(MoneyWatch) One of the most persistent mistakes made when building a portfolio is evaluating potential investments in isolation, instead of considering how their addition impacts the overall risk and return of the portfolio as a whole. The following is a great example of why this is a mistake. I happened upon it when preparing a presentation on commodities’ impact on portfolios.

We’ll use the S&P GSCI Index to represent commodities. The table below shows the annualized returns and annual standard deviation for the S&P GSCI as well as for the S&P 500 Index and five- and 20-year Treasuries over the period 1970-2012, the longest for which we have data.

We see that the S&P GSCI produced both lower returns and higher volatility than the S&P 500. In hindsight, with perfect knowledge of the return and volatility data, would you want to add a 5 percent or 10 percent allocation to commodities, taking that allocation away from the S&P 500? If you’re like most investors, your answer would be no. Yet, the data shows otherwise.

We’ll look at typical 60 percent stock/40 percent bond portfolios using the S&P 500 for the stock portion and both the 20-year and the five-year Treasury for the bond portion. Note that the Sharpe ratio is a measure of risk-adjusted returns. (The higher the more efficient the portfolio at delivery returns for a unit of risk.) In all cases, portfolios are rebalanced annually.

In both cases, we see that adding commodities while reducing the stock allocation both raised the return of the portfolio and lowered the volatility. The improvements in the efficiency of the portfolio were a result of the low/negative correlations of commodities to both stocks and bonds. And when you have negative correlation of returns, high volatility is actually a good thing. Below are the annual correlations of the S&P 500 and the S&P GSCI, plus the MSCI EAFE data so you could see that commodities also have low correlation to international stocks as well as domestic stocks.

While this example provides a clear illustration of the benefits of diversification and why you shouldn’t consider an asset in isolation, there’s a problem we should consider. Commodities shouldn’t be expected to produce returns so similar to the return on stocks. Would the diversification benefits hold up if commodities produced returns that were much lower than the returns to stocks?

To answer this question, we’ll look at the past 20 years. Limiting the data to this period also allows us to include the data on a broader commodity index: the DJ-UBS Index. The S&P GSCI has a higher concentration in energy-related commodities than does the DJ-UBS. The table below presents the data on returns and volatility.

In this period, the S&P GSCI underperformed the S&P 500 by 4.6 percent and did so with 7.5 percent greater volatility. So we’ll ask again: With the benefit of hindsight, would you want to include an allocation to commodities? As before, we’ll look at a typical 60/40 portfolio.

Whether we included an allocation to either the S&P GSCI or the DJ-UBS Index we find that while returns fell slightly, volatility fell more so, producing a more efficient portfolio. It’s important to note that this was a period of declining inflation, when the hedge that commodities provide against unexpected inflation wasn’t needed. Yet, even in this environment, including commodities led to a more efficient portfolio.

The reason we see that benefit is because of the low/negative correlations with both stocks and bonds. The table below presents the correlation data.

There’s one more point we need to make regarding viewing investments in the right way: in the whole, not in isolation. I hope that by going through the math here you’ll see the importance of viewing things the right way. Taking the time do go through the math will help you avoid the mistake of viewing things in isolation in the future.

For our example we’ll use the data for the period 1993-2012 and take the case of the portfolio with a 10 percent allocation to the S&P GSCI, which returned just 3.6 percent. If there was no diversification benefit (which comes from rebalancing the portfolio) the portfolio’s return would be equal to the weighted average return of its component parts. However, since we do rebalance, we need to see what the return contribution of the commodity allocation was. The math is straightforward and simple.

We begin with the 50 percent allocation to the S&P 500 which returned 8.2 percent, so its weighted impact on the portfolio was 4.1 percent. The 40 percent allocation to the 20-year Treasury earned 8.6 percent, so its weighted average impact was 3.44 percent. Combined, we have accounted for 7.54 percent of the portfolio’s 9.0 percent return. Thus, the 10 percent allocation to the S&P GSCI contributed the remaining 1.46 percent. Given the S&P GSCI’s 10 percent allocation, the weighted average impact on the portfolio’s return was 14.6 percent, or 11 percent greater than its return when viewed in isolation.

Commodities tend to perform best in periods of rising inflation (which can negatively impact the returns of both stocks and bonds) and during periods of supply shocks (when the supply of commodities is negatively impacted), though not demand shocks like we had in 1981, 2001, and 2008. Their addition to a portfolio has historically reduced the tail risk (both good and bad) of investing in a portfolio that only includes traditional stocks and bonds. Risk averse investors should be willing to trade off some upside potential to remove some downside risk. Thus, risk-averse investors should consider including a small allocation of commodities to their portfolio. Because of their high volatility and low/negative correlation with traditional assets, even a small allocation can have a meaningful impact on the overall portfolio, as you saw.

Finally, an irony is that the very people who might benefit the most from including commodities tend to avoid them due to their risk and low expected returns. However, when viewed correctly, retirees should view commodities favorably. The reason is that almost by definition they’re more risk averse because the risk of poor portfolio performance has a much greater impact when in the withdrawal phase of your investment career. In addition, retirees are often more subject to the risks of unexpected inflation, as they can no longer depend on labor income which tends to rise with inflation.

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