Question

The market risk of a portfolio is equal to the weighted average market risk of its components, and the total risk of a portfolio is equal to the weighted average total risk of its components. True or False? Please explain.

Answer 1

Ans. True

(1) The market risk of a portfolio is equal to the weighted average market risk of its components.

The market risk of a portfolio of assets is a simple weighted average of the betas on the individual assets.

Where wi denotes the fraction of the portfolio invested in stock i and Pi is market risk of stock i.

Example:

- Consider the portfolio consisting of three stocks A, B and C.

	Amount invested	Expected return	Beta
Stock A	1000	10%	0.8
Stock B	1500	12%	1.0
Stock C	2500	14%	1.2

- What is the beta on this portfolio?

- As the portfolio beta is a weighted average of the betas on each stock, the portfolio weight on each stock should be calculated. The investment in stock A is $1000 out of the total investment of $5000, thus the portfolio weight on stock A is 20%, whereas 30% and 50% are invested in stock B and C, respectively.

- The expected return on the portfolio is:

- Similarly, the portfolio beta is:

- The portfolio investing 20% in stock A, 30% in stock B, and 50% in stock C has an expected return of 12.6% and a beta of 1.06. Note that a beta above 1 implies that the portfolio has greater market risk than the average asset.

(2) The total risk of a portfolio is equal to the weighted average total risk of its components.

the portfolio's total risk is simply a weighted average of the total risk (as measured by the standard deviation) of the individual investments of the portfolio. Portfolio 1 is the most efficient portfolio as it gives us the highest return for the lowest level of risk.