Portfolio diversification remains the cornerstone of modern portfolio theory. The main concept of diversification is quite straight forward. Diversification minimizes the overall portfolio risk and therefore it protects investors against heavy drawdowns during times of market turbulences. Therefore, diversification increases the likelihood that the portfolio will be able to compound its way to long-term wealth accumulation.

However, during the financial crisis many so called "diversified portfolios" experienced significant losses and therefore this investment strategy faced widespread criticism afterwards. That happened only because the concept of diversification is often being misunderstood. Many portfolios only look balanced from a pure capital allocation point of view, but not from a risk perspective! In addition, many investments are classified as diversifiers, although they are not. For example, an investor is spreading its capital among emerging markets (NYSEARCA:EEM), real estate (NYSEARCA:RWR), large caps (NYSEARCA:IVV) and commodities (NYSEARCA:DBC). Despite the fact that this portfolio looks quite balanced from an asset class point of view, the portfolio will not be diversified at all, since those asset classes are highly correlated to each other (Correlation Matrix - Chart 1).

Chart 1: Correlation Matrix

Thus, in the following article, we would like examine the "diversification ratio", a metric which can help investors to measures the degree of diversification within their portfolio. This ratio is the weighted average of the volatilities of assets to the volatility of the portfolio of the same assets. The result of this calculation measures the essence of diversification. Since different asset classes are not perfectly correlated to each other, this ratio in general > 1. In other words, the volatility of a well diversified portfolio is greater than the sum of its underlying investments, as the overall risk of such a portfolio is less than the weighted-average risk of its component holdings. Therefore, every investor can measure the degree of diversification within every portfolio quite easily, with the following metric:

(wi = portfolio weight in asset i, σi = the risk of asset i, σp is the total risk of the portfolio)

In addition, there is only one portfolio combination that has the highest diversification ratio and thus represents a real diversified portfolio (Chart 2). After we have already written about how to construct the Most Diversified Portfolio, where the diversification ratio is being used in an advanced manner, we would now like to highlight the relationship between the diversification ratio, portfolio volatility and maximum drawdown in order to visualize the benefits of the so called diversification ratio.

For that reason, we will calculate the total portfolio volatility, the maximum drawdown as well as the diversification ratio for all possible portfolio combinations (231 portfolio combinations with 5% steps) with the following asset classes:

- Equities: iShares Core S&P 500 ETF (IVV)
- Bonds: iShares Barclays 20+ Year Treasury Bond ETF (NYSEARCA:TLT)
- Gold: SPDR Gold Shares ETF (NYSEARCA:GLD)

The asset classes have been chosen since they tend to be quite uncorrelated to each other. There is no allowance for transaction costs or brokerage fees. In order to minimize transaction costs, we rebalance the portfolio on a weekly basis, whereas 1 day slippage is included.

In Chart 2, we have highlighted the historical annualized portfolio volatility as well as the maximum drawdown for all three underlying asset classes, plus for all possible portfolio combinations. From 2005 until 2013, the annualized volatility of the iShares Core S&P 500 ETF was slightly higher than 20 percent and the maximum drawdown was slightly less than 60 percent. With 14 percent, the iShares Barclays 20+ Year Treasury Bond ETF had the lowest annualized volatility, whereas its maximum loss was 25 percent, during the same time period. The SPDR Gold Shares ETF has shown a 20 percent annualized volatility and a maximum drawdown of slightly more than 30 percent.

The blue points are representing all possible portfolio combinations. As shown in Chart 2, any given mixtures of asset classes are more efficient in terms of portfolio volatility and drawdown reduction than an investment in a single asset class. Moreover, it is possible to reduce the risk/volatility and the maximum drawdown of bonds significantly, by adding riskier uncorrelated asset classes! In our example, the most efficient portfolio, in terms of volatility and drawdowns, is a combination of 20 percent equities, 20 percent gold and 60 percent bonds. In other words, by adding equities and gold to a bond portfolio, the total portfolio volatility is nearly being reduced by 50 percent (from 14 percent to 8 percent), whereas the maximum drawdown is less than 14 percent, compared to 25 percent for a single bond portfolio!

Chart 2: Maximum Drawdown & Portfolio Volatility of all Portfolio Combinations

However, the main problem for investors remains the same: How to identify the perfect asset allocation mixture? To answer that question, investors should apply the diversification ratio, to measure the degree of diversification benefits within their portfolio since there is a strong relationship between the diversification ratio and the maximum loss of any given portfolio.

To show that strong relationship, we have plotted the diversification ratio and the maximum drawdown for all possible portfolio combinations in the chart below (Chart 3). As you can see, the most efficient portfolio has also the highest diversification ratio! Furthermore, any given mixtures of asset classes have a higher diversification ratio than a single asset class investment and are therefore reducing the maximum drawdown!

Chart 3: Maximum Drawdown & Diversification Ratio of all Portfolio Combinations

The bottom line: diversification is an extremely important investment strategy for every individual investor as it is the only free lunch an investor can achieve. Increased diversification reduces the overall portfolio risk/volatility/drawdown without a corresponding reduction in expected portfolio returns. Since creating a diversified portfolio is one of the most important tasks investors must accomplish, the diversification ratio can be a good measure to double check the strategic asset allocation of your portfolio.

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