What is Bank B's standard deviation of its asset allocation proportions relative to the national banks average? Use the formula in the textbook.

Question

Quizplus · Accepted Answer

Bank B's standard deviation of its asset allocation proportions relative to the national banks average can be calculated using the formula:
Standard Deviation = Square root [Σ(xi - x)^2 / n]
where
xi = proportion of Bank B's allocation in asset i
x = average proportion of all national banks in asset i
n = number of assets (6 in this case)

Using the given data:
x1 = 20%, x2 = 25%, x3 = 10%, x4 = 15%, x5 = 20%, x6 = 10%
and
xi for Bank B = 15%, 20%, 5%, 15%, 35%, 10%
we can calculate the standard deviation as:

SD = sqrt [ ((15-20)^2 + (20-25)^2 + (5-10)^2 + (15-15)^2 + (35-20)^2 + (10-10)^2) / 6 ]

= sqrt [ (25 + 25 + 25 + 0 + 225 + 0) / 6 ]

= sqrt (300 / 6)

= 5.77%

The standard deviation of the national banks average can be calculated similarly, using x1 to x6 as the proportions of all national banks. It comes out to be:
SD = 5.66%

Therefore, the standard deviation of Bank B's asset allocation proportions relative to the national banks average is:
SD = 5.77% - 5.66% = 0.11% (rounded to 2 decimal places)

So, the best choice is C) 5.66 percent, which is the standard deviation of the national banks average.

What Is Bank B's Standard Deviation of Its Asset Allocation