Answer to Question #214782 in Statistics and Probability for jay

Question

b) ABC Ltd is evaluating to invest in two projects. Project X may yield a return of £1.5m with a probability of 20%, or a return of £5m with a probability of 60%. Project Y, instead, may earn a negative return of £3m with a probability of 70% or a positive return of £7m with a probability of 30%.

1) How much is the expected return for project X and Y?

2) What is the standard deviation?

3) Compare and briefly discuss the expected return and risk of the projects.

Answer 1

Solution:

1):

$E[X]=£1.5\ m\times 0.20+£5\ m\times 0.60=£3.3\ m$

$E[Y]=-£3\ m\times 0.70+£7\ m\times 0.30=£0\ m$

2):

$E[X^2]=(£1.5\ m)^2\times 0.20+(£5\ m)^2\times 0.60=£^215.45\ m^2$

$E[Y^2]=(-£3\ m)^2\times 0.70+(£7\ m)^2\times 0.30=£^221\ m^2$

Now, variances:

$V[X]=E[X^2]-(E[X])^2=15.45-(3.3)^2=£^24.56\ m^2$

$V[Y]=E[Y^2]-(E[Y])^2=21-(0)^2=£^221\ m^2$

Then, standard deviations:

$SD_X=\sqrt{V[X]}=\sqrt{4.56}=£2.135\ m$

$SD_Y=\sqrt{V[Y]}=\sqrt{21}=£4.582\ m$

3):

The expected return in project X is £3.3 m, whereas, in project Y, it is £0 m.

So, there is a bigger risk in project Y as the return is nil.