Question

The Chahad Bank wants to open a new branch in a distant city with very different economic conditions. Currently, the bank has an expected return of 15% with a standard deviation of 7%. The new branch is expected to have a return of 20% with a standard deviation of 10%. The correlation between the bank's returns and the returns from the new branch is -0.3. The new branch is expected to contribute 10% of the bank's revenues. What is the expected return for the bank if they add the new branch?

please show work

Answer 1

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

Assume A = Old Business

b = Additional business.
SDb = SD of B

Particulars	Amount
Weight in A	0.9000
Weight in B	0.1000
SD of A	7.00%
SD of B	10.00%
r(A,B)	-0.3

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((0.9*0.07)^2)+((0.1*0.1)^2)+2*(0.9*0.07)*(0.1*0.1)*-0.3]
=SQRT[((0.063)^2)+((0.01)^2)+2*(0.063)*(0.01)*-0.3]
=SQRT[0.0037]
= 0.0608
= I.e 6.08 %

SD of Business along with new branch is 6.08%