CFA 2018 level 3 schweser practice exam CFA 2018 level 3 question bank CFA 2018 CFA 2018 r27 risk management IFT notes

LO.a: Discuss features of the risk management process, risk governance, risk reduction, and an enterprise risk management system.. While applying the risk management process to portfolio

Risk Management

1 Introduction 3

2 Risk Management as a Process 3

3 Risk Governance 4

4 Identifying Risks 5

5 Measuring Risk 6

5.1 Measuring Market Risk 6

5.2 Value at Risk 7

5.3 The Advantages and Limitations of VaR 11

5.4 Extensions and Supplements to VaR 11

5.5 Stress Testing 11

5.6 Measuring Credit Risk 12

5.7 Liquidity Risk 14

5.8 Measuring Nonfinancial Risks 14

6 Managing Risk 14

6.1 Managing Market Risk 14

6.2 Managing Credit Risk 15

6.3 Performance Evaluation 15

6.4 Capital Allocation 16

6.5 Psychological and Behavioral Considerations 17

Summary 17

Examples from the Curriculum 23

Example 1 Some Risk Governance Concerns of Investment Firms 23

Example 2 An Analysis of Risk Exposures 23

Example 3 An Operational Risk for Financial Services Companies: The Rogue Trader 24

Example 4 Accounting Risk: The Case of Derivative Contracts 24

Example 5 VaR with Different Probability Levels and Time Horizons 25

Example 6 Calculating VaR Using the Historical Method 26

Example 7 Value at Risk and the Management of Market Risk at Goldman Sachs 27

Example 8 Calculating Credit Risk Exposures 31

Example 9 Basel II—A Brief Overview 32

Example 10 A Fund Management Company and Risk Budgeting 33

Example 11 Repricing a Forward Contract 34

This document should be read in conjunction with the corresponding reading in the 2018 Level III CFA®

Program curriculum Some of the graphs, charts, tables, examples, and figures are copyright

2017, CFA Institute Reproduced and republished with permission from CFA Institute All rights reserved

Required disclaimer: CFA Institute does not endorse, promote, or warrant the accuracy or quality of the

products or services offered by IFT CFA Institute, CFA®, and Chartered Financial Analyst® are

trademarks owned by CFA Institute

1 Introduction

A portfolio manager needs to understand risk management as it relates to his firm He should also

understand the risk management process of firms where he invests

LO.a: Discuss features of the risk management process, risk governance, risk reduction, and an

enterprise risk management system

This LO is covered in sections 2 and 3

2 Risk Management as a Process

Risk management is a process that involves:

 Recognising the exposures to risk

 Creating appropriate ranges for exposures

 Constantly measuring these exposures

 Performing appropriate adjustments whenever exposure levels fall outside of target ranges

This is a constant process and may need adjustments in any of these activities to reflect new policies

Exhibit 1 shows the practical application of the process of risk management

While applying the risk management process to portfolio management, managers need to measure and

price the risks of financial transactions or positions Exhibit 2 demonstrates the process of pricing and

measuring risk

3 Risk Governance

LO.b: Evaluate strengths and weaknesses of a company’s risk management process

Risk governance is an element of corporate governance It is the process of setting overall policies and

standards in risk management

The two types of risk governance models are:

 Decentralized: Here each unit calculates and reports its risk exposures independently The main

advantage is that this model allows people who understand risk better to directly manage it

 Centralized: Here the risk management is moved closer to senior management The main

advantage is that it allows offsetting of risks across units For example, if one unit is exporting

goods to Japan and other unit is importing goods from Japan, then the Yen risk exposure can be

offset Centralized risk management is now called enterprise risk management (ERM)

Refer to Example 1 from the curriculum

LO.c: Describe steps in an effective enterprise risk management system

An effective ERM system usually includes the following steps:

1 Identify each risk factor to which the company is exposed

2 Quantify each exposure’s size in money terms

3 Map these inputs into a risk estimation calculation

4 Identify overall risk exposures as well as the contribution to overall risk deriving from each risk

factor

5 Set up a process to report on these risks periodically to senior management, who will set up a

committee of division heads and executives to determine capital allocations, risk limits, and risk

management policies

6 Monitor compliance with policies and risk limits

4 Identifying Risks

LO.d: Evaluate a company’s or a portfolio’s exposures to financial and nonfinancial risk factors

Exhibit 3 shows the main sources of risk Financial risk is the risk derived from events in the external

financial markets Non-financial risk refers to all other forms of risk

Refer to Example 2 from the curriculum

The various types of risks are:

Market Risk: Risk associated with interest rates, exchange rates, stock prices and commodity prices

Credit Risk: Risk of loss caused by a counterparty or debtor’s failure to make a promised payment

Liquidity Risk: Risk that a financial instrument cannot be purchased or sold without a significant

concession in price because of the market’s potential inability to efficiently accommodate the desired

trading size (large bid-ask spread)

Operational Risk: Risk of loss from failures in a company’s systems and procedures or from external

events

Refer to Example 3 from the curriculum

Model Risk: Risk that a model is incorrect or misapplied; in investments, it often refers to valuation

models

Settlement (Herstatt) Risk: Risk that one party could be in the process of paying the counterparty while

the counterparty is declaring bankruptcy

Regulatory Risk: Risk associated with how a transaction will be regulated or with the potential for

regulations to change

Legal/Contract Risk: The possibility of loss arising from the legal system’s failure to enforce a contract in

which an enterprise has a financial stake

Tax Risk: Risk associated with uncertainty in tax laws

Accounting Risk: Risk associated with uncertainty about how a transaction should be recorded and the

potential for accounting rules and regulations to change

Refer to Example 4 from the curriculum

Sovereign Risk: A form of credit risk in which the borrower is the government of a sovereign nation

Political Risk: Risk associated with changes in political environment

ESG Risk: Risk to a company’s market valuation resulting from environmental, social and governance

factors

Performance Netting Risk: Potential for loss resulting from the failure of fees based on net performance

to fully cover contractual payout obligations to individual portfolio managers that have positive

performance when other portfolio managers have losses and when there are asymmetric incentive fee

arrangements with the portfolio managers

Settlement Netting Risk: Risk that a liquidator or a counterparty in default could challenge a netting

arrangement so that profitable transactions are realized for the benefit of creditors

5 Measuring Risk

5.1 Measuring Market Risk

Several statistical tools are available to measure market risk:

 Volatility of the asset, measured by the standard deviation of asset prices

 Volatility relative to a benchmark (active risk, tracking risk) measured by deviation of a

portfolio’s returns in excess of a benchmark

 For stocks, beta measures the sensitivity to market movements

 For bonds, duration and convexity measure sensitivity of a bond to a small parallel shift in the

yield curve

 For options:

o delta measures an option’s sensitivity to a small change in the value of the underlying

o gamma measures the delta’s sensitivity to a change in the value of the underlying

o vega measures an option’s sensitivity to a change in the underlying’s volatility

o theta measures an option’s sensitivity to a change in the time to expiration

5.2 Value at Risk

LO.e: Calculate and interpret value at risk (VaR) and explain its role in measuring overall and

individual position market risk

VAR is a probability-based measure of loss potential More precisely, VAR is an estimate of the loss (in

money terms) that we expect to exceed with a given level of probability over a specified time period

Consider the following example of VaR for an investment portfolio: The VaR for a portfolio is $1.5 million

for one day with a probability of 0.05 This statement can be interpreted in the following two ways:

 There is a 5 percent chance that the portfolio will lose at least $1.5 million in a single day

 We can say with 95 percent confidence, that the maximum loss will be $1.5 million for one day

Elements of measuring VAR

VAR measures requires the user to make the following decisions about the calculation’s structure

1 Picking a probability level:

 The probability chosen is typically either 0.05 or 0.01

 Using 0.01 is more conservative and will give a higher VAR It is recommended to use 0.01 if

returns are non-linear

2 Selecting the time period over which to measure VAR:

 The choices are: day, week, two-week, month etc

 If the portfolio has a high turnover it is recommended to use a shorter period

 Using a longer period results in a higher VAR

3 Choosing the specific approach to modeling the loss distribution

Once these key parameters are selected, we can obtain the VAR estimate Exhibit 4 shows the

probability distribution for the returns on a portfolio over a specified time period

Return on Portfolio Probability

The first row in this table tells us that there is a 0.01 probability of a loss of 40% or worse The second

row tells us that there is a 0.01 probability of a loss between 30% and 40% The third row tells us that

there is a 0.03 probability of a loss between 20% and 30% Adding the three probability numbers we can

say there is 0.05 probability of a loss of 20% or worse

Assuming a portfolio of $100 million, the VAR with a probability of 0.05 can be calculated as:

20% of $100 million = $20 million

Methods to estimate VAR

The three standardized methods to estimate VAR are:

1 Analytical variance-covariance method

2 Historical method

3 Monte Carlo simulation method

Analytical variance-covariance method:

Here we assume that the portfolio returns are normally distributed Exhibit 5 shows the expected annual

returns and standard deviation of a portfolio obtained by combining the S&P 500 and NASDAQ

S&P 500 NASDAQ Combined Portfolio

Percentage invested (w) 0.75 0.25 1.00

Expected annual return (μ) 0.12 0.18 0.135

Standard deviation (σ) 0.20 0.40 0.244

Correlation (ρ) 0.90

Exhibit 6 demonstrates how we can calculate the annual VAR of this portfolio with a probability of 0.05

We start by determining the zvalue associated with a cumulative probability of 0.05 This zvalue is

-1.65 The distribution we are working with has a mean of 0.135 and a standard deviation of 0.244

Given these numbers it can be shown that 5% of the area under the curve is to the left of -0.268 The

calculations are outlined in the figure

If the portfolio is worth $50 million, we can express VaR as $50,000,000(0.268) = $13.4 million In other

words there is a 5% chance that the loss will be $13.4 million or worse in a year

To calculate the daily VAR, we can adjust the expected return to its daily average of approximately

0.135/250 = 0.00054 and the standard deviation to its daily value of 0.244 sqrt(250) = 0.01543 This is

based on the assumption of 250 trading days in a year and statistical independence between days With

these numbers the daily VaR is 0.00054 – 1.65(0.01543) = –0.0249 On a dollar basis, the daily VaR is

$50,000,000(0.0249) = $1.245 million

Refer to Example 5 from the curriculum

Historical method:

In this method we calculate the returns for a given portfolio using actual prices from a user-specified

period in recent past The advantage of using this method is that the user does not have to make any

assumptions about the type of probability distributions that generates returns The disadvantage is that

it relies on data from the past and past conditions might not hold in the future

Refer to Example 6 from the curriculum

Refer to Example 7 from the curriculum

Monte Carlo simulation method:

In this method we produce random outcomes according to an assumed probability distribution and a set

of input parameters

For example, consider a $50 million portfolio invested 75% in S&P500 and 25% in NASDAQ The annual

expected return is 13.5% and the standard deviation is 24.4% We use a random number generator to

produce a series of 300 random values The results are shown in Exhibit 9

To obtain the point in the lower tail with a 5 percent significance, we rank order the data and find the

15th-lowest outcome We use the 15th-lowest outcome because there are 300 iterations and 5 percent of

300 = 15 This corresponds to a portfolio value of $34.25 million – a loss of $15.75 million Based on this

information we can say: there is a 5% chance that the loss in one year will be $15.75 million or worse

LO.f: Compare the analytical (variance–covariance), historical, and Monte Carlo methods for

estimating VaR and discuss the advantages and disadvantages of each

The table below compares the three methods

Advantages:

Simple method

Disadvantages:

Relies on simplifying assumptions

such as normality of returns

If returns are not normally

distributed then we cannot rely

totally on standard deviation as a

measure of risk

Consider skewness and kurtosis

Portfolios containing options don’t

have normal distributions

Advantages:

Non-parametric (minimal probability-distribution assumptions)

LO.g: Discuss advantages and limitations of VaR and its extensions, including cash flow at risk,

earnings at risk, and tail value at risk

This LO is covered in sections 5.3 and 5.4

5.3 The Advantages and Limitations of VaR

Quantifies potential loss in simple terms

Most regulatory authorities accept VAR as an

acceptable risk measure

Some companies use VAR as a measure of

capital at risk across different lines of business

One sided Entire focus is on the left tail

Lulls into false sense of security Gives the incorrect impression that risk is properly understood and quantified

Often underestimates magnitude and frequency

of worst returns

Extremely difficult to calculate VAR for large organizations

Key points to remember are:

 No risk measure can precisely predict future losses; VAR is no exception

 Back testing allows you to determine accuracy level of VAR estimates

 Do not use VAR in isolation

 Ensure that inputs to VAR calculation are as reliable as possible and relevant to the current

investment mix

5.4 Extensions and Supplements to VaR

Incremental VAR (IVAR) measures the incremental effect of an asset on the VAR of a portfolio by

measuring the difference between the portfolio's VAR while including a specified asset and the

portfolio's VAR with that asset eliminated

Cash flow at risk (CFAR) is the minimum cash flow loss that we expect to be exceeded with a given

probability over a specified time

Earnings at risk (EAR) is the minimum earnings loss that we expect to be exceeded with a given

probability over a specified time

Tail value at risk (TVAR) is VAR plus the expected loss in excess of VAR when such excess loss occurs

5.5 Stress Testing

LO.h: Compare alternative types of stress testing and discuss advantages and disadvantages of each

Managers use stress testing to supplement VAR as a risk measure VAR quantifies potential losses under

normal market conditions Stress testing seeks to identify unusual circumstances that could lead to

losses in excess of those typically expected

The two broad approaches are: 1) scenario analysis and 2) stress modeling

Scenario analysis is the process of evaluating a portfolio under different states of the world Stylized

scenarios (one type of scenario analysis) involves simulating a movement in at least one interest rate,

exchange rate, stock price, or commodity price relevant to the portfolio

Derivatives Policy Group recommends the following scenarios:

 parallel yield curve shifting by ±100 basis points (1 percentage point);

 yield curve twisting by ±25 basis points;

 each of the four combinations of the above shifts and twists;

 implied volatilities changing by ±20 percent from current levels;

 equity index levels changing by ±10 percent;

 major currencies moving by ±6 percent and other currencies by ±20 percent;

 swap spread changing by ±20 basis points

Another approach to scenario analysis is to use actual extreme events that have occurred in the past

We can also create scenarios based on hypothetical events – i.e events that have never happened but

might happen

Stress modeling: It is difficult to estimate sensitivity of a portfolio to scenarios we design; so another

approach is to use an existing model and apply shocks and perturbations to the model inputs in some

mechanical way

Stressing models can take several forms:

 Factor push: Here we push the prices and risk factors of an underlying model in the most

disadvantageous way to calculate the combined effect on the portfolio’s value

 Maximum loss optimization: Here we try to optimize mathematically the risk variables that will

produce the maximum loss

 Worst case scenario analysis: Here we examine the worst case that we actually expect to occur

5.6 Measuring Credit Risk

LO.i: Evaluate the credit risk of an investment position, including forward contract, swap, and option

positions

Credit losses have two dimensions:

 Likelihood of loss

 Associated amount of loss

In risk management, credit risk exposure should be viewed from two different time perspectives:

 Current credit risk is the risk associated with events in the near future

 Potential credit risk is the risk associated with events at a later date

Cross-default provision: A owes B with a due date in 6 months and also owes C now Say A defaults on

the payment to C If there is credit-default provision then A has technically also defaulted to B

Credit VAR measures credit risk It reflects the minimum loss with a given probability during a period of

time

Option Pricing Theory and Credit Risk

The stock of a company with leverage can be viewed as a call option on assets All upside potential

above the value of debt belongs to the shareholders, if the asset value is less than debt value then

shareholders will receive nothing

Bond with credit risk can be viewed as a default free bond plus an implicit short put option written by

bondholders for the stockholders In other words, the bondholders have implicitly written the

stockholders a put on the assets From the stockholders’ perspective, this put is their right to fully

discharge their liability by turning over the assets to the bondholders, even though those assets could be

worth less than the bondholders’ claim

The Credit Risk of Forward Contracts

This is the risk that the party that owes the larger amount could default

Credit risk exposure is based on the market value which is calculated as:

PV or amount owed – PV of amount to be paid

For example: At T = 0, S = 100, I = 5%,  F = 105

Three months later asset price = 102

We can determine that the long forward contract’s value at that time is $102 – $105/(1.05)0.75 =

$0.7728 This is the value to the long because the contract is a claim on the asset, which is currently

worth $102, and an obligation to pay $105 for it in nine months To the holder of the long position, this

contract is worth $0.7728, and to the holder of the short position, it is worth –$0.7728

The long’s claim is positive; the short’s claim is negative Therefore, the long currently bears the credit

risk

The Credit Risk of Swaps

Swap’s market value is the PV of amounted owed – PV of amount to be paid

For interest rate and equity swaps the potential credit risk is the largest during the middle period of the

swap’s life:

1 Risk is low at the start because both counterparties will have performed sufficient current credit

analysis

2 Risk is low at the end because few payments remain

Currency swaps have greatest credit risk closer to the end of swap’s life This is because the notional

principal needs to be swapped at the end of the currency swap

Credit Risk of Options

Forward contracts and swaps have bilateral default risk This means that either party could face credit

risk Options have unilateral credit risk Only the long party faces credit risk

Refer to Example 8 from the curriculum.

5.7 Liquidity Risk

VAR assumes liquidity; however, some assets are not very liquid

Bid-ask spread relative to price is a measure of liquidity Assets which are traded very infrequently

present a larger problem because they provide a statistical illusion of low volatility

The selling price of illiquid assets might be much lower than expected A famous case of

underestimating liquidity risk is the LTCM failure

5.8 Measuring Nonfinancial Risks

Non-financial risks include the risk of fire, flood, tornadoes, terrorist attacks, and so on These risk are

very difficult to measure Most of these risks are more suitable for insurance

Refer to Example 9 from the curriculum

6 Managing Risk

6.1 Managing Market Risk

LO.j: Demonstrate the use of risk budgeting, position limits, and other methods for managing

market risk

We need to:

 identify sources of market risk

 define how these risks will be measured

 set appropriate risk tolerance levels

 identify corrective action if actual risk is outside tolerance levels

Risk budgeting focuses on where to take risk and how to efficiently allocate risk For example, consider a

bank with an FX unit and a fixed income unit The allocation of capital and risk budget for each unit is

shown below:

 FX desk: allocated capital = 100 mm and permitted daily VAR = 5 mm

 Fixed income desk: allocated capital = 200 mm and permitted daily VAR = 5 mm

 Permitted daily VAR for both desks combined = 9 mm

The FX desk has an allocated capital of 100 mm and a daily VAR limit of 5 mm The fixed income desk

has twice the allocated capital (200 mm) but the same daily VAR limit of 5 mm Clearly in percentage

terms the FX desk is allowed to take more risk This simple example also illustrates how the risk is

budgeted across the two desks

Note that the sum of risk budgets for individual units (5 mm + 5 mm = 10 mm) exceeds the risk budget

for the organization (9 mm) because of the diversification effect

Refer to Example 10 from the curriculum

6.2 Managing Credit Risk

LO.k: Demonstrate the use of exposure limits, marking to market, collateral, netting arrangements,

credit standards, and credit derivatives to manage credit risk

Credit risk is one sided and returns are not symmetric Hence this risk is not easily measured using

standard deviation and VAR

The various methods to reduce credit risk are:

Reducing credit risk by limiting exposure:

 Limiting exposure to a given party is the primary means of managing credit risk

 Banks have regulatory constraints on the amount of credit risk they can assume

Reducing credit risk by marking to market:

 Futures contracts typically require daily mark to market

 The same concept can also be applied in the OTC market

 Refer to Example 11 from the curriculum

Reducing credit risk with collateral:

 Futures markets require that all participants post collateral

 The same concept can be also be applied in OTC market

Reducing credit risk with netting:

 Payment netting reduces amount of money that must be paid

 Hence it reduces credit risk

Reducing credit risk with minimum credit standards and enhanced derivative product companies:

 Enhanced derivatives products companies (EDPCs) are separate from the parent organization

and are not liable for the parent’s debts

 They are also heavily capitalized

 The objective is to obtain good credit quality rating from the rating agencies

 EDPCs often have higher credit ratings than the parent company

Transferring credit risk with credit derivatives:

 Credit derivatives can be used to transfer risk to another party

 Examples include: credit default swap, total return swap, credit spread option, credit spread

forwards

6.3 Performance Evaluation

LO.l: Discuss the Sharpe ratio, risk-adjusted return on capital, return over maximum drawdown, and

the Sortino ratio as measures of risk-adjusted performance

In order to maximize the risk-adjusted return, we must measure performance against risks taken

The following measures can be used:

Sharpe ratio:

𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 =𝑀𝑒𝑎𝑛 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑟𝑒𝑡𝑢𝑟𝑛 − 𝑅𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒

𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑟𝑒𝑡𝑢𝑟𝑛Sharpe ratio is inaccurate when applied to portfolios with significant nonlinear risks such as option

positions

Risk-Adjusted Return on Capital (RAROC):

Here we divide the expected return on an investment by a measure of capital at risk Risk measurement

can be calculated in various ways A company may require that an investment’s expected RAROC exceed

a RAROC benchmark level for capital to be allocated to it

Return over Maximum Drawdown (RoMAD):

Drawdown is the difference between a portfolio’s maximum point of return (known as high water mark)

and any subsequent low point of performance Return over maximum drawdown is simply the average

return in a given year that a portfolio generates, expressed as a percentage of this drawdown figure

Sortino ratio:

Sortino ratio = (Mean portfolio return – MAR)/Downside deviation

Unlike Sharpe ratio, Sortino ratio only measures downside deviation below the minimum acceptable

rate (MAR) Thus it does not penalize portfolio managers for volatility due to extreme positive

performance

6.4 Capital Allocation

LO.m: Demonstrate the use of VaR and stress testing in setting capital requirements

Risk management is an important component in the process of allocating capital across units of a risk

taking enterprise Different capital allocation methods are shown in the table below:

Nominal, Notional or

Monetary Position Limits

Enterprise defines capital for each business unit

Simple and allows us to calculate percentage return on capital allocated

Does not capture effects of correlation and offsetting risks

Individual may be able to work around limits

VAR-Based Position Limits Use VAR limit as alternative or supplement to notional limit

Limit regime only as effective as VAR calculation

Relation between overall VAR and individual VARs is complex

Maximum Loss Limits Establish maximum loss limit for each risk-taking unit

Internal Capital

Requirements

Specify level of capital that will be appropriate for the firm

Example: Enough capital such that probability of insolvency over 1-year

6.5 Psychological and Behavioral Considerations

From a risk management perspective it is important to establish a risk governance framework when the

incentives of risk takers diverge from those of risk capital allocators

For example, when portfolio managers who are paid a percentage of profits in a given year fall in a

negative performance situation any incremental loss will not affect the manager’s compensation;

however, the organization will suffer from incremental losses In such situations a portfolio manager will

have an incentive to take a high level of risk to increase profits This high level of risk might not be

appropriate for clients who are the providers of capital

Summary

a discuss features of the risk management process, risk governance, risk reduction, and an enterprise

risk management system;

Risk management process: Includes:

 Recognising exposures to risk

 Creating appropriate ranges for exposures

 Constantly measuring these exposures

Risk governance (subset of corporate governance): process of setting overall policies and standards in

risk management

b evaluate strengths and weaknesses of a company’s risk management process;

The two types of risk governance models are:

 Decentralized: Each unit calculates and reports its risk exposures independently; allows people who

understand risk better to directly manage it

 Centralized: Risk management is moved closer to senior management The main advantage is that it

allows offsetting of risks across units Centralized risk management is now called enterprise risk

management (ERM)

c describe steps in an effective enterprise risk management system;

An effective ERM system usually includes the following steps:

1 Identify each risk factor to which the company is exposed

2 Quantify each exposure’s size in money terms