## Portfolio Diversification: When Not to Diversify

Diversification is not always good.  It’s common sense that having more shots on goal increases the probability of making a goal.  Financial advisors will always recommend diversifying your investment portfolio to improve returns.  Keep in mind, however, that blindly diversifying your portfolio does not always reduce risk.  I’m going to use some statistics to show you.

Let’s say that you invested in Gilead (GILD) stock, and the probability that it goes up \$1 is 25%.  In other words, the probability that you will make \$1 is 25%:

P(G)=25%

Now, let’s say you also invested in Allergan (AGN) shares, and the probability that the stock increases by \$1 is also 25%:

P(A)=25%

So if you invested in both GILD and AGN stocks, the probability that you make \$1 is now:

P(G or A)=P(G)+P(A)-P(G and A);

where P(G and A)=P(G)xP(A) assuming that P(G) and P(A) are independent events

P(G or A)=25%+25%-6.25%=43.75%

In the previous example, diversifying your investments improves your odds of making \$1 from 25% to 43.75%.  More often than not, however, the probability of success for different investments is not the same.  Let’s say that the probability that GILD stock increases \$1 is only 5%:

P(G)=5%

Therefore, your probability of making \$1 is not as good as before:

P(G or A)=25%+5%-1.25%=28.75%

In this last example, diversification does not reduce portfolio risk very much.  Keep in mind that the odds of the individual events will impact the odds of the entire portfolio before diversifying.  This is a common mistake made even by professionals.  It was “diversification” that led to the subprime crisis.  By combining a bunch of subprime home loans, bankers thought that they could reduce the risk of defaults.  Unfortunately, combining pieces of turd and putting frosting on it doesn’t make it a cake.