lecture Introduction Products of Credit Derivatives

Asset Swaps

• Investors use asset swaps because they are motivated by
arbitrage opportunities :

• Option 1 : Investor invests in LIBOR + x bp assets

• Option 2 : Same as option 1 but seeking arbitrage
opportunities by using an asset swap :
Fixed payments under the swap are less than payments
received from a fixed asset, then LIBOR + x bp spread is
created. If this spread is greater than the spread on a direct
FRN purchase then the asset swap arbitrage is effective

– Eg : Investor can receive 5.5% on a three-year, fixed-rate bond
and LIBOR +15bps on a three-year FRN, and can enter into a
three-year pay fix/receive LIBOR where the net return on the
synthetic asset is LIBOR +25bps, or 10 bps more than the
direct purchase.

Review of Last Lecture Introduction Products of Credit Derivatives

Asset Swaps Arbitrage

• Option 1 : LIBOR +15bps on a 3-year FRN or + Bond
• Option 2 : Using Swap and receiving LIBOR +25bps or +

Bond

Review of Last Lecture Introduction Products of Credit Derivatives

Callable Asset Swaps

• A callable asset swap is similar to the asset swap package,
except that the Swap bank selling the package retains a call
option on the underlying asset, allowing it to repurchase the
asset at a given spread at some future time

• The total package can therefore be regarded as a an ordinary
asset swap combined with a fixed-floating swap and an
underlying fixed or floating-rate bond

• The strike spread is typically set equal to the spread at which
the asset is placed with the investor.

Review of Last Lecture Introduction Products of Credit Derivatives

Callable Asset Swaps

• If the spread tightens during the life of the transaction (e.g.,
the price of the asset rises as a result of specific or general
credit improvements) the SWAP bank calls the package (the
underlying asset) away from the investor, delivering cash
proceeds equal to the strike spread times invested principal

• The Swap bank can then sell the underlying asset in the
market place at a profit, or enter into a new callable asset
swap with a new investor at the tighter market spread

• This process helps the bank realize the mark-to-market value
arising from credit improvement

• Naturally, if the spread widens instead of tightens, the swap
bank will abandon the option and the investor will preserve its
asset swap package until the contracted maturity date

Review of Last Lecture Introduction Products of Credit Derivatives

Callable Asset Swaps(Continued)

• In exchange the Swap bank has the right to call away the
package, the investor receives an incremental yield that
represents the premium from selling the option

• This synthetic structure gives both parties specific benefits :
• The Swap bank preserves the ability (on an off-balance sheet

basis) to efficiently crystallize value (cash benefit) by
liquidating or selling the structure if asset spreads tighten,

• While the investor earns an incremental yield for granting the
option.

Review of Last Lecture Introduction Products of Credit Derivatives

Callable Asset Swaps

a Initial and ongoing flows assuming no exercise

Review of Last Lecture Introduction Products of Credit Derivatives

Callable Asset Swaps

b Terminal Flows Assuming Swap Bank exercises

Review of Last Lecture Introduction Products of Credit Derivatives

Puttable Asset Swaps

• A puttable asset swaps functions in a similar way except that
the investor rather than the Swap bank, retains the option.
The investor acquires a package comprised of an asset (fixed
bond or FRN) and a puttable swap, where the put allows the
investor to sell the asset swap package back to the bank at a
predetermined strike spread

• The strike spread is typically set equal to the investor’s
original purchase spread

– If the spread widens (the price of the underlying asset falls)
during the life of the transaction, the investor puts the
package to the bank, receiving principal and interest defined by
the strike spread

– The bank may then retain the asset in its portfolio, sell it in
the market-place, or attempt to arrange a new asset swap
structure with another investor at the new (wider) spread level.

Review of Last Lecture Introduction Products of Credit Derivatives

Puttable Asset Swaps

• Depending on carrying value, the Swap bank may or may not
post a mark-to-market loss. If the spread tightens, the
investor will choose not to exercise the option, thus
preserving its package until the contracted maturity date

• The investor, in gaining the right to put the package back to
the bank, pays an option premium in the form of an up-front
payment or a lower yield on the asset swap coupon

• A puttable swap where the payer of the variable or floating
rate has the right, but not the obligation, to end the
contract before expiration.

Review of Last Lecture Introduction Products of Credit Derivatives

Puttable Asset Swaps

• Both parties obtain benefits through the synthetic structure :
• The Swap bank receives incremental income from selling the

put option (temporarily or permanently removing the
underlying asset from its balance sheet)

• The investor obtains de facto downside protection against
spread widening on the underlying asset

• The puttable asset swap structure is also an essential element
of callable bond investing, as investors must be assured that
they can terminate the swap component of an asset swap
strategy if the underlying bond is called back by the issuer.

Review of Last Lecture Introduction Products of Credit Derivatives

Puttable Asset Swaps

a Initial and ongoing flows assuming no exercise

Review of Last Lecture Introduction Products of Credit Derivatives

Puttable Asset Swaps

b Terminal Flows Assuming Swap Bank exercises

Review of Last Lecture Introduction Products of Credit Derivatives

Asset Swap Switches and Asset Swaptions
• Example : An investor may own an asset swap package on

credit reference ABC at LIBOR + 30bps and agrees with
Bank D to exchange it for as asset swap package on reference
XYZ, (currently trading at LIBOR +50bps), if XYZ’s trading
spread widens to +70 bps. Bank D has the right to put the
XYZ package to the investor while simultaneously calling back
the ABC package

• In order for this transaction to function from an economic
perspective, the investor and the bank must have different
views on the current and future creditworthiness of ABC and
XYZ

• The investor must believe that XYZ represents good value at
+70bps, but is too expensive at +50 bps

• The bank is exposed to 20 bps of spread widening before it
can trigger the swap, but effectively acquires default
protection through the structure.

Review of Last Lecture Introduction Products of Credit Derivatives

Credit Default Swaps (CDS)

• The CDS functions like an insurance policy, with the swap
buyer paying the swap seller a premium to protect against
losses resulting from a defined credit event such as
bankruptcy, moratorium etc

• The swap purchaser (beneficiary) ’swaps’ the credit risk with
the provider of the swap (the insurer or guarantor)
receiving a compensatory payment if the credit event is
triggered

• If the defined credit event occurs, the CDS seller must either :
– Accept delivery of the reference asset and pay par value
– Compensate the buyer for the difference between par and the

post default price through a process known as cash, or
financial settlement.

Review of Last Lecture Introduction Products of Credit Derivatives

Credit Default Swaps

• Note that while these products are called ’swaps’ they really
function more like an option or insurance

• Note that as discussed in Saunders and Allen (pages 250 to
252) a large scale default (e.g. Lehman Brothers) can result in
an auction process to arrive at market prices for settlement

• Though the CDS appears to be a form of insurance, it is
distinct in two respects :

– The swap is an OTC contract (OTC = over the counter, i.e.
a tailored financial product not quoted or traded on an
organised exchange)

– Note that as these contracts are OTC then the credit
worthiness of the writer is an important consideration.

Review of Last Lecture Introduction Products of Credit Derivatives

Credit Default Swaps

• Though the CDS appears to be a form of insurance, it is
distinct in two respects :

– Contracts can be arranged by a party not exposed to the
underlying risk, i.e. speculators and hedgers can participate
without needing to demonstrate proof of insurability

– E.g. prior to Enron’s default, many hedge funds speculated on
Enron’s default to the point where the volume of CDS on
Enron’s debt considerably exceeded the actual amount of debt
outstanding

• CDSs are generally written for maturities ranging from 6
months to 5 years, with trading size of $10-$50 mn

• Generally the value of CDS traded globally exceeds the global
value of relevant corporate debt

– Reason for this include (i) speculation (ii) creation of
synthetic asset portfolios with the need to write loans, and
(iii) changes in views of the future resulting in trading to
change already hedged positions

Review of Last Lecture Introduction Products of Credit Derivatives

Factors Affecting The Price of a CDS

• Time To Maturity : The longer the maturity, the greater the
likelihood of default, the higher the premium

• Default Probability Reference Credit : The higher the
probability of default, the higher the premium

• Credit Rating of CDS Counter-party (as Seller) : The
lower credit rating of the CDS counter-party, the lower the
premium

• Correlation between CDS Seller and Reference Credit :
The higher the correlation between the seller and reference,
the lower the premium

• Expected Recovery Rate : The higher the recovery rate, the
lower the premium

Review of Last Lecture Introduction Products of Credit Derivatives

Factors Affecting The Price of a CDS

• Time To Maturity : The longer the maturity, the greater the
likelihood of default, the higher the premium

• Default Probability Reference Credit : The higher the
probability of default, the higher the premium

• Credit Rating of CDS Counter-party (as Seller) : The
lower credit rating of the CDS counter-party, the lower the
premium

• Correlation between CDS Seller and Reference Credit :
The higher the correlation between the seller and reference,
the lower the premium

• Expected Recovery Rate : The higher the recovery rate, the
lower the premium

Review of Last Lecture Introduction Products of Credit Derivatives

Factors Affecting The Price of a CDS

• Time To Maturity : The longer the maturity, the greater the
likelihood of default, the higher the premium

• Default Probability Reference Credit : The higher the
probability of default, the higher the premium

• Credit Rating of CDS Counter-party (as Seller) : The
lower credit rating of the CDS counter-party, the lower the
premium

• Correlation between CDS Seller and Reference Credit :
The higher the correlation between the seller and reference,
the lower the premium

• Expected Recovery Rate : The higher the recovery rate, the
lower the premium

Review of Last Lecture Introduction Products of Credit Derivatives

Factors Affecting The Price of a CDS

• Time To Maturity : The longer the maturity, the greater the
likelihood of default, the higher the premium

• Default Probability Reference Credit : The higher the
probability of default, the higher the premium

• Credit Rating of CDS Counter-party (as Seller) : The
lower credit rating of the CDS counter-party, the lower the
premium

• Correlation between CDS Seller and Reference Credit :
The higher the correlation between the seller and reference,
the lower the premium

• Expected Recovery Rate : The higher the recovery rate, the
lower the premium

Review of Last Lecture Introduction Products of Credit Derivatives

CDS on Tobacco Company Reference

Review of Last Lecture Introduction Products of Credit Derivatives

CDS on Tobacco Company Reference

• The Bank is concerned about pending litigation that may
result in a deterioration of credit quality of its tobacco
company exposure ; It has extended a $10 million loan

• The Bank is eager to reduce its default exposure ; it enters
into a 5 yr CDS with a credit derivative dealer for $10 mn

• The reference under the transaction is the tobacco co’s
publicly traded 10-yr bond ; The transaction fee for the CDSs
is 50 bp, or $50,000 per year

• If the Tobacco co defaults on its bond and the reference bond
drops to a price of 60, the dealer pays 40 or $4mn.

Review of Last Lecture Introduction Products of Credit Derivatives

CDS on Tobacco Company Reference

• This provides coverage for the bank’s own $10mn loan. (e.g. if
my loan falls in value from $10mn to $6mm, the $4mn from
the CDS pays for the loss)

• The bank is exposed to the credit risk of the tobacco
company and the credit derivatives dealer as counter-party

• The correlation between the reference and the dealer must be
understood : High correlations between the dealer and the
tobacco co will allow the bank to pay a lower premium (but
bear more counter-party risk).

Review of Last Lecture Introduction Products of Credit Derivatives

CDS Index Swap

• A derivative contract covering a broad pool of credits that
together comprise a standardized index ; The CDS Index swap
uses a market index as its benchmark

• Example : the DJ CDX consists of a basket of 125 CDS
contracts on U.S. firms with liquid, investment-grade
corporate debt

• The buyer of an index swap pays the seller a premium in
exchange for a compensatory payment if a credit event
happens within the index

• If a credit event occurs, the reference asset is removed from
the index and the contract continues based on the remaining
reference assets

• The buyer is obliged to pay the same fixed premium on the
remaining references

Review of Last Lecture Introduction Products of Credit Derivatives

CDS Index Swap

Review of Last Lecture Introduction Products of Credit Derivatives

CDS Index Swap

• Assume the index price is 35bp, payable by the buyer quarterly
for the life of the trade

• If the fair price widens 1 month later 55bps, a protection buyer
entering the trade at that point musy pay an up-front fee
equivalent to the present value of the 20bps for the life of the
trade and then continue paying the fixed 35bps every quarter

• If one of the 125 reference entities defaults, the protection
seller pays the protection buyer $1mn

• The trade then continues at a premium of 35bps on the
remaining 124 credits and the lower notional amount.

Review of Last Lecture Introduction Products of Credit Derivatives

Credit Spread Forwards

• CSF is a forward contract on a risky credit spread that
allows the purchase or sale of a credit spread at a forward
price for settlement at some future date

• The seller agrees to pay the buyer a fixed credit spread and
receive a market spread

• The fixed spread is set at the trade date (today) and the
evaluation against the market spread occurs at transaction
maturity (in the future)

• The buyer agrees to pay the market spread in exchange for
the fixed spread

• This provides a mechanism to lock in a fixed spread on a risky
loan.

Review of Last Lecture Introduction Products of Credit Derivatives

Credit Spread Forwards

Review of Last Lecture Introduction Products of Credit Derivatives

Credit Spread Forwards Example

• If a bank agrees to pay a fixed 100bps for the spread on
Company ABC’s reference bond and receive ABCs market
spread, it will generate a gain as ABC’s market spread widens
beyond 100 bps and will post a loss as it tightens (i.e.
improves) ; the bank’s counter-party faces the opposite
scenario.

• If ABC defaults, the bank will receive a payment related to
ABCs post-default spread level.

• The payout on the forward is computed as the difference
between the fixed and market spreads.

Review of Last Lecture Introduction Products of Credit Derivatives

Total Return Swaps (TRS)

• TRS is a bilateral contract that transfers the economics of a
credit reference between two parties ; the contract covers the
entire spectrum of pay-offs, from credit strengthening to
credit deterioration and default

• Under a standard contract, the TRS receiver is entitled to
the total return on the reference asset in exchange for periodic
floating payments

• The TRS payer in turn is entitled to any depreciation that
occurs in the security along with a LIBOR spread

• If the price of the reference asset rises as a result of credit
improvement, the receiver benefits ; if it declines as a result of
depreciation or default, the payer benefits.

Review of Last Lecture Introduction Products of Credit Derivatives

Total Return Swaps

• The TRS can be arranged on a funded or unfunded basis

– A funded TRS requires the TRS receiver to purchase a
risk-free or low- risk floating asset that yields the LIBOR
stream payable to the TRS payer

An example of such an asset would be a AAA rated bond
paying LIBOR

– The receiver holds no such asset in the unfunded TRS , so
the LIBOR stream must be sourced from cash flow, this means
that the TRS position is leveraged.

• Total Return Swap may be applied to any underlying asset
but is most commonly used with equity indices, single stocks,
bonds and defined portfolios of loans and mortgages.

Review of Last Lecture Introduction Products of Credit Derivatives

Total Return Swaps

– Total Return = Interest Flows + (Final Value – Original Value)
– Total return receiver is long both the price and default risk of

the reference asset
– Total return payer is the legal owner of the reference asset and

has changed to credit risk of the reference asset into credit risk
of the total return receiver.

Review of Last Lecture Introduction Products of Credit Derivatives

Total Return Swaps

Review of Last Lecture Introduction Products of Credit Derivatives

TRS on Tobacco Company Reference

Review of Last Lecture Introduction Products of Credit Derivatives

Basket Swap Structure

• Basket swaps are credit derivatives that allow for the risk
transfer of a pool of reference credits ; this creates an
efficient and cost effective way of dealing with multiple credit
exposures

• A basket swap can be set up to include the credit risks you
nominate

– The seller may or may not own the underlying credit risks
when they sell the basket swap

• Baskets effectively give institutions the chance to
manage/hedge portfolios of reference credit risk exposures
and investors an opportunity to earn premium from the
creation of diversified portfolios of credit-risky assets.

Review of Last Lecture Introduction Products of Credit Derivatives

Basket Swap Structure

• The buyer of the credit protection receives a payment as each
component of the reference basket defaults

– Note that the assigned reading in not completely clear in this
area. The payout received will be : (1 – recovery rate) * face
value of reference credit

• The Standard basket swap will only terminate on the specified
maturity date

– Payment occur only on default, not in cases of credit
deterioration. The basket can have as few a 2 reference assets,
but larger numbers such as 20+ are more common

• The lower the correlation between the components of the
reference basket the lower the premium.

Review of Last Lecture Introduction Products of Credit Derivatives

Standard Basket Swap

Review of Last Lecture Introduction Products of Credit Derivatives

First-to-Default Basket Swap

Review of Last Lecture Introduction Products of Credit Derivatives

First-to-Default Basket Swap

• Under a first to default structure the buyer receives a payout
upon the first default of one of the assets in the basket

• The basket swap then terminates
• This has the advantage of a lower premium

• Alternatively the basket swap can be structured so that the a
payout only occurs after the second (or nth) default

– In a second to default structure the buyer would receive no
compensation for the first default and get compensation for
the second default

– After the second default the contract terminates
– Such a structure is cheaper than a first to default swap.

Review of Last Lecture Introduction Products of Credit Derivatives

Senior Basket Swap

• In this case the buyer is paid for any credit defaults that
occur, but only after a nominated loss threshold has been
reached

• Subordinated Basket Swaps
• A payout occurs for every default in the reference basket, but

there is a cap on the maximum payout to the buyer of the
credit protection.

Review of Last Lecture Introduction Products of Credit Derivatives

Senior Basket Swap

Review of Last Lecture Introduction Products of Credit Derivatives

Subordinated Basket Swaps

Review of Last Lecture Introduction Products of Credit Derivatives

Credit Spread Option

• The credit option grants the buyer the right, but not the
obligation to purchase (call) or sell (put) the credit spread of
a reference credit at a particular strike level ; in exchange for
this right, the buyer pays the seller an up-front premium
payment

• This mechanism provides protection against the deterioration
on credit risk in the case of a credit spread put.

Review of Last Lecture Introduction Products of Credit Derivatives

Credit Spread Option

Review of Last Lecture Introduction Products of Credit Derivatives

Lecture Recording

• Although lectures are recorded and
available on-line, it is highly
recommended and encouraged for
you to attend face-to-face lectures.

  • Review of Last Lecture
  • Introduction
  • Products of Credit Derivatives
    • Asset Swaps
    • Credit Default Swaps

effective cost of borrowing

You borrowed a home loan of $1638949 from Monash Bank for 25 years at a 10% nominal annual interest rate, compounded monthly. Monash bank charged 3.5% points on any home loans on the day of issuing. If you receive an extra-large income increase after 15 years of payments and want to pay off the rest of this debt at once immediately. What is the annual effective cost of this borrowing?
contract loan amount 1,638,949.00 Step 1 Original PMT Step 3 Finally payment if prepay
contract interest 10% PV 1,638,949.00 N 120.00
point charge 3.50% I 0.0083333333 I 0.0083333
Original terms 25.00 N 300.00 PMT ($14,893.14)
prepay in 15.00 PMT ($14,893.14) PV $1,126,981.36
Step 2 Bank actually Lend Step 4 compute the effective rate
Contract amount 1,638,949.00 PV 1,581,585.79
point 3.50% N 180.00
PV 1,581,585.79 PMT ($14,893.14)
FV ($1,126,981.36)
I 0.88%
yearly 10.51%

Point Charge

A loan amount of $240,000 with an ordinary term of 30 years at rate of 8%. 但是8%只是写在贷款合同之中为了吸引borrower,如果lender自己想要达到的预期收益率为8.5%,how many points are needed?
Step 1 Original PMT
contract loan amount 240,000.00 PV 240,000.00
contract interest 8% I 0.0066666667
Original terms 30.00 N 360.00
PMT ($1,761.03)
lender actually want 8.50%
Step 2 Bank actually Lend
N 360.00
I 0.0070833
PMT ($1,761.03)
PV $229,029.01
Step 4 Compute the charge point
PV $229,029.01
contract amount 240,000.00
point charge 4.57%

RORAC

A business borrower would like to apply for a 10-year $10 million loan to finance its new project form BB Bank. BB bank would like to charge this borrower a 1% spread and 0.5% of origination fee and expect a 0.2% of the expected loss. Since the project is very complicated to evaluate, and it will cost BB bank $18,000 to invite experts to assess it. Suppose that the risk-adjuested factor (ΔR)/(1+RL) and the tax rates are 1% and 28% respectively, what is the RORAC of this borrower?
% Amount
Spread 1.00% 100,000.00
Fees 0.50% 50,000.00
expected loss 0.20% 20,000.00
operating cost 0.18% 18,000.00
tax rate 28%
分子部分 80,640.00
duration 10
loan value 10,000,000
risk-adjusted factor 1%
分母 1,000,000.00
RORAC 8.06%

Prob of Repayment

A Company would like to borrow a $1 million loan from the bank for 3 years. This borrowe has a BBB credit rating on the bond market. The bank has collected related corporate bond returns and government bond returns, presented in the following table.
Table 1 Bond ratings and return rates with different maturities
1 year 2 Year 3 Year 4 Year 5 Year
AAA 3.50% 4.20% 4.30% 5.45% 6.60%
AA 3.60% 4.60% 4.80% 5.55% 6.90%
A 4.10% 4.90% 5.50% 5.95% 7.20%
BBB 5.30% 5.60% 5.80% 6.50% 7.90%
BB 6.00% 6.50% 6.80% 7.55% 8.10%
B 7.00% 7.50% 8.80% 9.55% 10.10%
CCC 7.50% 7.90% 8.90% 10.55% 11.10%
CC 7.80% 8.80% 9.60% 10.50% 12.80%
Governement Bond 1.50% 2.70% 3.10% 3.90% 4.20%
If the loan is granted, what’s the probability of default of this loan at maturity date?
Select one
a 3.61%
b 96.39%
c 5.42%
d 7.46%
e none of above
做题过程
Year Government Bond 分子 分母 prob. of repayment
1 0.015 i0,1 0.015 0,1 0.9639126306
2 0.027 i1,2 1.054729 1.015 0.0391418719 1,2 0.9812403071
3 0.031 i2,3 1.095912791 1.054729 0.0390467988 2,3 0.9783763407
Cumulative Prob. of Repayment 0.9253776216
Year BBB prob of default 0.0746223784
1 0.053 r0,1 0.053
2 0.056 r1,2 1.115136 1.053 0.059008547
3 0.058 r2,3 1.184287112 1.115136 0.0620113708

KMV

XXX Ltd. has banked with Bank of Australia for more than 10 years. XXX Ltd. would like to apply for a $ 10 million loan from the Bank of Australia and provides the following balance sheet report to the bank (in Table 1).  It’s estimated that XXX Ltd. will have a growth rate of 15% in the coming year.  The bank is provided the Expected Default Frequency Table from Moody (in Table 2).
Table 1 Table 2
Balance Sheets Expected Default Frequency From Moody’s
As at the end of Year 2019
$ m Distance to Default Expected Default Frequency
Current Assets 1 50%
Cash 50 2 35%
Debtors 150 3 10%
Stock 240 4 5%
Current liabilities 5 2%
Creditors 220 6 1%
Hire Purchase 50 7 0.10%
Bank Overdraft 120 8 0.05%
Directors’ Loans 14 9 0.01%
Current Tax 1
Net Current Assets 35 Suppose that the current market value of assets is $1100 million and its standard deviation is 12%.  What’s the Expected Default Frequency of this borrower under the KMV model?
Fixed Assets
Freehold Building 120 Answer: 2% – 过程如下
Plant & Machinery 150 Current liabilities 405
Long Term Liabilities 115
Long Term Liabilities
Mortgage Loan 50 Default point 462.5
Deferred Taxation 5
Corporate Bonds 60
Net Long Assets 155 Current Market Value of Asset 1100
Growth Rate 15%
Net Assets 190
Financed by Expected Market value of Asset 1265
Sushi: Sushi:
有的题目直接会给出来Future Market value of Asset / Expected Market value of Asseet

这种情况之下,题目仍给出Growth Rate就是迷惑的选项

Issued Share Capital 100
Profit and Loss Account 90
Total Capital 190 Volatility of Asset(%) 12%
Sushi: Sushi:
有的题volatility直接给数字,那就直接用具体的数字做DD的分母
Distance to Default 5.2865612648
Profit & Loss Amount Summary 分子部分 802.5
$ m 分母部分 151.8
Sales 1300
COGS 1050
including Credit Purchase 800 DD为5.28,四舍五入为5,对应Table 2,找到EDF为2%
Gross Profit 150
EBIT 74
Interest 10
Net Profit before Tax 60

Builder-minimum finance require

King Builder specialized in office building construction for more than 10 years,  has been banking with Banks of Australia for over 5 years.  It has been recently been awarded a contract to build an office building for JP Morgan.  The total contract price is $130 million and the construction length will be 13 months.  It is expected that labor costs and material costs will be 60 percent and 40 percent of costs, respectively.  It is estimated that the King Builder will make a profit of twenty-five (25) percent of the contract value.  As this is a relatively straightforward project for this builder, it is safe to assume that construction progress will be spread evenly over the life of the project.  Assume that monthly certificates will be issued at the end of the month and payments will occur 25 days after the issue of each certificate. A retention fund has been set up which will require retentions at the rate of 5 percent of the monthly payments and a minimum level 7 percent of the total contract value at the beginning of the construction.  As a well-established builder, King Builder expects no difficulties in obtaining two-month credit terms from the suppliers of the necessary construction materials.  What’s the minimum finance required of this builder at the end of the first month?
Total Contract Price 150,000,000 每个同学这一题的条件,最后的问题都会不一样,需要根据自己的题目调整计算思路
Duration 13 1月发生 2月发生 3月发生
Initial retention 7% 10,500,000 OUTFLOW
Initial Retention 10,500,000
Profit 25% 37,500,000 累计的人工费 5,192,308 5,192,308 5,192,308
Cost of construction 75% 112,500,000 累计的材料费 0
Sushi: Sushi:
材料费有两个月的赊销期限
0 3,461,538
Labor 60% 67,500,000 TOTAL OUTFLOW 15,692,308 5,192,308 8,653,846
Materials 40% 45,000,000 Cumulative TOTAL OUTFLOW 15,692,308 20,884,615 29,538,462
INFLOW
Monthly Payment 11,538,462 Net Monthly Payment 0 0 10,961,538
Monthly Retention 5% 576,923
Net Monthly payment 10,961,538 Finance require 15,692,308 20,884,615 18,576,923
Monthly labor cost 5,192,308
Monthly material cost 3,461,538 2 month credit term

minimum finance required at the end of the first month

Builder – Maximum loan amount

XXX is a builder and will complete one construction for its customer. It has 13 months to complete the building. The total contract price is $216 million. It is estimated that XXX will make a profit of 25% of the contract value. Labour costs and material costs are expected to be 65% and 35% of the construction costs, respectively. As this is a relatively striaghtforward project for XXX, it is safe to assume that construction progress will be spread evenly over the life of the project.
Interim payment certificates will be issued at the end of each month, and the corresponding payments received from its customer will occur two months after the issue of the progress certificate.
Eve Meng: Sushi:
每月底验工发证,发证再两个月收到相对应的工程款
也就是第一次收到工程款应该是在第三个月底/第四个月初

稳妥一些,应该算作是第四个月的inflow

At the beginning of the project, the retention fund of XXX should have 10% of the total contract value. Additionally, XXX has to set up a retention fund which will require retentions at the rate of 8% of the monthly paymanets. As a well-established construction company, XXX expects no difficults in obtaining two-month credit terms form the suppliers of the necessary construction materials.
The bank’s policy requires that XXX should provide at least 60% of the total cash requirements (as its own equity) for projects like this. What’s the maximum loan amount that the bank will grant to XXX?
Total Contract Price 216,000,000 每个同学这一题的条件,最后的问题都会不一样,需要根据自己的题目调整计算思路
Duration 13 1月发生 2月发生 3月发生 4月发生
Initial retention 10% 21,600,000 OUTFLOW
Initial Retention 21,600,000
Profit 20% 43,200,000 累计的人工费 8,640,000 8,640,000 8,640,000 8,640,000
Cost of construction 80% 172,800,000 累计的材料费 0
Sushi: Sushi:
材料费有两个月的赊销期限
0 4,652,308 4,652,308
Labor 65% 112,320,000 TOTAL OUTFLOW 30,240,000 8,640,000 13,292,308 13,292,308
Materials 35% 60,480,000 Cumulative TOTAL OUTFLOW 30,240,000 38,880,000 52,172,308 65,464,615
INFLOW
Monthly Payment 16,615,385 Net Monthly Payment 0 0 – 0 15,286,154
Monthly Retention 8% 1,329,231
Net Monthly payment 15,286,154 Finance require 30,240,000 38,880,000 52,172,308
Eve Meng: Sushi:
在这几个月中,累积到第三个月,需要的资金是最多
这个金额是builder的 minimum finance require


Eve Meng: Sushi:
每月底验工发证,发证再两个月收到相对应的工程款
也就是第一次收到工程款应该是在第三个月底/第四个月初

稳妥一些,应该算作是第四个月的inflow


Sushi: Sushi:
材料费有两个月的赊销期限
50,178,462
Monthly labor cost 8,640,000 Builder contribution 60%
Monthly material cost 4,652,308 2 month credit term Bank can provide 40%
Maximum loan amount 20,868,923

Return rate of loan

The Contractually Promised return on a loan
BB bank has granted a $1 m loan to APPLE CO. with an annual 0.09 loan rate. The bank keeps a capital ratio of 8%, and requires a minimum compensating balance ratio of 0.1. APPLE CO. has paid $5600 as loan origination fee to the bank. What is the gross return rate of this loan?
解题过程
其实就是求k
以下首先全部换算为百分数 amount principal %
分子 loan Origination fee (f) 5,600.00 1,000,000.00 0.0056
Base Rate (BR)
Sushi: Sushi:
BR + m 其实就是 loan contract 上面给到 borrower 的利率

在这题目中 0.09 的 loan rate,就已经是 BR + m 的总和了

0.09
Eve Meng: Sushi:

BR + m 总和为 loan contract 上面给到 borrower 的利率

在这题目中 0.09 的 loan rate,就已经是 BR + m 的总和了


Sushi: Sushi:
BR + m 其实就是 loan contract 上面给到 borrower 的利率

在这题目中 0.09 的 loan rate,就已经是 BR + m 的总和了

Credit risk premium (m)
0.0956
分母 Compensating balance requirements (b) 0.1
Reserve requirement (R) 0.08
0.908
Gross return (k) 0.1052863436

MMR Bond Price

Banana Ltd. Is rated as BBB on the bond market and the face value of the bond is $100 with a 6% coupon rate. Given that the risk-free rate is 4% annually and the bond will mature in 3 years. The mortality rates are provided in the following table
Cumulative Mortality Rates by Corporate Bond Ratings
Years after Issuance
1 2 3 4 5 6
AAA 0.00% 0.00% 0.00% 0.00% 0.03% 0.03%
AA 0.00% 0.00% 0.32% 0.48% 0.51% 0.54%
A 0.01% 0.11% 0.42% 0.51% 0.65% 0.74%
BBB 0.36% 3.11% 4.12% 5.51% 6.65% 7.34%
BB 1.21% 3.48% 4.42% 6.41% 8.65% 10.24%
What’s the current price of Banana Ltd’s bonds?
Year cash flow mortality rate surval cash flow PV
1 6 0.0036 5.9784 5.7484615385
2 6 0.0311 5.8134 5.3748150888
3 106 0.0412 101.6328 90.3511891215
Price 101.4744657487

Cumulative Mortality Rate

ABC Ltd. is rated as AAA on the bond market, and the face value of the bond is $100 with a 7% coupon rate. Given that the risk-free rate is 3.5% annually and the bond will mature in 5 years. The marginal mortality rates are provided in the following table
Table: Marginal Mortality Rates by Corporate Bond Ratings
Years after issuance
1 2 3 4 5 6
AAA Marginal Rates 0.00% 0.01% 0.05% 0.06% 0.09% 0.10%
AA Marginal Rates 0.04% 0.08% 0.32% 0.48% 0.51% 0.54%
A Marginal Rates 0.09% 0.22% 0.72% 0.81% 1.95% 2.74%
BBB Marginal Rates 0.36% 3.11% 4.12% 5.51% 6.65% 7.34%
BB Marginal Rates 1.21% 3.48% 4.42% 6.41% 8.65% 10.24%
B Marginal Rates 2.52% 5.44% 7.12% 8.82% 7.32% 6.19%
CCC Marginal Rates 7.55% 14.81% 18.28% 13.76% 9.54% 7.33%
What is the cumulative mortality rate of ABC Ltd’s bond?
1 2 3 4 5
AAA Marginal Rate 0.00% 0.01% 0.05% 0.06% 0.09%
100.00% 99.99% 99.95% 99.94% 99.91%
cumulative survival rate
99.7901489601027%
cumulative mortality rate
0.209851039897291%

Rating Migration

The Corporate Bonds of Banana company are rated as A rating on the market, and a table of transitions probabilities to different ratings and market values in provided below.
Ratings Transition Probability Market Value $
AAA 0.19%
Sushi: Sushi:
Banana公司的债券,评级变为AAA的可能性为0.19%
下同
108.00
Sushi: Sushi:
当前AAA类别的债券市价为108
若Banana的债券被评为AAA的情况下,市价为108
下同
AA 0.43% 107.00
A 91.00%
Sushi: Sushi:
现在Banana的债券评级为A,因此评级保持为A的可能性是最高的
106.00
BBB 3.00% 105.00
BB 4.00% 100.00
B 1.20% 90.00
C 0.12% 80.00
Default 0.06% 50.00
What is should be the price of this Banana Corporate bonds if considering the possible rating migration?
以上表格的解读为:市场价格变为108的概率为0.19%,等等。因此考虑了评级变化之后的价格就是以上表格的加权平均
Ratings Transition Probability Market Value $ weighted value
AAA 0.19% 108.00 0.2052
AA 0.43% 107.00 0.4601
A 91.00% 106.00 96.46
BBB 3.00% 105.00 3.15
BB 4.00% 100.00 4
B 1.20% 90.00 1.08
C 0.12% 80.00 0.096
Default 0.06% 50.00 0.03
Price 105.4813

Z socre

Consider the following data of a prospective borrower. Applying Altman’s Z score. What is this company’s Z score (round to two decimal)?
Curren Assets 490,300
Fixed Assets 4,006,000 Selected one
Total Assets 4,496,300 a 3.41
Current Liabilities 187,300 b 3.18
Long-term Liabilities 3,000,100 c 3.86
Liabilities 3,187,400 d 2.15
Book value of Equity 1,308,900 e 2.61 每个变量 系数
Working Captial 400,000 X1 0.0889620355 1.2 0.1067544425
sales 8,000,000 X2 0.0144563308 1.4 0.0202388631
EBIT 500,000 X3 0.1112025443 3.3 0.3669683962
Retained Earnings 65,000 X4 0.56 0.6 0.3388341595
Number of Shares 100,000 X5 1.779240709 1 1.779240709
Price per share 18 Z-score 2.6120365704

Regression model

Given the following regression model:
Pi = 0.8*Current Ratio + 0.4*Gross Margin + 0.3*(Equity/Debt)
Where Pi is the probability of repayment. The balance data of ABC Ltd. is shown in the following table
$
Curren Asset 150,000
Non current Assets 450,000
Total Asset 600,000
Equity 240,000
Current Liabilities 250,000
Book value of liabilities 360,000
Sales revenue 1,000,000
Gross income 15,000
EBIT 250,000
What is the probability of default of this company?
系数 变量值
0.8 0.6 0.48
0.4 0.015 0.006
0.3 0.6666666667 0.2
Prob. of repayment 0.686
Prob. of default 0.314

Topic 9 – Restruor liqu

Case 1 Case 2
Company A Ltd. owes Monash bank $300 and is in financial distress now. The owner of Company A has some special skills to run the firm, that costs him $15. With these skills, firm value can be $315 with a probability of 0.8, otherwise 0. The liquidation value of the firm is $200 Monash bank again is having problem with Company A Ltd.. Now Company A Ltd. Owes senior bond holders $75 and Monash bank $500. It still costs Company A Ltd. $15 to run the company, if it continues, the firm will be worth $520 with a probability 0.75, otherwise 0. The liquidation of the firm is $90 and the firm wants to default.
priority: Bank > shareholder priority: senior > junior > shareholder
Monash Bank 300 Senior bondholder 75
Monash Bank(junior) 500
If liquidate the firm 200
If Continue: If liquidate 90
Cost -15 If Continue:
Success 315 0.8 Cost -15
Failure 0 0.2 Success 520 0.75
Fisrt Step Failure 0 0.25
Choices of shareholders:
Continue -3 Fisrt Step
Liquidation 0 Choices of shareholders:
Continue -15
Choices of monash Bank Liquidation 0
Continue 240
Liquidation 200 Choices of senior bondholder
Continue 56.25
Second Step: Negociation and restructure Liquidation 75
Restructure the debt with the shareholders, make him continue the business Choices of junior debtholder(monash)
Continue 333.75
Break Even point if Owner choose to continue Liquidation 15 Loss -485
-15 + (315 – New Loan)*0.8 + 0*0.2 = 0
Monash will reduce its New Loan to 296.25
Second Step: Negociation and restructure
expected value of monash if restructure the loan 237
1. Overtake the bond
New debt owed by Monash 575
2. Convince the Shareholder
Break Even point if Owner choose to continue
-15 + (520 – New Loan)*0.75 + 0*0.25 >= 0
Monash (junior) will reduce its New Loan to <= 500
expected value of monash if restructure the loan 375 Loss 200

Topic 10 Basket Swap

Assume the following reference credit portfolio:
Credit 1: $100,000 notional, post-default value $31120.8
Credit 2: $200,000 notional, post-default value $51179.6
Credit 3: $250,000 notional, post-default value $89458.7
Given a $550,000 structure, if credits 2 ans 3 default in a second-to-default basket (in that order), how much will an investor receive?
此题说到的现在是一个second-to-default basket,所以只会对第二个违约的进行赔偿,因此只赔偿Credit 3违约的部分
Credit 3 notional post-default value
Eve Meng: Sushi:
违约之后的价值
赔偿金额
250,000.00 89,458.70 160,541.30

Topic 10 credit spread option

Senario 1
If an investor buys a 12-month credit spread call option on Company ABC’s bond with a strike spread of 100bps for a premium of 35 bps, what is the appropriate course of action if ABC’s spread tightens to 50bps? Widens to 150bps? What is the breakeven level of the trade?
Spread tighten: the investor should exercise the right
Then the investor can get the net gain of 15bps (100bps – 50bps – 35bps)
Spread widen: the investor should abandon the right
Breakeven level:
100𝑏𝑝𝑠 – 35𝑏𝑝𝑠 = 65 𝑏𝑝𝑠
Each 1bp tighten after 65 bps generates profit
Senario 2
If an investor buys a 12-month credit spread put option on Company ABC’s bond with a strike spread of 100bps for a premium of 35 bps, what is the appropriate course of action if ABC’s spread tightens to 50bps? Widens to 150bps? What is the breakeven level of the trade?
Spread tighten: the investor should abandon the right
Spread widen: the investor should exercise the right
Then the investor can get the net gain of 15bps (150bps – 100bps – 35bps)
Breakeven level:
100𝑏𝑝𝑠 – 35𝑏𝑝𝑠 = 65 𝑏𝑝𝑠
Each 1bp widen from 65 bps generates profit
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