Question

Find the expected value and variance of the following portfolio: Share 1 50% Share 2 30% Share 3 20%

Answer 1

Answer:

Given,

To give the expected value & variance

x	1	2	3
P(x)	0.5	0.3	0.2

Now consider,

Expected value = E(X)

= x*P(x)

= 1*0.5 + 2*0.3 + 3*0.2

= 0.5 + 0.6 + 0.6

= 1.7

Expected value = 1.7

let us consider,

E(X^2) = x^2*P(x)

= 1^2 * 0.5 + 2^2 * 0.3 + 3^2 * 0.2

= 0.5 + 1.2 + 1.8

= 3.5

Variance = E(X^2) - E(X)^2

= 3.5 - (1.7^2)

= 3.5 - 2.89

= 0.61

So variance = 0.61 & Expected value = 1.7