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Risk Management Selected Concepts


Risk Management Selected Concepts Agenda Definitions Basic Concepts of Modern Portfolio Theory Selected Risk Management Metrics Investment Policy and Conclusions – PowerPoint PPT presentation

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Title: Risk Management Selected Concepts

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

What is Risk?
  • Quite often risk is perceived only with negative
  • Dictionary.com defines risk as
  • 1. The possibility of suffering harm or loss
  • 2. A factor, thing, element, or course
    involving uncertain danger
  • 3. a. The danger or probability of loss to an
  • b. The amount that an insurance company stands
    to lose.
  • 4. a. The variability of returns from an
  • 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
  • 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
Investment Risks
Portfolio Concentration
Counterparty Risk
Human Factor
Market Risk
  • Market risk is the uncertainty of changes in the
    assets returns relative to changes in the
  • 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
Liquidity Risk
  1. 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
  2. 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.
  3. A position can be hedged against market risk but
    still entail liquidity risk.
  4. Accordingly, liquidity risk has to be managed in
    addition to market, credit and other risks.
  5. 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.
  6. Remember James Thompsons comment about matching
    assets and liabilities, this reduces exposure to
    liquidity risk!.

Systemic Risk
  1. Risk that a localized problem in the financial
    markets could cause a chain of events which
    ultimately cripple the market.
  2. 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.
  3. One of the purposes of financial regulation is to
    ensure that the market operates in a manner that
    minimizes systemic risk.
  4. 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
  • Termination (or mitigation) of risks via safety
    measures, quality control and hazard education.
  • Risk transformation also through the use of
  • 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
  • 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
  • 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
  • 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
  1. The green region corresponds to set of achievable
    risk-return portfolios (basket of instruments).
  2. 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
  3. Typically, the portfolios which comprise the
    efficient frontier are the ones which are most
    highly diversified.

  • A corollary of MPT.
  • Diversification (dont put all your eggs in one
  • 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
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)
  1. Beta measures the volatility of a security
    relative to the asset class (or to the market
  2. 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).
  3. 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.
  4. Investing in the asset class is possible and
    simple via investing in index funds that
    effectively replicate the market.

  1. Duration is a weighted measure of when an
    investor will get his money back from a fixed
    income investment.
  2. Duration considers coupon payments.
  3. The duration of a zero-coupon bond equals its
  4. For two bonds that mature at the same time, the
    bond with the higher coupon payment will have
    lower duration.
  5. Duration is also a metric of interest rate
  6. With a single number duration summarizes an
    instruments sensitivity to changes in interest
  7. Of the many risks facing investors (in fixed
    income), interest rate is probably the most
  8. Duration is one of the key metrics that allows
    identifying, measuring and controlling interest
    rate risk.
  9. The value of the instrument will decline if
    interest rates rise and rise if interest rates
  10. Bonds with higher duration face higher interest
    rate risk.

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
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
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.
  1. The variance is a metric of the spread of random
    variables probability distribution (around the
    arithmetic mean average).
  2. 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)
  1. Value at Risk (VaR) is metric that summarizes in
    a single number the portfolios market risk.
  2. VAR measures the maximum loss over an established
    time horizon (i.e. worst case scenario of losses
    in one month).
  3. 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).
  4. VaR uses standard deviation and statistical
    analysis (of price and volatilities) to determine
    the worst loss scenario for a given probability
    (confidence level).
  5. 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.
  6. The higher the variance and standard deviation,
    the greater the variability of possible returns
    from the investment (the greater the risk).

Credit VaR
  1. 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.
  2. This approach is based on the credit transition
    matrix, which defines the probability of one
    asset migrating or transiting to lower credit
  3. Industry limits, country and counterparty limits
    may be established to limit the credit exposure.

Credit rating transition matrix
Standardized Rating Standardized Rating
2 AA
3 A
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
  1. 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
  2. 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
  3. Tracking error is the standard deviation of the
    excess return.
  4. 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
Yield curve
Investment Instrument
Foreign currency
Active Management Asset classes
Active Risk
Different Active Management
Market Risk ß
Passive Management
US Euro Equities
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
  • Asset classes
  • Credit ratings
  • Limits
  • Currencies
  • Preferences

3rd Investment Restrictions
  • Absolute Return

4th Investment style
  • Relative Return

5th Risk Tolerance
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
  • 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
  • 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.

  • 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
  • William Sharpes idealized model proposed
    Tobins tangent portfolio must be the market
  • 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

  • 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.
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