The following are the returns and probability of returns of two securities:

The following are the returns and probability of returns of two securities:

Probability	0.10	0.30	0.40	0.20
Security-X	15%	20%	5%	10%
Security-Y	25%	30%	35%	40%

Calculate:

iii. Coefficient of variation for each security & iv. Which security is better and why?

i. Expected rate of return for each security,

ii. The standard deviation for each security,

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Solution

i. Expected Rate of Return [

]

• Security-X:

• Security-Y:

ii. Standard Deviation (

)

For Security-X [

]:

• State 1:
• State 2:
• State 3:
• State 4:

For Security-Y [

]:

• State 1:
• State 2:
• State 3:
• State 4:

iii. Coefficient of Variation (

)

• Security-X:

• Security-Y:

iv. Which Security is Better and Why?

Security-Y is significantly better.

Reasons:

1. Higher Return: Security-Y offers a much higher expected return (33.50%) compared to Security-X (11.50%).
2. Lower Absolute Risk: Security-Y has a lower standard deviation (4.50%) than Security-X (6.34%).
3. Lower Relative Risk: Security-Y’s Coefficient of Variation (0.1343) is much lower than Security-X’s (0.5517), meaning Security-Y carries far less risk per unit of return.

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