In 2005, someone asked me what I thought the best investment was. “Short the U.S. dollar or buy gold,” I responded—an unusual statement for an option trader. When I spoke those words, gold traded at $450 per ounce. Four years later, gold was trading at $1,150. The prediction was based on a couple of simple financial dynamics. Global Economic Forces and the Average Trader Joe In 2005, the world’s combined gross domestic product (GDP) was around $45 trillion, but the U.S. trade deficit had ballooned to $800 billion. Interest rates around the globe had already collapsed into a range of 1%–2%. Simply multiplying these numbers revealed that the U.S. trade deficit was consuming an amount of money equal to all the risk-free interest earned in the world (2% of $45 trillion is $900 billion). The situation had become unsustainable and the trade deficit was destined to unwind. Moreover, every conceivable mechanism for unwinding the trade imbalance involved a weaker dollar and a substantial increase in the money supply. The trade deficit problem was further compounded by the cost of the Iraq and Afghanistan wars, which were also consuming massive amounts of cash. The simple end result would almost certainly be a sharp increase in the price of gold as it is priced in dollars. That prediction turned out to be better than I had expected. The government went on a wild money printing binge, and by March 2006, the problem had become so severe that they stopped reporting the M3 money supply number. The dollar continued to plunge, and we eventually reached a point where the British pound was worth $2.00, the euro $1.57, and the Japanese yen $1.15. By 2008, everyone was buying gold; there were even television commercials about gold. So why did most investors and financial advisors miss this opportunity? The answer lies in the deceptive complexity of the analysis. Most investors have no idea what worldwide GDP is, and very few track the trade deficit— the two most significant components of this discussion. The concept of “risk-free” rate of return is also unfamiliar to most, as are the mechanisms by which the money supply is regulated. Where exactly does the money come from to fight a war? How does the U.S. government finance the trade deficit? Why does a weaker dollar help reduce the imbalance? How is gold priced in different currencies and when does its price move independently? What is the relationship between the federal funds rate, the typical interest rates paid by borrowers, and the riskfree rate of return? Most important of all, how does a weak dollar affect foreign investors who buy U.S. treasuries, and how does the money from these investments flow through the economy? The answers to these and many other questions form the underlying basis for understanding the trade imbalance. All the facts were readily available, but linking them together into a macro-level picture is never easy. Very few investors—or academic economists, for that matter—pay close attention to the underlying components of the trade deficit. Few realize, for example, that the imbalance is further exaggerated by differences in import-export content between nations. The U.S. tends to import manufactured products—cars, televisions, clothing—in addition to its largest import, crude oil. In return, it exports technology and less tangible products such as credit derivatives. Virtually nobody in the investment community during the early 2000s mentioned that complex banking products, including the infamous credit default swaps that ruined the banking system in 2008, were counted in the trade balance as a significant American export. In 2005, with the trade deficit approaching $800 billion, the major exports of the U.S. were dollars and jobs. In practical terms, the trade deficit became unsustainable because other countries—namely China—were lending the U.S. hundreds of billions of dollars each year to buy their products. The flow of money is always key to understanding the dynamics of any financial environment. In this case, dollars were flowing out of the U.S. to purchase foreign products. These dollars accumulated in foreign countries and were eventually lent back to the U.S. through the purchase of Treasury bonds, fixedincome securities sold directly by the government. The money worked its way through the banking system and ended up back in the hands of American citizens who continued borrowing and purchasing foreign products. The same dollars went around and around in a never-ending circle, with U.S. debt accumulating in the hands of foreign countries and foreign products piling up in American households. Another important dynamic, the one that ultimately hammered the final nail in the dollar’s coffin, was the selection of a Federal Reserve Chairman with a long history of support for “re-inflation” strategies. Ben Bernanke replaced Alan Greenspan as Chairman of the Board of Governors of the Federal Reserve System and the system’s monetary policymaking body, the Federal Open Market Committee, on February 1, 2006. His academic background includes a large number of research papers and books describing the benefits of “printing money.” In a now-famous 2002 speech, Bernanke stated: Like gold, U.S. dollars have value only to the extent that they are strictly limited in supply. But the U.S. government has a technology, called a printing press (or, today, its electronic equivalent), that allows it to produce as many U.S. dollars as it wishes at essentially no cost. By increasing the number of U.S. dollars in circulation, or even by credibly threatening to do so, the U.S. government can also reduce the value of a dollar in terms of goods and services, which is equivalent to raising the prices in dollars of those goods and services. We conclude that, under a paper-money system, a determined government can always generate higher spending and hence positive inflation. No statement could ever have been more foretelling of fiscal policy. By February 2006, we had a runaway trade imbalance and a Federal Reserve Chairman who had already articulated an inflationary strategy for addressing the problem by weakening the dollar to reduce the cost of American products for overseas buyers and increase the cost of foreign products for Americans. Wise investors recognizing gold’s history as a hedge against inflation bought gold—they were essentially betting with the house. For many of the same reasons, they also bought oil and other commodities, stocks, and bonds. Each of these markets skyrocketed on the power of a weakening dollar. Stocks became less expensive to foreign investors and the stock market climbed, bonds rallied as interest rates fell, and oil prices shot up from $55 per barrel in February 2006 to $140 during the summer of 2008. Oil was especially interesting because its price was driven by increased demand from a booming economy stimulated by low interest rates in addition to the effect of a weaker dollar. Speculators who recognized the trend jumped in and pushed prices even higher.
Forecasting with GARCH The naïve, long vol premium buy-and-hold strategy suffers large losses occasionally. For example, at the height of the financial crises in 2008, the naïve strategy would have suffered a loss of more than 14% in September. The key is to introduce simple indicators to alert yourself when turbulence threatens and avoid taking bad risk. There are endless ways of improving the naïve strategy, but two simple filters will be applied: The first filter is statistical and backward-looking, which uses its own history to draw an intelligent inference about its future. The second is forward-looking and derived from the most recent, traded market prices that contain vital information about financial market sentiment. A perfect forecast of upcoming actual volatility does not exist. A good statistical model can, however, help you build a sound forecast. By default many would use a rolling window standard deviation of daily returns as the forecast. Also popular is an exponential moving average of squared daily returns. These two proxies are easy to implement and are widely used by traders, analysts, and the like to get the first proxy of actual volatility. With the availability of intra-day data however, it is possible to just sum up high frequency return squares, which is itself a valid proxy for actual volatility. Figure 1-6 shows one-month historical volatility of USDJPY from July 29 to August 13, 2013, computed using tick-by-tick data compared with using only one data point a day. The difference can often be substantial. If high frequency data is not easy to obtain though, the next best thing you can do is use GARCH to measure and forecast actual volatility. GARCH stands for Generalized Autoregressive Conditional Heteroskedasticity. Simply speaking, it says: Volatility is time varying, meaning it changes over time from times of calm to times of anxiety, and periods of different volatility tend to cluster together, which any good forecasting model should incorporate. GARCH is a simple, elegant statistical model that incorporates all these observed properties. Financial markets tend to behave anxiously in response to disruptive events such as wars, natural disasters, or market crises. During these crisis periods, volatility tends to be much higher than it typically is as prices sharply fluctuate. This means that the volatility of the financial markets is not constant over time. A more sophisticated model would reflect that behavior. Also, dependencies in the data would have to be taken into account. Times of calm are generally followed by calm, and volatile days are followed by volatile days in a cluster. So if today’s stock price is extreme, it is likely tomorrow’s price will be extreme as well. Also, these events display mean reversion, meaning that in weeks or months, an anxious market will eventually calm back down and return to its typical long-term behavior. Hence, GARCH in the end can be thought of as a simple yet sophisticated way to describe the volatility process. It is seen as sophisticated because, rather than weigh events from yesterday and events from last month equally, recent events are given greater weight through an exponentially weighted moving average. And the model also recognizes that financial markets display mean reversion. There are countless varieties of GARCH models, and for our purposes the simplest case of GARCH (1,1) will suffice. In GARCH (1,1), today’s variance depends on yesterday’s variance, the first “1”, and yesterday’s shock (in squares), the second “1”. Figure 1-7 shows GARCH (1,1) predicted volatility against observed realized (measured using close-to-close returns), both with one-month tenor. GARCH(1,1) is the simplest model among the GARCH families. It uses only four parameters to describe the dynamics of return and its volatility. As you can see, GARCH mimics the up and downs of realized vol well, with some lags due to its backward-looking characteristic. The model relies on historical data only, so necessarily market events must occur (and be read as data) before the model can respond. Armed with a decent measure of actual volatility, the “sophisticated average” GARCH provides, you can now apply the first filter to the naïve vol premium strategy. Every month, you enter a volatility swap contract with one-month tenor in fixed amount of capital. The contract obligates you to receive a pre-determined strike level closely associated to the one-month at-the-money implied USDJPY volatility and pay upcoming realized volatility. If GARCH predicts upcoming high volatility, it indicates that recent market has experienced an unexpected large move. Something is happening behind the scenes that’s raising anxiety. If GARCH predicts a higher move, you don’t take the risk of paying upcoming actual vol in the coming month. You stay on the sideline. More specifically, if the difference between implied volatility and GARCH predicted actual volatility does not exceed a threshold, you will not take the risk of shorting volatility. Table 1-1 compares the result of vol investing with and without the GARCH filter. From January 2001 to June 2013, imposing the GARCH filter would achieve a similar level of return as the naïve strategy, which is annualized 4.74%. Standard deviation, however, is reduced from 10.1% to 8%, hence the Sharpe ratio increases from 0.47 to 0.59. In particular, the largest one-month loss of 14.7%, which occurred in September 2008, is avoided by the GARCH filter. Out of 150 months from January 2001 to June 2013, the GARCH filter switched off a total of 40 months to avoid taking risk in USDJPY vol premium. All these results assume a 0.4% transaction cost (that is, you pay 0.4% per month), which is a conservative assumption.