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

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```									Lecture 16. Tuesday Mar 30th

Risk and Diversification
Announcements

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)
“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

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

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