An investor is considering 3 securities R, C, and B. The details are as follows:
| Security | Return (r %) | Probability |
|----------|--------------|-------------|
| R | 13.4 | 0.3 |
| | 14.6 | 0.5 |
| | 16.8 | 0.2 |
| C | 9.4 | 0.2 |
| | 12.6 | 0.3 |
| | 15.1 | 0.3 |
| | 20.5 | 0.1 |
| B | -5 | 0.15 |
| | 6 | 0.25 |
| | 11.4 | 0.5 |
Find:
a) Which security should be chosen for investment?
b) What is the return an investor earns if he invests 50% of his funds in security R, 30% in C, and the balance in B?
Answer (1)
To determine which security should be chosen for investment and the return on a mixed investment:
a) Best Security Choice:
To find the best security, we need to calculate the expected return for each security. The expected return is calculated as the sum of the product of the return and its probability for each scenario of the security.
Security R: Expected Return for R = ( 13.4 × 0.3 ) + ( 14.6 × 0.5 ) + ( 16.8 × 0.2 ) = 4.02 + 7.3 + 3.36 = 14.68%
Security C: Expected Return for C = ( 9.4 × 0.2 ) + ( 12.6 × 0.3 ) + ( 15.1 × 0.3 ) + ( 20.5 × 0.1 ) = 1.88 + 3.78 + 4.53 + 2.05 = 12.24%
Security B: Expected Return for B = ( − 5 × 0.15 ) + ( 6 × 0.25 ) + ( 11.4 × 0.5 ) = − 0.75 + 1.5 + 5.7 = 6.45%
Conclusion: Security R has the highest expected return at 14.68%, so it should be chosen for investment based on expected return alone.
b) Return for Mixed Investment:
If the investor spreads their investment across the securities as 50% in R, 30% in C, and 20% in B, the overall return can be calculated by taking the weighted sum of the expected returns:
Mixed Investment Return = ( 0.5 × 14.68 ) + ( 0.3 × 12.24 ) + ( 0.2 × 6.45 ) = 7.34 + 3.672 + 1.29 = 12.302%
The investor will earn approximately a 12.30% return on their portfolio with the specified allocation.
