Lowering Portfolio Risk through Diversification

Investors have an important choice to make when deciding on the size and number of investments to hold in their portfolio. On the one hand, investors can lower the risk of their portfolio through diversification. On the other, transaction costs increase with the number of stocks purchased.

In this article, we're going to discuss the topic of portfolio risk and diversification.  We're going to start that discussion with a brief overview of the risks contained within a portfolio of stocks.  Next, we'll talk about diversification, and how this concept is different from hedging.  Finally, we'll talk about an approach that can be used to minimize risk by using an optimal diversification approach.

Portfolio Risk

The Capital Asset Pricing Model tells us there are two forms of risk to which all portfolios are exposed:

  • Systematic Risk:  also known as beta and market risk, this is a macro-level threat.  For example, a recession could depress the performance of the entire stock market.  Systematic risk is evident when a diverse set of stocks, such as the S&P 500 Index, experience a decline.  Hedging is the only means of mitigating this problem.
  • Individual Stock Risk:  also known as specific, idiosyncratic, and diversifiable risk, this is security-specific.  For example, a company could make a poor business decision that leads to a lowering of their stock price.  In this scenario, the stock market may continue to rise, but this particular stock's price would fall.  Holding a diversified portfolio of stocks can mitigate this type of risk.

Diversification versus Hedging

Portfolio risk can be lowered by utilizing two related, but different, techniques.  Systematic risk can be reduced through hedging, while individual stock risk can be reduced through diversification.  The difference between the two concepts is subtle, but worthwhile reviewing:

  • Diversification:  generally, as the number of assets in a portfolio increases, the risk of the portfolio decreases.  Diversification relies on a loose relationship between the returns of the assets in the portfolio.  For example, among a group of ten stocks, one company might make a poor business decision, which results in a decrease in that stock's price.  However, the return on investment for the remaining nine companies were unaffected by this decision.
  • Hedging:  when two assets are negatively correlated, they can be held together in a portfolio to reduce systematic risk.  For example, during an economic recession, the prices of stocks will be depressed.  Fortunately, the price of gold typically rises during a recession.  This negative correlation means that gold can be held as a hedge against inflation.

To summarize, the concept of diversification applies to similar assets with uncorrelated returns.  The concept of hedging applies to dissimilar assets with returns that are negatively correlated.

Creating an Optimized Portfolio

We've talked about how risky it is to hold a single stock, and how that risk is related to an unexpected event.  The example given earlier was a poor business decision that might hurt profits.  The forecasted, or actual, profits for this company varied from the market's original assumption.  Mathematically, we could describe this risk as variance.

In October 1977, The Journal of Business published Risk Reduction and Portfolio Size:  An Analytical Solution.  Written by Edwin J. Elton and Martin J. Gruber, this study examined the mathematical formulas needed to determine the effect of diversification on risk.  On a more practical level, Elton and Gruber also examined a portfolio of 3,290 securities, and calculated the variability in returns versus the number of stocks held in a portfolio.

The table below is based on information appearing in that 1977 publication.

Stocks in Portfolio versus Risk

Stocks Variance Risk Reduced
1 46.811  
2 26.934 24.1%
4 16.996 39.7%
6 13.683 45.9%
8 12.027 49.3%
10 11.033 51.5%
20 9.045 56.0%
50 7.853 59.0%
100 7.455 60.1%
200 7.256 60.6%
500 7.137 61.0%
1000 7.097 61.1%

The above information is interpreted in this manner.  The first column of data shows the number of stocks held in the portfolio.  The variance data represents the actual variance found by Elton and Gruber for each portfolio.  The last column of data demonstrates how much risk is reduced versus holding a portfolio consisting of a single stock.   For example, by holding ten securities in a portfolio versus a single stock, an investor can lower the variability of their portfolio's return by 51.5%.

Generally, the conclusion from this study is that diversification beyond 30 securities will not result in a significant reduction in diversifiable risk.  From a practical standpoint, a portfolio consisting of at least 10 stocks will contain less than half the risk of owning the stock of just one company.

Dollars Invested and Diversification

An investor can lower risk through diversification when they take an existing investment and spread the dollars over a larger number of stocks.  For example, an investor holding $500,000 in Google stock can mitigate individual stock risk by selling $450,000 of their Google stock and purchasing $50,000 in the stock of nine other companies.  In this example, the size of the portfolio did not increase, it remained at $500,000.

If that same investor purchased $50,000 in the stock of nine other companies, without selling their Google shares, they have increased the total dollars at risk.  Even though they own shares of stock in ten companies, they now have $950,000 invested in the market.  They didn't decrease the risk associated with Google stock.  Instead, they added additional risk by purchasing shares in nine other companies too.

This is an important point.  By increasing the total money invested in the stock market, the overall risk of the new portfolio increased.  On the other hand, hedging allows the investor to increase the size of their portfolio (in terms of dollars), and reduce their overall risk.  This occurs because the return of the new investment increases, when the existing investment declines.

About the Author - Lowering Portfolio Risk through Diversification (Last Reviewed on October 14, 2016)