The document contains information about returns and probabilities for different securities (A, B, C, D, E). It calculates the expected returns for A and B, which are both 8%. The risk (standard deviation) is lower for A at 1.14 than for B at 2.19. It recommends investing in security C, which has the highest return of 12% and moderate risk of 5%. For a portfolio with 75% in A and 25% in C, the expected return is 9% but the risk is higher at 6%; therefore, it recommends investing solely in E, which has the same return of 9% but lower risk.

1. • The probability distribution of annual return
on security are given below:
• Compute the expected return on security.
Return on Security Probability
-0.35 0.04
-.25 0.08
-0.15 0.14
-0.05 0.17
0.05 0.26
0.15 0.18
0.25 0.09
0.35 0.04
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2. • Expected return= 0.013 = 1.3%
Return on Security Probability Expected return
-0.35 0.04 -0.014
-.25 0.08 -0.020
-0.15 0.14 -0.021
-0.05 0.17 -0.009
0.05 0.26 0.013
0.15 0.18 0.027
0.25 0.09 0.023
0.35 0.04 0.014
Expected Value 0.013
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3. • Mr. Rajan wants to invest in company A or
company B. The return on stock A and B and
probabilities are given below:
Advice Mr. Rajan, whether he should invest in
company A or B
Company A Company B
Return % Probability Return % Probability
6 0.10 4 0.1
7 0.25 6 0.2
8 0.30 8 0.4
9 0.25 10 0.2
10 0.10 12 0.1
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4. • Calculation of Expected Return
Company A Company B
R (i) P ER R (i) P ER
6 0.10 0.60 4 0.1 0.40
7 0.25 1.75 6 0.2 1.20
8 0.30 2.40 8 0.4 3.20
9 0.25 2.25 10 0.2 2.00
10 0.10 1.00 12 0.1 1.20
∑ 8 ∑ 8
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5. • Calculation of Standard Deviation of stock A
• Mean R (i) = 40/5=8
• Standard Deviation: 1.14
R (i) R (i) – Mean R (i) [R (i) – Mean R (i)] 2 P P * [R (i) – Mean R (i)] 2
6 -2 4.00 0.10 0.40
7 -1 1.00 0.25 0.25
8 0 0.00 0.30 0.00
9 1 1.00 0.25 0.25
10 2 4.00 0.10 0.40
40 1.30
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6. • Calculation of Standard Deviation of stock B
• Mean R (i) = 40/5=8
• Standard Deviation: 2.19
R (i) R (i) – Mean R (i) [R (i) – Mean R (i)] 2 P P * [R (i) – Mean R (i)] 2
4 -4 16 0.10 1.60
6 -2 4 0.20 0.80
8 0 0 0.40 0.00
10 2 4 0.20 0.80
12 4 16 0.10 1.60
40 4.80
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7. Analysis
Stock A (%) Stock B(%)
Average Return 8 8
Risk 1.14 2.19
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8. • Following is the data relating to five securities.
• Which of the securities should be selected for
investment?
• Assuming prefect correlation, analyse whether
it is preferable to invest 75% in security A and
25% in security C
Security A B C D E
Returns (%) 8 8 12 4 9
Risk S.D (%) 4 5 12 4 5
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9. Analysis
• Which of the securities should be selected for
investment?
1. A
2. C
3. E
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10. Assuming prefect correlation, analyse whether it
is preferable to invest 75% in security A and 25%
in security C
In case of positive correlation exists between
two securities, their risk and return can be
averaged with the proportion. Hence proportion
of 3:1 for risk and return will be as follows:
Risk = [(3*4) + (1*12)]/ 4 = 6%
Return = [(3*8) + (1*12)]/ 4 = 9%
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11. • Comparing the above average risk and return
with security E, it is better to invest in E as it
has less risk for the same return of 6%
Stock A & C (%) Stock E (%)
Average Return 9 9
Risk 6 6
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