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September 29, 2009
These projections are relevant for the next several years, because we have calibrated the volatility of the S&P500 to this time-frame. Over much longer periods, we can expect (hope) that broad market volatility will settle down to a level more consistent with its long-term history. (For the S&P500, that’s around 15%.) In the immediate future, however, signs in the market suggest that volatility will remain high. The projected 8.7% expected return is higher than historical returns for gold over any of the periods of above, but the volatility is also substantially higher than for any long historical period. The projected volatility of 27.3% is very close to the current implied volatility in long-dated options on GLD (Jan 2011 options have implied volatility of 28%).
The Monte Carlo projections reflect expected values. When an asset class has substantially outperformed its expected returns over an extended period, it is because of a downward correction (and vice versa). When we compare the last three years to expected returns as a measure of valuation, the results are quite striking:
Expected vs. Trailing Returns
This approach to estimating valuation is purely statistical and uses no fundamentals—it is only part of the story. That said, it has historically been a useful indicator. Even though the projected average return for GLD is above the historical returns for gold for any of the long periods of history discussed at the start of this article, the trailing returns are higher still. It is also noteworthy that while GLD is the most overvalued of the asset classes in the table above, commodities (DJP) are the most undervalued. Investors have been selling off commodities as a whole at the same time that they have been buying gold! This suggests that the money flows into gold are not merely a rational response to inflation fears. Similarly, while TIPS have very slightly outperformed their expected returns, a fear of inflation is inconsistent with the fact that TIPS have underperformed nominal bonds (AGG and TLT). If fear of inflation was driving returns, TIPS would outperform nominal bonds.
The disproportionate run-up in gold may instead reflect some behavioral bias towards gold as a ‘safe’ store of value, but it mostly owes to simple performance-chasing. A good indication that the run-up in gold is largely driven by performance-chasing is the fact that the Morningstar investor returns lag the total returns on GLD by 2.2% per year over the trailing three years through August 2009.
The historical data suggest that gold is selling at a premium relative to other commodities and relative to inflation-protected bonds, which is consistent with the Monte Carlo projections.
The Monte Carlo projections of fair value must be understood in the context of the fact that projected returns using portfolio theory rest on somewhat shaky ground. Portfolio theory has trouble explaining the expected returns that have been observed for commodities. That said, our estimates for the expected returns from the Dow-Jones AIG Commodity Index are consistent with historical and projected values from Ibbotson, which provides some sense of consistency and rationality.
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