Professor Paulo Santos from ESGT Santarém and University of Lisbon in Portugal and I constructed diversified asset portfolios with strong flavor of precious metals for the daily period 1995-2011.  We examined the optimal weights of these differently diversified portfolios after subjecting them to downside risk as defined by value at risk (VaR) models which are used in conducting stress tests.

These are the three portfolios:

• Portfolio #1:  Gold, Silver, platinum and palladium. The estimated optimal weights for this portfolio are: Gold (58%), Silver (22%), Platinum (18%) and Palladium (2%).

• Portfolio #2:  Gold. Silver, platinum, palladium, Brent and the S&P500 index, with the following estimated optimal weights- Gold (44.62%), silver (3.67%), platinum (25.69%), palladium (1.95%), Brent (11.61%) and S&P 500 (12.46%).

• Portfolio #3:  Gold, Brent and the S&P500, with the following  derived optimal weights: Gold (66.44) , Brent  (22.65) and S&P 500 (10.91).

It's interesting to note the difference in weights of silver in Portfolio # 1 and Portfolio # 2, which suggests that oil and the S&P 500 index have the upper hand over the grey metal when all are included in a more diversified portfolio. We may add that when a highly volatile asset like silver is joined in an optimal diversified portfolio with key assets like oil and stocks, the highly volatile asset assumes a much lower weight in the portfolio. Silver is subject to much tighter supply than gold where the  mined amount of gold is about 100 times the amount of mined silver but both are demanded at the same time and at almost 1-1 dollar basis during strong investment demand.

This weight-losing phenomenon for silver did not happen in the optimal portfolios to gold which is the least volatile among the six assets include in the second portfolio. It seems that silver is moving away from gold and being the second safe haven to more of an industrial metal and closer to Dr. copper.

Optimal returns of these three portfolios on the basis of 250 business days in a year are consecutively:

           9%   8.5%    8.625%.

The historical upside and downside risk gauge (or the standard deviation) of these three portfolios also calculated on the basis of 250 business days in a year is consecutively:

            2.516   2.15575   2.342.

On the other hand, the downside risk only is measured by the value at risk (VaR) which expresses the probability for loss or the downside risk. The VaR for each of the three portfolios are: Portfolio # 1 is -0.028089, Portfolio # 2 is -0.022224 and Portfolio # 3 is -0.03168. This implies that the more diversified the portfolios are the lower their down side market risks.

The most diversified portfolio (Portfolio # 2 with six assets) has the lowest risk and lowest return, among the three portfolios. This is consistent with portfolio diversification.  It’s interesting to note that contrary to the other portfolios, the least diversified portfolio (Portfolio # 3) exhibits positive skewness compared to negative skewness for the other two portfolios, and it also has the least kurtosis. The positive skewness means this portfolio has greater chances to have positive returns than negative one, and still yields greater return slightly higher return than the most diversified portfolio but at marginally higher risk.

The difference in the characteristics of these precious metals-flavored portfolios is not much. It will be more interesting to do the same exercise for optimal portfolios that have more diversified hard and soft assets.

We should add that the results of the VaR models are sensitive to the time horizon on which they are based. Thus, our results are hindsight tests which would have maximized returns on portfolios if these derived optimal strategies had been followed over the last fifteen years.