Trading stocks using the correlation coefficient. Correlation in investments on Forex and stock exchange. Major world indices
The behavior of stock prices depends on many parameters. The most attractive for analysis, due to its simplicity, is the consistent behavior of prices or indices. The presence of this kind of consistency in behavior cannot be denied and is manifested in many examples. Thus, the share prices of many Russian companies change “with an eye on” the behavior of other shares. For example, despite significant differences in dynamics, it is easy to discern elements of consistency in the behavior of the shares of Gazprom and Sberbank - the most liquid securities of the Russian stock market. This kind of consistency of behavior does not seem strange given the involvement of shares in the dynamics of financial flows to the stock market. Although, from the point of view of analyzing the finances of a single company, it may seem that the dynamics of stock prices of companies from different sectors of the economy should be independent. Rice. 2, 3 Over a long period, the consistency of the behavior of stock prices and indices is most clearly manifested. The degree of consistency between the behavior of different curves can be assessed using the correlation coefficient. The correlation coefficients between the behavior of Sberbank share prices and the MICEX index, determined over an annual interval, change over time, often approaching unity, at which the behavior of the two curves is close to complete consistency. In the case of Sberbank share prices and the MICEX index, one can easily find an explanation for such a connection. In other cases, the relationship is not so obvious, even though the empirically determined correlation coefficients systematically exceed the values that could be obtained for pairs of independent variables. Using the correlation coefficient, you can try to build regression dependencies and evaluate the dynamics of assets based on the value and changes in other related quantities. However, there are a number of serious difficulties in such assessments, which sometimes leads to false conclusions about the uselessness of this kind of connectivity. However, the use of correlation coefficients can be useful for analyzing the dynamics of stock prices and indices. Moreover, these odds can be an essential element of trading systems, but when using them it is important to remember the most important limitations.
1. The correlation coefficient is only one characteristic of many parameters and there is no need to overestimate its values
Streams of price information coming from exchange terminals indicate the presence of both a chaotic random component in price behavior and some consistency with the prices of other assets. Mathematical statistics allows us to identify elements of coherence in the behavior of time series. To do this, Fourier analysis or other parameters can be estimated. The most convenient and simplest is the regression (correlation) coefficient K. It is often used to analyze the degree of connection between two time series. This coefficient can be determined for any two sets (including random ones) of variables Xi and Yi, where i ranges from 1 to n. Using a sample of length n, you can determine the empirical correlation coefficient, which is determined by the following formula:
K= , where Mx and Mu are estimates of the mathematical expectation of random variables (X) and (Y), and are the values of their standard deviations. K varies within (-1, 1).
The correlation coefficient turns out to be equal to unity for sets of two quantities X(ti) and Y(ti), the values of which change in phase with time, such as the sinusoids marked A and B in Figure 4. In a series of Figures 5, these sets of dependencies X(ti ) and Y(ti) are presented in coordinates (X and Y). For antiphase oscillations (curves A and D), the correlation coefficient is -1. When the phase of one of the processes shifts, the correlation coefficient decreases to become close to zero for orthogonal oscillations sin(t) and cos(t) (curves A and C). Similarly, we will find zero correlation for oscillations with oscillation periods sin(t) sin(2t) that differ by a factor of two (Curves A and F). The correlation coefficient also decreases due to the “noisiness” of the oscillations of two different processes. Thus, for synchronously oscillating curves G and H, in which there is random noise, the calculated correlation coefficient turns out to be less than unity. More often, it is precisely this noisy behavior that is observed for the prices of various assets. The correlation of a set of purely random numbers Yi with any dependence X(ti) will tend to zero as the sample grows, and a “graph” of pairs of numbers X(ti) and Yi will not give even a hint of the dependence, as depicted in the last graph for “ dependencies" of pairs of numbers Xi and Yi, where Xi was taken from the upper sinusoidal curve A, and Yi was read from curve I, which is a set of uniformly distributed random numbers.
2. It is necessary to remember about the possible accuracy of determining the correlation
In market dependencies, in addition to deterministic components that lead to the often observed coherence of their behavior, there are also other terms that can be interpreted as “random numbers.” Random terms also contribute to the determined correlation coefficient K. Thus, when calculating K for a finite sample of size N between two sets Xi and Yi of random variables, uniformly distributed over the interval (0-1), the results will also be non-zero meanings. The value of Kj(250) (for a sample size of 250 pairs) will depend on the number j of the sample itself. The correlation coefficient K will be a random variable, the realizations of which Kj, according to the law of large numbers, turn out to be distributed according to the normal law. In the presented figure we see how the correlation coefficients Kj(250) changed between samples of 250 pairs of random variables for thousands of implementations (j=1,2,3...1000). Standard deviation?? random variable K(250) is close to 0.062, which means that in 77% of cases the empirical value of the correlation coefficient Kj(250) for 250 pairs of random variables will be within ±2??. (The lines ±0.124 are shown in the figure). And beyond 3*?? (±0.186) the random variable Kj(250) will appear only in 1.35% of cases. Thus, the value of K(250) for a set of 250 pairs of numbers, greater modulo 0.2, most likely cannot be associated with random circumstances, and for time series with K>0.2 we have to discard the idea of their randomness change and one can look for possible reasons for their correlated behavior. For the normal distribution Kj(N) the value?? is inversely proportional to the square root of the sample size N. Therefore, for a sample size of 1000 pairs of random numbers?? will decrease by half compared to a sample of 250 pairs of random numbers, and a sample four times smaller, 62 pairs of points in size??, on the contrary, will double. If we assume that the stock price has a given deterministic component and a random term, then by increasing the sample size we can reduce the addition to the correlation coefficient that arises due to the random term. In the case of a time series, to reduce the contribution of random components, it is necessary to increase the period from which the points used are taken. However, it is also impossible to increase the study period too much, since over a long interval the nature of the consistency of the curves may well change. It is clear that using the correlation coefficient only the average correlation value for the period is estimated. Therefore, an annual interval is most often used as a study window, which, taking into account weekends and non-working holidays, gives about 250 daily closing prices. When choosing an annual interval, it should be remembered that random price components can make a contribution to the resulting correlation coefficient K(250), the value of which on a sample of 250 points can easily be ±0.1, and in some (albeit rare) cases reach even ±0.2. Therefore, in reality, when calculating the correlation coefficient on an annual interval, it makes sense to keep only one significant digit after the decimal point, and everything else may be associated with statistical errors. If the correlation coefficient K(250) turns out to be less than 10%, then it is better not to think about the relationship between the initial values. (There is no point in looking for non-random things where randomness dominates).
3. Index correlations
Taking into account the above assessment of accuracy, it is possible to calculate the correlation coefficients of potentially the most significant quantities for the RTS index. The figure below shows the relative changes in the RTS index, the American S&P 500 index, the Japanese Nikkei225 and the French CAC40. It turns out that in the last year the correlation coefficient of the RTS index with the indicated indices was negative. (K values for RTS with the above indices are given in the captions to the curves in the figure). The correlation becomes negative due to long periods of multidirectional movements of indices. Thus, the RTS index decreased in the first half of the year, while the indices of these countries showed growth. The N225 index grew especially strongly, which gave a high negative coefficient K. The correlation coefficient (from the given curves) turned out to be positive only for Brent oil prices. Although the coefficient K with oil +0.6 turns out to be not as high as one might expect, taking into account the dependence of our economy on the prices of this raw material.
From Table 1 of pairwise correlations we see that these assets are divided into two groups. One contains indices of developed countries, which have fairly high positive pairwise correlation values among themselves. Thus, the correlation coefficient of the S&P 500 index and the CAC 40 index is very high and amounts to +0.9. While the correlation coefficients with the indices of BRICS countries turn out to be negative for them.
The indices of BRICS countries are included in another group. The joint graph of relative changes in indices clearly shows their consistent behavior. The correlation coefficient of the RTS with the indices of China and Brazil turns out to be even slightly greater than the dependence of the RTS index on oil prices. This indicates a fairly high degree of coherence in the behavior of the BRICS countries' indices. From the curves shown in the two figures and the correlation coefficients of these curves with the RTS index, we can assume that over the annual horizon, the decision to invest in the stock market of Russia, Brazil and China by a set of main investors who determined the dynamics of the indices was made according to similar considerations. The same goes for decisions to invest in the US, Japanese and French markets.
4. Correlations of price increments
It is important to pay attention to one more important feature. For a speculator, what is much more important is not the correlation of stock prices, but the correlation of daily price changes. And this is not the same thing at all. Figure 9 shows three model graphs. Each of them represents the sum of a long-period sinusoid (annual changes) with the appropriate addition. But the additive for the three graphs is different. For schedule A, this is a “weekly” sinusoid with a period of 5 days. For graphs B and C, the weekly sinusoid has a negative sign, so on graphs A it is in antiphase with the addition on graphs B and C. On graph C, in addition, there is a random addition. The amplitudes of all additives are chosen to be equal to one-fifth of the amplitude of the main vibration. Pairwise correlation coefficients of the curves, despite the additions, are close to unity and equal to KA-B=+0.92; KA-S=+0.9; KB-C= + 0.9.
But for the “daily price increments” shown in the second chart the picture is completely different. Points on curves A, B, C in Fig. 10 were obtained as a result of calculating the differences of time-sequential values on the curves in Fig. 9: Fig. 10 = Fig. 9(t)-A Fig. 9(t-?t). As we can see, daily price increases are much less dependent on annual trends, but are largely determined by short fluctuations that have a period of several days. For the indicated difference curves (Fig. 10), the correlation coefficients have completely different values KA-B = -1.0; KA-C= -0.7; KB-C= + 0.7. Correlation coefficients were calculated using samples of 250 pairs. (Taking into account the previous point, we limit ourselves to one decimal place for curves containing a random component).
You can do the same with the indices used above and form sets of daily increments from them. For the obtained series of relative increments, the values of the correlation coefficients were calculated. As we see from Table 2 below, the values of the correlation coefficients are fundamentally different from the corresponding values given in Table 1.
The main difference is the greater stability of such coefficients. In addition, the correlations of increments are mostly positive. The exception turned out to be a negative correlation between oil price increments and increments of the Japanese Nikkei 225 index. However, the absolute values of the correlation coefficients for increments turn out to be, as a rule, noticeably smaller than for the values themselves and, in most cases, only slightly exceed the possible values for sets of purely random variables.
The degree of stability of the correlation coefficient can be demonstrated by their time dependences. As already mentioned, the correlation coefficient depends on time. Thus, for the two most liquid securities of the Russian market, the share prices of Sberbank and Gazprom, the correlation coefficient (calculated over the previous 250 days - an approximate annual interval) changes greatly over time. For example, at the end of 2008 the correlation coefficient was close to +1. This means that in 2008 the coordinated component predominated in the dynamics of stock prices. However, there were periods when the correlation coefficient dropped into the negative region. This means that during the year preceding such failures, the correlation values, the share prices of Gazprom and Sberbank changed in more different directions. This kind of multidirectionality is a fairly common occurrence in our market. So often the shares of Surgutneftegaz, Norilsk Nickel or some other shares showed counter-movement to the market. This happened either for specific corporate reasons, or when investors in the market chose some shares as a protective asset. But short-term changes in stock prices, even on average, are not so highly consistent, but they demonstrate greater stability of the correlation coefficient over different periods of time. This difference can be seen by comparing the behavior of the correlation of both the share prices of Sberbank and Gazprom (Fig. 12) and their changes (Fig. 13). Fig. 14 It is worth noting that even for periods of high correlation, the “dependence” of the increments in the prices of some shares on the increments in the prices of other shares does not look like a dynamic curve at all. Nevertheless, at large K, a linear regression relationship will work with a fairly high probability. As a result, it is possible, for example, to estimate the increase in the prices of Gazprom shares by the increase in Sberbank shares (and vice versa). However, the problem with this dependence is that the price increments of these shares occur over one time interval. And assessing the probability of an increase in the price of Sberbank shares on a certain day is only possible at the end of the same day for Gazprom shares.
Determining correlation coefficients between different data series allows you to quickly identify the simplest dependencies and find assets that correlate with what is being studied. Thus, based on changes in foreign market indices or prices for product groups, one can make estimates of the likelihood of current changes in indices in our market. But with the most important thing - the ability to make probabilistic forecasts on events that have already occurred - everything is a little worse. But it is precisely this kind of forecasts that have the greatest value. To do this, you need to study the correlations of today's index increments with past increments of other market indices or price increments of product groups. But in fact it turns out that information about the past devalues quite quickly over time. The well-known “maxim” of technical analysis “price history contains all the information about the market” works with great reserve and subject to taking into account on-line events. In reality, past prices determine future dynamics only to a limited extent. To determine which past most significantly influences the present, for initial analysis you can try to build a correlation of current increments with changes in index values and stock prices at previous points in time. In fact, it turns out that the correlation levels of increments from different time intervals, as a rule, have rather low values.
This can be illustrated using the example of the autocorrelation function of MICEX index increments. The correlation is taken for two consecutive series of daily changes in the MICEX index. And if the daily increment of the MICEX index for the current day is taken as the Xi values, then the index increments for the previous day are taken as the Yi values. From the graph shown in Figure 15 we see that, firstly, the value of autocorrelation does not greatly exceed the value of the correlation coefficient for pairs of purely random numbers. Secondly, K can change sign. And yet, during long periods of sign certainty of the correlation coefficient, using it you can make money in the market. To do this, with positive K, it is enough to buy the index at the close of trading on days when it closes with a positive increment, and sell on days when the index has a negative increment. As a result, during the period of positive certainty K it is possible to obtain a statistically significant positive increment in the count. During periods of negative K, a counter-trend technique to changes in the past day will be workable.
In conclusion, we note that from the data series that have the greatest correlation with the asset under study, it is possible to select sets that have the largest correlation coefficients in magnitude. Then, (weighing, for example, proportionally to the value of K) we can build synthetic assets that will potentially have a deeper connection with the asset we are interested in and have a higher correlation coefficient. In Fig. Figure 16 shows the correlation coefficients calculated for the previous year for the increments of the RTS index to the increments of the Bovespa index, Shanghai Com., and Brent oil prices. We see that all three of these coefficients have changed around the values of 0.3 over the past year. Having formed a hypothetical asset, the changes of which are equal to the average value of changes in the three indicated values, it is also possible to calculate the correlation coefficient for the daily increments of the resulting asset. The values of the correlation coefficient for increments of the RTS index and the specified synthetic asset, calculated according to the same rules, are shown in Fig. 16 thick line. We see that the correlation levels of the newly formed asset turned out to be systematically higher than for the components included in it. On this path, you can form other assets, achieving higher values of correlation coefficients. The most obvious practical value is the combination of such synthetic assets from data series that have already become history. So, in pair with Xi - changes in the RTS index, you can, for example, make up an asset Yi from three values: changes in oil prices and the Bovespa index on the previous day and the value of the Shanghai Comp. index, but on the current trading day, which China ends much earlier than trading in Moscow closes. As in the previous case, the correlation coefficient of RTS index increments with such a synthetic variable turns out to be higher than pairwise correlations with each of these values separately. Thus, the correlation coefficient helps to find a variable more closely related to changes in the RTS index, the values of which appear earlier in time than the closing time of the RTS index. By doing the same, you can select sets of such variables, choosing from them the most associated pair with the asset of interest.
(You need to be prepared for painstaking work on preliminary data cleaning, accounting for holidays, trading on weekends, as happens with Brent oil, etc.). And one more thing: it is more correct to take not the average value of the input quantities, but their weighted values according to the average value of the correlation coefficient. It is better to introduce changeable parameters, by selecting which you can achieve better results. However, it is better to optimize not by the value of the correlation coefficient, but by the potential profit that can be obtained using one or another trading technique. It is possible to use neural networks already at the stage of selecting the initial data, when the optimizing system at the training stage itself selects the most suitable coefficients. But all this most likely relates to the creation of a trading system. This text demonstrates how correlation coefficients can be used.
Finance is moving towards high interest rates because currency investors expect greater returns on cash investments. Foreign exchange flows also depend on how the world's population spends their money.
Demand for stocks, as well as for a commodity like gold or oil, causes the exchange rate of a currency to change. Why? To buy gold you need the currency of the producing country. Therefore, you will have to buy local currency.
If we are talking about South Africa, you will first need to buy the South African rand (ZAR) and then use it to pay the owners of gold mines. When there is a rush for gold and transactions become widespread, the prices of the South African currency and gold rise along with demand.
This dependence applies to all goods. Are you planning to buy shares traded on the German stock market? First you have to buy euros. There is a logic to this. But, watching the rise or fall of commodity prices, you need to clearly understand what exactly should be bought and what should be sold. Conducting a study of the correlation between commodity prices and the value of currencies can help with this. Analysis of the influence of financial instruments of different categories on each other is called intermarket analysis. Next, you will learn which currencies you need to work with in case of serious movements in the oil, gold and stock markets.
Correlation(from the Latin correlatio “correlation, relationship”) or correlation dependence is a statistical relationship between two or more random variables (or values that can be considered as such with some acceptable degree of accuracy). In this case, changes in the values of one or more of these quantities are accompanied by a systematic change in the values of another or other quantities.
Correlation with oil
In the modern world, the main driving mechanism of the global economy is a natural mixture of liquid hydrocarbons and organic compounds of sulfur and nitrogen. This mixture is also called crude oil. Most of the oil produced goes into the production of gasoline. Few people know that oil is also used to produce asphalt, plastics, textiles, for heating houses, and so on.
The wide versatility of oil as a raw material and the many areas of its application are the main reason for the high demand for it from growing economies. The rapid development of industry in India and China has led to a sharp change in the global balance of demand for black gold.
A Forex trader can make a profit by watching the movements of the oil market and trading currency pairs correlated with oil.
This may come as a surprise to some, but the most correlated currency with oil is the Canadian dollar. Statically, 84% of movements in the USDCAD currency pair depend on changes in oil prices. When the oil market goes up, the USDCAD pair tends to fall, which means the Canadian dollar increases in value against the US dollar.
This dependence is explained by Canada's high position in the world of oil production, which literally lies on huge oil reserves. The same dependence of the national currency on the oil exchange rate can be seen in the example of other leading countries in the production of black gold. For example, residents of Russia could not help but notice how the ruble exchange rate fell against the dollar when oil prices fell in 2014-2016.
Note that the oil market is not the only reason for changes in the prices of dependent currencies, even such as the Canadian dollar, but what is important is that these two variables move in tandem.
The figure below shows the USDCAD and oil rates superimposed on each other. The fates where there is a correlation and where there is none are noted. The ratio of the total lengths of the sections is approximately 50 to 50, which means that pure correlation trading is not the holy grail, but can be a good addition to an existing trading strategy or simply help determine the direction of opening a trade at a controversial moment.
Correlation between Brent oil and USDCAD 
At the bottom of the article you can download an indicator for overlaying the chart of one financial instrument on another. Charts with oil quotes can be viewed in the broker's terminal: "New chart" - CFD Futures - BRN (Brent) or WTI. Write in the comments if you have found currency pairs that are more strongly correlated with oil than USDCAD and do you use the correlation in your Forex trading?
Correlation with gold
As a rule, the demand for gold significantly exceeds the supply on the world market. In the recent past, gold miners have refrained from investing in exploration and development of new mines. However, demand for both jewelry and investment is increasing, especially amid the economic boom in India and China.
Gold's excellent electrical conductivity, malleability and resistance to corrosion have made the yellow metal indispensable in the production of components used in various electronics industries, including computers, cellular communications and household appliances. Since gold is a biologically inert substance, it is indispensable in medical research and is even used in the treatment of arthritis and other intractable diseases. In addition to jewelers, dentists also require gold. About 70 tons of gold are consumed annually in dental clinics.
In addition, market participants have a long-standing perception of gold as a safe haven for investment, which has a positive impact on the market prospects for this commodity.
Australia, being the world's third largest gold producer, benefits from its value. The correlation coefficient between the AUDUSD pair and the price of gold is approximately 0.78, which means that the rates are 78% identical. An increase in the price of gold is usually accompanied by an increase in the value of the Australian dollar against the US dollar. And often the fall in the AUD exchange rate is preceded by a decline in prices for the yellow metal.
The AUDUSD rate, with a slight lag, almost completely follows the movement of the price of gold 
Correlation with the stock market
Although stocks themselves are not commodities, they are highly correlated with foreign exchange markets.
But in this case, you should not track the correlation of currencies with any individual securities - there are too many of them; it is easier to track the largest stock indices, which reflect price movements across a basket of securities. The British FTSE, American S&P 500, Japanese Nikkei, German DAX are extremely important for the foreign exchange market; experienced traders around the world monitor these indices along with currencies.
A stock index is a large basket of stocks traded on a stock exchange. The general rise of the market attracts buyers of shares included in the indices, their price moves along with the value of the indices. The arrival of foreign money is preceded by its exchange into local currency. When the market falls, investors leave it, returning their “native” currency. Thus, stock markets have a direct impact on the value of currencies.
Does this mean that when the DAX rises, you need to buy the euro, and when the Nikkei declines, you need to sell the Japanese yen? Perhaps, but wouldn't it be better to have one recipe for all occasions? It's real. We are talking about indirect interdependence, but statistics indicate the effectiveness of the technique.
Trading the EURJPY pair is considered to be the basis for assessing the risk tolerance of traders around the world. The movement along this cross-rate closely correlates with changes in the values of the largest stock indices, not because currencies flow from one stock market to another, but due to the willingness of traders to enter the markets in general.
For this reason, if investors are confident that global markets are bullish, they will be more generous with their funds, expressing a willingness to put money into the line of fire. In such cases, the EURJPY rate usually rises. Falling stock markets have a negative impact on this currency pair. Not always, but in most cases.
The EURJPY rate almost completely follows the S&P 500 index rate 
conclusions
We learned that correlation of currency pairs on Forex is the relationship between two or more financial instruments, which can be commodities: gold, oil, shares, or other currency pairs. If a currency pair correlates with another financial instrument, then when the rate of this instrument changes, the rate of the dependent currency pair also changes.
The USDCAD currency pair depends on the oil rate, and AUDUSD on the gold rate. Gold in the Forex market is designated as GOLD or as XAUUSD. The EURJPY pair follows closely behind the S&P 500 stock index, which may show how this pair will behave in the near future.
If you decide to start trading by correlation, then you simply need this tool:
Download the currency pair correlation indicator for Forex:
Using this indicator, you can select the financial instruments that are most dependent on each other and start trading them, because not only CAD depends on oil and not only AUD depends on gold. By trading simultaneously on several correlated currency pairs, you can achieve good and stable profits.
Please write in the comments about your experience of trading on correlations, everyone will be very interested to know about it. Or maybe you found unusual or unexpected financial instruments that depend on each other? - Be sure to write.
The relationship between changes in the value of trading instruments, a situation where a change in the price of one asset leads to a change in the value of another.
To measure correlation in the practice of analyzing the behavior of stock prices, the corresponding indicator is used - the Pearson correlation coefficient, determined by the formula:
- rxy—correlation coefficient of stock values x and y;
- dx is the deviation of a certain value of the series x from the average value of this series;
- dy is the deviation of a certain value of the series y from the average value of this series.
Moreover, if the value of the calculated Pearson coefficient is plus one, then the relationship between the analyzed stock prices is of a direct functional nature.
If the value of the correlation coefficient in absolute value exceeds 0.7, then the relationship between the prices of two shares has a pronounced character.
When the value of the Pearson correlation coefficient modulus is between 0.4 and 0.7, the relationship between the values of stock prices is average. Less than the level of 0.4 - a weakly expressed relationship between stock prices.
If the value of this coefficient is minus 1, then the relationship between stock prices has an inverse functional nature.
The more values of the values of two shares are included in the sample, the lower the absolute value of the correlation coefficient can be stated about the presence of correlation.
The analytical value of calculating the Pearson correlation coefficient between stock prices allows you to obtain important fundamental data required for making an objective decision during stock trading.
For example, the stock market reacts to the release of news about price movements for major assets (oil, gold, industrial indices, government bond yields). As a result, the price of company shares changes. By carefully monitoring the dynamics of the relationship between market instruments and the cause-and-effect relationships between changes in price levels, you can effectively and quickly adjust your investment tactics and trading plan. At the same time, correlation analysis is necessarily used when forming an investment portfolio within the framework of the basic concepts of risk management.
Knowing the level of correlation between two stocks allows you to reduce the risk of the investment portfolio being formed.
Let's say our portfolio contains two assets, and the behavior of their prices depends on time according to the sinusoid law. When the correlation coefficient is equal to plus 1, a complete superposition of sine waves is obtained, and by buying both shares, we double our positions in each of them. A Pearson correlation coefficient value of minus 1, on the contrary, will allow mutual compensation of gains and losses on shares. Effectively selected sets of stocks in a portfolio grow over time. Then, when the price of one share decreases, growth in another stock will compensate for the overall drawdown of the portfolio and minimize the overall risk. The process of portfolio rebalancing allows you to generate income by quickly changing the shares of individual assets in the portfolio structure.
Let's say the initial composition of our portfolio of stocks A and B has an inverse correlation of minus one. And the ratio is one to one (50/50). The total value of the portfolio is $1 million. Over the course of six months, shares A fell in value by 10% and its price was reduced from the original $500 thousand. up to 450 thousand dollars Asset B, on the contrary, increased by 10% and its rate rose to 550 thousand dollars. The total portfolio value has not changed and amounts to $1 million. Now we will transfer half of the shares of B (550/2 = 275 thousand dollars) to A and its cost will now be 725 thousand dollars. A shares B - 275 thousand dollars.
In the next half of the year, the reverse process occurs - shares return to their previous price levels. Now shares A instead of 725 thousand dollars. costs 797.5 thousand dollars, and asset B instead of 275 thousand dollars. 247.5 thousand dollars The total value of the portfolio will now be 797.5 + 247.5 = 1045 thousand dollars. Thus, its profitability after rebalancing is 4.5% per year. Without rebalancing, the portfolio value would be zero percent. In practice, everything is much more complicated, since the correlation level of most stocks is in the range of plus 0.5 to minus 0.5.
Thus, we can conclude that the lower the value of the Pearson coefficient, the greater the probable return of the portfolio at the same level of risk, or the lower the level of risk at the same value of return. However, the calculation of the correlation coefficient must be used with caution.
Are they moving in the same directions? For example, the NZD/USD pair in most cases follows the trajectory of the AUD/USD pair. This phenomenon is called " correlation».
So, currency correlation – a measure of the mutual dependence of two currency pairs . The correlation coefficient is presented in decimal format and ranges from +1.0 to -1.0.
- Correlation +1 (positive, direct) means that two currency pairs move in the same direction 100% of the time.
- Correlation -1 (negative, inverse), on the contrary, means that the two pairs are moving in opposite directions 100% of the time.
- Zero correlation means that the two pairs do not depend on each other in any way.
The most striking examples of pairs that have a direct correlation are EUR/USD and GBP/USD, AUD/USD and NZD/USD, USD/CHF and USD/JPY.
Good examples of inversely correlated pairs are EUR/USD and USD/CHF, GBP/USD and USD/JPY, USD/CAD and AUD/USD, USD/JPY and AUD/USD.
How to use currency correlation in trading?
Understanding currency correlations will allow you to avoid dangerous mistakes in making trading decisions. The correlation value is especially high in medium- and long-term trading.
For example, you need to understand that unidirectional positions on positively correlated pairs increase the magnitude of potential losses. For example, we know that EUR/USD and GBP/USD traditionally have a strong direct correlation. This means that buying EUR/USD and GBP/USD at the same time effectively doubles your risk. If your expectations are not met and the euro becomes cheaper against the US dollar, the pound will most likely follow the euro down.
A similar situation arises when opening multidirectional positions on two pairs with an inverse correlation (for example, simultaneous purchase of EUR/USD and sale of USD/CHF).
In addition, simultaneous multi-directional trading on two correlated pairs does not make much sense - you actually have no position. For example, buying EUR/USD and selling GBP/USD at the same time is counterproductive. Any market movement increases your profit on one pair, but decreases it on the other. You may end up closing at a loss due to the difference in pip values. The same applies to unidirectional positions on inversely correlated pairs (for example, buying EUR/USD and USD/CHF at the same time).
Let's imagine that the EUR/USD pair is testing an important one. Before buying the euro on a breakout, we would recommend looking at how other dollar pairs behave at this time. If the dollar is weakening against most major currencies, we can assume that the current breakout in the EUR is not false.
Correlation of currencies and commodity prices
The foreign exchange market interacts closely with other financial markets. If you trade the currencies of raw material exporting countries, carefully study the factors influencing the price of this country’s “core” resource and try to make your own forecasts on it.
Let's look at the example of the Australian dollar (AUD). Australia's key exports are iron ore, dairy products and gold, so the state of the economy and the national currency are directly dependent on market prices for these goods. strengthens when prices for these goods rise, and vice versa, decreases when prices fall.
As you can see from the charts, there is indeed a long-term positive correlation between the price of gold and the AUD/USD pair. However, in the short term, the correlation may decrease. For example, a sharp sell-off in the American stock market, as is right, weakens the AUD/USD exchange rate's peg to gold.
Another good example of the correlation between currencies and commodities is the Canadian dollar (CAD) and oil. Canada is the largest supplier of oil to the United States, so with rising world oil prices, it is worth thinking about long-term purchases of the Canadian currency.
Correlation of exchange rates and stock market
The growth of the stock market, as a rule, is accompanied by a strengthening of the national currency, but there are also special cases. For example, The correlation between the S&P500 and the US dollar (USD) is not constant. On the one hand, a cheap dollar is a positive factor for the American stock market: the competitiveness of American goods on world markets increases, which leads to an increase in the profits of companies and, accordingly, their shares. This is why the launch of the quantitative easing (QE) program in the US sent stock indices to record heights. However, in addition to the exchange rate, the dynamics of American stocks are influenced by many other, local and global factors. The dollar exchange rate and US stock indices, as a rule, are a reflection of underlying economic processes.
In December 2013, the US Federal Reserve announced a gradual exit from the QE program, as well as a possible rate increase in early 2015. There are fears that tightening monetary policy could cause a collapse in the stock market, as the amount of cheap liquidity in the market will decrease. Meanwhile, the US dollar may strengthen. Despite this, many economists are not inclined to view the winding down of QE and raising rates as a clearly negative factor. The reduction in the volume of monetary stimulus signals that the world's largest economy is emerging from its crisis, and therefore is a positive signal for capital markets. In addition, the US authorities are phasing out QE gradually, making decisions based on the dynamics of economic indicators. There is a high probability that this will continue in the coming months. weak positive correlation between the dollar and stock indices.
The Japanese yen and the Nikkei 225 stock index are another interesting example of a changing correlation. Until 2005, the yen and Nikkei maintained a positive correlation, but then it changed to negative. This paradox is explained by the fact that in 2005-2007. in Japan there were exceptionally low interest rates, which made the yen the main funding currency in "" transactions (borrowing funds in the currency of the state that set low interest rates, converting and investing them in the currency of states that set high interest rates). The yen was declining amid an abundance of such operations (i.e. the USD/JPY pair was strengthening). The cheap national currency was beneficial to Japanese exporters - as a result, the Nikkei index also grew.
This situation continued until the start of the global economic crisis in 2008. During this tense time, investors began to get rid of risky assets and bought “reliable” yen. As a result, the JPY rose, which negatively affected the profits of Japanese exporters and, accordingly, the Nikkei index.
In 2012, the Bank of Japan chose a strategy to actively combat deflation, which is based on a decrease in the value of the national currency. The sharp fall of the yen led to a rise in Japanese stock markets. Thus, we see that the inverse relationship between the yen and Nikkei continues today.
Correlation of JPY and Nikkei 225
In statistics correlation coefficient (English Correlation Coefficient) is used to test the hypothesis about the existence of a relationship between two random variables, and also allows you to evaluate its strength. In portfolio theory, this indicator is usually used to determine the nature and strength of the relationship between the return on a security (asset) and the return on the portfolio. If the distribution of these variables is normal or close to normal, then you should use Pearson correlation coefficient, which is calculated using the following formula:
The standard deviation of the return on Company A shares will be 0.6398, on Company B shares 0.5241 and on the portfolio 0.5668. ( You can read about how standard deviation is calculated)
The correlation coefficient between the return on Company A shares and the portfolio return will be -0.864, and on Company B shares 0.816.
R A = -0.313/(0.6389*0.5668) = -0.864
R B = 0.242/(0.5241*0.5668) = 0.816
We can conclude that there is a fairly strong relationship between the return on the portfolio and the return on the shares of Company A and Company B. At the same time, the return on the shares of Company A shows multidirectional movement with the return on the portfolio, and the return on the shares of Company B shows a unidirectional movement.