Question

Consider a portfolio with 80% invested in asset X and 20% invested in asset Y . The volatility of each asset is the same and equals to 0.2. The correlation coefficient between the two asset returns is 50%. What is the portfolio volatility

Answer 1

The portfolio volatility is 26.83%.

Step-by-step explanation:

The portfolio volatility refers to the standard deviation of the rate of return of an investment portfolio.

To calculate the standard deviation, the variance of the of the return on the portfolio is first calculated using the following formula:

Portfolio return variance = (WX^2 * SDX^2) + (WY^2 * SDY^2) + (2 * WX * SDX * WY * SDY * CFxy) ......................... (1)

Where;

WX = Weight of Stock X = 80%

WY = Weight of Stock Y = 20%

SDX = Standard deviation of stock X return = 0.2

SDY = Standard deviation of stock Y return = 0.2

CFxy = The correlation between stock X and stock Y = 50%

Substituting all the values into equation (1), we have:

Portfolio return variance = (80%^2 * 0.2^2) + (20% * 0.2) + (2 * 80% * 0.2 * 20% * 0.2 * 50%)

Portfolio return variance = 0.072

The standard deviation of the return on this portfolio can be calculated as using the following formula:

`PRSD =√(PRV)` ........................... (2)

Where;

PRSD = Portfolio return standard deviation = ?

PRV = Portfolio return variance = 0.072

Substituting the values into equation (2), we have:

`PRSD=√(0.072)`

PRSD = 0.2683, or 26.83%

Therefore, the portfolio volatility is 26.83%.