Lecture 16. Tuesday Mar 30th Risk and Diversification by sparkunder22

VIEWS: 5 PAGES: 33

									Lecture 16. Tuesday Mar 30th

  Risk and Diversification
Announcements

  Start reading
  Chapter Nine
       (Material from this
       chapter will be on
       second midterm)
Tuesday Mar 30th   Risk and Diversification   2
Uncertainty
 Uncertainty arises when we do not
 know and have no way of quantifying
 the choices or options that we have in
 front of us
                          Probability                           Probability

   Gamble 1        $100         ?%      Gamble 4           $?      45%
                   $100         ?%                         $?      55%

   Gamble 2          $0         ?%      Gamble 5           $?      60%
                   $200         ?%                         $?      40%

   Gamble 3         $50         ?%      Gamble 6          $10            ?
                   $150         ?%                       $210            ?
Tuesday Mar 30th              Risk and Diversification                        3
Risk
 Risk is quantifiable uncertainty.
 Bring knowledge or information to
 bear on the situation.
                          Probability                           Probability

   Gamble 1        $100       ?%
                             50%        Gamble 4           $?
                                                           $0      45%
                   $100       ?%
                             50%                           $?
                                                         $200      55%

   Gamble 2          $0       ?%
                             50%        Gamble 5           $?
                                                           $0      60%
                   $200       ?%
                             50%                           $?
                                                         $200      40%

   Gamble 3         $50       ?%
                             50%        Gamble 6          $10       ?%
                                                                     ?
                                                                   50%
                   $150       ?%
                             50%                         $210       ?%
                                                                     ?
                                                                   50%
Tuesday Mar 30th              Risk and Diversification                        4
                There are five “correct
                   #1 (Page 50)(PRS)
 Class Applicationanswers” and one
                   “wrong
 To play you pay $100. answer”!
  Which gamble do you make?
Gamble 1            $100   50%       Gamble 4           $0   45%
                    $100   50%                        $200   55%

Gamble 2              $0   50%       Gamble 5           $0   60%
                    $200   50%                        $200   40%

Gamble 3             $50   50%       Gamble 6          $10   50%
                    $150   50%                        $210   50%

       Use PRS #7 if don’t know!
 Tuesday Mar 30th          Risk and Diversification                5
Gamble 1 – Expectation

    Put $100 down,
        50% of time get $100 back
        50% of time get $100 back.
    Return is $0 → $100 gets you
    $100 every time!
    Risk is zero
Tuesday Mar 30th   Risk and Diversification   6
Gamble 2 – Expectation

    Put $100 down
        50% of time get $0 back
        50% of time get $200 back.
    Return is $0 → $100 gets you $100
    on average!
    Risk is you might lose $100 every
    time
Tuesday Mar 30th   Risk and Diversification   7
Gamble 3 – Expectation

    Put $100 down
        50% of time get $50 back
        50% of time get $150 back.
    Return is $0 → $100 gets you $100
    on average!
    Risk is you might lose $50 every
    time
Tuesday Mar 30th   Risk and Diversification   8
Gamble 4 – Expectation

    Put $100 down
        45% of time get $0 back
        55% of time get $200 back.
    Return is $10 → $100 gets you
    $110 on average!
    Risk is you might lose $100 every
    time
Tuesday Mar 30th   Risk and Diversification   9
     Gamble 5 – Expectation
                                             Gamble 5 gets you
Gamble 4                 $0   45%
                                             $200, 40% of the
                  $200        55%            time
Gamble 5                 $0   60%
                                             Gamble 4 gets you
                                             $200, 55% of the
                  $200        40%            time
Gamble 6                $10   50%            Gamble 6 gets you
                                             $210, 50% of the
                  $210        50%
                                             time.
     Tuesday Mar 30th         Risk and Diversification       10
Gamble 6 – Expectation

    Put $100 down
        50% of time get $10 back
        50% of time get $210 back.
    Return is $10 → $100 gets you
    $110 on average!
    Risk is you might lose $90 every
    time
Tuesday Mar 30th   Risk and Diversification   11
Your Attitude to Risk

    If 1 → don’t really like risk
    If 2 → really like risk
    If 3 → will take some risk
    If 4 → want reward for taking risk
    If 6 → want same reward as in 4,
    for taking a little less risk

Tuesday Mar 30th   Risk and Diversification   12
Measurement of Return




Tuesday Mar 30th   Risk and Diversification   13
                                                         Value of Shares
                   54 days from       February 1st 2004 to March 26th 2004
Measurement of Return
      Bank Of America 5,000.00                                             4,916.52
                   Bank One                       5,000.00                 5,290.41




Tuesday Mar 30th              Risk and Diversification                            14
  Measurement of Return
                                   Value of Shares
54 days from         February 1st 2004 to March 26th 2004
Bank Of America               5,000.00               4,916.52
Bank One                      5,000.00               5,290.41

Formula 8.1
R W = [End Value - Start Value] / Start Value
R BoA = [4,916.52 - 5,000.00] / 5,000.00 = - 0.016696
R ONE = [5,290.41 - 5,000.00] / 5,000.00 = + 0.058082
  Tuesday Mar 30th        Risk and Diversification              15
        Measurement of Return
                           Value of Shares        Dividend
54 days from      Feb 1 2004 to Mar 26 2004
Bank Of America     5,000.00           4,916.52 No Dividend in Period
                                                March 10 Dividend of 44.8 cents per share
Bank One            5,000.00           5,290.41 on 98.44 shares. Total Dividend $44.10



  Formula 8.1 (with dividends) End Value for Bank One
  = Value of Share + Value of Dividend Paid
  R W = [End Value - Start Value] / Start Value
  R ONE = [(5,290.41+44.10) - 5,000.00] / 5,000.00 = + 0.066902
        Tuesday Mar 30th                 Risk and Diversification                       16
        Measurement of Return
                           Value of Shares        Dividend
54 days from      Feb 1 2004 to Mar 26 2004
Bank Of America     5,000.00           4,916.52 No Dividend in Period
                                                March 10 Dividend of 44.8 cents per share
Bank One            5,000.00           5,290.41 on 98.44 shares. Total Dividend $44.10




Simple Annualized Return = Periodic Return * Periods in Year

R BoA = - 0.016696 * 365 54 = - 0.11285 or - 11.285%
R ONE = + 0.066902 * 365 = 0.4522 or 45.22%
                          54

        Tuesday Mar 30th                 Risk and Diversification                       17
Measurement of Return 1 Asset

Assume we can calculate the
return for a share under several
different economic scenarios
(states of nature) that occur
with know probability…
For example: Good Economy
Prob=.35 R=25%
Tuesday Mar 30th   Risk and Diversification   18
Measurement of Return 1 Asset
   E ( R ) = ∑ i =1,n R i * Prob i
  Economy          Probi                Returni    i
  Boom             Prob1                      R1   1
  Good             Prob2                      R2   2
  Fair       Prob3                            R3   3
  Recession Prob4                             R4   4
  Depression Prob5                            R5   5
Tuesday Mar 30th   Risk and Diversification            19
Measurement of Return 1 Asset
  E ( R ) = ∑ i =1,n R i * Prob i
  Economy          Probi                Returni       i
  Boom             0.20                       0.28    1
  Good             0.25                       0.25    2
  Fair       0.30                              0.15   3
  Recession 0.20                               0.08   4
  Depression 0.05                             -0.05   5
Tuesday Mar 30th   Risk and Diversification               20
Measurement of Return 1 Asset
 i    Econ Probi                   Ri
 1    B            0.20   *    0.28             =     0.0560
 2    G            0.25   *    0.25             =     0.0625
 3    F            0.30   *    0.15             =     0.0450
 4    R            0.20   *    0.08             =     0.0160
 5    D            0.05   *   -0.05             =     -.0025
                              Sum               =    0.1770
Tuesday Mar 30th          Risk and Diversification             21
Expected Returns of Gambles 1
and 4          E ( R ) = ∑ R * Prob                           i =1, n     i           i

                              Probability                               Probability

   Gamble 1            $100       50%        Gamble 4            $0           45%
                       $100       50%                         $200            55%

    $100 to play, so
        E(R ) = ($100-$100)*.50 + ($100-
                   1

        $100)*.50 = 0 a return of 0%
        E(R ) = ($0-$100)*.45 + ($200-
                   4

        $100)*.55 = $10 a return of 10%
Tuesday Mar 30th                   Risk and Diversification                               22
Measurement of Risk

σ                    ( Ri − E ( R ) )
                                                                
                                                    2
          = ∑ i =1,n 
      2
                                                        * Prob i 
                                                                
    Finance uses the variance in
    the return over the different
    scenarios as a measure the
    riskiness of the asset.

Tuesday Mar 30th         Risk and Diversification                    23
    Variance of Returns on Gambles
                           σ    = ∑ ( R i − E ( R ) ) * Prob 
                                                                                                     2

    1 and 4
                                                              2
                                                                          i =1, n                                  i
                                                             

σ = ( R1− E ( R ) ) * Prob + ( R 2 − E ( R ) ) * Prob
                                2                                                       2
  2
  1                                               1                                                2



σ = ( 0−0 ) * 0.50 + ( 0−0 ) * 0.50 = 0
                2                                         2
  2
  1

                    Return          Probability                                                    Probability

 Gamble 1                 0%           50%                Gamble 4                      -100%          45%
 E(R1)= 0%                0%           50%                E(R2) = 10%                       100%       55%

                              ( R1− E ( R ) ) * Prob + ( R 2− E ( R ) ) * Prob
                                                                  2                                            2

               σ
                      2
                      2
                          =                                                         1                                  2



                   ( −1.0−0.10 ) * 0.45 + (1.0−0.10 ) * 0.55
                                                                      2                                    2

               σ
                      2
                      2
                          =

               σ = ( −1.10 ) * 0.45 + ( 0.90 ) * 0.55 = .99
                                                      2                                 2
                      2
                      2
      Tuesday Mar 30th                                    Risk and Diversification                                         24
Expected Returns and Variances
of Gambles σ = σ 2 = ∑ ( Ri − E( R ) ) * Prob 
                                            i =1, n
                                                          2

                                                              i




   Gamble          E(R)              VAR              StDev
     1              0.00             0.00             0.000
     2              0.00             1.00             1.000
     3              0.00             0.25             0.500
     4              0.10             0.99             0.995
     5             -0.20             0.96             0.980
     6              0.10             1.00             1.000
Tuesday Mar 30th     Risk and Diversification                 25
PRS Q – Which 2 Gambles might
it be “sensible” to take??

    1 for 1 and 2
                                      6 for 1 and 3
    2 for 2 and 3
                                      7 for 1 and 4
    3 for 3 and 4
                                      8 for 1 and 5
    4 for 4 and 5
                                      9 for 1 and 6
    5 for 5 and 6

Tuesday Mar 30th   Risk and Diversification           26
      Return 2 Projects (or Assets)
 i Econ              George         RGi           Probi          RKi   Kramer

1 Recession              0.000   = 0.00       *    0.2       *   0.00 = 0.000

2   Slow                 0.018   = 0.06       *    0.3       *   0.05 = 0.015
   Growth
3 Moderate               0.032   = 0.08       *    0.4       *   0.10 = 0.040
   Growth
4 Prosperity             0.010   = 0.10       *    0.1       *   0.15 = 0.015
                         0.060   = Sum                           Sum = 0.070
Course Notes
  Page 53
      Tuesday Mar 30th            Risk and Diversification                      27
                           Course Notes Page 53
George                                                           Kramer
        Variance 2 Projects (or Assets)
i Ec      [RGi -E(RG)]^2 RGi - Probi                  RKi -   [RKi -E(RK)]^2
             * Probi     E(RG)                        E(RK)      * Probi
1   R         0.00072        0.00 -       0.2        0.00 -     0.00098
                              0.06                    0.07
2 SG          0.00000        0.06 -       0.3        0.05 -     0.00012
                              0.06                    0.07
3 MG          0.00016        0.08 -       0.4        0.10 -     0.00036
                              0.06                    0.07
4   P         0.00016        0.10 -       0.1        0.15 -     0.00064
                              0.06                    0.07
              0.00104        = VAR                  VAR =       0.00210
        Tuesday Mar 30th         Risk and Diversification                  28
       Covariance 2 Projects (or Assets)

σ   xy
       = ∑ i =1,n 
                  
                     (R   xi
                              − E ( R x)   )(R     yi
                                                      −E      ( R )) * Prob 
                                                                  y         
                                                                                  i


i Ec       RGi -E(RG)             RKi -E(RK)                  Probi       Probability
                                                                          Weighted
                                                                           Product
1 R        0.00 -0.06        *    0.00 - 0.07           *      0.2    =   0.00084
2 SG       0.06 -0.06        *    0.05 - 0.07           *      0.3    =   0.00000
3 MG       0.08 -0.06        *    0.10 - 0.07           *      0.4    =   0.00024
4 P        0.10 -0.06        *    0.15 - 0.07           *      0.1    =   0.00032
                                                              COV     =   0.00140
    George                       Kramer
       Tuesday Mar 30th            Risk and Diversification                            29
Correlation 2 Projects (or Assets)
Correlation = ρ = σ GK σ Gσ K
                                 GK
   ρ   GK
            = 0.0014 ( 0.032249*0.045826)
             ρ     GK
                        = 0.0014 0.001477842674 = 0.9473

                          George            Kramer       Geo / Kra
       E(R)                 0.06             0.07
     Variance             0.00104          0.00210
      St. Dev.           0.032249         0.045826
   Covariance                                            0.00140
   Correlation                                           0.9473
Tuesday Mar 30th              Risk and Diversification               30
Historical Relationship
Risk/Return (Notes page 51)
Investment         Average Low                  High   Standard
                   Return                              Deviation
Treasury Bills      3.8%    1%                  15%      3.3%

Treasury Bonds      5.4%         -9%            31%      5.8%

Large Common       12.7%        -44%            54%     20.3%
Stock
Small Common       17.7%        -50% 143%               34.1%
Stock

Tuesday Mar 30th     Risk and Diversification                      31
Current Relationship Risk / Return




     Spread is
     percentage
     above the “risk
     free rate” paid.
     100 basis
     points = 1
     percent.
      Tuesday Mar 30th          Risk and Diversification   32
Articles from The Economist
Links on the Course Web Site “News”
Page to 5 articles:
  Australian Economy. House Price Inflation.
  Investment Research. Separation of
  Traders from Analysts.
  US Monetary Policy. About Interest Rates.
  Warren Buffet. About Risk/Reward
  Tradeoff.
  Appetite for Risk. About Risk.

Tuesday Mar 30th   Risk and Diversification    33

								
To top