The Clearwater National Bank is planning to set up a new branch.This new branch is...

The Clearwater National Bank is planning to set up a new branch. This new branch is anticipated to generate 5 percent of the total business of the bank after it is opened. The bank also expects the return for this branch to be 15 percent with a standard deviation of 5 percent. Currently the bank has a 10 percent rate of return with a standard deviation of 5 percent. The correlation between the bank's current return and returns on the new branch is expected to be -0.3. What is this bank's expected risk (measured by the standard deviation) after adding this branch?

*please provide work

Expert Solution

Portfolio SD:

It is nothing but volataility of Portfolio. It is calculated based on three factors. They are
a. weights of Individual assets in portfolio
b. Volatality of individual assets in portfolio
c. Correlation betwen individual assets in portfolio.
If correlation = +1, portfolio SD is weighted avg of individual Asset's SD in portfolio. We can't reduce the SD through diversification.
If Correlation = -1, we casn reduce the SD to Sero, by investing at propoer weights.
If correlation > -1 but <1, We can reduce the SD, n=but it will not become Zero.

Wa = Weight of A
Wb = Weigh of B
SDa = SD of A
SDb = SD of B

Assume A = Old Business

B = New Branch

Portfolio SD:

Particulars	Amount
Weight in A	0.9500
Weight in B	0.0500
SD of A	5.00%
SD of B	5.00%
r(A,B)	-0.3

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.95*0.05)^2)+((0.05*0.05)^2)+2*(0.95*0.05)*(0.05*0.05)*-0.3]
=SQRT[((0.0475)^2)+((0.0025)^2)+2*(0.0475)*(0.0025)*-0.3]
=SQRT[0.0022]
= 0.0468
= I.e 4.68 %

New risk of entire business after new branch is 4.68%

jeff jeffy answered 2 years ago

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