Stochastic model & statistical method to estimate gold exposure
By Tim Leung, Ph.D.
Gold is often viewed as a safe haven asset or a hedge against market turmoils, currency depreciation, and other economic or political events. For instance, during the credit crisis, the Dow and S&P 500 declined by about 20% while gold prices rose from $850 to $1,100 per troy ounce. And then this year, S&P500 has experienced a sharp drop before returning to pre-COVID level lately. Meanwhile, gold ETF (GLD) has gained more than 25% since Feb 2020.
During the Feb 18, 2020 — Aug 17, 2020 (6 months), the S&P500 ETF (SPY in green) has experienced a sharp drop before returning to pre-covid level. Meanwhile, gold ETF (GLD in blue) has gained more than 25%.
To gain exposure to gold, there are a number of related products, including gold exchange traded funds (ETFs), leveraged ETFs (LETFs), gold futures, and gold miner equities.
However, the price of gold does not exist in a vacuum. Gold must be mined and the companies that perform this mining process are themselves traded companies. This gives another avenue for investors to achieve exposure to gold, while allowing them to determine investment decisions through standard equity research techniques.
In addition to the spot gold, there are a number of single-name gold miner stocks and (L)ETFs available for trading. Even though general equity sector ETFs are by far the largest by market capitalization, gold miner (L)ETFs are some of the most popular vehicles for short-term trading available on the market. On the other hand, not a single gold miner ETF appears in the top 20 when ranked by AUM, which suggests that the recent primary interest in gold and gold miner stocks is heavily driven by speculative traders seeking gold-like exposure. Therefore, understanding the underlying factor dynamics of gold miner ETF returns are practically useful for analyzing popular trading strategies, such as pairs trading.
Gold miner stocks are leveraged play on physical gold.
Standard equity market research has established several rules of thumb to understand the differences of investing in gold miners vs. gold itself. While in the long run there is a clear correlation between gold prices and miner equity prices, price divergence is not unusual. For example, the short-term performance of gold miners is very sensitive to both the market discount rate and payments of future dividends, which are dictated by the general equity markets. Furthermore, at the individual firm level, management could have a significant impact on the equity returns through superior investment skills, mine openings and closures, cost cutting, or market timing. However, in the long run, the only way for gold miners to make money is to dig gold from the ground and sell it on the open market.
Therefore, in our recent paper we propose a model to describe the connection between gold and miner stocks. It is a tractable structural model that directly relates gold prices to the value of gold miner equity via a combined optimal control and stopping problem. This real options model requires gold miners to set an internal production function, liquidating the company assets when gold prices decline past a certain level. In particular, our model suggests that a dynamic portfolio of physical gold would perform identically to an actual portfolio of gold miners.
Our model gives explicit analytical expressions for the value of firm’s assets, the value of the firm’s equity, and precisely identifies the parameters which affect firm’s leverage. In fact, we examine the predictions of our real options model, finding that a significant part of gold miner firm’s leverage can be explained within the real options framework!
Furthermore, we use the insights from our structural model to develop a method to replicate gold miner stocks, using only physical gold and the market equity portfolio, that can explain about 70% of the variation in gold miner stock returns. Our main empirical insight suggests that gold-miner equities have a call option-like payoff, which results in higher implied leverage and negative alpha relative to physical gold.
Plots of model implied gold leverage (raw) vs. Kalman filtered time series (red) and simple moving average (green) of the implied gold leverage, for Barrick Gold (ABX), Gold Corp (GG), Gold Miners ETF (GDX), Junior Gold Miners ETF (GDXJ).
K. Guo, T. Leung, and B. Ward, How to Mine Gold Without Digging, International Journal of Financial Engineering, Vol. 6, №1, 2019 [PDF]
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