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Managerial Economics e Hirschey Currency Risk

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Managerial Economics e Hirschey Currency Risk Powered By Docstoc
					Risk Analysis
Concepts and Calculations

              Md. Al Mamun MBA (Finance, DU)
              MBA (HRM, Finance, AUS)
              ACCA in Progress (UK)
    Topics
- Risk and Uncertainty
- General Risk Categories
- Probability
- Probability Distributions
- Payoff Matrix
- Expected Value
- Variance and Standard Deviation
  (Measurement of Absolute Risk)
- Coefficient of Variation
  (Measurement of Relative Risk)
Topics (Con’t)
- Risk Attitudes
      Risk Aversion
      Risk Neutrality
      Risk Loving (Taking)

-   Utility Theory and Risk Analysis
-   Risk Premium
-   Decision-Making Under Risk
-   Certainty Equivalent
Definition of Risk and Uncertainty

- Risk/Uncertainty: Both concepts
   deal with the probability of loss or
   the chance of adverse outcomes
- Risk: All possible outcomes of
   managerial decisions and their
   probabilities are not completely
   known
- Uncertainty: The possible outcomes
   and their probabilities are known
General Risk Categories

Business Risk – the chance of loss
  associated with a given managerial
  decision; typically a by-product of the
  unpredictable variation in product
  demand and cost conditions
Market Risk – the chance that a portfolio
 of investments can lose money because
 of overall swings in financial markets

Currency Risk – the chance of loss due to
  changes in the domestic currency value
  of foreign profits
General Risk Categories
Inflation Risk – the danger that a general
  increase in the price level will undermine
  the real economic value of corporate
  agreements

Interest-rate Risk – another type of
  market risk that can affect the value of
  corporate investments and obligations

Credit Risk – the chance that another
  party will fail to abide by its contractual
  obligations
General Risk Categories (Con’t.)
Liquidity Risk – the difficulty of selling
  corporate assets or investments that
  have only a few willing buyers or are
  otherwise not easily transferable at
  favorable prices under typical market
  conditions

Derivative Risk – the chance that volatile
  financial derivatives such as commodity
  futures and index options could create
  losses by increasing rather than
  decreasing price volatility
 Probability
- Probability: likelihood of particular outcome
  occurring, denoted by p. The number p is
  always between zero and one.
- Frequency: estimate of probability, p=n/N,
  where n is number of times a particular
  outcome occurred during N trials.
- Subjective probability: If we do not have
  frequency, we often resort to         informed
  guesses. Subjective probabilities must follow
  the same rules of the probability calculus, if
  we are dealing with rational decision-makers.
Probability Distribution

 A probability
  distribution is
  simply a listing of
  the probabilities
  and their                Potential Outcomes

  associated
  outcomes
 Probability
  distributions are
  often presented          Potential Outcomes

  graphically as in
  these examples
 Probability Distribution
                                 Event          P
 Discrete probability
                                State of    (probabi
  distribution: deals with      Economy
  “events” whose “states of                   lity)
  nature” are discrete. The     Recession     0.2
  “event” is the state of the    Normal       0.6
  economy. The “states of
  nature” are recession,         Boom         0.2
  normal, and boom.
 Continuous probability
  distribution: deals with
  “events” whose “states of
  nature” are continuous
  values. The “event” is
  profits, and the “states of
  nature” are various profit
  levels.
The Expected Value
 The expected value
  of a distribution is
  the most likely
  outcome
 For the normal dist.,
  the expected value
                                 E(R)
  is the same as the
  arithmetic mean                    N

 All other things
  being equal, we
                          E R      R
                                     t 1
                                            t   t


  assume that people
  prefer higher
  expected returns
The Expected Return: An Example
 Suppose that a
  particular
  investment has
  the following                           60%




                            Probability
  probability                             40%
  distribution:                           20%
   25% chance of -                       0%
    5% return                                   -5%   5%       15%
                                                      Rate of Return
   50% chance of 5%
    return
   25% chance of
    15% return
 E ( Ri )  0.25 (0.05 )  0.50 (0.05 )  0.25 (0.15 )  0.05
 This investment has an expected return of 5%
Standard Deviation

 The formula for the standard
  deviation when analyzing population
  data (realized returns) is:

             n

             ( Ri  ERi ) 2
          i 1
                   n 1
Standard Deviation

 The formula for the standard
  deviation when analyzing forecast
  data (ex ante returns) is:
             n
           ( R  ER )
            i 1
                   i   i
                           2
                               Pi

 it is the square root of the sum of
  the squared deviations away from
  the expected value.
The Variance & Standard
Deviation
 The variance and
  standard deviation Less Risky
  describe the
                                               Riskier
  dispersion
  (spread) of the
  potential
  outcomes around

                                               
                                 N
  the expected                                  2
                        R 
                           2
                                     t R t  R
  value
                                t 1
 Greater dispersion
  generally means        R  2     R
  greater
  uncertainty and
Calculating variance and standard deviation


 Using the same example as for the
  expected return, we can calculate the
  variance and standard deviation:
i2  0.25 (0.05  0.05 ) 2  0.50 (0.05  0.05 ) 2  0.25 (0.15  0.05 )  .005
i  0.25 (0.05  0.05 ) 2  0.50 (0.05  0.05 ) 2  0.25 (0.15  0.05 )  0.071


   Note: In this example, we know the probabilities. However,
    often we have only historical data to work with and don’t know
    the probabilities. In these cases, we assume that each outcome
    is equally likely so the probabilities for each possible outcome
    are 1/N or (more commonly) 1/(N-1).
The Scale Problem: an
Example
               Potential Returns
      Prob       ABC       XYZ
      10%       -12%       -24%
      15%        -5%       -10%
      50%         2%        4%
      15%         9%       18%
                                   Is XYZ really twice
      10%        16%       32%     as risky as ABC?
   E(R)          2.0%      4.0%
   Variance    0.00539 0.02156
   Std. Dev.    7.34%     14.68%
   C.V.         3.6708    3.6708       No!
The Coefficient of Variation
 The coefficient of variation
  (CV)provides a scale-free measure
  of the riskiness of a security
 It removes the scaling by dividing
  the standard deviation my the
  expected return (risk per unit of
  return):            
                       CV       R

                              E R

   In the previous example, the CV for XYZ and ABC
    are identical, indicating that they have exactly the
    same degree of riskiness
Risk Measurement
Absolute Risk:
 - Overall dispersion of possible payoffs
 - Measurement: variance, standard deviation
 - The smaller variance or standard deviation, the lower
    the absolute risk.

Relative Risk
 - Variation in possible returns compared with the
    expected payoff amount
 - Measurement: coefficient of Variation (CV),
 - The lower the CV, the lower the relative risk.
         
 CV 
        EV
Risk Attitudes

 Risk Aversion
 Characterizes decision makers who seek to
 avoid or minimize risk.

 Risk Neutrality
 Characterizes decision makers who focus on
 expected returns and disregard the dispersion
 of returns.

 Risk Seeking (Loving)
 Characterizes decision makers who prefer risk.
Risk Attitudes
Scenario: A decision maker has two choices, a
sure thing and a risky option, and both yield the
same expected value.
Risk-averse behavior:
Decision maker takes the sure thing

Risk-neutral behavior:
Decision maker is indifferent between the two
choices

Risk-loving (or seeking) behavior:
Decision maker takes the risky option
Risk Attitudes


                 (MU)
                             (MU)




                                    (MU)



                        Risk averter: diminishing MU
                        Risk neutral: constant MU
                        Risk lover: increasing MU
Utility Functions

  Utility is a measure of well-being.
  A utility function shows the relationship
   between utility and return (or wealth) when
   the returns are risk-free.
  Risk-Neutral Utility Functions: Investors
   are indifferent to risk. They only analyze return
   when making investment decisions.
  Risk-Loving Utility Functions: For any
   given rate of return, investors prefer more
   risk.
  Risk-Averse Utility Functions: For any
   given rate of return, investors prefer less risk.
Utility Functions (Continued)
 To illustrate the different types of
  utility functions, we will analyze the
  following risky investment for three
  different investors:
       Possible Return (%)   Probability
               (ri)             (pi)
           _________         _________
              10%                .5
              50%                .5
  E(ri )  .5(10%) .5(50%) 30%

 σ(ri )  .5(10% 30%)2  .5(50% 30%)2  20%
    Risk-Neutral Investor

     Assume the following linear utility function:
                       ui = 10ri

 Return (%)      Total Utility     Constant
    (ri)             (ui)        Marginal Utility
__________       __________       __________
      0               0
     10              100               100
     20              200               100
     30              300               100
     40              400               100
     50              500               100
Risk-Neutral Investor (Continued)


 Expected Utility of the Risky
  Investment:
           E(u)  .5 * u(10%) .5 * u(50%)
           E(u)  .5(100) .5(500) 300

 Note: The expected utility of the risky
  investment with an expected return
  of 30% (300) is equal to the utility
  associated with receiving 30% risk-
  free (300).
Risk-Neutral Utility Function
ui = 10ri


      Total Utility
         600

         500

         400

         300

         200

         100

           0
               0   10   20   30   40   50   60

                    Percent Return
Risk-Loving Investor
 Assume the following quadratic utility
  function:
              ui = 0 + 5ri + .1ri2
  Return (%)      Total Utility     Increasing
     (ri)             (ui)        Marginal Utility
 __________       __________       __________
       0               0
      10               60                60
      20              140                80
      30              240               100
      40              360               120
      50              500               140
Risk-Loving Investor (Continued)

                       ui = 0 + 5ri + .1ri2

    Expected Utility of the Risky Investment:
               E(u)  .5 * u(10%) .5 * u(50%)
               E(u)  .5(60) .5(500) 280
    Note: The expected utility of the risky
     investment with an expected return of 30%
     (280) is greater than the utility associated
     with receiving 30% risk-free (240).
                                                      )
                                  - 5 + 25 - 4(.1)(-280
          C e rtainty
                    Equivale nt
                              :                            33.5%
                                              2(.1)
    That is, the investor would be indifferent
     between receiving 33.5% risk-free and
     investing in a risky asset that has E(r) = 30%
     and (r) = 20%
Risk-Loving Utility Function

ui = 0 + 5ri + .1ri2


     Total Utility
      600

      500



      280
      240


       60
        0
            0    10           30 33.5   50   60
                       Percent Return
Risk-Averse Investor



    Assume the following quadratic utility
     function:
                 ui = 0 + 20ri - .2ri2
     Return (%)        Total Utility    Diminishing
        (ri)               (ui)        Marginal Utility
    __________         __________       __________
          0                 0
         10                180               180
         20                320               140
         30                420               100
         40                480                60
         50                500                20
Risk-Averse Investor (Continued)



    Expected Utility of the Risky Investment:
              E(u)  .5 * u(10%) .5 * u(50%)
              E(u)  .5(180) .5(500) 340
    Note: The expected utility of the risky
     investment with an expected return of 30%
     (340) is less than the utility associated with
     receiving 30% risk-free (420).

                                                  0)
                             - 20 + 400- 4(-.2)(-34
     C e rtainty
               Equivale nt
                         :                              21.7%
                                     2(.2)
    That is, the investor would be indifferent
     between receiving 21.7% risk-free and
     investing in a risky asset that has E(r) = 30%
     and (r) = 20%.
Risk-Averse Utility Function
ui = 0 + 20ri - .2ri2

  Total Utility
  600

  500
  420
  340


  180


    0
        0     10     21.7 30        50   60
                   Percent Return
Indifference Curve

 Given the total utility function, an indifference
  curve can be generated for any given level of
  utility. First, for quadratic utility functions, the
  following equation for expected utility is
  derived in the text:

    E(u)  a0  a1E(r)  a 2E(r) 2  a 2σ 2 (r)
    Solving σ(r) :
           for
           E(u) a0 a1E(r)        2
    σ(r) =               E(r)
            a2   a2   a2
Indifference Curve (Continued)




   Using the previous utility function for the
    risk-averse investor, (ui = 0 + 20ri - .2ri2),
    and a given level of utility of 180:
                       180 20 E(r)
              σ(r)                   E(r) 2
  
                        .2      .2
      Therefore, the indifference curve would be:


                    E(r)   (r)
                     10     0
                     20    26.5
                     30    34.6
                     40    38.7
                     50    40.0
Risk-Averse Indifference Curve
When E(u) = 180, and ui = 0 + 20ri - .2ri2
     Expected Return
       60

       50

       40

       30

       20

       10

        0
            0    10     20     30      40       50
                Standard Deviation of Returns

				
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