Suppose an investor starts with a portfolio consisting of onerandomly selected stock. As more and...

Suppose an investor starts with a portfolio consisting of one randomly selected stock. As more and more randomly selected stocks are added to the portfolio, what happens to the portfolio’s risk? Explain the formula that relates total risk, market risk, and diversifiable risk.

Expert Solution

As more and more randomly selected stocks are added to the portfolio, the portfolio risk is reduced due to the benefit of diversification.

Diversification means a reduction in the overall risk of the portfolio when 2 or more stocks are present in the portfolio. The overall risk of the portfolio is less than its weighted average risk of Individual stocks in the portfolio.

how can an investor have a diversified portfolio?

As per modern portfolio theory:

The benefit of diversification is when non perfectly correlated stocks are added then if the stock return of stock falls then it's offset by a rise in the stock return of another stock.

The standard deviation of the portfolio is not the weighted average standard deviation. it is due to the benefit of diversification due to non-perfect relationship between the stocks.

It is usually less than the weighted average standard deviation.

If there is a perfect correlation between stocks in the portfolio then it is the weighted average standard deviation. Although, this is not the case in almost any scenario.

The standard deviation of the portfolio of two stocks is:

[(Weight*Sd)^2+(Weight*Sd)^2+2*(Weight*Weight)*Sd*Sd*correlation]^0.5

Where Sd= Standard Deviation.

The formula that relates total risk, market risk and diversifiable risk is:

Total risk= Market risk + Diversifiable risk.

jeff jeffy answered 2 years ago

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