Risk Management Selected Concepts

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Risk Management Selected Concepts

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

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Definitions
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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

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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.
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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
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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.).

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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.

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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!).
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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
   credit.
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!.

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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.

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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).

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Basic Concepts of Modern Portfolio Theory
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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.

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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.

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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
   return.
3. Typically, the portfolios which comprise the
   efficient frontier are the ones which are most
   highly diversified.

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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.

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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.

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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).

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Capital Asset Pricing Model (CAPM)

1. Beta measures the volatility of a security
   relative to the asset class (or to the market
   portfolio).
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.

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Metrics
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Duration

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
   maturity.
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
   sensitivity.
6. With a single number duration summarizes an
   instruments sensitivity to changes in interest
   rates.
7. Of the many risks facing investors (in fixed
   income), interest rate is probably the most
   worrisome.
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
   fall.
10. Bonds with higher duration face higher interest
    rate risk.

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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
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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.

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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.

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).

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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).

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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
   ratings.
3. 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
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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
   benchmark.
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
   performance.
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.

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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
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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
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Setting Investment Policy and Conclusions
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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
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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
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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.

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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

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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.