Question

Portfolio Risk

Assume

A portfolio consists of two assets, Investment A and Investment B.

Market Value of Investment A at beginning of period: $600

Market Value of Investment B at beginning of period: $300

Investment A has an expected return of 8%

Investment B has an expected return of 3%

Investment A has a standard deviation (volatility) of returns 15%

Investment B has a standard deviation (volatility) of returns of 6%

The correlation of returns for Investment A and Investment B is 20%

Deliverable

Word or Excel spreadsheet items.

1. Calculate the portfolio standard deviation (volatility) of returns. Show your work.
2. If the correlation of returns was negative 20%, i.e., -20%, what is the portfolio standard deviation (volatility) of returns? Show your work.
3. Did risk increase or decrease when the correlation declined from 20% to -20%? Why? Briefly explain your answer using non-mathematical terminology.

Answer 1

a. Answer; Portfolio Standard deviation = 10.625% ( see below calculation and image calculation)

Calculation of Portfolio standard deviation.

INVESTMENT	MARKET VALUE	WEIGHTS	EXPECTED RETURN	STANDARD DEVIATION
A	$600	0.67	8%	15%
B	$300	0.33	3%	6%
TOTAL	$900

Correlation (r) of Investment A and B = 20% OR 0.2

Covariance of Investment A and B = r*standard deviation of A * standard deviation of B

Covariance (Cov(A,B)) of Investment A and B = 0.2*15%*6% = 18%

When Correlation (r) is negative 20% or -0.2

Answer = Standard deviation of portfolio is 9.847% ( see the calculation in below image )

Due to change in correlation the Covariance will also be change

Covariance (COV(A,B)) of investment A and B = r*standard deviation of A* standard deviation B

Cov(A,B) = -0.2*15%*6% = -18%

Risk got decrease from 10.625% to 9.847%.

Reason of Risk reduction is the decrease in correlation between investment A and B. Because when the Correlation is between +1 and -1  there is a some benefit of diversification which means minimum risk portfolio can be possible.