Merrill
Liechty
Lance Stover
Murray Spence
TABLE OF CONTENTS
Part 1: Dual Moving Average Crossover
Part 3: In Sample Results Analysis
Part 4: Parameter Selection for Out-of-Sample Analysis
Part 5: Out-of-Sample Forecasts
Part 7: Where Do We Go From Here?
The concept of a dual moving average crossover is fairly straightforward. Calculate two moving averages of the price of a security, or in this case exchange rates of a currency. One average would be the short term (ST) (strictly relative to the other moving average) and the other long term (LT). Mathematically speaking, the long term moving average (LTMA) will have a lower variance and will move in the same direction as the short term moving average but at a different rate. The different rates of direction, induces points where the values of the two moving averages may equal and or cross one another. These points are called the crossover points.
In the dual moving average crossover trading strategy, these crossovers are points of decision to buy or sell the currencies. What these crossover points imply depends on the approach the investor has in their strategy. There are two schools of thought: Technical and Value.
The Technical Approach suggests that when the Short Term Moving Average (STMA) moves above the LTMA, that represents a Buy (or Long) signal. (Conversely, when the STMA moves below the LTMA, the Technical Approach indicates a Sell (or Short) signal.) The intuition behind this strategy can be explained in terms of momentum. Basically, the principle of momentum states that a price that is moving up (or down) during period t is likely to continue to move up (or down) in period t+1 unless evidence exists to the contrary. When the STMA moves above the LTMA, this provides a lagged indicator that the price is moving upward relative to the historical price. Buy high, sell higher.
The Value Approach offers the opposite trading signals to the Technical Approach. The Value Approach claims that when the STMA crosses from below to above the LTMA, that the investment is now overvalued, and should be sold. Conversely when the currency STMA moves below the LTMA then the currency is undervalued it should be bought. The intuition behind the Value Approach can be thought simply as a mean reversion approach. Buy low (value), sell high (overvalued).
Both strategies try to achieve the same goal, but do it in opposing ways to one another. In this paper, we will analyze both the technical and value strategies as applied to the Euro/USD currency exchange rates.
The following graph shows how the dual moving crossover trading strategy produces buy and sell signals. Note that the gains and losses are calculated by taking the difference between the price (not the moving average value) at signal points. So, the actual price traded will, with great probability not equal the corresponding moving average values.
Below is a table that summarizes the data that we used for this assignment:
Type of Data |
Interval |
Start Date |
End Date |
# Total Observations |
# Observations (excluding weekends) |
Out of Sample “Hold Out” Observations |
Euro/USD FX |
5 minute |
January 3, 1999 |
February 6, 2002 |
328,000 |
228,000 |
75000 |
Note about Software:
Microsoft Excel was unable to handle the number of observations that we were able to obtain. It was therefore necessary to use a different software package to do the calculations or write software ourselves. We decided that C++ was an appropriate language to use.
Methodology:
We wrote C++ code to do the following functions with the data:
1. Clean data, including filtering out weekends, holidays, and stale periods.
2. Breakout the specified long and short term moving averages.
a. Used Fibonacci Series as a starting point for short term and Long term (first 12 – 5,8,13,21,34,55,89,144,233,377,610,987 – examined. Results not different from below).
b.
Calculate all combinations of 10 period increments up to
1000.
e.g. 10,50; 230, 740 (runtime of approximately 30 minutes, 5050 possible
combinations)
3. Calculate the crossover points,
4. Identify crossover as a Buy or Sell
5. Calculate results: (with and without slippage of 0.0003)
a. Profit
b. # wins/losses/
c. #trades
d. Max win/loss
e. Average win/loss
f. # periods below initial investment
g. Max portfolio value
h. Min portfolio value
6. Determine which moving averages to use in out of sample testing.
7. Perform out of sample analysis.
8. Compare in sample with out of sample.
The table below summarizes the in sample trial results that were conducted.
The following are three key analyses from the in sample calculations:
At this point in the process we developed a selection methodology for determining what range of STMA and LTMA parameters we would recommend for out of sample analysis. The process follows:
The table below summarizes the out-of-sample trial results that were conducted.
From the out-of-sample analysis, we discovered that by utilizing a well-conceived parameter selection process, it appears that we did indeed succeed in selecting profitable DMAC combinations. The out-of-sample combinations showed considerable improvement over the in-sample combinations. Compare 89% profitability (screened, out-of-sample) versus 35% (all possible combinations, in-sample). Also, compare 2.5% average return (screened, out-of-sample) versus –4.0% average return (all possible combinations, in sample). Perhaps even more importantly, the screened, out-of-sample results showed a far lower standard deviation and downside risk. In fact, the worse return among the out-of-sample results was a –2.7% return.
There are portions of our analysis that must be analyzed to determine where there may be underlying hazards (i.e. risks) that may not be readily apparent:
1) Data – Clean and unbiased data is vital to good analysis. Given the reliability in the source of the data, we feel fairly confident that the data is indeed accurate; however, our analysis only examined a single currency for a 2 ½ year period. Although our approach was purely technical in nature, this single data set does not justify generalization across other currencies or asset classes (e.g. futures, equities).
2) Methodology – A fine line exists between good optimization and data mining. By examining all possible combinations of DMAC with STMA and LTMA parameters between 10 and 990, we opened ourselves to the temptation of data mining to generate favorable results; however, by employing a well-conceived parameter selection methodology, we felt confident taking the recommended range of parameter values out-of-sample. Considering that nearly 90% of the selected DMAC combinations were indeed profitable out-of-sample, it is rather unlikely that we could achieve these results through a data mining or “over-optimized” parameter selection methodology.
3) Risk – Besides taking a rather cursory look at the standard deviation of the expected return and the minimum total return, we did not complete a thorough evaluation of the risks involved. Investors would also be interested in metrics such as maximum drawdown at any period in time. (This information would also be relevant to the incentive structure for hedge fund managers.) In sum, a more thorough examination of risks should be explored. Perhaps this analysis could yield a “filter” approach to buy and sell signals. As a result, we would not need to adopt an “always in (excluding weekends)” strategy.
.
It is clear from our results from both the in sample and out of sample analyses, that there must be even smarter ways capture the available profits with the DMAC trading strategy.
Capture
more profit through better timing strategies
We can see from the DMAC graph (see Section 1) that much of the potential profit is lost when the trading signal is provided. This is because the moving average is a trend-following, lagged indicator that only reflects past price action. As we have shown in our analysis and results, most of the profit potential is lost at that point to trading costs (i.e. the banks get it in the foreign exchange market). In order to capture more of the available profits, we recommend investigating the following ideas and strategies.
Selection of Asset Classes (Currencies, Securities, Futures)
In our analysis, we used data that was provided to us by Professor Campbell Harvey. It is reasonable to assume that it is possible to go through an analysis to select more profitable currencies and securities. Some possible methods for selection include
Catastrophic Event Analysis
In the wake of multiple major or catastrophic events in the last 3 years including: August 1998 (Russian default); March 2000 (fall in US stock market); September 11, 2000 (Terrorist Attack). Although we have included two of these three events in our data, we still feel that an analysis should be done to plan for such events (i.e. exit strategies), and their impact to our positions.