The principle idea of diversification is that by investing in more than two different stocks that are not positively correlated you reduce the overall risk of your portfolio. You can lower your overall risk further then an individual investment could. By choosing stocks that are more negatively correlated or uncorrelated you lower the risk you take on.

The analogy of not to put all your eggs in one basket relates heavily to the concept of diversification. Positive stock are anything that have some relationship with each other, both can be affected by externalities in similar ways. So for example, Intel processors and HP computers might be positively correlated. If demand falls for HP Computers and HP computers use Intel processors, than Intel stock could be directly affected by the fall in demand for HP computer. Uncorrelated is just that, Hp computers and Boat engines for example.

Negative correlated stock could be Apple and Microsoft. Both compete for roughly the same market share and both are trying to appeal to the same youth generation, especially since the release of Windows phone 7 series. When one gains traction by releasing a blockbuster gadget or new software, the other company will be negatively affected. So why is it good to diversify by broadening your negative stock? Because it helps offset variance or in other words helps decrease your risk in these stocks.

If you buy both Apple and Microsoft shares, and Apple releases a product that gets underwhelming responses by the public, the shares of Apple might decrease. To help offset that loss, your Microsoft shares might increase because investors will be looking at competing firms with similar or better products and invest in Microsoft. Microsoft might use that opportunity to release promising devices/software to dampen Apple even further. By diversifying your portfolio with negative or uncorrelated investments you are cushioning your fall if one of your investments has a negative return. The positive performance of some of your other investments can dampen the effects of a negative return investment.

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Here is an mathematical example, don’t get turned away because its math and math is scary, its relatively straightforward 😉

To show algebraically how diversification using negative correlated stock can reduce risk, consider this 2 Asset example:

Assume total shares are divided between these two stocks. Assume given variance. Assume expected return is known.

Your portfolio is made up of 2 stocks, X1 and X2.

Asset X1= .6

Asset X2= .4 where X1+X2= 1

Your variance for both stocks are; V1= 100, V2= 100 so with that, we know the standard deviation which is the square root (S) of variance, so S1=10 and s2=10.

Your expectations of your rate of return for both stocks are:

E1= 30%

E2= 20%

Therefore, we know the expected yield of your portfolio using the following equation:

Ep= X1E1+X2E2

Ep= .6(30) + .4(20)

=26%

So you expect a 26% return.

Did you get all that? If not, that’s OK. Just know that basically in the above, we’re just setting up the equation with information we need to calculate the variance (aka risk associated with a positive, negative, and uncorrelated stocks). Lets continue to whats important…

The portfolio risk equation is: Vp = X1²V1 + X2²V2 + 2X1X2√V1√V2P12

**The equation above will tell us have much risk would be associated with a positive, negative, or uncorrelated stocks. The P12 at the end of the equation for portfolio variance will be replaced with either 1 (positive), 0 (uncorrelated), -1 (negative). Here are the equations below:
**

Thus a portfolio with 2 assets that are uncorrelated (0) and/or negatively (-1) correlated can reduce the overall risk moreover than a positively correlated (1) and/ or individual asset.

The uncorrelated and negative investments lower the standard deviation from 10 (risk) to 7.211 and 2 respectively. The positively correlated and individual assets remain at standard deviation 10. This interestingly shows that by investing in different assets that have a positive correlation is ineffective at reducing risk, and one would be just as well off by investing into an individual asset. So even if your anti-Microsoft, it would be beneficial in buying Microsoft stock to offset the potential loss in value from Apple stock.

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