Unsystematic Risk

Question

Have a question on this. When the explanation mentions "decreases at a decreasing rate." Why is that? The chart on adding stocks to a portfolio makes it seem like the curve is decreasing at an increasing rate. Can someone explain this? As the number of stocks in a portfolio increases, the portfolio's systematic risk:A) can increase or decrease.B) decreases at a decreasing rate.C) decreases at an increasing rateWhen you increase the number of stocks in a portfolio, unsystematic risk will decrease at a decreasing rate. However, the portfolio's systematic risk can be increased by adding higher-beta stocks or decreased by adding lower-beta stocks. (LOS 53.c)

cfachris · Answer

Hi @pcunniff , when you increase the number of stocks in your portfolio, unsystematic risk (diversifiable risk) reduces, but at a slower/decreasing rate. I presume you meant this chart below.As you can see below, to take an extreme, if you add infinite number of stocks, there comes a point where adding 1 extra stock to your portfolio doesn't do much to reducing your unsystematic risk, i.e. the impact of adding 1 stock to unsystematic risk decreases at a DECREASING rate. If it were to decrease at an INCREASING rate, you wouldn't see the shape of the red curve below, but instead a mirror image where the curve hits zero eventually as stocks are added to portfolio - which doesn't make sense. Does this help?

pcunniff · Answer

thanks @cfachris makes sense!So I wrapped up portfolio management today and thought of the theory regarding shorting a risk free asset (such as a government bond) while borrowing on margin to purchase a riskier stock (say amazon) to create a risk-less asset. Could it be possible to eliminate unsystematic risk by diversifying to your 30 stocks and effectively eliminating systematic risk by diversifying in uncorrelated market stocks? For example, diversifying in stocks holding betas of .5, 1.0, and 1.5?