Question

There is a 30% chance that demand will be strong for both A and B's products. If demand is strong, A’s return is 100% and B's return is 20%. Suppose there is a 40% chance that demand is normal. If demand is normal, A's return is 15% and B's return is 15%. Finally, suppose there is a 30% chance that demand is weak, in which case, A's return is -70% and B's return is 10%. What is the expected return for both A and B? What is the standard deviation of both A and B? Given your return and risk results, which investment do you think is best?

Answer 1

The expected value can be obtained as - E (x) a Enplu) As per the expected return for each demand type. x 0.30 0.40 0.30) [P(x) 1 0.15 -0.70 Therefore, expected value of A ds. E (A) - Emplo) - (0.30201) +(014090.15)+(0:30 00:40) z 0.30 + 0,06 + (-0.21) 2 0.15

As per the expected return for each type of demand of B, Ty 10.30 0.40 0.80) Ply) 10.20 0.15 0.10) Therefore, expected value of B, E (B) z Eyply) = (0.3000 120) + (0.4oxo18) + (0.308 0.10) Further, s.D obtained as, v(x) E (m2) - [E(r)] ~ 'Here, E(x²) En ²p(u) 2 (0.30) 1+ (0.40) 60.15+ (0.30) x-oto 20.051. and, Ely) z Ey?ply) = (0:3) % 020 +(0.40)0:15+ (0-20) no 1o 26.054 Therefore, s. o of A is obtained, V(A) - E (m2) - [E60] . 2 0.051 - (0.15) ? 20.0285 Standard Deviation of B is obtained V(B) = E(ge) - [E(y)] 20.051 - (0.15) ² 20.0285 Now, from the above we see, for both A and B returm is same as 5.1% (0.051) And ,S.D is also same for both A and B so risk is also equivalent at 2.85% (0.0285). Either of the product can be choßen A