IFRS 9 Implementation : Using the Z-score approach as a KRI to identify adverse credit deterioration for Stage Transition from 1 to stages 2/3 in IFRS 9 Modeling
IFRS 9 Implementation : Using the Z-score approach as a KRI to identify adverse credit deterioration for Stage Transition from 1 to stages 2/3 in IFRS 9 Modeling
It should be my presentation at R in Insurance CASS conference at 15th July 2013. It shows how R can be successfully applied to price life, non - life and reinsurance contracts.
It is not difficult to find situations of marked change in variables and with unpredictable event risk implies estimation problems. E.g.,
Credit spreads in 2008 rise to levels that could never have been forecast based upon previous history. The subprime crisis of 2007/8: credit spreads & volatility rise to unseen levels & shift in debtor behavior (delinquency patterns)
E.g., estimating the volatility from data in a calm (turbulent) period implies under (over) estimation of future realized volatility
In-spite of large volumes of Contingent Credit Lines (CCL) in all commercial banks, the paucity of Exposure at Default (EAD) models, unsuitability of external data and inconsistent internal data with partial draw-downs has been a major challenge for risk managers as well as regulators in for managing CCL portfolios. This current paper is an attempt to build an easy to implement, pragmatic and parsimonious yet accurate model to determine the exposure distribution of a CCL portfolio. Each of the credit line in a portfolio is modeled as a portfolio of large number of option instruments which can be exercised by the borrower, determining the level of usage. Using an algorithm similar to basic the CreditRisk+ and Fourier Transforms we arrive at a portfolio level probability distribution of usage. We perform a simulation experiment using data from Moody\'s Default Risk Service, historical draw-down rates estimated from the history of defaulted CCLs and a current rated portfolio of such.
We construct a model to value the tranches of Freddie Mac
Multi Class Offering Series 2884, and conduct sensitivity analysis in order to make a recommendation in accordance with our client’s goals.
It should be my presentation at R in Insurance CASS conference at 15th July 2013. It shows how R can be successfully applied to price life, non - life and reinsurance contracts.
It is not difficult to find situations of marked change in variables and with unpredictable event risk implies estimation problems. E.g.,
Credit spreads in 2008 rise to levels that could never have been forecast based upon previous history. The subprime crisis of 2007/8: credit spreads & volatility rise to unseen levels & shift in debtor behavior (delinquency patterns)
E.g., estimating the volatility from data in a calm (turbulent) period implies under (over) estimation of future realized volatility
In-spite of large volumes of Contingent Credit Lines (CCL) in all commercial banks, the paucity of Exposure at Default (EAD) models, unsuitability of external data and inconsistent internal data with partial draw-downs has been a major challenge for risk managers as well as regulators in for managing CCL portfolios. This current paper is an attempt to build an easy to implement, pragmatic and parsimonious yet accurate model to determine the exposure distribution of a CCL portfolio. Each of the credit line in a portfolio is modeled as a portfolio of large number of option instruments which can be exercised by the borrower, determining the level of usage. Using an algorithm similar to basic the CreditRisk+ and Fourier Transforms we arrive at a portfolio level probability distribution of usage. We perform a simulation experiment using data from Moody\'s Default Risk Service, historical draw-down rates estimated from the history of defaulted CCLs and a current rated portfolio of such.
We construct a model to value the tranches of Freddie Mac
Multi Class Offering Series 2884, and conduct sensitivity analysis in order to make a recommendation in accordance with our client’s goals.
We use GARCH model to calculate the probability to default.
Our innovation is to use two dimensional GARCH model through a formula that combines both the firm's risk and the market risk.
The method is calculating the total risk by taking into consideration the different influences of the firm’s and market’s risk, i.e. Beta, using different weights for each one.
Ch05 P24 Build a Model Spring 1, 201372212Chapter 5. Ch 05 P24 B.docxtidwellveronique
Ch05 P24 Build a Model Spring 1, 20137/22/12Chapter 5. Ch 05 P24 Build a ModelExcept for charts and answers that must be written, only Excel formulas that use cell references or functions will be accepted for credit. Numeric answers in cells will not be accepted.A 20-year, 8% semiannual coupon bond with a par value of $1,000 may be called in 5 years at a call price of $1,040. The bond sells for $1,100. (Assume that the bond has just been issued.)Basic Input Data:Years to maturity:20Periods per year:2Periods to maturity:Coupon rate:8%Par value:$1,000Periodic payment:Current price$1,100Call price:$1,040Years till callable:5Periods till callable:a. What is the bond's yield to maturity?Periodic YTM =Annualized Nominal YTM = Hint: This is a nominal rate, not the effective rate. Nominal rates are generally quoted.b. What is the bond's current yield?Current yield = Hint: Write formula in words.Current yield =/ Hint: Cell formulas should refer to Input SectionCurrent yield =(Answer)c. What is the bond's capital gain or loss yield?Cap. Gain/loss yield =- Hint: Write formula in words.Cap. Gain/loss yield =- Hint: Cell formulas should refer to Input SectionCap. Gain/loss yield =(Answer)Note that this is an economic loss, not a loss for tax purposes.d. What is the bond's yield to call?Here we can again use the Rate function, but with data related to the call.Peridodic YTC =Annualized Nominal YTC =This is a nominal rate, not the effective rate. Nominal rates are generally quoted.The YTC is lower than the YTM because if the bond is called, the buyer will lose the difference between the call price and the current price in just 4 years, and that loss will offset much of the interest imcome. Note too that the bond is likely to be called and replaced, hence that the YTC will probably be earned.NOW ANSWER THE FOLLOWING NEW QUESTIONS:e. How would the price of the bond be affected by changing the going market interest rate? (Hint: Conduct a sensitivity analysis of price to changes in the going market interest rate for the bond. Assume that the bond will be called if and only if the going rate of interest falls below the coupon rate. That is an oversimplification, but assume it anyway for purposes of this problem.)Nominal market rate, r:8%Value of bond if it's not called:Value of bond if it's called: The bond would not be called unless r<coupon.We can use the two valuation formulas to find values under different r's, in a 2-output data table, and then use an IFstatement to determine which value is appropriate:Value of Bond If:Actual value,Not calledCalledconsideringRate, r$0.00$0.00call likehood:0%$0.00$0.00$0.002%$0.00$0.00$0.004%$0.00$0.00$0.006%$0.00$0.00$0.008%$0.00$0.00$0.0010%$0.00$0.00$0.0012%$0.00$0.00$0.0014%$0.00$0.00$0.0016%$0.00$0.00$0.00f. Now assume the date is 10/25/2010. Assume further that a 12%, 10-year bond was issued on 7/1/2010, pays interest semiannually (January 1 and July 1), and sells for $1,100. Use your ...
Mercer Capital | A Layperson's Guide to the Option Pricing ModelMercer Capital
Mercer Capital's whitepaper on the option pricing model, often used to value ownership interests in early-stage companies. Developed in response to the need to reliably estimate the value of different economic rights in complex capital structures, the OPM models the various capital structure components as a series of call options on underlying total equity value. Through a detailed example, Travis W. Harms explains key concepts including breakpoints and tranches in a straightforward and non-technical way, taking the mystery out of OPM terms such as “breakpoint” and “tranche”. Relative to the probability-weighted expected return method, the principal strengths of the OPM include the small number of required assumptions and auditability. The PWERM, in contrast, offers greater flexibility and transparency. Harms closes with some thought on reconciling OPM results with the market participant perspective.
Testing and extending the capital asset pricing modelGabriel Koh
This paper attempts to prove whether the conventional Capital Asset Pricing Model (CAPM) holds with respect to a set of asset returns. Starting with the Fama-Macbeth cross-sectional regression, we prove through the significance of pricing errors that the CAPM does not hold. Hence, we expand the original CAPM by including risk factors and factor-mimicking portfolios built on firm-specific characteristics and test for their significance in the model. Ultimately, by adding significant factors, we find that the model helps to better explain asset returns, but does still not entirely capture pricing errors.
Case Notes on MW Petroleum Corporation (A)Why Should We Care A.docxwendolynhalbert
Case Notes on MW Petroleum Corporation (A)
Why Should We Care About Real Options?
Ignoring real options in a project often leads to an underestimation of the true project value. Because real options are not explicitly linked to cash flows, they may seem difficult to identify. Here are some typical examples of real options.
· The option to expand an existing investment project.
· Research and development (R&D) is an example of a growth option.
· The option to delay an investment project.
· The option to abandon a project that has already been undertaken.
From the above examples, we find that real options reflect the flexibility inherent in any capital investment process, which is often ignored by the DCF analysis because flexibility is hard to quantify in terms of cash flows. Fortunately, the breakthrough in option pricing theory provides us with the tools to find the value of these real options.
Types of Reserves
MW Petroleum’s estimated reserves can be classified into four major categories:
· proved developed reserves
· proved undeveloped reserves
· probable reserves
· possible reserves
Exhibits 3 through 6 tell us the production and cash flow projections for each of the four types of reserves.
Risk-adjusted Discount Rate (RADR)
For valuation purposes, we need an estimate of MW's WACC to discount cash flows. Unfortunately, the case does not provide many details. This presents a very realistic problem that is often faced when attempting to do analysis in the real world. For example, because MW is a subsidiary of Amoco, its (market) equity value is not available. We do not have a clear idea about the debt and equity mix of MW either. However, we do have the following information:
The average asset (unlevered) beta for Oil companies = 0.64 (footnote b of Exhibit 2).
Given this information, we can use the CAPM to calculate the cost of equity for MW.
· Cost of equity = risk-free rate + beta * market risk premium
For the risk-free rate, we can use the 1990 year-end 30-year US government bond yield given in the MW case in Exhibit 10. We choose the 30-year bond because the time horizon of the cash flows given in the case is 15 years, which is longer than 10 years. Remember, projects in this industry are long-term and, therefore, call for a longer-term Treasury yield to proxy for the risk-free rate.
To determine the market risk premium, we can rely on a report that is maintained by the Stern School of Business at New York University. This report maintains historic annual returns on stock, T-bonds, and T-bills from 1928 – Current. The report also maintains the historic market-risk premium, starting in 1960. To be consistent with our risk-free rate, we want to use the historical market-risk premium for 1990 in the following report:
· http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html
Next we assume that Miller Equilibrium holds. This implies:
· The WACC, which is the risk-adjusted discount rate for discoun ...
In this paper, we construct a Credit Default Swap pricing model for default recovery rates under
distributional uncertainty based on a structured pricing model and distributional uncertainty theory. The model
is algorithmically transformed into a solvable semi-definite programming problem using the Lagrangian dual
method, and the solution of the model is given using the projection interior point method. Finally, an empirical
analysis is conducted, and the results show that the model constructed in this paper is reasonable and efficient
The European Unemployment Puzzle: implications from population agingGRAPE
We study the link between the evolving age structure of the working population and unemployment. We build a large new Keynesian OLG model with a realistic age structure, labor market frictions, sticky prices, and aggregate shocks. Once calibrated to the European economy, we quantify the extent to which demographic changes over the last three decades have contributed to the decline of the unemployment rate. Our findings yield important implications for the future evolution of unemployment given the anticipated further aging of the working population in Europe. We also quantify the implications for optimal monetary policy: lowering inflation volatility becomes less costly in terms of GDP and unemployment volatility, which hints that optimal monetary policy may be more hawkish in an aging society. Finally, our results also propose a partial reversal of the European-US unemployment puzzle due to the fact that the share of young workers is expected to remain robust in the US.
Turin Startup Ecosystem 2024 - Ricerca sulle Startup e il Sistema dell'Innov...Quotidiano Piemontese
Turin Startup Ecosystem 2024
Una ricerca de il Club degli Investitori, in collaborazione con ToTeM Torino Tech Map e con il supporto della ESCP Business School e di Growth Capital
when will pi network coin be available on crypto exchange.DOT TECH
There is no set date for when Pi coins will enter the market.
However, the developers are working hard to get them released as soon as possible.
Once they are available, users will be able to exchange other cryptocurrencies for Pi coins on designated exchanges.
But for now the only way to sell your pi coins is through verified pi vendor.
Here is the telegram contact of my personal pi vendor
@Pi_vendor_247
Empowering the Unbanked: The Vital Role of NBFCs in Promoting Financial Inclu...Vighnesh Shashtri
In India, financial inclusion remains a critical challenge, with a significant portion of the population still unbanked. Non-Banking Financial Companies (NBFCs) have emerged as key players in bridging this gap by providing financial services to those often overlooked by traditional banking institutions. This article delves into how NBFCs are fostering financial inclusion and empowering the unbanked.
what is the best method to sell pi coins in 2024DOT TECH
The best way to sell your pi coins safely is trading with an exchange..but since pi is not launched in any exchange, and second option is through a VERIFIED pi merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and pioneers and resell them to Investors looking forward to hold massive amounts before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade pi coins with.
@Pi_vendor_247
USDA Loans in California: A Comprehensive Overview.pptxmarketing367770
USDA Loans in California: A Comprehensive Overview
If you're dreaming of owning a home in California's rural or suburban areas, a USDA loan might be the perfect solution. The U.S. Department of Agriculture (USDA) offers these loans to help low-to-moderate-income individuals and families achieve homeownership.
Key Features of USDA Loans:
Zero Down Payment: USDA loans require no down payment, making homeownership more accessible.
Competitive Interest Rates: These loans often come with lower interest rates compared to conventional loans.
Flexible Credit Requirements: USDA loans have more lenient credit score requirements, helping those with less-than-perfect credit.
Guaranteed Loan Program: The USDA guarantees a portion of the loan, reducing risk for lenders and expanding borrowing options.
Eligibility Criteria:
Location: The property must be located in a USDA-designated rural or suburban area. Many areas in California qualify.
Income Limits: Applicants must meet income guidelines, which vary by region and household size.
Primary Residence: The home must be used as the borrower's primary residence.
Application Process:
Find a USDA-Approved Lender: Not all lenders offer USDA loans, so it's essential to choose one approved by the USDA.
Pre-Qualification: Determine your eligibility and the amount you can borrow.
Property Search: Look for properties in eligible rural or suburban areas.
Loan Application: Submit your application, including financial and personal information.
Processing and Approval: The lender and USDA will review your application. If approved, you can proceed to closing.
USDA loans are an excellent option for those looking to buy a home in California's rural and suburban areas. With no down payment and flexible requirements, these loans make homeownership more attainable for many families. Explore your eligibility today and take the first step toward owning your dream home.
Poonawalla Fincorp and IndusInd Bank Introduce New Co-Branded Credit Cardnickysharmasucks
The unveiling of the IndusInd Bank Poonawalla Fincorp eLITE RuPay Platinum Credit Card marks a notable milestone in the Indian financial landscape, showcasing a successful partnership between two leading institutions, Poonawalla Fincorp and IndusInd Bank. This co-branded credit card not only offers users a plethora of benefits but also reflects a commitment to innovation and adaptation. With a focus on providing value-driven and customer-centric solutions, this launch represents more than just a new product—it signifies a step towards redefining the banking experience for millions. Promising convenience, rewards, and a touch of luxury in everyday financial transactions, this collaboration aims to cater to the evolving needs of customers and set new standards in the industry.
What website can I sell pi coins securely.DOT TECH
Currently there are no website or exchange that allow buying or selling of pi coins..
But you can still easily sell pi coins, by reselling it to exchanges/crypto whales interested in holding thousands of pi coins before the mainnet launch.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and resell to these crypto whales and holders of pi..
This is because pi network is not doing any pre-sale. The only way exchanges can get pi is by buying from miners and pi merchants stands in between the miners and the exchanges.
How can I sell my pi coins?
Selling pi coins is really easy, but first you need to migrate to mainnet wallet before you can do that. I will leave the telegram contact of my personal pi merchant to trade with.
Tele-gram.
@Pi_vendor_247
What price will pi network be listed on exchangesDOT TECH
The rate at which pi will be listed is practically unknown. But due to speculations surrounding it the predicted rate is tends to be from 30$ — 50$.
So if you are interested in selling your pi network coins at a high rate tho. Or you can't wait till the mainnet launch in 2026. You can easily trade your pi coins with a merchant.
A merchant is someone who buys pi coins from miners and resell them to Investors looking forward to hold massive quantities till mainnet launch.
I will leave the telegram contact of my personal pi vendor to trade with.
@Pi_vendor_247
Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
how to sell pi coins on Bitmart crypto exchangeDOT TECH
Yes. Pi network coins can be exchanged but not on bitmart exchange. Because pi network is still in the enclosed mainnet. The only way pioneers are able to trade pi coins is by reselling the pi coins to pi verified merchants.
A verified merchant is someone who buys pi network coins and resell it to exchanges looking forward to hold till mainnet launch.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
how to sell pi coins in South Korea profitably.DOT TECH
Yes. You can sell your pi network coins in South Korea or any other country, by finding a verified pi merchant
What is a verified pi merchant?
Since pi network is not launched yet on any exchange, the only way you can sell pi coins is by selling to a verified pi merchant, and this is because pi network is not launched yet on any exchange and no pre-sale or ico offerings Is done on pi.
Since there is no pre-sale, the only way exchanges can get pi is by buying from miners. So a pi merchant facilitates these transactions by acting as a bridge for both transactions.
How can i find a pi vendor/merchant?
Well for those who haven't traded with a pi merchant or who don't already have one. I will leave the telegram id of my personal pi merchant who i trade pi with.
Tele gram: @Pi_vendor_247
#pi #sell #nigeria #pinetwork #picoins #sellpi #Nigerian #tradepi #pinetworkcoins #sellmypi
how can I sell pi coins after successfully completing KYCDOT TECH
Pi coins is not launched yet in any exchange 💱 this means it's not swappable, the current pi displaying on coin market cap is the iou version of pi. And you can learn all about that on my previous post.
RIGHT NOW THE ONLY WAY you can sell pi coins is through verified pi merchants. A pi merchant is someone who buys pi coins and resell them to exchanges and crypto whales. Looking forward to hold massive quantities of pi coins before the mainnet launch.
This is because pi network is not doing any pre-sale or ico offerings, the only way to get my coins is from buying from miners. So a merchant facilitates the transactions between the miners and these exchanges holding pi.
I and my friends has sold more than 6000 pi coins successfully with this method. I will be happy to share the contact of my personal pi merchant. The one i trade with, if you have your own merchant you can trade with them. For those who are new.
Message: @Pi_vendor_247 on telegram.
I wouldn't advise you selling all percentage of the pi coins. Leave at least a before so its a win win during open mainnet. Have a nice day pioneers ♥️
#kyc #mainnet #picoins #pi #sellpi #piwallet
#pinetwork
how to sell pi coins at high rate quickly.DOT TECH
Where can I sell my pi coins at a high rate.
Pi is not launched yet on any exchange. But one can easily sell his or her pi coins to investors who want to hold pi till mainnet launch.
This means crypto whales want to hold pi. And you can get a good rate for selling pi to them. I will leave the telegram contact of my personal pi vendor below.
A vendor is someone who buys from a miner and resell it to a holder or crypto whale.
Here is the telegram contact of my vendor:
@Pi_vendor_247
1. The 2013 Center for Financial Studies
Modeling Competition
Dongyang Wang (661181660)
Yulin Li (661181660)
Wenhua Xiao (661128134)
Jingli Li (661138638)
1
2. Contents
1. Introductions:........................................................................................................................................ 2
2. Ascertain the Importance of the Anchors to Real Estate Portfolio (shopping center). ........................ 2
3. Value lease obligations based on the information given and prevailing market conditions................ 3
4. Measure the Risk and Probability of Default ........................................................................................ 4
5. Hedging Strategies ................................................................................................................................ 6
6. Recommend Specific Derivatives .......................................................................................................... 7
7. Additional Risks Based on Hedging Strategies: ..................................................................................... 9
8. Conclusions: ........................................................................................................................................ 10
Appendix ................................................................................................................................................. 11
1. Introductions:
This case’s target is to hedge the credit risk faced by Muck River Plaza because of there exist
potentialprobability of default of two anchors in this plaza, Best Buy and Barnes & Noble. Beyond those
anchors’ risk, other small tenants’ rent are mostly depend on the anchors behaviors and their rents are
much higher than anchors’ rents, which is roughly 75% of the total rents. Our target is to quantify these
risks and then devise proper strategy to hedging these risks efficiently. We use both accounting skills
and computation skills to do the credit risk management and list some proper strategies Muck River
Plaza may utilize to construct the portfolio and management the real estate.
2. Ascertain the Importance of the Anchors to Real Estate Portfolio (shopping
center).
For the operation of the major anchors, we consider two scenarios for the Muck River
Associates: good case and bad case. Good case represents that two major anchors, Best Buy
and Barnes & Noble, run successfully and pay for the rent and surcharges and small anchors
also rent the space as much as possible, while bad case represents that all anchors run into the
worst case. Specifically, the two anchors, Best Buy and Barnes & Noble, will argue with Muck
River Associate on interests for lease at most 5 dollars instead of 8 dollars. For the first year, the
revenue, cost and profit are calculated and showed in the Table 1.
2
3. Scenarios
Tenants
Revenue
Cost
Profit
Table 1 Profit of The Real Estate Portfolio
Good Case
Bad Case
Major Anchors
Small Anchors
Major Anchors
Small Anchors
$640,000
$1,760,000
$430,000
$647,000
$950,000
$950,000
$1,450,000
$127,000
Compared with these two results, we find that the profit difference is $1,323,000, which means
the profit of the bad case decreased by 91.24% of the profit under the good case. It
demonstrates that the performance of both major anchors is important to the real estate
portfolio.
3. Value lease obligations based on the information given and prevailing
market conditions.
In this section, it is important to evaluate the lease obligations based on the scenarios: Best Buy
and Barnes & Noble boom, cease or limit operations, and bankrupt. Correspondingly, the small
anchors are combined with the situations of the major anchors.
We believe that for small anchors, they will stay boom or bankrupted when the major anchors
go boom or bankrupted because for example major anchors, Best Buy and Barnes & Noble,
attract people to go shopping and then the small anchors will benefit from it.
The Table 2 explains the expected profits for the Muck River Associate when two major anchors,
Best Buy and Barnes & Noble go bankrupted while small anchors stay between boom and
bankrupted and go bankrupted respectively.
Table 2 Expected Profit Under Bankruptcy ForTwo Major Anchors
Scenarios
Bankrupted
Expected Return
$-814,771
3
4. The Table 3 shows the expected profits for the Muck River Associate when two major anchors,
Best Buy and Barnes & Noble cease or limit operations while small anchors boom, stay between
boom and bankrupted and go bankrupted respectively
Table 3 Expected profit under ceased or limited operation in two major anchors
Scenarios
Stay between boom and bankrupted
Expected Return
$176,484
The Table 4 shows the expected profits for the Muck River Associate when two major anchors,
Best Buy and Barnes & Noble boom while small anchors boom, stay between boom and
bankrupted and go bankrupted respectively. This is a little bit better scenario than that one in
Table 3.
Table 4 Expected profit under boom in two major anchors
Scenarios
Stay between boom and bankrupted
Expected Return
$328,928
4. Measure the Risk and Probability of Default
The risks faced by Muck River based on the lease payment uncertainties are the credit default
risk and operational risk of the anchors. In this project, we use the KMV-Merton model to
calculate the probability of default. The KMV-Merton default forecasting model produces a
probability of default for the two firms at any given point in time. To calculate the probability,
the model subtracts the face value of the firm’s debt from an estimate of the market value of the
firm and then divides this difference by an estimate of the volatility of the firm (scaled to reflect
the horizon of the forecast). The distance to default is then substituted into a cumulative density
function to calculate the probability that the value of the firm will be less than the face value of
debt at the forecasting horizon.
The KMV-Merton model employs the Merton bond pricing model. KMV model is based on the
structural approach to calculate probability of default. KMV model is best when it is applied to
publicly traded companies, where the value of equity is determined by the stock market. It
translates firm’s stock price and balance sheet to an implied risk of default. It works best in
highly efficient liquid market conditions. One assumption for Merton model is that the total
value of the firm follows geometric Brownian motion(equation 1), where is the total value of
the firm, is the expected continuously compounded return on ,
is the annualized firm value
volatility, and
is a standard Weiner process.
4
5. What’s more, we price the value of equity using Black Scholes Merton formula. According to
put-call parity, the value of the firm’s debt is equal to the value of a risk-free discount bond
minus the value of a put option written on the firm, again with a strike price equal to the face
value of debt and a time to maturity of (see in equation (2)), where E is the market value of the
firm’s equity, F is the face value of the firm’s debt, is the instantaneous risk-free rate,
is
the cumulative standard normal distribution function:
Because Merton’s model assumes the value of equity is a function of the value of the firm and
time, it follows from Ito’s lemma:
In the Black Scholes Merton model, we can get
, where
is already defined above.
So, combining these two equations, we get the volatilities of the firm’s value and its equity are
related by equation (3).
. is the volatility of
equity. is the volatility of firm value. is the total value of the firm.
From the equations above, we get the values of and , which are the volatility of firm value
and the total value of the firm respectively. Then the distance to default can be calculated as
equation (4), where is the expected return on firm’s value.
So the corresponding implied probability of default is calculated in equation (5).
5
6. The most critical inputs to the model are clearly the market value of equity, the face value of
debt, and the volatility of equity. As the market value of equity declines, the probability of
default increases. This is both a strength and weakness of the model. For the model to work well,
both the Merton model assumptions must be met and markets must be efficient and well
informed.
In its promotional material, KMV points to the Enron case as an example of how their method is
superior to that of traditional agency ratings. When Enron’s stock price began to fall, its distance
to default immediately decreased. The ratings agencies took several days to downgrade Enron’s
debt. Clearly, using equity values to infer default probabilities allows the KMV-Merton model to
reflect information faster than traditional agency ratings. However, when Enron’s stock price
was unsustainably high, KMV’s expected default frequency for Enron was actually significantly
lower than the default probability assigned to Enron by standard ratings. If markets are not
perfectly efficient, then conditioning on information not captured by
probably makes sense.
Table 5 Results from KMV Model (B: billion dollars)
Firm Name
Best Buy
Barnes&
Noble
Total Value of
Firm( )
24.7289 B
Volatility of Total
Value( )
0.3280
Distance of
Default ( )
0.8960
Probability of
Default( )
0.1851
2.7813 B
0.2266
-0.3097
0.6216
Table 6 Key Statistic for Best Buy and Barnes& Noble (B: billion dollars)
Firm Name
Debt
( )
Value of
Equity( )
Volatility of
Equity( )
Expected Return
on Firm Value ( )
Best Buy
12.26 B
14.66 B
0.5159
0.0449
Barnes&
Noble
2.44 B
0.868 B
0.5635
Risk Free
Rate( )
Time to
Maturity( )
-0.0319
0.0251
5
5. Hedging Strategies
Through our former analysis, we know that Best Buy has an impressive performance during last
year and Barnes & Noble shut down a bookstore in July after more than 12 years. We try to
hedge all these risks and the further risks derive from smaller sales volume. Small Tenants’ rent
fees are generally higher then anchors and they also affects Muck River Plaza’s profit
tremendously.
6
7. Based on the principle of simplicity and effectiveness, we want to find two kinds of derivatives
to hedge two anchors’ risks separately. The advantages of using derivatives are:
(1) Trading actively in the derivative market and easy to buy or sell depends on different
strategies;
(2) Derivatives have higher leverage ratio and the cost of strategy will be less;
(3) Two derivatives are the simplest strategy to hedge credit default risk;
(4) We can simply expand the numbers of derivatives contract to hedge the additionally risk
derive from smaller tenants.
6. Recommend Specific Derivatives
After searching the market and collect the historical data, we found that CDS (Credit Default
Swap) is the best way hedge the credit risk in this situation. Best Buy have an impressive
performance on its equity in last year, it increased from $15 to $42 in this period. Its 5-year CDS
is 227bp right now, which implies roughly an 18% chance of default in 5 years. 1 year ago, its 5year CDS is about 890bp, which implies roughly a 50% chance of default in 5 years.
Consequently, we just need to pay 2.27% of the notional amount annually to hedge the credit risk
of Best Buy.
But the condition of Barnes & Noble is totally different. Barnes & Noble shut down a bookstore
in this July after more than 12 years and its stock prices fluctuated upside down in this year.
Essentially, Barnes & Noble doesn’t offer CDS to the market and then we can’t use the same
strategy as Best Buy. After doing a lot of research of Barnes & Noble’s stock, we find out that its
expected return on equity is -19%. If it keeps going down in the next year, Barnes & Noble may
expand its shutdown plan in the future. Our Strategy is simple, buy the put option of Barnes &
Noble’s stock in one year and using it to hedge the risk.
These Tables below are the calculation results based on the accounting method and we use these
risk expose to calculate the number of contracts we need to buy. Furthermore, we also measure
the risks derive form the small tenants and divide them equally to two company’s derivative by
expanding the numbers of contracts. But it’s easily to find that the probability of default for
Barnes & Noble is much higher than the probability of default for Best Buy, and that means we
need to pay more to hedge the risk exposure of Barnes & Noble.
Table 7 The Risk Exposure for Two Anchors
Year 1
Year 2
320,000
333,200
Cash Flow (Normal)
64,500
68,460
Cash Flow (Bankrupt)
255,500
264,740
Risk Exposure
Year 3
346,400
72,420
273,980
Year 4
361,600
199,480
162,120
Year 5
376,800
204,040
172,760
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8. Table 8 The Risk Exposure for Other Tenants
Year 1
Year 2
1,760,000
1,786,400
Cash Flow (Normal)
352,000
357,280
Cash Flow(Bankrupt)
1,408,000
1,429,120
Risk Exposure
Year 3
1,812,800
362,560
1,450,240
Year 4
1,843,200
368,640
1,474,560
Year 5
1,873,600
374,720
1,498,880
For Best Buy, we just need to pay 2.27% of the notional amount annually to hedge the credit risk.
In this case our notional amount is $250,000 and then the price of Best Buy CDS is $5,675.
Finally, multiplying a scalar of 3 to hedging additional risks derives from the small tenants and
then we need to pay $22,700 totally.
For Barnes & Noble, we consider three put options expire in Jan 2015. Their strike price and
option prices respectively are $15, $17, $20 and $3.42, $5.4, $7.6. The stock price of Barnes &
Noble is $14.57 right now and then the risk premiumsof these put options are different. Based on
the principle of simplicity and effectiveness, we prefer the one with lower risk premium and then
we choose the put option with strike price equal to $20. The expected of return on equity is -19%
and our estimation of return on equity for Barnes & Noble is -40%. Then we use the risk
exposure divided by estimated profit of our put option to calculate the numbers of derivatives we
need to use to hedge the credit risk. Same procedure in CDS of Best Buy, the price of Barnes &
Noble Put Option is $334,400. Finally, multiplying a scalar of 3 to hedging additional risks
derives from the small tenants and then we need to pay $1,337,600 totally.The results are shown
in Table 9.
Table 9 Dollar Values of Derivative Contracts
Anchors' Risk
Small Tenants’ Risk
5,675
17,025
BBY CDS 5Y
334,400
1,003,200
BKS Put(K=20) 1Y
Total Risk
22,700
1,337,600
Interpreting the results of hedging portfolios:
(1) CDS cost less to hedge the credit risk than put options;
(2) The probability of default of Best Buy is smaller and that results the cost of hedging
portfolio be lower in this year;
(3) The shutdown news of Barnes & Noble makes us pay more attentions to its credit risk
and it also increases the cost of put options;
(4) Higher strike price of option price increases the cost of hedging portfolio but we can get
most of them at the maturity because our option is deep in the money;
(5) The times to maturity of two derivatives are different and then we need to choose another
put option after 1 year depends on Barnes & Noble’s performance at that time.
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9. 7. Additional Risks Based on Hedging Strategies:
There are three risks in our Hedging Strategies: The first one is the residue risk exposure because
the imperfect hedging; the second one is the interest rate risk based on principles we have paid
on the derivatives; the third one is the operational risk derive form the Plaza’s business strategy.
In the first situation, we buy 44,000 contracts of put options of Barnes & Noble. But actually we
just need to buy 43,840 contracts of put options. As the result show, we pay additional $1,215 in
put options and that may produce additional risk. For the CDS of Best Buy, the notional amount
of CDS should be 255,000 and our notional amount is 250,000.As the result show, we still need
to pay another $125 to hedge the credit risk of Best Buy but we can’t do that because the
imperfect hedging.
In the second situation, we pay $1,360,300 to construct hedging portfolio, which will lead to
interest risk for this 1 year period. If the interest rate is 2.66%, the interest during 1year should
be $36,670 at the interest rate exposure. But these risks are acceptable for Muck River Plaza
because the payments are annually and then the interest rate risk is limited.
But these two additional risks are hard to be eliminated in this scenario. Our final target is to
hedge the credit risk, and the additional risk exposure is roughly 3.01% of the total amount of
principle of our hedging strategy.
The third one is the operational risk derive form Muck River Plaza’s business strategy. Best Buy
and Barnes & Noble are kind of competitors to each other. Best buy are electronic store and
Barnes & Nobles is bookstore. But actually they are all selling videos, music CD, etc. Essentially,
Barnes& Noble’s selling their new product, NOOK, which is a kind of e-reader. This is a one
source of major profit of Barnes& Nobleand there are a lot of similar electronic devices, such as
iPad, sold in Best Buy. For some extent, they are competitors and they depress the each other’s
sales. So our suggestion to eliminate this risk is to substitute the Barnes& Noble to another
different anchor, such as Wal-Mart, Macy’s or IKEA. We prefer to keep Best Buy because it has
a pretty good performance in its stock market and it just needs a little bit money to hedge its
default risk. After this substitution the cost of our hedging will be lesser and we can receive more
payment from the anchors, because of they are diversified, and also more payment form other
tenants because the volume of costumers increases.
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10. 8. Conclusions:
Beside to consider the impact value of the credit risk management, the cost to manage the risk
also must be balanced. The costs can be measured in actual monetary values. In this project, the
implementation cost associated with our risk management strategy is $1,360,300. We use the
credit default swap to hedge the default risk of Best Buy lease. The cost to manage this risk is
22,700. The cost is very low for the small probability of default based on the great performance
of Best Buy business in these years. What’s more, we can see that the credit default swap used to
hedge the risk is perfectly matched which makes us manage this risk easy. Furthermore, as no
credit default swap is available for us, we use the put options to hedge the default risk of Barnes
& Noble lease. The cost to manage this risk is 1,337,600. The cost is much higher than the cost
to hedge the default risk of Best Buy lease. In order to balance the cost effectively, we buy the
deep-in-the money put options to hedge the default risk. Deep-in-the money put option has the
lower premium because the time value is small. After considering these factors for the risk
management costs, we believe that the cost to manage the risk can be balanced against the
impact value.
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