Correlations create diversification [Crypto indexing part 2]

Portfolio theory has had a huge impact on finance. Markowitz, who won the 1990 Nobel Memorial Prize in Economic Sciences, invented portfolio theory in 1952 with his famous paper “Portfolio Selection” published in the Journal of Finance. Portfolio theory changed the lens through which assets are considered. Before Markowitz, investors held a small number of stocks and tended to evaluate their stocks in isolation. Today, almost all investors evaluate their portfolio as a whole before buying or selling assets.

To understand why portfolios are attractive investments, we can study Figure 2. Most standard textbooks on portfolio theory contain a version of this figure, in which we see a collection of assets with their historical volatility on the x-axis and their expected return on the y-axis. Holding one of these assets will give the investor a certain risk (volatility) for a certain reward (return). The line is called the efficient frontier.

Figure 2: Portfolios on the efficient frontier are more attractive than single assets.

Investors want high returns and low volatility, so the upper left corner is an ideal place to be. When comparing assets against each other there is, of course, a trade-off between risk and reward: taking on more risk (by for example selling some treasury bills and investing in a startup) does increase the expected return but also leads to higher volatility.

The efficient frontier is the set of (volatility, return)-points the investor can get if she buys a portfolio of assets, and it is illustrated with a solid black line in Figure 2. Every single point on the efficient frontier is a portfolio the investor can have. The efficient frontier is located close to the ideal upper left corner, reflecting the fact that efficient portfolios are more attractive than owning a single asset. The reason for this is diversification.

Figure 3: American stocks exhibit low correlation with each other, hence basketing them is smart.

Correlation is the driver of diversification. When assets are correlated less than 1.00 with each other, it is possible to increase the risk-adjusted returns by diversifying. The lower the correlations between the assets, the more the efficient frontier will expand to the upper left corner.

In Figure 3 we see the correlation between 10 important constituents of the SP500: Apple, Microsoft, Amazon, Johnson & Johnson, J.P. Morgan, Facebook, Exxon and Google. Since the correlation between individual equities is below 1.00 they are suitable to be put into a basket like the SP500.

Here is an important but subtle point: Even though an asset like gold might have inferior risk-adjusted returns to some stocks, it can be rational for an investor to include gold in his portfolio because doing so improves the portfolio as a whole. Diversification stems from correlation, and if gold has a low correlation with stocks then including it will lead to better risk-adjusted returns for the entire portfolio.

Diversification analogy: Don’t put all eggs in one basket. Photo by Katherine Chase on Unsplash

More content from the author

This blog post is a part of our intro blog series on crypto indexing. In this post, we looked at the correlation between stocks, and in the next article we study the correlations between cryptocurrencies.

Jacob Lindberg, the author of this post, is the founder & CEO of Vinter — an index provider and data analysis firm specialized in cryptocurrencies