CFA level 3 CFA level 3 CFA level 3 CFA level 3 CFA level 3 finquiz curriculum note, study session 14, reading 27

Risk Management

1.

INTRODUCTION

managing risk i.e. reducing, increasing, avoiding risk
exposures etc.

Risk management is considered to be a critical
component of the investment process. Risk
management is not only hedging risk rather, it involves
2.

RISK MANAGEMENT AS A PROCESS

Risk management is a continuous process that involves:
1. Proper identification of risks (i.e. all callable bonds
have call risk).
2. Identification of the firm’s desired level of risk i.e.
determining risk tolerance.
3. Measurement of risks (i.e. how to measure risk e.g.
duration to measure interest rate risk, beta to measure
risk of stocks).
4. Monitoring and adjusting the exposures to align
actual risk exposures with desired target levels.

3.

Risk governance structure can be centralized or
decentralized.

1) Centralized risk management system: In this system,
the responsibility of risk management is put at the senior
management level where it is supposed to belong. It is
also known as Enterprise Risk Management (ERM).

• Allows economies of scale.
• Allows firm to recognize offsetting nature of
different risk exposures.
• It considers risk exposures both in isolation and at
portfolio level.
• In centralized system, risk management
responsibility is on a level closer to senior
management who are actually responsible for
managing it.
• It provides an overall picture of the company’s risk
position.

NOTE:
• Some risks are preferred to be taken on a regular
basis, some should be taken occasionally and
some should be avoided altogether.
• The execution of transactions for managing risk is
also a distinct process e.g. for portfolios, it involves
trade identification, pricing and execution.

RISK GOVERNANCE

Risk governance is a process of setting risk management
policies and standards for an organization. The risk
management process should be overseen by the senior

management who is responsible for all organizational
activities. The quality of risk governance is determined by
its transparency, accountability, effectiveness
(achieving objectives), and efficiency (economical use
of resources to achieve objectives). Risk governance is
an important part of corporate governance.

Advantages:

Risk should be taken in those areas in which business has
expertise and competitive advantage (in order to earn
profits).

NOTE:
It is important to note that due to less than perfect
correlation between risk exposures, overall risk is less than
the individual risks.
2) Decentralized system: In this system, risk
management responsibility is placed on individual
business unit managers. Each unit calculates and reports
its exposures independently.
Advantage:
It allows people closer to the actual risk taking to directly
manage it.
Disadvantage:
It does not take into account portfolio effects across
different units.
Enterprise Risk Management (ERM):
It is a centralized risk management system in which there
is a firm-wide perspective on risk. Effective ERM system

typically incorporates the following steps:
1.
2.
3.
4.

Identify risk exposures of the company.
Quantify each exposure in money terms.
Estimate risks.
Identify overall risk exposures of the firm as well as the
contribution of each risk factor to overall risk.
5. Report risks periodically to senior management by
establishing a proper process and determine capital
allocation, risk limits and risk management policies.
6. Monitor compliance with policies and risk limits.

–––––––––––––––––––––––––––––––––––––– Copyright © FinQuiz.com. All rights reserved. ––––––––––––––––––––––––––––––––––––––

FinQuiz Notes 2 0 1 8

Reading 27


Reading 27

Risk Management

Benefits of Enterprise-wide Risk Management (ERM):
1) It facilitates to put all firm’s risk on a comparable basis.
2) It allows managing risk in diversified and global firms.

3) It promotes discipline of collecting, storing and
analyzing all positions both individually and at firmwide level.
4) It helps in detecting fraud.
5) It provides risk information to stakeholders.
6) It facilitates firms to be more flexible as decisions are
based on risk-return trade-off.
Main characteristics of an ERM system:
• Centralized data warehouse: It collects and stores
data in a technologically efficient manner from all
business units.
• Risk analysis i.e. market risk (using parametric,
historical, Monte Carlo), stress testing, credit risk,
4.

1. Financial Risks:
Risks that are derived from events in the external
financial markets.
They include:
i. Market risks are associated with adverse movements
in firm or portfolio values. These risks are linked to supply
and demand in various marketplaces. It includes:
a) Interest rate risk
b) Exchange rate risk
c) Equity price risk
d) Commodity price risk
ii. Credit risk: It is the risk of loss that arises when a
counterparty or debtor fails to perform or meet the
obligation on the agreed terms. OTC derivatives (unlike
Exchange traded), are subject to credit risk as they
contain no explicit credit guarantee.

• This risk arises in both initiating and liquidating
transactions for both long and short positions but is
particularly serious for liquidating transactions
when there is a need to reduce exposure to avoid
large losses.
• Liquidity risk is a serious problem and often is
difficult to observe and quantify.
• Short squeezes: i.e. start to buy in panic and price
keeps on rising; thus increasing losses.

liquidity risk
• Monitoring and evaluation.
• Decision making i.e. reporting risk information to
stakeholders and adjusting risks to a desired level.
Some risk governance concern of investment firms:
• The risk manager is responsible for monitoring risk
levels for all portfolio positions and portfolio as a
whole and controlling the level of risk.
• It is generally recommended that risk manager
should work together with the trading desks in the
development of risk management specifications.
• For an effective risk governance system, the back
office of an investment firm must be fully
independent from the front office.

IDENTIFYING RISKS

Following are the categories of risks:

iii. Liquidity risk: It is the risk that arises when a financial
instrument cannot be purchased or sold without a
significant price impact i.e. unwinding a position may
become costly or impossible.

FinQuiz.com

Derivatives do not help in managing liquidity risk
because: They are usually no more liquid than the
underlying.
Indicators of liquidity:
a) Size of Bid-ask spread is used as an indicator of
liquidity for traded securities i.e. the bid-ask spread
widens when markets are illiquid. However, bid-ask
quotations can be applied when trades are of small size.
b) Illiquidity ratio: It measures the price impact per $1
million traded in a day, expressed in % terms.
c) Transaction volume i.e. the greater the average
transaction volume, the more liquid the instrument.
However, there is no certainty that historical volume
patterns will repeat themselves.
NOTE:
Funding risk refers to a risk associated with the availability
of cash.
2. Non-financial risks:
It includes
i. Operational risk: It is the risk of loss that arises from
failures in the company’s operating systems and
procedures or from external events due to technological
factors, human errors, natural disasters etc.

• These risks can be managed by using insurance
contracts (which involves a transfer of risk)
because these risks do not have a developed
derivative market.
• Most companies manage operational risks by
monitoring their systems, taking preventive actions,
and having a plan in place to swiftly respond if
any adverse event occurs.


Reading 27

Risk Management

ii. Model risk: It is the risk that arises due to the use of
incorrect valuation model or misapplication of the
model.
iii. Settlement risk (or Herstatt risk):It is the risk that arises
when a counterparty defaults in its obligation while the
other counterparty is paying. These payments can be
associated with the purchase and sale of cash securities
i.e. equities and bonds along with cash transfers
executed for swaps, forwards, options and other types of
derivatives.
• Exchange traded transactions (unlike OTC) do not
have settlement risk because all transaction take
place between an exchange member and the
central counterparty (clearing house).
• Two-way payments involve settlement risk
because one party could owe payment to its

counterparty while that counterparty declares
bankruptcy and fails to make its payments.
• Netting arrangements can be used to reduce
settlement risk.
iv. Regulatory risk: It is the risk associated with the
uncertainty of how a transaction will be regulated and
with the potential for regulations to change.
• Regulated markets face the risk that the existing
regulatory regime may become harder, more
restrictive or more costly.
• Unregulated markets face the risk of being
regulated which results in costs and restrictions.
• Regulatory risk is difficult to estimate.
• Equities, bonds, futures and exchange traded
derivatives markets usually are regulated at the
federal level, whereas OTC derivative markets and
transactions in alternative investments are loosely
regulated.
• Regulatory risk and the degree of regulation vary
widely from country to country.
• Regulatory risk is affected by the priorities of
politicians and regulators.
• Derivatives may be regulated indirectly when they
are used by regulated companies.
v. Legal/contract risk: It refers to risk of loss arising that
arises when the legal system fails to enforce a contract
in which a firm has a financial stake.
vi. Tax risk: Tax risk arises because of the uncertainty
associated with tax laws i.e. impact of level and type of
taxation.

• E.g. transactions exempt from taxation could later
be found to be taxable.
• Equivalent combinations of financial instruments
do not have identical tax treatment.
• Like regulatory risk, tax risk is affected by the
priorities of politicians and regulators.
vii. Accounting risk: It arises from uncertainty associated
with recording and accounting rules regarding

FinQuiz.com

transactions and risk of changes in these accounting
rules and regulations.
• Accounting standards vary from country to
country.
• Companies have to deal with trade-off between
protecting proprietary information from
competitors and adequately informing investors
and the public.
3. Sovereign/political risk:
Sovereign risk is a form of credit risk in which the
borrower/debtor is the government of a sovereign
nation.
• It involves current and a potential credit risk.
• Its magnitude has two components: Likelihood of
default and the estimated recovery rate.
• It is relatively difficult to evaluate sovereign risk.
• Risk evaluation involves evaluating debtor nation’s
asset/liability/cash flow, willingness, alternative
means of financing etc.

Political risk: It is the risk associated with changes in the
political environment i.e. change in political regime or
the potential impact of a change in party control in a
developed nation.

Practice: Example 2,
Volume 5, Reading 27.

4.12

Other Risks

1) ESG Risk: It is the risk caused by environmental, social
and governance factors.
• Environmental factors: Environmental factors
include decisions related to products & services i.e.
process of production etc.
• Social factors: Social factors are related to
company’s policies, practices regarding human
resources, contractual arrangements and the
workplace. Risks include labor strikes etc.
• Governance factors: These factors include
corporate governance policies and procedures.
2) Performance netting risk: This risk arises when firm’s
incentive is based on net performance whereas there
are asymmetric incentive fee arrangements with the
portfolio managers. This risk occurs only in multi-strategy,
multimanager environments.
Example:
• Manager A generated positive $10 million returns

while manager B generated $10 million loss.
• Firm’s net performance = 10 – 10 = 0.


Reading 27

Risk Management

Solution: This risk can be managed by establishing
absolute negative performance thresholds for individual
accounts.

• Thus, firm does not get any incentive fee from the
client.
• However, firm is required to pay manager A his
incentive fee.

5.

5.1

FinQuiz.com

3) Settlement Netting risk: It refers to risk that arises when
there are no “netting arrangements” i.e. contract is
based on “two-way payments”.
MEASURING RISK

Measuring Market Risk

• Volatility (represented by sigma σ) is measured by
S.D.
• Volatility is preferred to describe portfolio risk for
portfolios that contain instruments with linear
payoffs.
• Relative volatility: The volatility of the deviation of a
portfolio’s returns from benchmark portfolio returns
is known as active risk, tracking risk, tracking error
volatility or tracking error.

how interest rate sensitivity changes with changes
in interest rates.
• Gamma measures the delta’s sensitivity to a
change in the underlying’s value.

Market risk has two dimensions:
1. Primary or first-order measures of risk:
Sensitivity of the assets to the factor (e.g. duration).
These measures reflect the expected change in price of
a financial instrument for a unit change in the value of
another instrument.
Examples:
• Beta measures sensitivity to market movements
and is a linear risk measure.
• Duration for bonds
• Delta for options (measures option’s sensitivity to a
small change in the value of its underlying).
• Volatility (Vega) measures the change in the price
of an option for a change in underlying’s volatility.
o Options are very sensitive to a change in

volatility due to their non-linear pay-off structure.
o Swaps, futures and forwards are much less
sensitive to changes in volatility because they
have linear pay-offs.
o Certain options may have risk associated with
correlation.
• Time to expiration (theta) measures the change in
the price of an option for a change in time to
expiration (i.e. 1 day reduction in its time to
expiration). Both theta and Vega are exclusively
associated with options.

5.2

Value at Risk

Value at Risk (VAR): is the minimum loss that would be
exceeded with a specified probability in a specified
period. Equivalently, it is the maximum loss that will not
be exceeded with a specified confidence (1 –
probability) in a specified period.
Characteristics:
• VAR is considered as the financial service industry’s
premier risk management technique.
• It is expressed in currency (e.g. dollar terms) or in
percentage terms.
• VAR can be used as a standalone risk measure or
can be applied to a portfolio of assets.
• VAR represents a dollar value risk measure i.e.
translates the volatility in portfolio value in dollar

value unlike other measurements of risk i.e. beta
and standard deviation.
• VAR measures Total Risk whereas beta measures
Systematic (or Non-Diversifiable Risk).
• It is easily used to measure the loss from Market risk,
but it involves complexity in measuring the loss
from credit risk and other types of exposures.

2. Secondary or second-order measures of risk:
Change in the sensitivity to its respective factor
(sensitivity) e.g. convexity.
Examples:
• Convexity for fixed-income portfolios measures

Example:
A one day VAR of $10mn using a probability of 5%
means that there is a 5% chance that the portfolio could
lose more than $10mn in the next trading day.


Reading 27

Risk Management

FinQuiz.com

To estimate Daily VAR, expected returns and S.D are
adjusted as follows:
Daily E(R) = Annual E(R) / 250
Daily S.D = Annual S.D. / √250

Similarly, other conversions include:
Monthly E(R) = Annual E(R) / 12
Monthly S.D = Annual S.D. / √12
Daily E(R) = Monthly E(R) / 22
Daily S.D = Monthly S.D. / √22

Three implications of this definition:
1. VAR measures minimum loss only i.e. the actual loss
can be much greater than the specified amount.
2. VAR is associated with a given probability i.e. 5%, 1%
etc. The lower the probability, the greater will be VAR
in magnitude.
3. VAR is based on specified time period; thus it cannot
be compared directly for different time intervals.
Generally, the longer the period, the greater is the
potential loss. But mostly, longer time periods increase
VAR in a non-linear fashion.
NOTE:
The objective of estimating VAR is to identify the
probability distribution characteristics of portfolio returns.
5.2.1) Elements of Measuring Value at Risk
Three important decisions regarding VAR calculations:
1. Selection of an appropriate probability: typically 5%
or 1% is used.
• 1% is more conservative approach because it
results in higher VAR.
• Different probabilities provide identical information
for portfolios with linear risk characteristics.
• No rule exists for selection of probability.
2. Selection of an appropriate time period to match

turnover or reporting period: e.g.
• Derivative dealers use one day
• Banks use two weeks
• Industrial firms use quarterly or annually
o The longer the period, the greater the VAR in
magnitude.
3. Selection of an appropriate modeling technique i.e.
analytical, historical method, Monte Carlo simulation
technique.
Three Methods to Measure VAR
5.2.2) Analytical or variance-covariance method
(Delta Normal Method)
It assumes normally distributed portfolios. The key to using
the analytical method is to estimate the portfolio’s
expected return and S.D of returns.
VAR = E(R) – z-value (S.D)

Advantages:
•
•
•
•

It is easy to calculate.
It is easy to understand.
It allows to model the correlation of risks.
It can be applied to any time period according to
industry custom.

Disadvantages:

• It assumes normal distribution. Portfolios that
contain options are not normally distributed. In
addition, real life returns often exhibit leptokurtosis.
Therefore, it tends to give poor results for portfolios
with non-normal return distributions.
• It leads to understatement of actual magnitude
and frequency of large losses for portfolios with
excess kurtosis (fat tails).
• It is difficult to estimate correlation between
individual assets in large portfolios.
Implications of Using of Zero expected value in VAR
estimation:
• It leads to greater VAR because expected returns
are typically positive for longer time horizons.
• It represents a more conservative approach as it
leads to higher VAR.
• It avoids the problem to estimate expected return
since E(R) = 0.
• It makes easier to adjust VAR for a different time
period i.e. short term VAR cannot be converted to
long term VAR (or vice versa) * when average
return is not zero.
*Conversion:
Annual VAR = Daily VAR×√250
Delta-Normal Method: The problem associated with nonnormal distribution e.g. in options can be solved by using
option’s delta (delta = ∆ in option price / ∆ in
underlying’s price).
• We know that normally distributed random
variable remains normally distributed when they
are multiplied by a constant (i.e. delta is constant

here).
∆ in option price = ∆ in underlying price × delta.


Reading 27

Risk Management

• This trick converts the non-normal distribution of
option return into a normal distribution.
• However, delta is appropriate to use only for small
changes in the underlying. But when second-order
effects (i.e. gamma) are used to improve results,
the relationship between the option price and the
underlying price begins to approximate the true
non-linear relationship. This further creates problem
in using normal distribution assumption.

Practice: Example 5,
Volume 5, Reading 27.

5.2.3) Historical Method or Historical Simulation Method
This method uses actual historical returns from a userspecified period in the recent past i.e. plotting these
returns using a histogram or ranking these returns in
descending order e.g. if there are 100 observations of
returns, 5% of 100 is 5. Thus, VAR at 5% probability will be
5th worst return. Note that if nth return is not a discrete
number then average is taken.
Key assumption: Future returns will be the same as actual
returns over some historical period.

Example:
Total returns = 248. To calculate 5% VAR:
5% × 248 = 12 returns→ thus, VAR would be the 12th worst
return in the observations. Assume that after rankordering the data, the 12th worst return is -0.0294. If total
value of portfolio is $50 million, then one-day VAR would
thus be 0.0294 × $50,000,000 = $1.47 million.

FinQuiz.com

Example:
A 5 year duration bonds, after 1 year, will be of 4 year
maturity. Using historical simulation requires using a 4year duration bond (probably held by someone else).
NOTE:
Total VAR is not simply the sum of individual VARs
because risks of individual positions are less than
perfectly correlated. This is known as diversification
effect. It is equal to:
Sum of individual VARs – Total VAR

Practice: Example 6,
Volume 5, Reading 27.

5.2.4) Monte Carlo Simulation Method
It generates random outcomes according to assumed
probability distribution and a set of input parameters. It
examines outcomes given a particular set of risks. In this
method:
• Random portfolio returns are generated.
• These returns are assembled into a summary
distribution

• From this distribution, it is determined that at which
level the lower 5% (or 1%) of return outcomes
occur.
• This value is then applied to portfolio value to
obtain VAR.
Key assumption: common risk factors affect asset
returns.

Advantages:
• It is a non-parametric approach i.e. it does not
involve any assumption regarding probability
distribution.
• It is easy to calculate and easy to understand.
• It can be applied to any time period according to
industry custom.

Important to note: Both Monte Carlo and analytical
methods provide identical results when sample size is
large i.e. sample VAR converges to the true population
VAR when sample size increases.
Advantage:
It does not require normal distribution assumption i.e. any
distribution can be used.

Disadvantages:
Disadvantage:
• It is based on historical data, which may not hold
in the future. This problem is also included in other
two approaches.
• Characteristics of bonds and derivatives change

over time; therefore, it is inappropriate to base
results on historical data.
Historical simulation: In this approach, current weights
are applied to a time-series of historical returns. In this
method, the history of a hypothetical portfolio using the
current position is reconstructed.

It involves making a large number of assumptions
regarding inputs of the return distributions and their
correlations.
5.2.5) “Surplus at Risk”: VAR as It Applies to Pension Fund
Portfolios
• Pension fund managers seek to enhance and
protect the value of the fund surplus (plan assets –
plan liabilities).
• Pension fund managers apply VAR methodologies
to the surplus by:
o Treating the liability portfolio as a short position


Reading 27

Risk Management

and
o Calculating VAR on the net position
• All three VAR methodologies can be used by
pension fund managers.
5.3

The Advantages and Limitations of VAR

Advantages of VAR:
1) It measures total risk.
2) It quantifies the potential losses in simple and easy to
understand terms.
3) It is easily understood by senior management.
4) It is a versatile measure of risk because it can be used
to compare performance of different units with
different risk characteristics.
5) It can be used to allocate capital at risk.
Disadvantages of VAR:
1) VAR is difficult to estimate.
2) VAR ignores information given in the tails of loss
distribution i.e. it does not tell the extent to which loss
can exceed.
3) The VAR estimate is sensitive to the assumptions made
and to the method used. Thus, different estimation
methods produce different values.
4) It gives a false sense of security that risk is measured
and controlled properly.
5) When wrong assumptions and models are employed,
it may understate the magnitude and frequency of
losses.
6) VAR is difficult to apply in complex organizations.
7) Portfolio VAR is not equal to sum of VAR from
individual positions.
8) It does not take into account the positive results into
its risk profile; thus, it provides an incomplete picture of
the overall exposures.

9) VAR has an inherent limitation that distribution of past
changes in market risk factors cannot provide
accurate predictions of future market risk.
Back-Testing: Back testing refers to tests performed to
evaluate whether VAR estimates prove accurate in
predicting results.

FinQuiz.com

Similarly, for the recent quarter, it is expected to exceed
= 0.05 × 60 = 3 days
For recent month, it will be = 0.05 × 20 = 1 day
5.4

Extensions and Supplements to VAR

Incremental VAR: It is used to measure the incremental
effect of an asset on portfolio VAR. it incorporates the
effects of correlation of an asset with the portfolio. It is
measured as follows:
Incremental VAR=Portfolio’s VAR including a specified
asset – Portfolio’s VAR excluding that asset.
Cash Flow at Risk (CFAR): It represents minimum cash
flow loss that is expected to be exceeded with a given
probability over a specified time period.
Earnings at Risk (EAR): It represents minimum earnings
loss that is expected to be exceeded with a given
probability over a specified time period.
• CFAR and EAR are used for companies that
generate cash flows or profits/earnings but are not

readily valued publicly.
Tail Value at Risk (TVAR) or Conditional Tail Expectation =
VAR + expected loss in excess of VAR when such excess
loss occurs.
5.5

Stress Testing

• VAR objective is to quantify potential losses under
normal market conditions.
• Stress testing is used to analyze nonnormal/unusual conditions that could result in
higher than expected losses. It involves the
following two approaches:
5.5.1) Scenario Analysis
It is used to analyze portfolio under different scenarios.
1. Stylized Scenarios:

• If the VAR is systematically “too low”, the model is
underestimating the risk and there will be too
many occasions where the loss in the portfolio
exceeds the VAR.
• If the VAR is systematically “too high”, the model is
over estimating the risk and there will be frequent
changes in regulatory capital.
Example:
Daily VAR at 5% is $1 million; then over 1 year, a loss of at
least $1 million is expected to exceed approximately
0.05 × 250 = 12.5 days. If the results are quite different
from that the model predicts, then the model is
inappropriate and needs to be adjusted.

It involves simulating a change in at least one factor i.e.
interest rate, exchange rate, stock price or commodity
price relevant to the portfolio. There are industry
standards of stylized scenarios as well.
Limitation:
In stylized method, shocks are applied in a sequential
fashion; it does not take into account their simultaneous
effects.
2. Actual Extreme Events:
The analyst measures the impact of actual past extreme
events on portfolio value.


Reading 27

Risk Management

Advantage:

FinQuiz.com

5.6

Measuring Credit Risk

It is useful to use when higher probability of extreme
event is expected relative to the probability given by
valuation models or historical time period.

Credit Risk: It is the risk associated with failure of
counterparties to meet their obligations.

3. Hypothetical Events:

There are two dimensions of credit risk:

The analyst measures impact of events that never
happened in the past or were assigned small probability
in the past but can be expected to occur in future.

1. Probability of default:

Limitations of Scenario Analysis:
• Only provides information that loss will result in a
given scenario but does not provide the
probability of occurrence of that scenario.
• Different estimation methods produce different
values.
• It is difficult to identify the sensitivity of a portfolio’s
instruments to the designed scenarios.
• It requires analyst to have good skill and expertise.
Scenario analysis complements VAR because: VAR tells
the minimum loss with a specified probability (assuming
normal market conditions) but does not provide
information regarding unusual events and underlying
factors that would result in actual losses in excess of
specific amount.
5.5.2) Stressing Models
This involves examining how well a portfolio performs

under some of the most extreme market moves.
• It involves analyzing a range of possibilities rather
than a single set of scenarios.
• It is computationally more difficult to perform.
1. Factor Push:
It involves pushing the prices and risk factors of an
underlying model in the most unfavorable way (that
indicates extreme risk climate) and analyzing their
combined effect on portfolio’s value.
• It is used as a complement to VAR because it gives
actual loss in scenarios for which probability
estimation is difficult.
• Limitation: It involves higher model risk.
2. Maximum Loss Optimization:
It involves mathematically optimizing the risk
variable/factor that will result in maximum loss to the
portfolio’s value.
3. Worst case scenario analysis:
It involves analyzing the impact of worst cases on
portfolio’s value.
Stress tests are used to supplement VAR because VAR
does not measure "event" (e.g., market crash) risk.

It refers to the probability that counterparty will default
on its obligation. It is present within every credit-based
transaction.
2. Amount of loss:
It is expressed in terms of recovery rate i.e. fraction of
total amount that is owed.
It is difficult to estimate credit risk compared to market

risk because:
• Default events are infrequent.
• There is lack of market data regarding such
events.
• The inability to determine the correlation between
different credit events.
There are two different time perspectives in credit risk:
1. Jump-to-default/ current credit risk:
It is the risk associated with immediate/current credit
events i.e. risk of not receiving payment that is currently
due.
2. Potential Credit Risk:
It is the risk associated with events that may occur in
future i.e. risk of not receiving future payment.
Cross-default Provision: It refers to a provision according
to which if a borrower defaults on any outstanding credit
obligations, the borrower ultimately defaults on all of
them.
Credit VAR: Credit VAR refers to maximum loss that is
expected to occur over a specified period with
specified confidence level e.g. amount of credit loss
that will not be exceeded in one year with 99% certainty.
• In credit VAR the main focus is the upper tail unlike
market VAR where focus is on the lower tail. Credit
VAR cannot be separated from market VAR due
to the fact that credit risk results from gains on
market positions held.
5.6.1) Option Pricing Theory and Credit Risk
According to this theory, credit risk can be explained as
follows:

A bond with credit risk can be viewed as: Default-free
bond + implicit short put option


Reading 27

Risk Management

• A put option is written explicitly by the bondholders
to the shareholders.
• This put option gives shareholders the right to fully
discharge their liability by giving assets to
bondholders despite the fact that those assets
could be of less value relative to claim of
bondholders.
5.6.2) Credit Risk of Forward Contracts:
Credit risk is faced by each party until contract is settled
i.e. forward contract has no current credit risk.
Market value of forward contract at a given time reflects
the potential credit risk.
Market value indicates the amount of a claim that
would be subject to loss when credit default occurs.
Value Long = Spot t – [Forward / (1 + r) n]
When counterparty declares bankruptcy before
contract expiration, then market value of a forward
contract at the time of bankruptcy (if positive)
represents the claim of non-defaulting counterparty.
5.6.3) Credit Risk of Swaps
A swap is equivalent to a series of forward contracts.

FinQuiz.com

5.6.4) Credit Risk of Options:
Forward and swap contracts have bilateral credit risks.
Options have unilateral risks i.e. the buyer of the option
pays a cash premium at the initiation and owes nothing
to the seller of the option unless he decides to exercise
the option.
Options do not have current credit risk until expiration
like forward contracts.
American options have greater value because option
holder has the right to exercise the option early.
Market price of option represents the amount at risk.
When seller of an option defaults before option
expiration, value of an option represents claim of option
buyer.
Value of the side held by the firm determines the
treatment of derivative contract in bankruptcy:
• When value to firm is negative, it is the creditor’s
claim.
• When value to firm is positive, it is an asset of the
firm.

At each periodic payment, current credit risk exists.
Market value of swaps at a given time reflects the
potential credit risk.
In interest rate swaps and equity swaps, potential credit
risk is largest during the middle period of the swap’s
contract maturity period.
In currency swaps, potential credit risk is largest during

the middle period and at the end of the life of the swap
due to exchange of notional amount at the termination.
Swap ValueLong = PV inflows – PV outflows
ࡲ࢕࢘࢝ࢇ࢘ࢊࢉ࢕࢔࢚࢘ࢇࢉ࢚࢜ࢇ࢒࢛ࢋࡸ࢕࢔ࢍୀ ቎
െ

ܵ‫݁ݐܴܽݐ݋݌‬

൫1 ൅ ܴ‫ܴܨ‬ி௢௥௘௜௚௡ ൯

‫݁ݐܴܽ݀ݎܽݓݎ݋ܨ‬

ሺ1 ൅ ܴ‫ܴܨ‬஽௢௠௘௦௧௜௖ ሻ

ೃ೐೘ೌ೔೙೔೙೒೟೔೘೐
೅೚೟ೌ೗೟೔೘೐

ೃ೐೘ೌ೔೙೔೙೒೟೔೘೐
೅೚೟ೌ೗೟೔೘೐

቏ ൈ ܰܲ

When a party to which value is negative defaults → that
value represents claim of counterparty.
When a party to which value is positive defaults → asset
with positive market value is held by the defaulting party.
When counterparty defaults before a payment on swap
is due, the claim of creditor will be either the market
value at that time or the asset held by bankruptcy party
in bankruptcy proceedings.

Practice: Example 8,
Volume 5, Reading 27.

Derivatives credit risk v/s Loans credit risk: Credit risk of
derivatives is smaller relative to credit risk of loans
because:
• Unlike loans, derivatives e.g. forwards, swaps have
netting arrangements.
• Unlike loans, most of the derivative contracts do
not involve exchange of notional principal.
• Currency swaps involve exchange of notional
amount; however, in case of default of
counterparty, the amount owed to the defaulting
party can serve as collateral.
5.7

Liquidity Risk

Liquidity adjusted VAR can be estimated to incorporate
liquidity risk.
5.8

Measuring Nonfinancial Risks

Non-financial risks are difficult to estimate. Therefore,
these risks are managed by using insurance rather than
measuring and hedging them.

Reading 27

Risk Management

6.

FinQuiz.com

MANAGING RISK

The key components of managing risk include:
1. Effective risk governance model i.e. Policies which
• Determine overall responsibility of senior
management
• Effectively allocate resources among units
• Separate revenue generation activities from
controlling side of the business.
2. Appropriate systems and technologies i.e.
Methodologies used to implement policies.
3. Sufficient and suitably trained personnel to evaluate
risk information and distribute this information to those
responsible for proper decision making.

NOTE:
• Return on capital = Profit ($) / Capital ($)
• Return on VAR = Profit ($) / VAR ($) → higher return
on VAR indicates that manager has outperformed
on a risk-adjusted basis.
For Details refer to Reading 27, Curriculum, Volume 5.

Practice: Example 10,
Volume 5, Reading 27.

6.2

Managing Credit Risk

Principles of Effective Risk Management:
1) Return cannot be generated without taking risks.
2) Transparency i.e. risk should be fully understood.
3) Risk should be measured and managed by
experienced people instead of mathematical
models.
4) Assumptions used in the valuation models should be
critically analyzed.
5) Proper communication of risks i.e. risks should be
discussed openly.
6) Risk should be diversified to obtain consistent returns.
7) A disciplined approach should be followed i.e. should
not take extreme positions.
8) It is preferred to use common sense and be
approximately right instead of precisely wrong.
9) Investment decisions should be based on risk-return
trade-off.
6.1.1) Risk Budgeting
Risk budgeting refers to allocating risk among units,
divisions, portfolio managers or individuals in an efficient
manner.
• Risk capital is allocated by the firm before the fact
in order to provide guidance to the units, divisions

etc. on the acceptable level of risk that a given
unit/division can undertake.
• Generally, total sum of risk capital allocated to
individual units is greater than the risk budget of
the firm as a whole because of the impact of
diversification.
• Risk budgeting is used to allocate funds to portfolio
managers according to their Information ratios
(IRs).
Note: It is recommended to use correlationadjusted IR (to evaluate manager’s ability to add
value) to eliminate the effect of asset class
correlations.

Ways to manage Credit Risk:
6.2.1) Reducing Credit Risk by Limiting Exposure
Credit risk can be reduced/managed by limiting
exposure to a single party e.g. single broker.
6.2.2) Reducing Credit Risk by Marking to Market
It involves recalculating forward or swap price after
party to which value is negative pays out the party to
which value is positive. It is important to note that option
contracts are not marked to market because in options
value is always positive to one party of the contract.
Option credit risk is managed by using collateral.
6.2.3) Reducing Credit Risk with Collateral
Credit risk can be reduced by requiring parties to a
contract to post collateral.
6.2.4) Reducing Credit Risk with Netting
By using netting arrangements credit risk can be
reduced as it results in lower amount of money that must

be paid. It is useful in reducing credit risk in the following
cases:
• Payment netting
• Close out netting: It refers to a situation when after
netting, defaulting party ultimately has a claim on
non-defaulting party (i.e. in spite of being
bankrupt, party has claim on other party). This
scenario assumes that the non-defaulting party
owes the defaulting party a greater amount.
• Cherry picking: It refers to a practice when
bankrupt party attempts to enforce favorable
contracts while neglects non-profitable contracts.
It is important to note that netting arrangements are
effective only when they are recognized by the legal
system


Reading 27

Risk Management

6.2.5) Reducing Credit Risk with Minimum Credit
Standards and Enhanced Derivative Product
Companies:
It involves setting minimum credit standards and
undertaking business with SPVs to reduce credit risk.
• EDPCs are highly capitalized and are willing to
hedge their own derivative positions.
• EDPCs have higher credit rating relative to parent
because EDPCs are not liable for the parent

company’s debts.

2. Sortino Ratio:
It uses minimum acceptable return as threshold and
downside deviation as a measure of risk.
Sortino Ratio =

୑ୣୟ୬୮୭୰୲୤୭୪୧୭୰ୣ୲୳୰୬ି୑୧୬୧୫୳୫ୟୡୡୣ୮୲ୟୠ୪ୣ୰ୣ୲୳୰୬ሺ୑୅ୖሻ
ୈ୭୵୬ୱ୧ୢୣୢୣ୴୧ୟ୲୧୭୬

Limitation:
It assumes normal distribution of returns and provides
inaccurate results if this assumption is violated.
• Both Sortino and Sharpe ratios are useful and give
detailed idea of risk-adjusted return when used
together instead of in isolation.
• The higher the Sortino ratio, the more attractive
the investment will be.

6.2.6) Transferring Credit Risk with Credit Derivatives:
Credit risk can be transferred by using credit derivatives
i.e. CDS, total return swap, credit spread options, credit
spread forwards etc. Credit derivatives can be used to
eliminate or assume credit risk.

FinQuiz.com

3.

Risk Adjusted Return on Capital (RAROC):

It is stated as:

Total return Swap:
• Asset owner pays seller total return on reference
asset.
• Seller pays asset owner floating rate i.e. LIBOR +
spread.
• In these types of transactions, seller (dealer) bears
both credit risk and interest rate risk.
NOTE:
Credit risk is one-sided risk.

RAROC =

୉୶୮ୣୡ୲ୣୢ୰ୣ୲୳୰୬୭୬ୟ୬୧୬୴ୣୱ୲୫ୣ୬୲
ୡୟ୮୧୲ୟ୪ୟ୲୰୧ୱ୩

where,
Capital at risk is the capital required for credit risk,
market risk or operational risk.
• The higher the RAROC, the more attractive the
investment will be.
• RAROC is compared against historical RAROC,
expected RAROC or benchmark RAROC.
4. Return over Maximum Drawdown (RoMAD):

Practice: Example 11,
Volume 5, Reading 27.

It is stated as:
RoMAD =

6.3

Performance Evaluation

Performance Measures:
1. Sharpe Ratio:
It uses risk-free rate as the minimum return threshold and
S.D as a measure of risk.
Sharpe Ratio =

୑ୣୟ୬୮୭୰୲୤୭୪୧୭୰ୣ୲୳୰୬ିୖ୧ୱ୩ି୤୰ୣୣୖୟ୲ୣ

୉୶୮ୣୡ୲ୣୢ୰ୣ୲୳୰୬୭୬ୟ୬୧୬୴ୣୱ୲୫ୣ୬୲୧୬ୟ୥୧୴ୣ୬୷ୣୟ୰
୫ୟ୶୧୫୳୫ୢ୰ୟ୵ୢ୭୵୬

• Using maximum drawdown as a measure of risk is
more intuitive compared to S.D. as a measure of
risk because it deals with concrete numbers.
• However, like S.D., it assumes normally distributed
returns.
• The higher the RoMAD, the more attractive the
investment will be.
6.4

Capital Allocation

ୗ.ୈ୭୤୮୭୰୲୤୭୪୧୭୰ୣ୲୳୰୬ୱ

• The higher the Sharpe ratio, the more attractive
the investment will be.
Advantage:
• It is based on sound financial theory.
• It is most widely used performance measure.
Limitation:
It assumes normal distribution of returns, which is not
appropriate in case of portfolio that contains options
and other instruments with non-symmetric payoffs.

Every business unit has a target marginal risk-adjusted
return for new investments where marginal risk-adjusted
return refers to change in firm’s risk-adjusted return when
a unit invests one more dollar.
Goal of Capital Allocation: The goal is to make marginal
contributions to return = marginal contributions to risk i.e.
Setting capital requirements: Following are the types of
position limits:
1) Nominal position limits: In this approach, the amount
of capital that the individual portfolio or business unit
can use in a specified activity is defined by the firm.


Reading 27

Risk Management

• The exposure is defined in terms of amount of
money exposed in the markets.

• The defined nominal position can be replicated by
an individual using other assets e.g. using options.
Advantages:
• Easy to understand
• Easy to monitor
Disadvantages:
• It ignores effects of correlation and offsetting
nature of risks.
2) VAR based position limits: In this approach, capital is
allocated based on pre-assigned VAR limit.
Advantages:
• This measure takes into account portfolio size,
diversification and leverage.
• It facilitates the measurement of the business unit’s
risk exposures in a comparable manner.
• It plays an important role in effective capital
allocation.
• It is adjusted automatically to changes in volatility.
Limitation:
• The effectiveness of VAR based limits depend on
effectiveness of VAR calculation.
• Sum of VAR of individual positions is not equal to
portfolio VAR i.e. it can be > portfolio VAR.
Therefore, sum of individual VARs cannot be used
to obtain “maximum” overall VAR.
3) Maximum loss limits: It involves establishing a
maximum loss limit for each business (risk-taking) unit.
Rule: It should be both large enough to meet
performance objectives and small enough to meet
objective of preservation of capital.

• Setting maximum loss limits ensures that the total
maximum loss never exceeds firm’s capital.
• However, these limits can be violated in case of
extreme market conditions.

FinQuiz.com

4) Internal capital requirements: It refers to the level of
capital specified by the management of the firm that is
considered appropriate for the firm. When regulatory
capital requirements are higher relative to internal
capital requirements, they overrule internal capital
requirements.
• They have traditionally been specified in terms of
capital ratio (ratio of capital to assets).
• Modern tools permit a more thorough approach. If
decrease in value of an asset is greater than value
of capital, firm is considered insolvent.
Examples:
• 1% probability of insolvency over a one-year
horizon is acceptable.
• Capital must be at least one-year aggregate VAR
at 1% probability level. Using aggregate VAR takes
care of correlations. Stress tests can be done in
case of unusual conditions.
• When normally distributed returns can be
assumed, required capital can be stated in terms
of S.D.
5) Regulatory capital requirements: It involves meeting
regulatory capital requirements. When demanded by

regulations, these regulatory capital requirements must
be included as a part of overall capital allocation
process of firm.
Limitations:
• Meeting regulatory capital requirements is a
difficult process.
• Regulatory requirements are at times inconsistent
with rational capital allocation objectives.
Recommended Approach:
The most effective approach to capital allocation
involves combination of different methodologies with
dual objective of profit maximization and capital
preservation.
NOTE:
• All position limits must be revised periodically with
the change in risk-return expectations.
• Position limits should not be changed in response
to temporary changes in risk.
• Position limits are adjusted gradually to
incorporate permanent changes in risk.


Reading 27

6.5

Risk Management

Psychological and Behavioral Considerations

Implication of behavioral aspects of portfolio
management in risk management:
• Risk takers behave differently during different
points of the portfolio management cycle.
Their behavior depends on:
o Recent performance
o Risk characteristics of their portfolios
o Market conditions
Risk management process can be improved when ERM
system and senior management take steps to avoid
conflicts of interest between management which is
responsible for allocating risk and portfolio managers
who make investment decisions. This can be done
through effective monitoring and designing efficient
performance incentive schemes.

Practice: End of Chapter Practice
Problems for Reading 27 & FinQuiz
Item-set ID# 7441.

FinQuiz.com