Question

Ann's portfolio has 20% of its funds invested in Security A, 75% of its funds invested in Security B, and 5% invested in the risk free asset. The risk-free asset earns 4%. Security A has an expected return of 8% and a standard deviation of 18%. Security B has an expected return of 10% and a standard deviation of 22%. Securities A and B have a coefficient of correlation of 0.60.

What is the standard deviation of the portfolio?

What is the expected return of the portfolio?

Answer 1

 

Weight of Security A = 20%

Weight of Security B= 75%

Weight of Security of Risk free Asset = 5%

Expected return on A = 8%

Expected return on B= 10%

Return on Risk free Asset = 4%

Standard Deviation of Security A= 18%

Standard Deviation of Security B= 22%

Correlation Coefficient between A and B = 0.60

We know that

Expected return on the Portfolio is the Weighted Average return

Expected return on Portfolio = Return on A* Weight of A+Return on B* Weight of B+Return on risk free asset* Weight of Risk free asset

= 8 ( 0.20) + 10( 0.75) +4( 0.05)

= 9.3%

Hence Expected return on Portfolio is 9.3%

Standard Deviation of Portfolio =

0.18880

Hence the Standard deviation of the portfolio is 0.1888 or 18.88%

Note: Standard Deviation of Risk free Asset is 0.

WA= Weight of A, WB = Weight of B, WR = Weight of Risk free Asset

SDA= Standard deviation of A, SDB = Standard deviation of B, SDR = Standard deviation of Risk free asset

rAB = Correlation between A and B

rBR = Correlation between B and risk free asset

rRA= Correlation between Risk free Asset and A.