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Risk Measures - Solutions

The document presents statistical data for two discrete distributions (A, B, C, D, E) along with their probabilities and various calculated metrics such as expected values, variances, and standard deviations. It also includes information on two assets modeled using Binomial and Poisson distributions, detailing their expected returns and variances. Additionally, the document provides calculations for specific scenarios involving the distributions and their respective probabilities.

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Kathryn Smith
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39 views2 pages

Risk Measures - Solutions

The document presents statistical data for two discrete distributions (A, B, C, D, E) along with their probabilities and various calculated metrics such as expected values, variances, and standard deviations. It also includes information on two assets modeled using Binomial and Poisson distributions, detailing their expected returns and variances. Additionally, the document provides calculations for specific scenarios involving the distributions and their respective probabilities.

Uploaded by

Kathryn Smith
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Discrete1 - a & b

Condition
1
2
3

A
16
10
4

B
30
10
-10

C
15
8
7

D
9
6
3

E
2
5
8

Prob1

Prob2

0.333333
0.5
0.333333 0.333333
0.333333 0.166667

(Note for equal prob case, A,B,D,E are symmetrical distributions)


prob1

E
V
SD
DSV
SP0
SP6.5
SP8.5

10
24
4.8989795
12
0
0.3333333
0.3333333

10
266.66667
16.329932
133.33333
0.3333333
0.3333333
0.3333333

10
6
5
12.66667
6
6
3.559026 2.4494897 2.44949
4.333333
3
3 Note case E in different order.
0
0
0 P(X<0)
0 0.6666667 0.666667 P(X<6.5)
0.666667 0.6666667
1 P(X<8.5)

prob2

E
V
SD
DSV
SP0
SP6.5
SP8.5

12
20
4.472136
12
0
0.1666667
0.1666667

16.666667
222.22222
14.90712
133.33333
0.1666667
0.1666667
0.1666667

11.33333
13.55556
3.681787
6.833333
0
0
0.5

7
4
5
5
2.236068 2.236068
3
2
0
0
0.5 0.833333
0.5
1

133.3333
133.3333

Binomial Poisson.
Asset1:
n
p
E[X]
E[R]
V[X]
V[R]

Bin[3,0.5]
3
0.5
1.5
6
0.75
12

Asset2:
lamda

Poisson[3]
3

E[Y]
E[R]

3
6

V[Y]
V[R]

3
12

SV
2 cases where x<1.5
2
=(0-1.5) *P[X=0]+(1-1.5)2*P[X=1]
SV[X]
0.375
SV[R]
6

SV

use y = 0,1,2,3

SV[Y]
SV[R]

1.2695702
5.078281

SP[R;3]

SP[R;3]

=SP[Y;1.5]
0.0497871
0.0497871 check

=SP[X;0.75]
0.125

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