Hi!!
Consider two securities, A and B, with standard deviations of 30% and
40%, respectively. Calculate the standard deviation of a portfolio
weighted equally between the two securities.
Start defining the variables:
WA = weight of Stock A in the portfolio
WB = weight of Stock B in the portfolio
STDA = standard deviation of security A
STDB = standard deviation of security B
STDP = standard deviation of the portfolio
1. If correlation is 0.9:
Variance = (WA)^2*(STDA)^2 + (WB)^2*(STDB)^2 +
+ 2*(WA)*(WB)*(STDA)*(STDB)*[Correlation(rA, rB)] =
= (0.50)^2*(30)^2 + (0.50)^2*(40)^2 +
+ 2*(0.50)*(0.50)*(30)*(40)*(0.9) =
= 1165
STDP = sqrt(Variance) = sqrt(1165) = 34.13%
2. If correlation is 0.0:
Variance = (WA)^2*(STDA)^2 + (WB)^2*(STDB)^2 +
+ 2*(WA)*(WB)*(STDA)*(STDB)*[Correlation(rA, rB)] =
= (0.50)^2*(30)^2 + (0.50)^2*(40)^2 + 0 =
= 625
STDP = sqrt(Variance) = sqrt(625) = 25.00%
3. If correlation is -0.9:
Variance = (WA)^2*(STDA)^2 + (WB)^2*(STDB)^2 +
+ 2*(WA)*(WB)*(STDA)*(STDB)*[Correlation(rA, rB)] =
= (0.50)^2*(30)^2 + (0.50)^2*(40)^2 +
+ 2*(0.50)*(0.50)*(30)*(40)*(-0.9) =
= 85
STDP = sqrt(Variance) = sqrt(85) = 9.22%
-------------------------------------------------------
Monika Vasquez owns a portfolio composed of three securities with the
following characteristics:
Standard Deviation
of
Security Beta Random Error Term Proportion
A 1.20 5% .30
B 1.05 8% .50
C 0.90 2% .20
If the standard deviation of the market index is 18%, what is the
total risk of Monika's portfolio?
I prepared an Excel file to answer this part of the question, download
it from here:
http://www.geocities.com/artistaflores/MonikaVazquez.xls
------------------------------------------------------
I hope that this helps you, and feel free to request for a
clarification if you need it before rate this answer.
Regards,
livioflores-ga |
