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Risk Management Selected Concepts

- Agenda
- Definitions
- Basic Concepts of Modern Portfolio Theory
- Selected Risk Management Metrics
- Investment Policy and Conclusions

Definitions

What is Risk?

- Quite often risk is perceived only with negative

connotations - Dictionary.com defines risk as
- 1. The possibility of suffering harm or loss

danger. - 2. A factor, thing, element, or course

involving uncertain danger - 3. a. The danger or probability of loss to an

insurer. - b. The amount that an insurance company stands

to lose. - 4. a. The variability of returns from an

investment. - b. The chance of nonpayment of a debt.
- 5. One considered with respect to the

possibility of loss a poor risk. - However, risk may also contain another element
- The Chinese use two symbols to define risk
- 1. The first symbol is for danger
- 2. The second is for opportunity

What is Risk Management ?

- From our previous definition, Risk Management

(RM) would entail administering a mix of danger

and opportunity. - A more classic approach defines RM as a process

(an attempt, really) to identify, measure,

monitor and control uncertainty in an orderly and

methodical manner (often using mathematical

models). - Both approaches to RM are correct.
- However, RM is more of avoiding dangers than

seeking the opportunities. RM in a modern

acception entails following a pre-established

management process and performing mathematical

models (Greek letters and other sophisticated

financial metrics). - RM is about understanding human behavior and

finding a comfortable trade-off between

expected reward and potential loss.

RM entails managing exposure and uncertainty.

Risk Topology in the Investment Management context

Equity/commodity (price)

Market Risk

Interest Rates

Currency

Issuer

Credit

Investment Risks

Portfolio Concentration

Liquidity

Counterparty Risk

Operational

Regulatory

Systemic

Human Factor

Legal

Market Risk

- Market risk is the uncertainty of changes in the

assets returns relative to changes in the

market. - Derives from market-wide factors which affect

issuers and investors. Such factors will include

(but will not limited to) - Interest rates
- Inflation rates
- Currency exchange rates
- Demographics (remember Michael Cichons comments

about demographic implications!) - Unemployment rates
- General legislation
- Risk of natural disasters (Katrina, Rita,

earthquakes, floods, fire, etc.).

Credit Risk

- - Credit risk is the uncertainty in a

counterpartys (or obligors) ability to meet

payment of its obligations. - Associated concepts
- Default probability is the likelihood that the

obligor will default on its obligation either

over the life of the transaction or at an

specific timeframe. - Credit exposure is the amount of outstanding at

the time of a potential default. - Recovery rate is the fraction of the exposure

that might be recovered. - Credit quality is the perceived ability (usually

by a credit rating agency) of an issuer or

counterparty to meet its obligation. - Credit rating is assigned by credit analysts to

the counterparty (or specific obligation) and can

be used for making credit decisions.

Standard Poors Credit Ratings

AAA Best credit quality - Extremely reliable with

regard to financial obligations AA Very good

credit quality - Very reliable A More

susceptible to economic conditions - still good

credit quality BBB Lowest rating in investment

grade BB Caution is necessary - Best

sub-investment credit quality B Vulnerable to

changes in economic conditions - Currently

showing the ability to meet its financial

obligations CCC Currently vulnerable to

nonpayment - Dependent on favorable economic

conditions CC Highly vulnerable to a payment

default C Close to or already bankrupt -

Payment on the obligation currently continued D

Payment default on some financial obligations

has actually occurred

Simple, market wide, common, homogeneous (to a

broad range of assets), easily available and ( -

) objective. But have limitations (remember

Enron!).

Liquidity Risk

- Liquidity risk is the uncertainty of being able

to easily and without undue cost avail oneself of

cash either through converting financial assets

to cash (liquidate a position) or through

credit. - A person or institution might be exposed to

liquidity risk if sudden unexpected cash outflows

occurs and the markets on which it depends are

subject to loss of liquidity, or if a financial

asset it holds losses marketability or if the

credit rating of the institution falls. - A position can be hedged against market risk but

still entail liquidity risk. - Accordingly, liquidity risk has to be managed in

addition to market, credit and other risks. - Cash flow exercises and stress testing (along

with asset-liability matching) cab be applied to

assess liquidity risk. However, Comprehensive

metrics of liquidity risk due to systemic

failures are not easily available. - Remember James Thompsons comment about matching

assets and liabilities, this reduces exposure to

liquidity risk!.

Systemic Risk

- Risk that a localized problem in the financial

markets could cause a chain of events which

ultimately cripple the market. - A default by a major market participant (i.e.

Government default, and even maybe foreign

currency depletion and/or inability to access

international markets) might cause liquidity

problems for a number of that institutions

counterparties. This might cause those

counterparties to fail to make payment on their

own obligations, and a liquidity crisis could

spread throughout the market. - One of the purposes of financial regulation is to

ensure that the market operates in a manner that

minimizes systemic risk. - This issue might be discussed by Edgardo Podjarny

for the Argentina case.

Basic Risk Management Concepts

- Risk management as it is understood today,

largely emerged during the early 1990s. It is

different from earlier forms (it is more oriented

to financial solutions using derivatives). - The four approaches to risk management are
- Risk Transfer through the purchase of

traditional insurance products, or through the

acquisition of derivative products to hedge

exposures. - Termination (or mitigation) of risks via safety

measures, quality control and hazard education. - Risk transformation also through the use of

derivatives. - Tolerate risks alternative risk financing,

including self-insurance and captive insurance

(assume expected value of impact or loss is lower

than cost of hedging, transferring risk or

preventive measures).

Basic Concepts of Modern Portfolio Theory

Modern Portfolio Theory (MPT)

- Markowitz (1952) Portfolio Selection
- Harry Markowitz proposed that investors focus on

selecting portfolios based on their overall

risk-reward characteristics instead of merely

compiling portfolios form securities that have

(individually) attractive risk-reward

characteristics. - MPT treats volatility and expected return as

proxies for risk and reward. - Out of the entire set of possible portfolios, a

certain sub-set will optimally balance risk and

reward. (sub-set efficient frontier of

portfolios) - An investor should select a portfolio that lies

on the efficient frontier. - MPT provides a broad context for understanding

the structuring of a portfolio.

Efficient Frontier

- Today, it is possible to monitor daily the values

(reflecting price changes, coupon payments,

dividends, stock splits, etc.) for most of the

traded financial instruments. However, their

future values behave in what seems a random

pattern. - Observing their past behavior and using several

algorithms we may estimate their future returns

and volatilities and correlations (for each pair

of instruments). - With these inputs (expected returns, volatilities

and correlations) we may calculate the expected

return and volatility of any portfolio. - The notion of optimal portfolio can be defined

in one of two ways - For any expected return, consider all the

portfolios which have that expected return and

select the one which has the lowest volatility. - For any level of volatility, consider all the

portfolios which have that volatility and select

the one which has the highest expected return.

Efficient Frontier

- The green region corresponds to set of achievable

risk-return portfolios (basket of instruments). - Portfolios on the efficient frontier are optimal

in both the sense that they offer maximal

expected return for some given level of risk and

minimal risk for some given level of expected

return. - Typically, the portfolios which comprise the

efficient frontier are the ones which are most

highly diversified.

Diversification

- A corollary of MPT.
- Diversification (dont put all your eggs in one

basket) - A portfolio that is invested in multiple

instruments whose returns are uncorrelated will

have an expected simple return which is the

weighted average of the individual instruments

returns, but its expected volatility (risk) will

be less than the weighted average of the

individual instruments volatilities. - Expected behavior need to be uncorrelated
- To diversify it is not sufficient to add

instruments to a portfolio. Suitable

diversification requires reduction of risk

concentrations and unrelated risks taken on.

Capital Market Line

Borrow at risk free rate and purchase more

efficient portfolio

Risk-Free Rate

CML

Loan at risk free rate and sell

efficient portfolio

- James Tobin (1958) added the notion of leveraging

the efficient portfolio by combining it with a

risk-free asset. - Investors who hold the super-efficient portfolio

using the risk-free asset may - Leverage their position by shorting the risk-free

asset and investing the proceeds in additional

holdings in the super-efficient portfolio. - De-leverage their position by selling some of

their holdings in the super-efficient portfolio

and investing the proceeds in the risk-free asset.

Capital Asset Pricing Model (CAPM)

- William Sharpe (1964) extended MPT by introducing

notions of systematic and specific risk. - CAPM demonstrates that (given simplifying

assumptions), the super-efficient portfolio must

be the market portfolio. - All investors should hold the market portfolio

(leveraged or de-leveraged to achieve whatever

level of risk they desire). - CAPM decomposes a portfolios risk into
- Systematic risk risk of holding the market

portfolio for which an investor is compensated. - Specific risk risk which is unique to an

individual asset and can be diversified (the

investor doesnt receive compensation for it). - When an investor holds the market portfolio, each

individual asset in that portfolio entails

specific risk, but through diversification the

risk may be nullified (the net exposure ends up

as only systematic risk of the market portfolio).

Capital Asset Pricing Model (CAPM)

- Beta measures the volatility of a security

relative to the asset class (or to the market

portfolio). - If a securitys Beta is known, then CAPM can

establish the required return (a higher Beta

that is higher expected risk- requires higher

expected returns). - CAPM simplifies the task of finding the efficient

frontier because it is necessary to calculate the

correlations of every pair of asset classes

(proxies of the market) instead of every pair of

instruments in the entire universe. - Investing in the asset class is possible and

simple via investing in index funds that

effectively replicate the market.

Metrics

Duration

- Duration is a weighted measure of when an

investor will get his money back from a fixed

income investment. - Duration considers coupon payments.
- The duration of a zero-coupon bond equals its

maturity. - For two bonds that mature at the same time, the

bond with the higher coupon payment will have

lower duration. - Duration is also a metric of interest rate

sensitivity. - With a single number duration summarizes an

instruments sensitivity to changes in interest

rates. - Of the many risks facing investors (in fixed

income), interest rate is probably the most

worrisome. - Duration is one of the key metrics that allows

identifying, measuring and controlling interest

rate risk. - The value of the instrument will decline if

interest rates rise and rise if interest rates

fall. - Bonds with higher duration face higher interest

rate risk.

Duration

Geometrically, duration is defined to be the

slope of that tangent line, multiplied by

negative one.

A good rule of thumb regarding duration and

changes in interest rates

Duration Change in price Change in price

Duration Rates fall 1 Rates rise 1

1 year 1 -1

5 years 5 -5

10 years 10 -10

Volatility

Example Time series of prices of two assets

The asset on the left is more risky (more

volatile of the two)

- Volatility may be defined as the uncertainty

surrounding an expected value - Volatility usually refers to movements in

financial prices and rates. - Fluctuations (of prices or rates in financial

markets) are generally random and independent

from one period to the next (there are no serial

correlations or other dependencies). - Usually, we refer to volatility as the mean of

the standard deviation of expected returns.

Variance and Standard Deviation

Example High vs. Low Variance

µ

µ

Probability density functions (PDFs) are

indicated for two random variables. The one on

the left is more dispersed (it has a higher

variance) than the one on the right.

- The variance is a metric of the spread of random

variables probability distribution (around the

arithmetic mean average). - The most commonly used measure of spread is the

standard deviation (which is calculated as the

square root of the variance).

Value at Risk (VaR)

- Value at Risk (VaR) is metric that summarizes in

a single number the portfolios market risk. - VAR measures the maximum loss over an established

time horizon (i.e. worst case scenario of losses

in one month). - VaR is applicable to any liquid portfolio (any

portfolio that can reasonably be marked to market

on a regular basis and that its assets may be

readily converted to cash). - VaR uses standard deviation and statistical

analysis (of price and volatilities) to determine

the worst loss scenario for a given probability

(confidence level). - If the returns are normally distributed

(bell-shaped curve distribution), approx. 68 of

the outcomes will fall within one standard

deviation on either side of the expected value

(mean) and approximately 95 will fall within 2

standard deviations on either side of it. - The higher the variance and standard deviation,

the greater the variability of possible returns

from the investment (the greater the risk).

Credit VaR

- Credit VaR is similar to market VaR, but it

refers specifically to the maximum exposure and

expected maximum loss (through default or price

change) a firm is willing to take in an

investment (or loan) portfolio. - This approach is based on the credit transition

matrix, which defines the probability of one

asset migrating or transiting to lower credit

ratings. - Industry limits, country and counterparty limits

may be established to limit the credit exposure.

Credit rating transition matrix

Standardized Rating Standardized Rating

1 AAA

2 AA

3 A

4 BBB

5 BB to C

6 Default

Short term 1 2 3 4 5 6

1 93.92 3.60 0.56 1.91 0.00 0.00

2 0.54 98.04 0.81 0.41 0.21 0.00

3 0.29 2.76 90.20 4.08 2.57 0.10

4 2.42 0.00 1.69 91.37 1.85 2.66

5 0.00 0.00 1.33 1.35 97.32 0.00

6 0.00 0.00 0.00 0.00 0.00 100.00

Source CONSAR. March 2005

Alpha (a) and Information Ratio

- Alpha is a measure of the incremental reward (or

loss) that an investor gained in relation to the

market. This is measured as performance of a

selected portfolio relative to a market

benchmark. - Alpha can be used to directly measure the value

added or subtracted by a a funds manager. It is

calculated by measuring the difference between a

funds actual returns and its expected

performance. - Tracking error is the standard deviation of the

excess return. - The information ratio (IR) is one measure of

volatility-adjusted return. IR is defined as

alpha divided by tracking error.

Alpha as a tool of active investors

- Alpha is used by investors that follow an active

management style. That is, they diverge from the

benchmark or index trying to generate more

returns (alpha).

The benchmark (usually an index, represents the

market or asset class). The assumption is the

market is efficient

Divergence versus the chosen benchmark

Long

Short

Duration

Flattening

Slope

Yield curve

Over-weight

Under-weight

Investment Instrument

Over-weight

Under-weight

Foreign currency

Long

Short

Volatility

Active Management Asset classes

Active Risk

Different Active Management

Market Risk ß

Passive Management

US Euro Equities

Cash

Long term bonds

Emerging Markets Equities

Short medium term bonds

High yield bonds

Asset class or portfolio composition

Setting Investment Policy and Conclusions

Prudent Risk Management Starts by Setting an

Adequate Investment Policy

1st Clearly articulate the primary objective and

nature of the Fund

Balance risks and returns

2nd Investment Targets

Returns

Risks

- Asset classes
- Credit ratings
- Limits
- Currencies
- Preferences

3rd Investment Restrictions

- Absolute Return

4th Investment style

- Relative Return

Benchmarks

Active

5th Risk Tolerance

Passive

Investment Policy IMSS as an exampleremember Dr.

Levys presentation

- Reserve Structure
- Economic Fluctuations
- Catastrophes
- Random fluctuations in income and expenditure
- Future benefit expenditures (pre-funding)
- Buffer fund for pensions DB (normalize

expenditure level)

Clearly state the primary objective (or nature)

of the Fund

- One asset class, no derivatives
- Investment grade
- Limits (VaR, Credit VaR, Tracking error, issuer,

sector, international markets) - No Hedging
- Accepted currencies, US dollar, Euro, MX peso

Investment Restrictions

- Mostly passive
- i.e. For ROs
- 50 PIP Guber.
- 50 PIP Bancario

Risk Tolerance

Risk-Averse positive real returns certain

liquidity requirements

Conclusions

- Risk involves exposure and uncertainty.
- RM is a process to identify, measure, monitor and

control uncertainty in an orderly and methodical

manner (often using mathematical models). - Harry Markowitzs Modern Portfolio Theory showed

that all the information needed to choose the

best portfolio for any given level of is risk is

contained in three simple metrics - Expected investment returns
- Standard deviation of expected returns
- Correlations of the pairs of instruments in the

portfolio. - A portfolio is a basket or set instruments that

presents, in a comprehensive and accumulated

manner, a risk return profile that responds to

the goals and risk tolerance of the investor.

Conclusions

- James Tobin showed that it is possible to combine

the efficient portfolios with the risk free

asset, thus creating a set of portfolios with

superior characteristics (super efficient

frontier). - William Sharpes idealized model proposed

Tobins tangent portfolio must be the market

portfolio. - Investors use asset classes to determine

Strategic Asset Allocation (for which the number

of correlations is small and more of less stable

and easier to determine). - Practical Lessons
- Volatility worsens as the time horizon shrinks (

there are benefits to long term investing,

remember Sudhir Rajkumars presentation on 20 yr.

volatility of US stocks! ) - Diversification reduces volatility efficiently

Conclusions

- Practical Lessons
- A practical way to invest in a diversified

portfolio is through representative market

indices or index funds - Dont go for Alpha until investment and risk

management process is mature (remember Lesson 8

of Jay Collins presentation! ) - Modern Portfolio Theories provide simple,

intuitive solutions to investing, but have their

limitations and should be one of many elements to

be considered - Strong governance and prudence! should be

prerequisites for safe and efficient investment

of Social Security Funds - Sound Risk Management starts with an adequate

policy statement. - Thank you.