Question

A companys cash position, measured in millions of dollars, follows a generalized wiener process with a drift rate of 0.5 per quarter and a variance rate of 4.0 per quarter. How high does the companys initial cash position have to be for the company to have a less than 5% chance of a negative cash position by the end of 1 year

Answer 1

Answer:

The initial cash position should be $4.58 million.

Step-by-step explanation:

If the initial cash position of company is x . The total distribution of cash’s probability at the end of 1 year is ϕ (x+4 x 0.5,4 x 4) = ϕ (x+ 2.0, 16)

where ϕ (m & v) is a normal distribution of probability with m & v  where m is mean and v is variance. The negative cash position’s probability at the end of one year is:

N [ -x + 2.0/ 4]

where N (x) = cumulative probability that a standardized normal variable (with zero mean and S.D. 1.0) is less than x . As according to the standard normal distribution table,  

N [ -x + 2.0/ 4] = 0.05

when:  

-x + 2.0/ 4 = -1.6449

As,  

x = 4.5796. Hence, the initial cash position should be $4.58 million.