Diversify, Diversify, Diversify! Every investment book and guru will drill that into you. But, have you ever wondered why diversification works? And, when it does not?

Here is an explanation using simple math.

Imagine the stock market consists of only two stocks – Nike and Berkshire Hathaway. Let’s say you have $200,000 to invest in stocks. You have been taught to diversify, so your policy is to keep 50% in each stock.

Over the next two years, Nike and Berkshire produce the following returns.

Nike: Year 1 +20%, Year 2 -10%, Cumulative +8%

Berkshire: Year 1 -10%, Year 2 +20%, Cumulative +8%

Two questions

1.      What is the value of your portfolio after two years – $216,000 or $220,500?

2.      Did diversification between the two stocks add value?

The answer depends on whether you rebalanced at the end of Year 1 or not.

If you rebalanced back to a 50% Nike and 50% Berkshire at the end of Year 1, you will have $220,500; otherwise, you will have $216,000.

Next two questions.

1.      Was there any other benefit to diversifying besides the extra $4,500?

2.      Does rebalancing always work?

Think about the volatility. Your diversified portfolio had zero volatility if you rebalanced the portfolio. You earned exactly 5% in each year. Positive returns with no volatility will get you some peaceful sleep!

Even if you did not rebalance the portfolio, the volatility of your diversified portfolio was fairly low – a return of 5% in Year 1 and 2.8% in Year 2.

If you did not diversify, the ups and downs of the portfolio – +20% in one year and -10% in the second – might have given you a headache, if not something worse.

One of the readers of my first post, Dan Myers, CFA, CFPP® summarized it perfectly, “Psychologically and emotionally – where most investors operate – diversification adds tremendous value as many investors are tempted to sell after downturns and buy more after rises. Annual rebalancing would clearly add to the end results both in dollars gains and peace of mind in this example”. Thank you, Dan!

Next Question

Does rebalancing always work?

It seems that diversification not only reduced the volatility of your portfolio but, with rebalancing, it added real dollars to your portfolio.

But what if Nike and Berkshire had a different performance pattern that what we had assumed. What if their return pattern was like this?

Nike: Year 1 -10%, Berkshire +20%, Cumulative +8%
Berkshire: Year 1 -10%, Berkshire +20%, Cumulative +8%

If you do the calculations you will find that in this case despite diversification, there is no improvement in volatility and there is no opportunity to add value via rebalancing.

What happened?

As you probably surmised, in this example, Nike and Berkshire have identical patterns of return, whereas in the previous example they had opposite patterns of return. In statistical terms, Nike and Berkshire have a correlation of +1.0 above, whereas they had a correlation of -1.0 in Post 1. The closer the correlation is to +1, the less likely the diversification benefit.

Low correlation assets are highly desirable but their are few of them, and fewer yet are accessible by individual investors at a reasonable cost. There is one exception – Intermediate-term Inflation-Linked Bonds.

Summing up the lessons of diversification.

1.   Diversification, even without rebalancing, can lower the volatility of the portfolio.

2. Diversification, with rebalancing, can add real dollars to the portfolio, if the assets ultimately have the same cumulative return.

3. Diversification works when assets in the portfolio have a correlation of less than +1.0.

4. The lower the correlation the more the possibility of lowering volatility and adding real dollars to the portfolio.

5. If everything in your portfolio is going up, it is not necessarily a good thing. It might mean you are not properly diversified. Thank you Weston Tompkins for sharing this quote “diversification means always saying you’re sorry.”

6. If some of the assets in your portfolio are going down, it does not automatically mean you have made mistakes. It may just be the price one has to pay for logical diversification that will ultimately pay off.

Photography by Alesia Kozik at Pexels.com