Concept Of Risk And Measurement Techniques
Illustration 107
Suppose an investment in offshore oil exploration, there are two feasible results, the success of the project capitulating a payoff of $45 per share with a possibility 0.35 and the failure capitulating a payoff $5 per share with a possibility of 0.65. What is the anticipated value of investment per share.
Also determine what would be the investment per share in case of 5 probabilities as given below.
Cash Flows Value in Million $ - Xi |
Possibilities |
25 |
0.4 |
35 |
0.5 |
45 |
0.6 |
55 |
0.5 |
65 |
0.4 |
Solution
- The anticipated value of investment per share
Formula to ascertain the anticipated value per share in case of two possibilities is,
__
E (X) or X = P1X1 + P2X2
= 0.35 * 45 + 0.65 * 5
= 15.75 + 3.25
= 19
- Formula to ascertain 2 probable outcomes is
E (X) or X = P1X1 + P2X2 + ….
PnXn
n
= Σ PiXi
t=1
Therefore,
= (0.4 * 25) + (0.5 * 35) + (0.6 * 45) + (0.5 * 55) + (0.4 * 65)
= 10 + 17.5 + 27 + 27.5 + 26
= 108
Or
Cash Flows Value in Million $ - Xi |
Possibilities |
Anticipated Value |
25 |
0.4 |
10 |
35 |
0.5 |
17.5 |
45 |
0.6 |
27 |
55 |
0.5 |
27.5 |
65 |
0.4 |
26 |
Σ PiXi = 108 |
__
E(X)
or X = 108
Illustration 108
Determine the standard deviation for the following probable outcomes.
Cash Flow |
Probability |
15 |
0.15 |
25 |
0.25 |
35 |
0.35 |
45 |
0.45 |
55 |
0.55 |
Solution
Cash Flow |
Probability |
_ |
_ |
_ |
15 |
0.15 |
- 20 |
400 |
60 |
25 |
0.25 |
- 10 |
100 |
25 |
35 |
0.35 |
0 |
0 |
0 |
45 |
0.45 |
10 |
100 |
4.5 |
55 |
0.55 |
20 |
400 |
11 |
_ |
0 |
100.5 |
Σ = √ 100.5 = 10.02
Illustration 109
Determine the standard deviation and Coefficient Variation for the following.
Project A
Cash Flow |
Probability |
50 |
0.50 |
60 |
0.75 |
70 |
0.90 |
80 |
0.75 |
90 |
0.50 |
Project B
Cash Flow |
Probability |
40 |
0.75 |
55 |
0.85 |
70 |
0.95 |
85 |
0.85 |
100 |
0.75 |
- Standard Deviation and Variance for the Project A is as follows:
Cash Flow |
Probability |
_ |
_ |
_ |
50 |
0.50 |
- 20 |
400 |
200 |
60 |
0.75 |
- 10 |
100 |
75 |
70 |
0.90 |
0 |
0 |
0 |
80 |
0.75 |
10 |
100 |
75 |
90 |
0.50 |
20 |
400 |
200 |
_ |
550 |
n __
Standard Deviation σ = Σ √ (X1 – X1)^
2. P1
t=1
= √550 = 23.45
Co-efficient Variance = VA = σ A = 23.45
R
A 550
= 0.04
- Standard Deviation and Variance for the Project B is as follows:
Cash Flow |
Probability |
_ |
_ |
_ |
40 |
0.75 |
- 30 |
900 |
675 |
55 |
0.85 |
- 15 |
225 |
191.25 |
70 |
0.95 |
0 |
0 |
0 |
85 |
0.85 |
15 |
225 |
191.25 |
100 |
0.75 |
30 |
900 |
675 |
_ |
1766.25 |
n __
Standard Deviation σ = Σ √ (X1 – X1)^
2. P1
t=1
= √1766.25 = 42.02
Co-efficient Variance = VA = σ A = 42.02
R
A 1766.25
= 0.02
Therefore, the standard deviation as well as the variance is greater for Project B. This entails the relative risk of project B is comparatively lesser than that of project A.
Thus, as the anticipated value of project B is greater and its relative risk too is greater, the manager will decide to invest in this project.
Illustration 110
The table presents the probability allocation and anticipated value on investments. Determine the less risk project among the two.
State of Nature |
Probability Pi |
Outcome Monetary Return Xi |
Investment in Project C |
||
Inflation Null |
0.25 |
100 |
Reasonable Inflation |
0.40 |
175 |
Huge Inflation |
0.30 |
300 |
Investment in Project D |
||
Inflation Null |
0.25 |
150 |
Reasonable Inflation |
0.40 |
200 |
Huge Inflation |
0.30 |
250 |
Investment Project C
Anticipated Value E(X) = P1X1 + P2X2 + P3X3
= 0.25 * 100 + 0.40 * 175 + 0.30 * 300
= 25 + 70 + 90
= 185
S D σ = √ P1 (X1 – E(X)) ^2 + P2 (X2 – E(X)) ^ 2 + P3 (X3 – E(X)) ^2
= √ 0.25 (100 –185) ^2 + 0.40 (175–185) ^2 + 0.30 (300 –185) ^2
= √ 0.25 (85) ^2 + 0.40 (-10) ^2 + 0.30 (115) ^2
= √ 0.25 (7225) + 0.40 (100) + 0.30 (13325)
= √ 1806.25 + 40 + 3997.5
= √ 5843.75 = 76.44
Investment Project D
P1X1 + P2X2 + P3X3
= 0.25 * 150 + 0.40 * 200 + 0.30 * 250
= 37.5 + 80 + 75
= 192.5
S D σ = √ P1 (X1 – E(X)) ^2 + P2 (X2 – E(X)) ^ 2 + P3 (X3 – E(X)) ^2
= √0.25(150–192.5)^2+0.40(200–192.5)^2 + 0.30 (250–192.5)^2
= √ 0.25 (42.5) ^2 + 0.40 (-7.5) ^2 + 0.30 (57.5) ^2
= √ 0.25 (1806.25) + 0.40 (56.25) + 0.30 (3306.25)
= √ 451.56 + 22.5 + 991.875
= √ 1466 = 38.28
- It is unambiguous from the above that anticipated return from investment Project C and D are slightly different, that is 185 and 192.5.
- However the investment Project C integrates double the risk as compared to investment D that is 76.44 and 38.28 correspondingly.
- Thus, the manager would choose Project D which has lesser risk comparatively.
- It is thus unambiguous that decision making involving risk is based not only on the anticipated value but also on the degree of risk incorporated and in the person’s approach toward risk.
- It has to be noted that the scrutiny of decision making by a person integrating risk and uncertainty is helpful not only for choosing the investments but also scrutinising between any performance integrating risk and uncertainty.
- Therefore, selection among different ways of accomplishment that vary in both anticipated value and risk, needs to be scrutinised the individuals preference towards risk.
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