Question

You are a hotel manager and you are considering four projects that yield different payoffs, depending upon whether there is an economic boom or a recession. The potential payoffs and corresponding payoffs are summarized in the following table. Project Boom (50%) Recession (50%) A $20 -$10 B -$10 $20 C $30 -$30 D $50 $50 If a manager adopted both project A and B simultaneously, the variance in returns associated with this joint project would be:

Answer 1

Solution:-

Following Formula is used to Calculate the Mean

Mean=Total observation/No. of observations

The following formula is used to calculate the Variance

Variance=[∑(X-Mean)^2]/No. of Observation

Find the mean and Variance of A and B Projects:

­Project A:

Mean=20-10/2=10/2=5

Variance=[(20-5)^2+(-10-5)^2]/2

                =[(15)^2+(-15)^2]/2

                =225+225/2

                =225

So, the Variance of Project A is 225.

­Project B:

Mean=-10+20/2=10/2=5

Variance= [(-10-5)^2+(20-5)^2]/2

                =[(-15)^2+(15)^2]/2

                =225+225/2

                =225

So, the Variance of Project A is 225.

Thus,the variance in returns associated with this joint project would be 225.