The past two years have brought research into the area of price momentum, where past winning assets continue to perform well while past losing assets continue to perform poorly. One way to study this phenomenon is through the angle of information of an asset. Investors perceive information, namely news of the asset and of the economy, and react accordingly, leading to a momentum effect on the price.
We will develop a rigorous expression of this idea by developing a framework that divides investors into “news traders” and “momentum traders.” News traders use current and projected fundamental information about an asset and trade on it. They look at what they think is useful information, for example an announcement of lower interest rates thereby slowing down bond investments, and take positions accordingly. Momentum traders look for established trends in an asset’s price and then take positions with the belief that the trend will continue.
Information is the glue between these two groups of traders. As information diffuses into the market, price experiences underreaction as news watchers slowly adjust to the new information. It then experiences overreaction as momentum traders seek to profit from the moves that follow the under-reaction. Knowing this, a trader wants to get into the market before it has fully absorbed this new information, which by then is too late for any gains as the market has stabilized to it.
As we shall see, identifying assets whose information takes longer to diffuse into the market can be instrumental in creating a profitable strategy. But before looking into the process of information diffusion, a quick update on momentum strategies is in order.
Excess returns in foreign exchange spot can be made by adopting a momentum strategy comprising technical rules. The strategy starts by ranking currencies using a metric. The most common one advocated by momentum traders is price.
Unlike the equity market where each asset is valued in U.S. dollars, currencies are valued vs. movement against another currency, usually the U.S. dollar. This gives rise to the difficulty in capturing movement of a currency. A simple way around this is to define a basket of currency pairs that will represent a currency. The average value of the indicators applied on the individual pairs will determine the rank of this currency.
The pairs selected to represent a currency each will have their base pair as the currency represented. For example, we define the basket of pairs EUR/USD, EUR/JPY and EUR/AUD to represent the euro currency. The premise here is that a large enough basket is significant to capture the true movement of that single currency. As the euro appreciates, market forces will dictate that the majority of currency pairs whose base is the euro will appreciate too. The indicator used to rank the euro currency would then be the average of each of the three pair’s returns. We do the same for other currencies by swapping the base of the pairs with that currency, such as GBP/USD, GBP/JPY and GBP/CHF to represent the pound.
The top-ranked currencies are assumed to continually perform better and the lower ranked ones worse. Seeking to profit from this assumption, a trader buys the pair whose base is the top-ranked pair and whose quote is the lowest-ranked pair. This is the classic momentum strategy. We shall now enhance it by exploring how we can exploit the diffusion of information into the spot market.
That the foreign exchange market has an estimated average daily turnover of $4 trillion makes us appreciate the sheer wealth of information circling the currency market, which itself comprises spot and derivatives. Too much information can also be a bad thing, so we seek a portion of it that we can quantify and then capitalize on during its diffusion into spot.
The goal, then, is to choose a market, other than spot, that contains information that reflects the interactions between investors’ decisions and price action, as well as includes as many market participants as possible. Also, to move away from the bane of lagging indicators as found in most strategies, we need a market that is representative of implied movement, usually by way of its prices being dealt in the future but being agreed upon now, i.e., futures.
Implementing our model on the futures markets brings quantitative and qualitative benefits. Daily turnover of exchange-traded currency futures and options is said to be $166 billion. A market of that size provides a data set with extensive coverage from which we can draw meaningful observations. In addition, the data are highly qualified because there is a larger ratio of sophisticated to retail investors trading futures as compared to that ratio trading spot. Therefore, the information should better reflect decisions made by hedge funds and asset managers, who in turn have done their research before placing bets in the futures market. It is the information in the futures market that we hope will enhance our profits.
After observing price movements in the futures market, news watchers decide to take positions in the spot market. Momentum traders in the spot market then react, observing a trend developing in spot from this new inflow of information (see “Volatility reactions,” below). Our goal is to take advantage of the inefficiency where the spot price reflects all the information inflow from the futures during this reactive process. To quantify this idea, we have American Finance Association Fischer Black Prize winner and M.I.T. Ph.D. Harrison Hong to pave the way.
Hong understood that flow of information from the futures markets to the spot market is characterized by the volatility of the asset. The slow diffusion of volatility found in futures prices generates an under-reaction and overreaction, which are the driving forces of momentum. Assuming interest rate parity, we know that the futures contract price is the expectation of the price of the actual currency in the future. (Interest rate parity is a theory in which the interest rate differential between two countries is equal to the differential between the forward exchange rate and the spot exchange rate. It plays an essential role in connecting foreign exchange rates with interest rates.) Futures prices exhibit volatility, either in the form of price action of a single contract or deviation of prices between contracts. This volatility, derived from expected prices, would itself be an expected volatility.
As the market evolves, what is expected becomes realized, and so this expected volatility, as calculated from the futures market, will find its presence in the spot market. Volatility is the fuel that, when lit, drives the fire.
Hong tested this idea in the equity market and concluded that small changes in the implied volatility of a stock preceded a large jump in the underlying price. In his study, information flow is characterized by the diffusion of options volatility. In addition, he also concluded that stocks are heterogeneous in their information diffusion speed, which implies momentum traders can benefit if they know where stocks are in their diffusion cycle. This is an important point we’ll use to formulate our strategy.
In casting Hong’s conclusion to the currency market, options volatility is analogized to futures volatility, making the theme of spot reacting to futures akin to underlying reacting to options. For currencies whose futures volatility has yet to diffuse into the spot, momentum traders should then take positions before the diffusion to capitalize on the impending big moves. For those whose diffusion has already occurred, spot prices would have stabilized, hinting that positions are being closed out. Now, we quantify futures market volatility using models developed for such.
A cash asset such as spot gives rise to only one calculation of volatility: The historical volatility from its time series. Futures contracts introduce an additional element, time to expiry. Volatility models built on this contract brings the possibility of quantifying volatility in different ways. We either can use a model implemented on a futures curve or a model implemented on a futures’ price series. We’ll consider both types of models.
Consider a volatility model that looks at the futures curves to calculate the expected volatility. On the close of a trading day, we’ll consider the futures settlement price of all contracts available on that day. For currency trading, these typically would be the quarterly contracts March (H), June (U), September (M) and December (Z). The expected volatility would then be the standard deviation between the settlement prices of these contracts at the close of a day. The standard deviation can either be a normal one or a weighted one. We call this our curve volatility model (see “Futures curve volatility model,” below).
Next, consider a more involved volatility model that allows each contract to exhibit its own volatility measure. It is important to differentiate between the modeling of spot prices and the modeling of futures prices. While the uncertainty in spot price usually is due to a volatility model that is left unchanged throughout the entire price series, futures behave slightly differently. The earlier months of the futures curve tend to be more volatile than the later months. That is, futures price volatility increases as the futures contract nears maturity. Our volatility model on the futures prices needs to incorporate this market behavior. Our volatility model on the futures series needs to incorporate this market behavior.
One way is to model the spot price of the currency as a mean-reversion process and extract the volatility from there. Those familiar with options pricing will recognize this as the typical assumption that the underlying follows Brownian motion. The math will show, as it should, that for contracts nearer to expiry, the expected volatility is given as the historical volatility amplified by a factor.
Another way to calculate futures volatility is to consider the volatility term structure. By studying the price distribution of futures, the futures price of a currency changes due to two distinct components: The delivery horizon in relation to the expected spot price and the new information up to settlement date. The conclusion is a volatility term structure where futures volatility nearer to expiration, the short term, is emphasized differently than that further to expiration, the long term.
In the short term, futures prices that respond to new information are subjected to the same mean reversion, devoid of any other influences. We’ll then use that same model to calculate the volatility, but only in the duration of three months leading to expiry. In the long term, volatility tends to level off at a positive point, reflecting uncertainty in interest rate changes. So volatility is taken to be the usual realized volatility for other times not in the short duration period. As both short-term and long-term volatilities are independent, the expected volatility is then an addition of the short and long volatilities. No weights are required as the time issue is already considered separately in each of the volatilities (see “Term structure volatility model,” below).
Hong believes that the flow of expected volatility from the news to actual volatility in the market is given by the daily change of volatility, called the volatility growth, of the contract. Implicit in the price of futures is the market sentiment of sophisticated investors. By looking at the change of expected volatility, we are studying the diffusion speed at which expected volatility will find its way in the spot market. Knowing that diffusion is slow is key for timing our trades. The ideal scenario is to take positions on currencies that are trending, but with slow diffusion speeds. The rationale is that we want to be in the trade just before a big move happens.
Given any momentum portfolio, the volatility growth can be used to enhance it in two ways: Double sorting and dynamic sizing. Each algorithm itself can be paired with any of the three volatility models we mentioned. If our theory is sound, either enhancement with any volatility model will improve the profits of a given momentum portfolio.
Double sorting works like this: After an initial ranking of currencies by returns, we form a group of the best three performers and a group of the worst three performers. Within the best (worst) group, we’ll re-rank them by their volatility growth where those with lower growths are ranked better (worse) than those with higher growths. Volatility growth is a non-directional measure, meaning that it is always better to have a lower growth value that implies the anticipation of volatility flowing to the market. Our buy signal now becomes the currency pair whose base currency is the best performer with lowest growth and the quote currency is the worst performer with the lowest growth. Sell signals are vice versa (see “Double sorting benefits,” below).
The double sorting algorithm can be seen as a filter to pick the best of the best or the best of the worst. Our trust is that the volatility growth will give us that added confidence in placing a trade which has a trend, that is not yet fully realized. On the other hand, dynamic sizing is more of a risk management technique where we trust the volatility growth to tell us the appropriate amount of capital to risk in a trade.
After the initial ranking by returns, we buy the currency pair whose base is the best performer and quote the worst. But this time, our trade size is scaled linearly depending on where the base currency is ranked by volatility growth. As we have 10 currencies, we’ll risk 100% of the trade size if our base currency is the lowest ranked. The second lowest ranked will risk 90%. Third lowest will risk 80%, and so on. For a notional value of $1 million, this equates to trade sizes of $1 million, $900,000 and $800,000, respectively. As seen, we are risking a small trade size for positions whose expected volatility is close to being realized. Somewhere between news watchers acting on information in futures and momentum traders reacting to changes in spot is the transient for us to make profits, but not risk too much capital as we know that markets are midway through stabilizing from the volatility diffusion.
Exit rules for all systems will be a moving average crossover, namely close long trade when fast signal crosses under slow signal, along with a trailing stop loss which starts an average true range multiple from the entry and moves to breakeven when price moves another ATR multiple into the money. As our model’s focus is timing entries, exits are basic. Our test period is two years and slippage is a realistic two basis points per trade.
With the exception of one system, the volatility diffusion enhancements worked like a charm. Our reference momentum portfolio started with a Sharpe of 0.61. By applying double sorting using the futures curve weighted volatility model, we improved the Sharpe to 1.14. Annual return is 8.4%. The cumulative profit and loss of double sorting using any volatility model is always higher than that of our original portfolio. It is always best to wait for a currency to have a low expected volatility at the cusp of its breakout before taking a position ( “Returns: Double sorted momentum,” below).
Enhancements through dynamic sizing also showed benefits. The biggest improvement comes when we size our trades based on the volatility growth calculated using a one factor term structure model. It has a Sharpe of 0.83, up 0.22 from our original number, and an annual return of 5.03%. Performances of the four different sizing models are similar in 2012 and 2013. Only in 2014 did they start to diverge where term structure models performed better than curve volatility models. Particularly, the curve weighted model’s returns dipped -0.02% from our initial momentum portfolio (“Returns: Dynamic sizing,” below).
Curve models are best used for double sorting, and term structure models are best used for dynamic sizing. In deciding which currency among momentum currencies has the largest imminent move, the futures curves seem to contain all the information needed. As institutional traders inspect the futures curve every day, this information is indicative of what sophisticated investors think. Therefore, the curves of two different currencies whose volatility is going in different directions should tell us clearly which currency to trade.
For dynamic sizing, we are placing half our confidence in the idea that trading on volatility diffusion works. Because term structure models emphasize the realized volatility differently based on how far it is from expiration, it could be that our confidence is in the half that correctly characterizes the volatility, short-term or long-term, thereby producing a signal reflective of the currency’s real momentum. Volatility diffusion has its value in enhancing a momentum portfolio.
Volatility in the currency market has been at record lows. Traders are blaming central banks for their monetary easing policies. Hedge funds have shuffled allocations as equities have provided more movement. Will a slow currency market lead to the demise of currency managers?
Of course not all volatility will return, but our model suggests there is another way to look at this market. Instead of trying hard to find movement when it’s not there, momentum traders should wait for the signs of volatility diffusing from futures to spot and capitalize. It may sound demeaning to linger as others move, but profiting by knowing where and when big trends will emerge is witty and fruitful.
Donny Lee works as a quantitative analyst for an Asian-based hedge fund. Reach him at firstname.lastname@example.org.