Question

ou only have four stocks in your portfolio. What will happen to your portfolio if you add some randomly selected stocks to it? Question 4 options:

a) The diversifiable risk will remain the same but the market risk will rise.

b) The diversifiable risk to your portfolio will probably decline while the expected market risk will not change.

c) The total portfolio risk should decline along with the expected rate of return, but the market risk will remain unchanged.

d) The diversifiable risk and the market risk will both decline.

Answer 1

Portfolio Risk :

The variance of a portfolio's return is a function of the variance of the component assets as well as the covariance between each of them. Covariance is a measure of the degree to which returns on two risky assets move in tandem. A positive covariance means that asset returns move together. A negative covariance means returns move inversely. Covariance is closely related to "correlation," wherein the difference between the two is that the latter factors in the standard deviation.

Although the diversifiable risk of a portfolio obviously depends on the risks of the individual assets, it is usually less than the risk of a single asset because the returns of different assets are up or down at different times. Hence, portfolio risk can be reduced by diversification—choosing individual investments that rise or fall at different times from the other investments in the portfolio. For most portfolios, diversifiable risk declines, quickly at first, then more slowly. However, how rapidly risk declines depends on the covariance of the assets composing the portfolio.

Portfolio risk consists of 2 components: systemic risk and diversifiable risk. Systemic risks, also known as systematic risks, are risks that affect all assets, such as general economic conditions, and, thus, systemic risk is not reduced by diversification. Diversifiable risks are risks specific to particular assets, such as factors that affect particular businesses and their stocks. Diversifiable risks can be reduced to the extent that the coefficients of correlation of the assets in the portfolio approaches 0.

Total Portfolio Risk = Systemic Risk + Diversifiable Risk

This can be explained by the below illustrated graph:

Expected Return:

Expected return is calculated as the weighted average of the likely profits of the assets in the portfolio, weighted by the likely profits of each asset class. Expected return is calculated by using the following formula :

E(R) = w1R1 + w2Rq + ...+ wnRn

So, the expected returns of the portfolio will be weighted average returns of all the stocks and thus as the number of stocks increases the expected returns is likely to come down as it averages all the returns.

Market Risk:

Market risk is the risk that the value of an investment will decrease due to changes in market factors. Market risk is the possibility of an investor experiencing losses due to factors that affect the overall performance of the financial markets in which he or she is involved. Market risk, also called "systematic risk," cannot be eliminated through diversification.

So, on the basis of above exlanations, it can be concluded that, with an increase in number of stocks in the portfolio, the diversifiable risk will come down, expected rate of return will come down but the market risk will remain unchanged.

So, Option C should be the choice.