Shares of company A are sold at 10 per share Shares of compa

Shares of company A are sold at $10 per share. Shares of company B are sold at $50 per share. According to ta market analyst, 1 share of each company can either gain $1, with probability 0.5, or lose $1, with probability 0.5, independently of the other company. Which of the following portfolios has the lowest risk:

(a) 100 Shares of A

(b) 50 shares of A + 10 shares of B

(c) 40 shares of A + 12 shares of B

Please explain why or why not on each. Thanks :D

Solution

Portfolio c has the least risk.

All the three portfolio have a value of $1000.

For the first portfolio there is equal probability of an upside or downward movement of $100, thus a total deviation of $200.

For the second portfolio there is equal probability of an upside or downward movement of $60,  thus a total deviation of $120.

For the third portfolio there is equal probability of an upside or downward movement of $52, thus a total deviation of $104

Hence in the third portfolio the risk is least as the deviation is minimum.