Problem
Z Corp produces widgets using two inputs, let's call them X and Y. It has estimated the following characteristics of its sales revenue and costs:
|
|
Expected Value
|
Standard Deviation
|
Correlation Coeff with Sales Rev
|
Correlation Coeff with Cost of X
|
|
Sales Revenue
|
100
|
15
|
1.0
|
|
|
Cost of X
|
40
|
10
|
0.5
|
1.0
|
|
Cost of Y
|
40
|
8
|
0.0
|
0.0
|
The CFO is concerned that the firm's profit is too volatile (the variance/standard deviation is too high), where Profit is defined as
Profit = Sales Revenue - Cost of X - Cost of Y
Suppose that the uncertainty or variability in the cost of X can be eliminated through derivative contract or through a fixed price contract (do not worry about how this done). Similarly, the variability in the cost of Y can be eliminated using derivative contracts or fixed priced contracts (again do not worry about this is done).
If the goal is to reduce variability in profit as much risk as possible and you could eliminate the variability of only one input, X or Y, which would you choose? Intuitively explain your logic. No calculations are necessary.