When more than one position opens up, risk management methods more akin to traditional portfolio management come to the rescue.** Compared to trading, portfolio management is characterized by longer-term investment objectives and investments in different asset classes (stocks, bonds, commodities, ****derivatives****).** Their selection and relative weightings are made in a way aimed at achieving a certain risk profile. The portfolio manager expects losses in a particular asset class when another asset class makes gains.

**Various quantitative (statistical) methods are used to assess the risk of such portfolios. They could also be useful in forex trading when more than one ****position is open**** at the same time – a kind of ****investment ****portfolio.** For example, being long AUD/USD and NZD/USD at the same time, intuitively alarms us that identical price changes in both pairs could be expected. This is due to the common factors influencing Australia and New Zealand. This pattern is worth measuring to avoid over-concentration on identical risks. What would be the risk if we bought one currency pair and sold the other?

In this chapter we will look at some traditional risk management methods.

__Standard deviation__

__Standard deviation__

**Standard deviation is the most common risk indicator of volatility. It ****examines ****the dispersion****s**** of individual observations relative to the population (or sample) mean.** When these dispersions are large, the standard deviation will be high. When individual observations are concentrated close to the mean, the standard deviation will be low.

**Statisticians ****pay special attention to** **the data they work with. The final conclusions may be wrong if the sample material is misinterpreted.** This line of analysis is not a priority of this chapter but let us introduce in brief the most popular distribution structure – the normal distribution. For simplicity, **we will assume that the data in the following examples follow a normal distribution. **This means that the individual observations (gains and losses) are symmetrically located with respect to the mean.

The normal distribution has some key characteristics. The mean is zero (since half the observations are larger than the mean and the other half are mirror and lower than the mean). The number of observations located within +/- 1, 2 and 3 standard deviations is statistically established**. 68% of the observations lie within 1 standard deviation, 95% of the data lie within 2, and 99.7% of the observations lie within 3 standard deviations. **

Let’s use a classic example with human height. If on average people in the world are 1.70 m tall, and one standard deviation is 0.1 m, then 68% of all people will be between 1.60 m – 1.80 m tall (1.70 +/- 0.1 m). 95% of people will be within two standard deviations (1.50 m/1.90 m). 99.7% of people worldwide will be between 1.40 m and 2.00 m or within 3 standard deviations.

The same logic applies in finance. If an index realizes an average annual return of 5% with a standard deviation of 2%, we can expect the return in 68% of cases to be between 3% and 7% (1 standard deviation from the mean). In 95% and 99.7% of cases, the return will be between 1% and 9% and between -1% and 11%, respectively.

**Based on this historical return and volatility information, portfolio managers build their reasoned expectations for the future. **Of course, history does not always repeat itself, but this is a good starting point.

Let’s turn to another indicator that, combined with standard deviation, plays an important role in the diversification across asset classes – the correlation.

__Correlation__

__Correlation__

**As the name suggests, the correlation coefficient indicates the levels of ****linear relationship ****between two different assets.** Linear correlation, also known as Pearson Correlation, is most commonly used in finance. It compares the periodic changes in the return on two assets to establish the degree of correlation between them.

**The correlation can range from -1 to +1. A correlation of +1 means that the two assets have a perfect positive correlation. An appreciation or depreciation in one instrument will be accompanied by an identical movement in the other.** In this situation, the portfolio manager will be indifferent whether he invests his funds in only one or both assets. Because diversification effects will not be achieved.

**When we have a perfect negative correlation of -1, changes in one asset will be accompanied by opposite changes in the other. ****Thus, in practice****, a portfolio of these two financial instruments will realize zero return and carry no risk.**

**It is important to understand that the correlation coefficient reflects the linear relationship between the two assets. A positive correlation of 0.8 does not mean that a 10% appreciation in one asset will lead to an 8% appreciation in the other.** This coefficient simply indicates that historically their value has changed in an identical manner very often. If the correlation coefficient is 0.9, then the correlation will be even stronger. If it is -0.9, then a strong negative correlation will be present.

**A correlation of zero means no linear correlation – no conclusions can be drawn from the change in the value of one about the movement in the other. **

**Why is this coefficient so important? **

**Correlation is a determinant of diversification. A diversified portfolio reduces risk. **

Let us imagine two stocks of companies, each of which realizes an annual return of 10% with a standard deviation of 5%. At first glance, it seems irrelevant whether you will invest in one, the other, or equally in both.

**Equal investment allocation will yield a return of 10% (0.5** **x** **10% + 0.5** **x** **10%) – the same as investing in each one separately.** If there is a perfect positive correlation of +1 between the two stocks, then the portfolio standard deviation will remain 5% (0.5 x 5% + 0.5 x 5%).

However, **when the correlation is other than +1, the standard deviation of this two-asset portfolio will decrease.** This is because the two stocks have followed their own path of achieving the 10% return. In some cases, one stock has appreciated while the other has declined. For this reason, an investment in both companies reduces the risk. **That is precisely** **the point of diversification – to achieve a better risk-return ratio. **** **

This concept is commonly used in portfolio optimization by asset management companies. All of them consider indicators based on standard deviation and correlations, especially when their focus is market risk.

__Does this have anything to do with the foreign exchange markets____?__

**It is important to know one key difference between ****foreign exchange and equity markets****. By their very nature, equities are an asset class that appreciates over the long term.** Even for purely inflationary reasons, a company raises the prices of its products, the salaries of its employees, etc. In this process, the value of shares should also rise. Of course, some companies succeed, others fail. But the general pattern remains. It is clearly evident in the chart on the S&P 500 index. Since its inception, it has achieved an average annual return of about 10%.

**Foreign exchange markets follow a different logic of behavior. One currency pair represents two separate economies. Buying one currency means selling the other.** When quotes rise, one currency appreciates while the other depreciates.

Rarely in the developed world does one economy dominate the other in the long term. Sooner or later there comes a time when the process reverses. In this sense, foreign exchange markets tend to revert to their mean (mean reverting). For example, EUR/USD has traded in the range of 0.80 to 1.60 since its inception. At the time of writing this chapter, the pair is trading close to parity. An exchange rate of 3.00 or 5.00 or 10.00 dollars per euro is not impossible. However, this sounds unlikely. **In this sense, unlike the stock market, the historical calculation of the mean value on individual currency pairs tends towards zero. **

**However, traders often form their expectations on the basis of ****different models****. Thus****,**** a portfolio of currency pairs will have its expected return and its risk parameters as ****a ****standard deviation.** If at the beginning of 2020 a trader had forecast an appreciation of the Australian or New Zealand dollar against the US dollar, he faced 3 investment options – a long position in AUD/USD, a long position in NZD/USD, or an equal purchase of both pairs. The standard deviation for the year was 12.24% in AUD/USD and 11.35% in NZD/USD, respectively. If a perfect positive correlation existed between the two pairs, there would be no benefit from diversification. The standard deviation of this portfolio would be the average of the two (12.2+11.4)/2 = 11.8%. As might be expected, the correlation is actually high, but less than +1, namely +0.89. As a result, the portfolio standard deviation has fallen to 11.5%. In this sense, systematic risk has been reduced and diversification has been achieved.

**Portfolio optimization is typically applied to a broader set of asset classes and financial instruments. ****Each of them ****has its own inherent characteristics, is influenced by different factors and reacts in its own way to different market circumstances. The ultimate goal is to build a portfolio with a defined risk profile.**

Some forex traders follow a similar investment logic and are interested in the behaviour of their basket of currency pairs as a whole rather than as individual positions. The table below presents a correlation matrix with the major currency pairs for 2019.

It is noteworthy that in 2019 the correlation between AUD/USD and NZD/USD is 0.77, which is lower than the correlation of 0.89 realized in 2020. This comes to show that the correlation, as well as other indicators such as standard deviation, change periodically. However, a matrix like the one above helps traders assess at a glance the correlation between individual pairs (or other assets).

**Final words:**

**Traders often ****place their stops based on technical analysis or following some other subjective method. However, statistical science can offer a more consistent approach. **For example, the daily standard deviation for the EUR/USD pair is 0.3% for 2019. This means that in 68% of cases the pair will end the day within a 0.3% rise/fall. A trader could calculate how many times the quotes will end up in a certain range. In other words, they can develop their risk controls based on statistical indicators.

**The same approach is often implemented at the portfolio level**** – calculating expected return and risk (portfolio standard deviation)****.**

The above examples by no means exhaust the directions in which risk management finds application in forex trading. They are only intended to highlight the existence of an alternative approach to investment control. Each individual trader should find the best application of quantitative methods to his trading strategy.