Question

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%

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

1. Calculate the portfolio standard deviation (volatility) of returns. Show your work.

Below is worked in excel and formula is given which is easy to understand.

	Amount	Portfolio Weight	Std Dev	Correlation
Investment A	600	0.67	0.15	0.20
Investment B	300	0.33	0.06
Formula	σP = √(wA2 * σA2 + wB2 * σB2 + 2 * wA * wB * σA * σB * ρAB)

σP	0.11
where
σP	PF Std Dev
wA	Weight of investment A in PF
wB	Weight of investment B in PF
σA	Investment A Std Dev
σB	Investment B Std Dev
ρAB	Correlation between investment A and Investment B

2. If the correlation of returns was negative 20%, i.e., -20%, what is the portfolio standard deviation (volatility) of returns? Show your work

	Amount	Portfolio Weight	Std Dev	Correlation
Investment A	600	0.67	0.15	-0.20
Investment B	300	0.33	0.06
Formula	σP = √(wA2 * σA2 + wB2 * σB2 + 2 * wA * wB * σA * σB * ρAB)

σP

0.098

3. Did risk increase or decrease when the correlation declined from 20% to -20%? Why? Briefly explain your answer using non-mathematical terminology.

Answer to this question is simple - Diversification. Negative correlation mean if return on one investment goes up, the other goes down. Hence standard devistion of PF is less in the second option when correlation is -20%.