The expected return and the variance

expected return- the weighted average of the distribution of possible returns in the future.

The variance of returns- a measure of the dispersion of the distribution of possible returns.

rational investors like returns and dislike risk.

example of calculating expected returns. the economy can have three stages of Booming, Normal or recession situation. lets assume that the probability of each stage is 25%, 50%, and 25%. if the return in each case is 35%, 15% and -5% resectively, what will be the expected return of the investment?

= 0.25*35%+0.5*15%+0.25*(-5%)= 15%

now we calcualte the variance.

- calculate the differences between expected return and the return at each stage.
- Square it.
- then we multiply it with the probablity.

the sum of that give us the variance, and the standard deviation will be the value to the power of .5.

right now consider the economy that can have two different states:

state of economy | Pi (Probability)| Return on asset A | Return of asset B

— — — — — — — — — — — — — — — — — — — — — — — — — — —

Boom | 0.4 | 30% | -5%

Bust | 0.6| -10% | 25%

Expected returns:

E(R_A)=(0.4*30%)+(0.6*-10%)=6%

E(R_B)= (0.4*-5%)+(0.6*25%)=6%