Today we shall look at a few more areas of interest relating to diversification.

In *An Introduction to Diversification ^{[4]}*, we saw that Investopedia recommends holding a “wide variety of investments” to benefit from diversification.

Further, that a diversified portfolio will generate “higher returns and pose a lower risk than any individual investment found within the portfolio”?

Is this true? What does it mean?

**A Wide Variety of Investments?**

The greater the number of investments in one’s portfolio, the greater the diversification.

This implies that you should have as many investments as possible in your portfolio.

However, the greater the number, the less the impact from any one additional investment.

If you have a single asset portfolio and add a second asset to the mix, there will be significant impact from the new asset. But if you have 1000 assets equally in your portfolio, the addition of one more will have minimal influence.

So what is the ideal number?

The optimal number of individual investments, excluding such things as funds, fluctuates slightly from study to study. Some claim that 20-30 proper investments will result in strong diversification. Other studies found that 15-20 stocks can provide adequate diversification to eliminate nonsystematic risk. Some studies even believe that the benefits of diversification are exhausted in portfolios with more than 15 investments.

As to what is the right number, I think it varies depending on the investor. I could build a portfolio of 10 or less assets that managed to diversify efficiently. Others might need 40 to properly diversify.

The key to effective diversification is the correlation between the investments.

If you are comfortable investing in fine art as part of your investment portfolio, you do not require many assets to diversify. If you only want to invest in North American based public companies, you will require significantly more assets to diversify.

Regardless of the “right” number, you can see that it is not substantial. And by that, I mean less than 50 individual assets.

Less investments are also better for long term compounding. Buying and selling multiple investments results in transaction costs and potentially taxes payable on any gains. As we discussed during our compound returns review, these two costs can significantly erode long term portfolio growth.

Another factor to bear in mind is that researching and monitoring 30-50 investments can require substantial time and energy.

**Higher Returns Through Diversification?**

I have thought a bit more about the Investopedia statement. It is still inaccurate, but I think I can explain it.

I do not believe that you can get higher returns just by diversifying. As I explained previously, a portfolio’s expected return is simply the weighted average of every component’s expected return.

But diversification does allow the ability to add higher return assets to the portfolio to improve the overall expected return of the portfolio.

Say you have a two asset portfolio. Asset A has an expected return of 10.0% and a standard deviation of 5.0%. Investment B has a 14.0% expected return and a standard deviation of 8.0%. Your portfolio is 50% of each and the correlation between the two assets is 0.70.

Skipping the calculations, click here if you want to see the basic formulas ^{[5]}, the portfolio has an expected return of 12.0% and a standard deviation of 6.0%. Note that we have already breached the Investopedia statement that a diversified portfolio will yield higher returns than any individual investments in the portfolio.

But we can get a nice increase in expected returns by adding a high risk investment to the mix. Let us add asset C with an expected return of 50.0%, but a standard deviation of 30.0%. Further the correlation between asset A is 0.60 and 0.90 with asset B.

The ABC portfolio will have an expected return of 24.6%, a huge increase from the 12.0% expected return of an AB portfolio. But again, the higher average is less than the return of asset C on its own.

So while you may be able to increase expected performance in a portfolio, it will never be greater than the return of all individual assets.

What about risk though?

**Lower Risk Through Diversification?**

As we saw with our correlation calculations, proper diversification will lower portfolio risk. Again, not necessarily lower than all individual assets though.

In our two asset AB portfolio, the standard deviation is 6.0%. Less than asset B’s risk of 8.0% but more than asset A’s 5.0%.

Now let us look at adding asset C to the risk calculation.

The standard deviation of ABC portfolio is 13.5%. Now the combined risk is higher than both A and B on their own and even the AB portfolio itself.

Like returns, Investopedia’s statement on lower risk is faulty.

**What Should Investopedia Have Stated?**

I might have looked at the impact of diversification on portfolio returns and risk.

For a given return level, proper diversification will reduce the portfolio risk.

Or for a given risk level, proper diversification will provide higher returns.

But that is for the portfolio as a whole, not compared to its individual investments.

For example, you have a single asset portfolio, asset X. Its expected return is 20.0% and its standard deviation is 10.0%.

You like the return but are concerned about the amount of risk. You decide to add another asset in a 50% mix of the two assets.

You find two other potential investments that both have 20.0% expected returns.

Investment Y has a standard deviation of 10.0%, the same as your current asset X. Asset Y has a 0.20 correlation to asset X.

Investment Z has a standard deviation of 7.0%, lower than asset X. Its correlation to asset X is 0.90.

An XY portfolio will have an expected return of 20.0%. But an XY standard deviation will only be 7.8%.

An XZ portfolio will also have an expected return of 20.0%. But the XZ standard deviation will be 8.3%.

Both portfolios are more efficient than holding asset X alone.

For further points, note that the XY is more efficient than XZ even though Y has a higher amount of risk than Z. That is because of the differences in correlations.

The same may be said for someone wanting to enhance portfolio returns while keeping risk stable.

You own asset X and are comfortable with portfolio risk of 10.0%. However, you would like to increase your potential returns.

Perhaps you find investment option S with an expected return of 28.0%, a standard deviation of 13.0% and a correlation with X of 0.50.

In combining the two assets equally, the expected return of XS has increased to 24.0%, but the standard deviation remains the same at 10.0%.

Again, correlation plays a significant role in risk reduction. Had the correlations been 0.90 rather than 0.50, the standard deviation of XY would be 11.2%. For investment options with high correlations, you would need to accept lower risk-return profiles to equal the risk of X alone.

Okay, I hope that helps clarify diversification.

If not, do not worry. It is a rather complicated subject. I just want to lay the groundwork now for when we look at asset allocation and portfolio construction strategies.

I think we will move on to a discussion of investment returns next.