In my previous article, we discussed whether bonds, gold, and commodities have a role to play in a balanced portfolio based on their correlation with equities and volatility.

Now let's decide whether the balance of returns and volatility for bonds, gold, and commodities warrants adding these asset classes to a stock portfolio.

As we now know, the correlation between stocks and other asset classes is extremely variable. However, when measuring the volatility of asset classes, one finds that volatility is more stable over time and therefore easier to measure when developing an asset allocation strategy.

The key is to understand the relationship between the expected returns and the volatility of an asset class.

First, one must understand that volatility can flatten returns like a pancake. Let me give you an example to illustrate my point.

Below are two investments, both with an average annual return of 10% yet drastically different volatility. Investment "A" has volatility of 3%, and Investment "B" has volatility of 39%. Here's how their value appreciates over five years, given an initial investment of \$1,000 each:

Year

Investment A Price Change

Investment A Value

Investment B Price Change

Investment B Value

Year 1

6%

\$1,060

60%

\$1,600

Year 2

12%

\$1,187

(40%)

\$960

Year 3

10%

\$1,306

10%

\$1,056

Year 4

16%

\$1,515

(25%)

\$792

Year 5

8%

\$1,636

45%

\$1,148

As you can see, the cumulative gains for these investments with the same 10% annual returns are 64% versus 15%! As I said, volatility can flatten your return.

So how much volatility is too much?

The answer lies in how big of a return you expect for the amount of volatility you take on -- i.e., how efficient the asset class is.

Asset class efficiency is measured by the Sharpe Ratio, which is calculated by subtracting the expected return on Treasury Bills from the asset class' expected return and dividing the result by the corresponding historical volatility of the asset class.

For investors with a long-term time horizon, below are the major asset-class options, along with the corresponding hypothetical expected returns, historical volatility, and efficiency numbers (Sharpe Ratios). The assumed rate on Treasury Bills is 0.5%.

Asset Class

ETF

Return

Volatility

Efficiency

Stocks

Vanguard Total Stock Market Index

10%

16%

0.59

Bonds

Vanguard Total Bond Market Index

3%

4%

0.63

Gold

SPDR Gold Shares

7%

19%

0.34

Commodities

iShares S&P GSCI Commodity-Indexed Trust

10%

25%

0.38

For long-term investors with an allocation of 70% to 90% in stocks, the question becomes which asset classes have the same efficiency as stocks or higher and can improve the overall efficiency of the portfolio through low or negative correlation.

Bonds are the most efficient asset class and have a long-term correlation to stocks of -0.34.

Gold and commodities both have lower efficiency and positive correlations to stocks.

From a long-term asset-allocation standpoint, clearly 10% to 30% of your asset allocation strategy should include bonds to improve the efficiency of the overall portfolio.

Adding gold or commodities to a stock portfolio will drag on returns, increase volatility, decrease efficiency, and, most importantly, decrease the cumulative gains of the overall portfolio.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.