Kaplan Schweser 2016 FRM Part I 10-Week Online Class … · Kaplan Schweser 2016 FRM Part I 10-Week...
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1 Fixed Income Investments Kaplan Schweser 2016 FRM Part I 10-Week Online Class Week 10 Fixed Income Investments External and Internal Ratings Topic 62 2
Transcript of Kaplan Schweser 2016 FRM Part I 10-Week Online Class … · Kaplan Schweser 2016 FRM Part I 10-Week...
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Fixed Income Investments
Kaplan Schweser2016 FRM Part I
10-Week Online ClassWeek 10
Fixed Income Investments
External and Internal Ratings
Topic 62
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©2016 Kaplan, Inc.
The Rating Process
External rating scales are designed to convey information about either a specific instrument, called an issue-specific credit rating, and/or information about the entity that issued the instrument, which is called an issuer credit rating
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Book 4, LO 62.1
©2016 Kaplan, Inc.
The Rating Process (continued)
After the initial rating, the ratings agency monitors the firm and adjusts the rating as needed utilizing transition matrices that show the frequency of default (see next slide)
These tables show that the higher the credit rating, the lower the default frequency
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Book 4, LO 62.6
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©2016 Kaplan, Inc.
Transition Matrix From Moody's
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Rating From:
Rating To:
Aaa Aa A Baa Ba B Caa-C Default
Aaa 91.75% 7.26% 0.79% 0.17% 0.02% 0.00% 0.00% 0.00%
Aa 1.32% 90.71% 6.92% 0.75% 0.19% 0.04% 0.01% 0.06%
A 0.08% 3.02% 90.24% 5.67% 0.76% 0.12% 0.03% 0.08%
Baa 0.05% 0.33% 5.05% 87.50% 5.72% 0.86% 0.18% 0.31%
Ba 0.01% 0.09% 0.59% 6.70% 82.58% 7.83% 0.72% 1.48%
B 0.00% 0.07% 0.20% 0.80% 7.29% 80.62% 6.23% 4.78%
Caa-C 0.00% 0.03% 0.06% 0.23% 1.07% 7.69% 75.24% 15.69%
Book 4, LO 62.6
©2016 Kaplan, Inc.
Example: Transition Matrix
Starting Ending
A B C Default
A 90% 5% 5% 0%
B 10% 80% 5% 5%
C 5% 15% 70% 10%
Company X starts with B rating in year 1. Calculate the cumulative default probability over a 2-year period.
Book 4, LO 62.6
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©2016 Kaplan, Inc.
Example: Transition Matrix (continued)
In year 1, 5% chance of default
In year 2, 5% chance of default if rated B after one year (80% ×5% = 4%). 0% chance of default if rated A after one year (10% ×0% = 0%). 10% chance of default if rated C after one year (5% ×10% = 0.5%).
The probability of default is 5% from year 1 plus 4.5% chance of default from year 2 (i.e., 4% + 0% + 0.5%) for a total probability of default over a 2-year period of 9.5%
Book 4, LO 62.6
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©2016 Kaplan, Inc.
Impacts on External Ratings
Time horizon: The probability of default given any rating at the beginning of a cycle increases with the time horizon
Economic cycle: Ratings agencies try to give a rating that incorporates the effect of an average cycle
Industry: For a given rating category, default rates can vary from industry to industry
Geography: Geographic location does not seem to cause a variation of default for a given rating class
Book 4, LO 62.2
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Rating Changes on Bond and Stock Prices
For bonds:
A rating downgrade is likely to make the bond price decrease (stronger evidence)
A rating upgrade is likely to make the bond price increase (weaker evidence)
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Book 4, LO 62.3
©2016 Kaplan, Inc.
For stocks:
A rating downgrade is likely to lead to a stock price decrease (moderate evidence)
A rating upgrade is somewhat likely to lead to a price increase (evidence is mixed)
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Rating Changes on Bond and Stock Prices (continued)
Book 4, LO 62.3
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©2016 Kaplan, Inc.
Evolution of Internal Credit Ratings
In order to continually make solid lending decisions, it is increasingly important for banks to create their own internal credit ratings
Today, internal credit ratings are largely based on techniques developed and applied by external credit rating agencies
Since external ratings models have been thoroughly tested, it makes sense for banks to apply these techniques when assessing the creditworthiness of their own borrowers
Book 4, LO 62.4
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©2016 Kaplan, Inc.
Internal Credit Ratings
At-the-point approach: Predict the credit quality over a relatively short horizon of a few months or, more generally, a year
Through-the-cycle approach: Focuses on a longer time horizon and includes the effects of forecasted cycles. Given the stability of the ratings over an economic cycle high-rated firms may be underrated during growth periods and overrated during the decline of a cycle.
Book 4, LO 62.5
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Internal Credit Ratings (continued)
The use of at-the-point approaches may be pro-cyclical.The reason for this is as follows:
economic downturn → rating downgrades → decrease in loans and economic activity
economic upturn → rating upgrades → increase in loans and economic activity
Furthermore, the changes in ratings and lending policies can lag the economic cycle
Book 4, LO 62.5
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©2016 Kaplan, Inc.
Sample Exam Question
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Given the 1-year transition matrix below, what is the probability that a company that is currently B rated will default over a given 2-year period?
Initial Period State Next Period State
A B Default
A 85% 13% 2%
B 10% 85% 5%
a. 7.00%.
b. 8.05%.
c. 9.45%.
d. 12.32%.
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©2016 Kaplan, Inc.
Answer
Answer: c
After year 1, there is a 5% chance of default, an 85% chance of still being B, and a 10% chance of being A
In year 2, there is a 4.25% chance of default if B rated (or 85% × 5% = 4.25%) and a 2% chance of default if A rated (10% × 2% = 0.2%)
The total probability is therefore 9.45%15
Fixed Income Investments
Capital Structure in Banks
Topic 63
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©2016 Kaplan, Inc.
Economic Capital for Credit Risk
Probability of Default (PD)
Exposure Amount (EA) [a.k.a. Exposure at Default (EAD)]
Loss Rate (LR) [a.k.a. Loss Given Default (LGD)]
LR = 1 – Recovery Rate
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Book 4, LO 63.2
©2016 Kaplan, Inc.
Expected and Unexpected Loss
Expected Loss (EL)
EL = EA × PD × LR
Unexpected Loss (UL) = variation in EL
Assuming 2-state world
σPD= PD × (1 – PD)
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Book 4, LO 63.3, 63.4, & 63.5
2 2 2LR PDUL = EA × PD×σ +LR ×σ
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Expected and Unexpected Loss
Suppose XYZ bank has booked a loan with the following characteristics: total commitment of $2,000,000 of which $1,800,000 is currently outstanding.
The bank has assessed an internal credit rating equivalent to a 1% default probability over the next year.
The bank has additionally estimated a 40% loss rate if the borrower defaults.
The standard deviation of PD and LR is 5% and 30%, respectively.
Calculate the expected and unexpected loss for XYZ bank.
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Book 4, LO 63.3 & 63.4
©2016 Kaplan, Inc.
Expected and Unexpected Loss Answer
We can calculate the expected and unexpected loss as follows:
EL = EA × PD × LR
Exposure amount = $1,800,000Probability of default = 1%Loss rate = 40%
EL = $1,800,000 × 0.01 × 0.40 = $7,20020
Book 4, LO 63.3 & 63.4
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©2016 Kaplan, Inc.
Expected and Unexpected Loss Answer
The unexpected loss represents 3.61% of the exposure amount: ($64,900 / $1,800,000).
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2 2 2LR PDUL = EA × PD×σ +LR ×σ
2 2 2UL = $1,800,000× 0.01×0.3 + 0.4 ×0.05 = $64,900
Book 4, LO 63.3 & 63.4
©2016 Kaplan, Inc.
Portfolio Unexpected Loss and Risk Contribution
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Book 4, LO 63.6
P i i i ii i
EL = EL = EA ×LR ×PD
P ij i ji j
UL = ρ UL UL
i j ijj
iP
UL UL ρ
RC =UL
1 1,2 21 1
P
2 1,2 12 2
P
UL +(ρ ×UL )RC = UL ×
UL
UL +(ρ ×UL )RC = UL ×
UL
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©2016 Kaplan, Inc.
Portfolio Unexpected Loss and Risk Contribution
Bigger Bank has two assets outstanding. The features of the loans are summarized below. Assuming a correlation of 0.3 between the assets, compute ELP and ULP as well as the risk contribution of each asset.
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Asset A Asset B
EA $8,250,000 $1,800,000
PD 0.50% 1.00%
LR 50.00% 40.00%
σPD 2.00% 5.00%
σLR 25.00% 30.00%
Book 4, LO 63.6
©2016 Kaplan, Inc.
Portfolio Unexpected Loss and Risk ContributionAnswer
Step 1: Compute EL for both assets.
ELA = EA × PD × LR
= $8,250,000 × 0.005 × 0.50
= $20,625
ELB = EA × PD × LR
= $1,800,000 × 0.01 × 0.40
= $7,200
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Book 4, LO 63.6
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©2016 Kaplan, Inc.
Portfolio Unexpected Loss and Risk ContributionAnswer
Step 2: Compute UL for both assets.
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2 2 2LR PDUL = EA × PD×σ +LR ×σ
2 2 2AUL = $8,250,000× 0.005×0.25 + 0.5 ×0.02 = $167,558
2 2 2BUL = $1,800,000 × 0.01× 0.3 + 0.4 × 0.05 = $64,900
Book 4, LO 63.6
©2016 Kaplan, Inc.
Portfolio Unexpected Loss and Risk ContributionAnswer
Step 3: Compute ELP.
ELP = $20,625 + $7,200
= $27,825
Step 4: Compute ULP.
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2 2PUL = 167,558 + 64,900 + 2 0.3 167,558 64,900 = $197,009
Book 4, LO 63.6
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Portfolio Unexpected Loss and Risk ContributionAnswer
Step 5: Compute RC for both assets.
RCA + RCB = $197,009 = ULP
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A
167,558 + 0.3×64,900RC = 167,558 =159,070
197,009
B
64,900 + 0.3×167,558RC = 64,900 = 37,939
197,009
Book 4, LO 63.6
©2016 Kaplan, Inc.
Portfolio Unexpected Loss and Risk ContributionAnswer
ELP = $27,825
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2 2PUL = 167,558 + 64,900 + 2 0.1 167,558 64,900 = $185,641
Book 4, LO 63.6
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©2016 Kaplan, Inc.
Economic Capital
Loan loss reserves are set aside for expected losses
Economic capital is set aside for unexpected losses
The amount of economic capital needed to absorb credit losses is the distance between the unexpected (negative) outcome and the expected outcome for a given confidence level
By knowing the shape of the loss distribution, ELP, and ULP, the difference between the expected outcome and the confidence level (typically 99.97%) can be estimated
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Book 4, LO 63.1, 63.7
©2016 Kaplan, Inc.
Economic Capital (continued)
0
expected loss
unexpected loss = capital
VaR = loss at a very high confidence level (99.97%)
Pro
bab
ility
of
Lo
ss
Potential Loss
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Book 4, LO 63.1, 63.7
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Fixed Income Investments
Operational Risk
Topic 64
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©2016 Kaplan, Inc.
Operational Risk
The Basel definition of operational risk is “the risk of direct and indirect loss resulting from inadequate or failed internal processes, people, and systems or from external events”
Be able to calculate the operational risk capital under both the basic indicator approach and the standardized approach
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Book 4, LO 64.1
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©2016 Kaplan, Inc.
Basic Indicator Approach
Under the basic indicator approach, operational risk capital is based on 15% of the bank's annual gross income over a 3-year period. Gross income in this case includes both net interest income and noninterest income.
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Book 4, LO 64.1
©2016 Kaplan, Inc.
Standardized Approach
Under the standardized approach, the beta factor of each business line is multiplied by the annual gross income over a 3-year period. The results are then summed to arrive at the total operational risk capital charge.
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Investment banking (corporate finance) 18%
Investment banking (trading and sales) 18%
Retail banking 12%
Commercial banking 15%
Settlement and payment services 18%
Agency and custody services 15%
Asset management 12%
Retail brokerage 12%
Book 4, LO 64.1
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©2016 Kaplan, Inc.
Standardized Approach (continued)
To use the standardized approach, banks must:
Be able to identify, assess, monitor, and control operational risk
Document losses for each business line
Report operational risk losses on a regular basis
Have a system that has the appropriate level of documentation
Conduct audits with both internal and external auditors35
Book 4, LO 64.1
©2016 Kaplan, Inc.
Loss Frequency and Loss Severity
Loss frequency is the number of losses over a period
Loss severity is the value of the loss suffered
In a Monte Carlo process, we make random draws from the loss frequency data and then draw the indicated number of draws from the loss severity data to create a potential loss event. This process is continued several thousand times to create the potential loss distribution.
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Book 4, LO 64.3
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©2016 Kaplan, Inc.
Data Limitations
Historical operational risk loss data is inadequate. To combat this problem, banks are building a database of potential loss events.
Internal data should be used when estimating the frequency of losses
Both internal and external data should be used when estimating the severity of losses
When viewing external data from other banks it is necessary to scale the loss event to your bank's situation
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Book 4, LO 64.4
©2016 Kaplan, Inc.
Scenario Analysis
A method for obtaining additional operational risk data points is to use scenario analysis
Regulators encourage this approach as it allows management to incorporate events that have not yet occurred
The drawback is the amount of time spent by management developing scenarios and contingency plans
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Book 4, LO 64.5
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©2016 Kaplan, Inc.
Forward-Looking Approaches
Risk and control self assessment (RCSA) program. An RCSA program surveys those managers directly responsible for the firm's operations. It is presumed that they are in the best position to evaluate the risks.
Key risk indicators (KRIs). When attempting to identify operational risks, KRIs are valuable if they (1) have a predictive relationship to losses and (2) are accessible and measurable in a timely fashion.
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Book 4, LO 64.6
©2016 Kaplan, Inc.
Scorecard Data
Allocating operational risk capital to each business unit encourages managers to improve their management of operational risks
The scorecard approach to allocating capital involves surveying each manager regarding the key features of each type of risk. Survey answers are quantified to gauge the total amount of risk for each business unit. Scores are compared across business units and validated by comparison with historical losses.
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Book 4, LO 64.7
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©2016 Kaplan, Inc.
The Power Law
The power law is useful in extreme value theory (EVT) when we evaluate the nature of the tails of a given distribution. The law states that for a range of variables:
Since low values of α will represent the extreme tails, α also represents the VaR from potential operational risks
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P V X K X
Book 4, LO 64.8
©2016 Kaplan, Inc.
Moral Hazard and Adverse Selection
A moral hazard occurs when an insurance policy causes an insured company to act differently with the presence of insurance protection. To help protect against this, firms use deductibles, policy limits, and coinsurance provisions.
Adverse selection occurs when an insurance company cannot decipher between good and bad insurance risks. Since the insurance company offers the same polices to all firms, it will attract more bad risks since those firms with poor internal controls are more likely to desire insurance.
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Book 4, LO 64.9
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Fixed Income Investments
Stress Testing
Topic 65
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©2016 Kaplan, Inc.
Stress Testing
While VaR is useful for normal market conditions, history clearly tells us that large and unexpected losses do occur (e.g., Black Monday, Russian debt crisis)
VaR cannot make predictions about the magnitude of the losses beyond a threshold, and it cannot identify the causes or conditions that can lead to large losses
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Book 4, LO 65.1
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©2016 Kaplan, Inc.
Stress Testing (continued)
The use of stress testing addresses these shortcomings in VaR
Should be used as a complement to VaR measures rather than a substitute
Book 4, LO 65.1
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©2016 Kaplan, Inc.
Scenario Analysis
Scenario analysis involves estimating portfolio value from extreme movements in model inputs. In effect, “shocking”the model parameters by large amounts creates a distribution of portfolio values.
Book 4, LO 65.2
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©2016 Kaplan, Inc.
Scenario Analysis (continued)
For an event-driven scenario, the scenario is generated from events that would likely cause movements in relevant risk factors
For a portfolio-driven scenario, the risk vulnerability of the portfolio is first identified and is then translated into adverse risk factor movements
For example, an institution that borrows short and lends long would be vulnerable to an increase in interest rates. The scenarios chosen should reflect this vulnerability.
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Book 4, LO 65.2
©2016 Kaplan, Inc.
Common One-Variable Sensitivity Tests
1. Parallel yield curve shifts
2. Changes in steepness of yield curves
3. Changes in equity indexes
4. Changes in foreign exchange currencies
5. Changes in volatilities of above
6. Changes in swap spreads48
Book 4, LO 65.3
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©2016 Kaplan, Inc.
Scenario Analysis
Unidimensional scenario analysis involves identifying key variables, assuming larger movements than predicted by recent history, and revaluing the portfolio
Correlation across risk factors is ignored
Multidimensional scenario analysis attempts to overcome the correlation drawback. The generalized process involves two steps:
1. Hypothesize various states of the world
2. Consider the impact on all relevant variables
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Book 4, LO 65.5
©2016 Kaplan, Inc.
Prospective and Historical Scenarios
The historical approach is backward looking. Historical scenarios will examine previous market data to infer the joint movement of key financial variables during times of market stress.
Prospective scenarios are hypothetical based on reasonable and relevant scenarios that could generate large losses. Prospective scenarios are either factor push or conditional.
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Book 4, LO 65.6
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©2016 Kaplan, Inc.
Prospective Scenarios
The factor push method pushes each risk factor up or down the same amount in the direction that would cause adverse price effects
The conditional scenario method includes correlations across risk factors. By focusing on changes in a subset of variables, the unchanged variables are zeroed out.
Book 4, LO 65.6
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©2016 Kaplan, Inc.
Sensitivity Analysis
Sensitivity analysis is a form of stress testing that examines how model output variation relates to model input variation
A variety of alternative models can be used to price derivatives. Some of these models might be good approximations for small changes in the current environment but could break down during large movements in key variables.
Stress testing should consider the robustness of the risk forecasts to not only changes in model inputs but also the model itself
Book 4, LO 65.7
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Improving Stress Tests
The purpose of stress tests is to identify potential exposures. It is possible that the magnitude of the loss may be unacceptably large. There are several tools at management's disposal to alleviate this problem.
Buy protection through insurance contracts
Modify portfolio to decrease exposure
Alter business strategy
Contingency plan in case of trigger event
Secure alternative funding in liquidity stress
Book 4, LO 65.8
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Fixed Income Investments
Principles for Sound Stress Testing Practices and Supervision
Topic 66
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Stress Testing in Risk Management
Stress testing is an important tool that enables a bank to identify, assess, monitor, and manage risk
Recent financial turmoil has substantially increased the need for flexible, comprehensive, and forward-looking stress testing
Book 4, LO 66.1
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©2016 Kaplan, Inc.
Stress Testing and Risk Governance
Major weaknesses and recommendations for stress testing and integration in risk governances are as follows:
Lack of involvement of board and senior management
Lack of overall organizational view
Lack of fully developed stress testing
Lack of adequate response to crisis
Book 4, LO 66.2
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Stress Testing and Risk Governance (continued)
Recommendations: Stress testing should form an essential ingredient of overall governance of risk management plan, encompass multiple techniques and perspectives, involve a sound infrastructure and regular assessment, produce written policies and recommendations, and generate comprehensive firm and market-wide scenario testing
Book 4, LO 66.2
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©2016 Kaplan, Inc.
Weaknesses of Stress Testing Methodologies and Scenarios
Stress testing methodologies were based on inadequate infrastructure, inadequate risk assessment approaches, inadequate recognition of correlation, and inadequate firm-wide perspectives
Stress testing scenarios lacked depth and breadth because they were based on mild shocks, shorter duration, and smaller correlation effects among various markets, portfolios, and positions
Book 4, LO 66.2
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Recommendations to Improve Stress Testing Methodologies and Scenarios
Stress testing methodologies should be based on:
Comprehensive testing approaches that include risk exposures at the firm-wide level
Inclusions of differential risk exposure concentrations and correlated risk factors
Evaluating multiple performance measures and capital requirement definitions
Book 4, LO 66.2
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©2016 Kaplan, Inc.
Risks Arising From Complex Structured Products
Banks evaluated the risk of complex structured products based on the credit rating of similar cash instruments
In order to identify, assess, monitor, and control risk exposure of complex structured products, stress testing plans should utilize all the relevant information about the underlying asset pool, market conditions, contractual obligations, and subordination levels
Book 4, LO 66.2
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Risks Arising From Complex Structured Products
Basis risks due to ineffective hedging instruments that do not move in lock-step with exposures. Convergence may not even occur at hedge horizon depending on deviation between exposure and instrument characteristics.
Counterparty credit risks become an issue with initiation of any agreements. Wrong way risks may creep into position, generating unexpected exposures.
Book 4, LO 66.2
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©2016 Kaplan, Inc.
Pipeline Risk and Liquidity Risk
Due to a lack of access to the securitization market under stress conditions, a bank may be forced to park assets on the balance sheet longer than planned. Such risk is called pipeline risk.
Stress testing did not fully recognize funding liquidity risk and its correlation with other risks. Future stress tests should focus more on correlations of various factors and risks, including funding liquidity risk.
Book 4, LO 66.2
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Recommendations to Supervisors
Supervisors should make frequent and comprehensive assessments of a bank's stress testing procedures
In the event that stress testing procedures or analysis is deemed inadequate, a supervisor should push for corrective actions
It is necessary for supervisors to question the use of stress tests that produce unrealistic results
Book 4, LO 66.3
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©2016 Kaplan, Inc.
Recommendations to Supervisors
Under the Basel II Accord, banks should conduct an analysis of their stress tests when assessing both capital requirements and liquidity
It is prudent for supervisors to conduct additional stress tests using common scenarios within a bank's jurisdiction
In order to expand their knowledge of stress testing, supervisors should consult with other experts to identify potential stress vulnerabilities
Book 4, LO 66.3
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Fixed Income Investments
Valuation and Risk Models
Sample Problems and Solutions
2016 FRM Exam Part I
©2016 Kaplan, Inc.
1. Coherent Risk Measures
Which coherent risk measure property infers that if a random future value R1 is always greater than a random future value R2, then the risk of the return distribution for R1
will be less than the risk of the return distribution for R2.
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1. Coherent Risk Measures Answer
Monotonicity: Y ≥ X → ρ(Y) ≤ ρ(X)
Monotonicity infers that if a random future value R1 is always greater than a random future value R2, then the risk of the return distribution for R1 is less than the risk of the return distribution for R2
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©2016 Kaplan, Inc.
2. Binomial Option Pricing
Stock ABC is priced at $50
Risk-free rate is 3%
What is the value of a 2-period European call option with a strike price of $60 on a share of ABC stock using a binomial model with an up factor of 1.20 and a (risk-neutral) up probability of 67%?
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©2016 Kaplan, Inc.
2. Binomial Option Pricing Answer
Two up moves produce a stock price of 50 × 1.44 = 72 and a call value at the end of two periods of 12
All other movements result in the option being out of the money
The value of the call option is discounted back one year and then discounted back again to today
C1-year = [12(0.67) + 0(0.33)] / 1.03 = 7.806
Ctoday = [7.806(0.67) + 0(0.33)] / 1.03 = 5.07869
©2016 Kaplan, Inc.
3. Black-Scholes-Merton
Using the Black-Scholes-Merton (BSM) model, compute the value of a European put option using the following information:
Stock price = $100
Exercise price = $102
Risk-free rate = 3%
Time to expiration = 1 year
N(d1) = 0.64
N(d2) = 0.56 70
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©2016 Kaplan, Inc.
3. Black-Scholes-Merton Answer
BSM put price
= Xe–rt × [1 – N(d2)] – S0 × [1 – N(d1)]
= 102e(–0.03 × 1)(0.44) – 100(0.36)
= 43.55 – 36 = $7.55
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©2016 Kaplan, Inc.
4. Delta of Futures Contract
Suppose that a portfolio of options is delta-neutral when a short position of $100,000 is entered into
If the risk-free rate in the United States is 5%, what is the alternative required position in futures contracts for delta-hedging if you hedge with 9-month futures contracts?
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©2016 Kaplan, Inc.
4. Delta of Futures Contract Answer
Recall that the delta of a futures position is erT on a long stock or stock index that pays no dividends
Therefore, the equivalent short position in futures contract is:
hedge(futures) = e–rT × hedge(asset)
e–(0.05)(9×12) × $100,000 = $96,319
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©2016 Kaplan, Inc.
5. Spot and Forward Rates
If the 1-year spot rate is 6% and the 1-year forward rate is 7.5%, what is the 2-year spot rate?
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5. Spot and Forward Rates Answer
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T he 2 -year spo t ra te
= (1 + 0 .06)(1 + 0 .075) – 1
= 0 .0675, o r 6 .75%
©2016 Kaplan, Inc.
6. Yield to Maturity
A zero-coupon bond with a face value of $1,000 has a price of $250
The bond matures in 20 years
Assuming annual compounding periods, what is the yield to maturity of this bond?
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©2016 Kaplan, Inc.
6. Yield to Maturity Answer
PV = –250
N = 20
FV = 1,000
PMT = 0
CPT → I/Y = 7.18%
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©2016 Kaplan, Inc.
7. Duration
A 10-year, 10% annual coupon bond with $100 par value currently yields 8%
What is the effective duration of the bond given a 50 basis point change in yield?
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7. Duration Answer
I/Y = 8.00; FV = 100; N = 10; PMT = 10;
PV = BV0 = 113.42
I/Y = 7.50; FV = 100; N = 10; PMT = 10;
PV = BV– = 117.16
I/Y = 8.50; FV = 100; N = 10; PMT = 10;
PV = BV+ = 109.84
effective duration = [(BV– – BV+) / (2BV0(Δy)]
= (117.16 – 109.84) / (2 × 113.42 × 0.005)
= 6.4579
©2016 Kaplan, Inc.
8. Transition Matrix
Starting Ending
A B C Default
A 90% 5% 5% 0%
B 10% 80% 5% 5%
C 5% 15% 70% 10%
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Company ABC starts with C rating in year 1; calculate the cumulative default probability over 2 years.
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©2016 Kaplan, Inc.
8. Transition Matrix Answer
In year 1, 10% chance of default
In year 2, 10% chance of default if rated C after 1 year (70% × 10% = 7%). There is a 0% chance of default if rated A after 1 year (5% × 0% = 0%). There is a 5% chance of default if rated B after 1 year (15% × 5% = 0.75%).
The probability of default is 10% from year 1 plus 7.75% chance of default from year 2 (i.e., 7% + 0% + 0.75%) for a total probability of default over a two-year period of 17.75%.
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©2016 Kaplan, Inc.
9. Expected Loss
Bank XYZ has two equal sized and equal maturity loans
Exposure amount for each loan is $5 million
Both loans have a 1% probability of default and 80% loss rate
Loan 1: σPD = 2%; σLR = 5%
Loan 2: σPD = 3%; σLR = 6%
What is the expected loss for the loan portfolio?
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©2016 Kaplan, Inc.
9. Expected Loss Answer
Compute EL for both loans:
EL1 = EA × PD × LR
= $5,000,000 × (0.01) × (0.8) = $40,000
EL2 = EA × PD × LR
= $5,000,000 × (0.01) × (0.8) = $40,000
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©2016 Kaplan, Inc.
9. Expected Loss Answer (continued)
Compute ELP:
ELP = $40,000 + $40,000
ELP = $80,000
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©2016 Kaplan, Inc.
10. Loss Rate and Recovery Rate
Given the following information, compute the loss rate and recovery rate.
Expected loss = $150,000
Exposure at default = $6,000,000
Probability of loss = 3%
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10. Loss Rate and Recovery Rate Answer
EL = EA × LR × PD
LR = (1 – recovery rate)
$150,000 = ($6,000,000) × (1 − RR) × (0.03)
Recovery rate = 16.67%
Loss rate = 83.33%
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Fixed Income Investments
Exam Tips and Strategies
2016 FRM Part I Exam
Kaplan Schweser
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FRM Exam Format
The Part I Exam will be four hours in length and contain 100 multiple-choice questions
Part I Exam will be administered in the morning, and Part II Exam will be administered in the afternoon
Admission ticket: Available late April. You will receive an email that includes instructions on how to download your ticket.
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Exam Day Schedule
FRM Part I Session
7:00 a.m. Candidates may check in
7:45 a.m. Doors promptly close. No late candidates are allowed to enter.
7:46 a.m. Exam is distributed, and instructions are read
8:00 a.m. Exam begins
12:00 p.m. Exam ends, materials are collected, and candidates are released
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What to Bring on Exam Day
Government-issued photo ID
Admission ticket
Approved calculator(s)—see next slide
#2 pencils (no pens should be used)
Lunch, food, and drink must be consumed outside of the testing room but can be brought into the room in a clear bag
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Calculator Policy
GARP will strictly enforce its calculator policy. The following calculators are permitted:
Texas Instruments BA II Plus and Professional
Hewlett Packard 12C and 12C Platinum
Hewlett Packard 10B II and 10B II+
Hewlett Packard 20B91
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What to Wear on Exam Day
Dress comfortably and in layers
The exam room can go from hot to cold and back
You will probably be allowed to keep extra clothing at your table
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The Big Picture
Focusing on the big picture means you should know at least a little about every concept
For example, if you draw a blank on the formula for hedging a long stock portfolio with stock index futures, you can still eliminate any responses suggesting that you buy futures
By remembering some basic information on exam day, you will be able to narrow your answer choices
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The Big Picture (continued)
You probably won’t answer many questions correctly with only a basic grasp of the concept, but you can improve your odds on a multiple-choice question from 25 to 33%, or even 50%
Also, by having a big picture grasp of the material you will be better able to distinguish between relevant and irrelevant information in a question
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Formulas
The big-picture approach will help you master large parts of the curriculum, but there is some material that will be tested with a significant level of detail
Being able to work with formulas will be critical to your exam day success
Try to get comfortable with as many formulas as possible
The longer, more complex formulas are a pain for all of us. The good news is that these equations are less likely to show up on the exam.
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Formulas (continued)
Don’t spend time memorizing formulas that your calculator is programmed for, such as the net present value of an uneven cash flow stream or the yield to maturity
However, you should be very confident in using your calculator to solve these types of problems
In other words, you don’t want to learn how to use the time value of money functions on your calculator during the exam
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Question Answering Tips
Tips for answering multiple-choice questions:
Watch for double negatives
Avoid unnecessary calculations—sometimes, quantitative questions can be answered by logically reasoning through the answer choices
Select the best answer choice—several choices may seem correct, so select the choice that best answers the question
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Question Answering Tips (continued)
Do not look for patterns in the answer choices
Make sure you mark the right answer on the answer sheet
Rely on your first impression. Only change your answer if you can justify the change.
Be confident in yourself. Do not worry if you miss some questions. You only need a passing score on the exam, not a perfect score.
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Time Management
Candidates who fail to pass the FRM exam cite time management as their biggest downfall
Do not let poor time management determine your exam results
The following slides have some tips to help you manage your time wisely
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Practice Exams
Take at least one practice exam where you time yourself
This will give you some indication of whether you will have problems on exam day
However, do not let your positive results on practice exams lull you into overconfidence
The stress of exam day, plus possible distractions like noise or a cold exam room, can make a big difference in how fast you work
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Monitor Your Progress
Keep an eye on the time as you work through the exam
There will be 100 questions, which means 25 questions per hour or about 6 questions every 15 minutes
You may deviate some as you work through easier or more difficult questions, but be careful not to let yourself fall too far behind
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Monitor Your Progress
One way to alleviate time pressure is to bank a few minutes by doing an easy question first
Select questions that you feel comfortable with and start there
If you begin to struggle, move to a different question
This strategy will help you gain confidence as you progress through the exam and will also allow you to get a little ahead with your time allocation
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Never Panic!
Even if you fall behind, panicking will only make things worse
You won’t think clearly, and you’ll miss easy questions
If you need a short break, put your pencil down and take a few deep breaths
The 30 seconds or so that this takes may very well help you think clearly enough to answer several additional questions correctly
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After the Exam
You will be sent an email stating your pass/fail status two months after the exam
If you pass the Part I exam, you must pass the Part II exam within a 4-year time span
In order to become a certified FRM, after passing the Part II exam, candidates must demonstrate a minimum of two years of risk-related full-time professional experience
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