Understanding Portfolio Risk in FX: Strategies for Mitigation
When multiple positions are opened, risk management techniques from traditional portfolio management are applied.
Portfolio management, unlike trading, is centered on long-term investment objectives. It emphasizes diversification across asset classes, including stocks, bonds, commodities, and derivatives. The choice of investment securities and their respective weightings are carefully structured to match a predetermined risk profile.
Quantitative (statistical) methods are often used to evaluate portfolio risk. These methods can also be applied to forex trading when managing multiple positions.
For example, holding long positions in both AUD/USD and NZD/USD suggests that the two currency pairs may move similarly due to shared economic factors affecting Australia and New Zealand. But what would the risk be if we bought one currency pair and sold the other?
This chapter will discuss traditional risk management techniques in the context of forex trading.
Standard Deviation
Standard deviation measures volatility by assessing how much individual observations deviate from the mean. A high standard deviation indicates that the data points are widely spread, while a low standard deviation shows that they are closely clustered around the mean.
Statisticians carefully examine the data they work with because wrong assumptions can lead to incorrect conclusions. Although analyzing data distribution is not the focus of this chapter, we will briefly introduce the standard normal distribution.
Individual observations (such as gains and losses) are symmetrically spread around the mean in a standard normal distribution.
Graph 1: Standard Normal Distribution. Source: tradepretty.com
The mean is zero because half of the observations are above the mean, and the other half are below it. Statistically, the distribution of observations within +/- 1, 2, and 3 standard deviations is well-defined: 68% of observations fall within one standard deviation, 95% within two, and 99.7% within three standard deviations.
Consider the classic example of human height. If the average global height is 1.70 meters with a standard deviation of 0.1 meters, then 68% of the population will be between 1.60 meters and 1.80 meters tall (1.70 +/- 0.1 meters). Within two standard deviations, or between 1.50 and 1.90 meters, 95% of people will fall. Finally, 99.7% of people worldwide will have heights ranging from 1.40 to 2.00 meters, which covers three standard deviations.
The same logic applies to finance. Suppose an index has an average annual return of 5% with a standard deviation of 2%. In that case, we can expect the yearly return to fall between 3% and 7% (within one standard deviation) in 68% of cases. In 95% of cases, the return will range between 1% and 9%, and in 99.7% cases, it will be between -1% and 11%.
Many risk models use historical returns data to measure volatility. While history may not always repeat itself, it provides valuable input information to these models.
Next, we will explore another critical factor in portfolio management—the correlation coefficient.
Correlation Coefficient
The correlation coefficient measures the strength of the linear relationship between two assets. The most used measure in finance is the Pearson Correlation, which compares the periodic returns of two assets to determine how closely they are correlated.
Correlation ranges from -1 to +1. A correlation of +1 indicates a perfect positive correlation, meaning both assets move similarly—when one appreciates or depreciates, the other does the same. In this case, investing in both assets offers no diversification benefit, so a portfolio manager would be indifferent between investing in one or both.
When two assets have a perfect negative correlation of -1, changes in one asset are offset by opposite changes in the other. As a result, a portfolio consisting of these two assets would experience no return and carry no risk.
It’s important to understand that the correlation coefficient measures the linear relationship between two assets. A positive correlation of 0.8 does not imply that a 10% increase in one asset will cause an 8% increase in the other. Instead, it means that historically, the values of the two assets have often moved identically. A correlation of 0.9 indicates a stronger positive relationship, while -0.9 denotes a strong negative correlation.
A correlation of zero means there is no linear relationship between the two assets, so changes in the value of one provide no information about the movement of the other.
Why is the correlation coefficient so significant?
Correlation is a determinant of diversification. A diversified portfolio reduces risk.
Consider two stocks, each with an annual return of 10% and a standard deviation of 5%. Investing in both stocks equally would yield an overall return of 10% (0.5 x 10% + 0.5 x 10%), identical to the return from investing in each stock individually. If the correlation between the two stocks is perfectly positive (+1), the portfolio’s standard deviation will remain 5% (0.5 x 5% + 0.5 x 5%).
However, if the correlation is not perfectly positive (less than +1), the portfolio’s standard deviation will decrease. This is because the two stocks, while both achieving a 10% return, may not move in tandem. Sometimes, the price of one stock may increase while the other decreases. Investing in both companies reduces overall risk due to their different performance paths, which is the essence of diversification—improving the risk-return ratio.
Does this concept apply to the FX markets?
Recognizing a key difference between forex and equity markets is essential. Equities tend to appreciate over the long term. While individual companies may fail, the overall stock market trend is upward, as illustrated by the S&P 500 index, which has averaged an annual return of about 10% since its inception.
Chart 1: S&P Long-Term Trend. Source: Investing.com
Forex markets perform differently from equity markets. Each currency pair involves two distinct economies, where buying one currency means selling the other. When exchange rates rise, one currency appreciates while the other depreciates.
In developed economies, it’s uncommon for one economy to dominate another over the long term. Eventually, trends tend to reverse. This tendency for currency pairs to revert to a mean value is called mean-reversion.
For instance, the EUR/USD pair has historically fluctuated between 0.80 and 1.60. As of this writing, the pair is near parity. Although extreme exchange rates like 3.00, 5.00, or even 10.00 dollars per euro are theoretically possible, they are unlikely. In this sense, unlike the stock market, the historical mean returns of individual currency pairs tend toward zero.
Traders often use various models to forecast the expected returns of currency pairs. For example, at the beginning of 2020, a trader predicting an appreciation of either the Australian dollar (AUD) or the New Zealand dollar (NZD) against the US dollar was investigating three investment options: a long position in AUD/USD, a long position in NZD/USD, or an equal investment in both pairs. That year, the standard deviation was 12.24% for AUD/USD and 11.35% for NZD/USD.
If the two currency pairs were perfectly positively correlated, there would be no benefit from diversification, and the standard deviation of an equal-weighted portfolio would be the average of the two standard deviations: 11.80% = (12.24% + 11.35%) / 2. However, the actual correlation was high (+0.89) but not perfectly positive. As a result, the portfolio’s standard deviation decreased to 11.5%, demonstrating that diversification effectively reduced systematic risk.
Portfolio optimization is typically applied to different asset classes and financial instruments. The objective is to create a portfolio with a specific risk profile.
Similarly, some forex traders focus on the behavior of a basket of currency pairs rather than individual trading positions. The table below shows the correlation matrix for major currency pairs for 2019.
Table 1: Correlation Matrix 2019, FX Majors. Source: tradepretty.com
In 2019, the correlation between AUD/USD and NZD/USD was 0.77, lower than the 0.89 observed in 2020. This illustrates that correlation and other metrics, such as standard deviation, change dynamically over time. However, a matrix like the one shown provides traders a quick overview of the relationship between different currency pairs (or other assets).
Conclusion
Traders often rely on technical analysis or subjective methods for making investment decisions. However, statistical science provides an alternative approach. For instance, the daily standard deviation of the EUR/USD pair in 2019 was 0.3%. This means that, in 68% of all cases, the pair’s daily price change fell within a 0.3% increase or decrease. Traders can use this information to estimate how frequently prices fall within a specific range and develop risk controls based on these statistical indicators.
A similar approach can be applied to portfolios by calculating expected return and risk (standard deviation).
These examples illustrate how diversification across different investments can optimize risk-adjusted returns. Traders should explore and adapt these methods to best suit their trading strategies.
Next: Intro to Fundamental Analysis
