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Systematic risk

I keep getting this question wrong because I feel like two answers are correct. 

Which of the following statements about systematic and unsystematic risk is most accurate?

A. As an investor increases the number of stocks in a portfolio, the systematic risk will remain constant.

B. The unsystematic risk for a specific firm is similar to the unsystematic risk for other firms in the same industry

C. Total risk equals market risk plus firm-specific risk. 

I know C is correct, but I thought A was also correct. Does systematic risk change? I thought it was a constant risk that was undiversifiable. 

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I’d have thought that A could be incorrect because when you add a stock to the portfolio, the new portfolio beta will be dependent on the beta of any new stocks you add. You may of just invested in a stock with a Beta of 0.5 with a portfolio beta of 1 meaning the beta has now reduced.

I think systematic risk can be diversified by investing in other countries. I could be wrong though.

Systematic risk can not be diversified away.

When you add more stocks in your portfolio that  may be led to more/less risk depends on the weight of stocks in your portfolio.

While if your portfolio has all market stock at same index weight, you simply replicate the index by passive approach and get same mark systematic risk.

Let’s think about the question differently. If I asked whether this was true: as an investor increases the number of stocks in a portfolio, beta will remain constant.

The answer is clearly no as a portfolio’s beta can fluctuate depending on what it hold;. note that systematic risk is typically measured by beta. Hence, the first answer is clearly false, even if systematic risk cannot be diversified away.

Thanks for that answer.  I was with the original question writer but you cleared it up.  Thanks