Quantitative trading involves developing and executing trading strategies based on quantitative research. The quants traders start with a <a href="https://financetrain.com/hypothesis/">hypothesis </a>and then conduct extensive data crunching and mathematical computations to identify profitable trading opportunities in the market. The most common inputs to these mathematical models are the price and the volume data, though other data inputs are also used. Traders who develop these quant-based trading strategies and execute these strategies are called&nbsp;<a href="https://financetrain.com/how-to-become-a-trader/">quant traders</a>.



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/Quantitative_Trading_With_R_Thumb.png" alt="" class="wp-image-26321"/></figure></div>



<h3>Trading Infrastructure</h3>



While the infrastructure to support quantitative and algorithmic trading is quite robust, the key to finding success is in identifying the right opportunities and&nbsp;building a solid trading strategy. Quants traders make use of programming tools such as R, Python, and Matlab to build and <a href="https://financetrain.com/backtesting-quantitative-trading-strategies/">backtest</a> their trading strategies before deploying them for real trade execution.



<h3>Who Uses Quantitative Trading?</h3>



Quantitative trading is used mostly used by financial institutions and hedge funds, though individuals are also known to engage in such strategy building. Once the trading strategy is built, the trades can be executed manually or automatically using those strategies. The key idea is to pick investments or build a trading strategy solely based on mathematical analysis.



<h3>Algorithmic Trading</h3>



Algorithmic trading is a subset of quantitative trading that makes use of a pre-programmed algorithm. The algorithm, using the quantitative models, decides on various important aspects of the trade such as the price, timing, and quantity, and executes the trades automatically without human intervention. The algorithmic trading process involves making use of powerful computers to run these complex mathematical models and execute the trade orders. This involves automating the full process including order generation, submission, and the order execution. Algorithmic trading is often used by large institutional investors such as pension funds, and mutual funds, to break large orders into several smaller pieces. Since the information is received electronically, algo trading is also used by players such as hedge funds to automatically make decisions to order before other human traders even receive the information, thereby providing them with a huge advantage.



<h3>What We Will Learn</h3>



In this course, we will focus on understanding the process of designing a successful trading strategy, and learning to use R to build and backtest a trading strategy. We will be making use of some popular R packages such as quantmod and quantstrat.



It is important to note that R can be used for analyzing data, building a strategy and backtest it. It is great for trading analytics. However, once you are ready to execute the strategy, i.e, ready to place orders based on strategy, you are going to do that in a real-time order execution system.



Note: Backtesting is one of the most important steps in building a successful quantitative trading strategy. Quants use their computational finance and programming skills to build complex trading strategies. However, before these strategies are executed in the live market, they are tested using historical data. Basically, the traders will feed the historical data into these algorithmic trading programs which will tell them how well their strategies performed on this historical data. This refers to backtesting and can help traders in finding flaws in their trading strategies and improvise them.

Introduction to Quantitative Trading

<h3>Advantages</h3>



Quantitative trading has many advantages over the discretionary approach of trading.&nbsp;



<ul><li>The performance of a quantitative strategy can be tested with historical market data. This process is known as backtesting where we test the strategy using historical data to help us determine if the strategy is likely to be profitable in the future.&nbsp;</li><li>The automation of the strategy is more efficient as there is no need for an individual or a team to constantly monitor market prices or news.&nbsp;</li><li>Traders and investors have gained more computational power to perform tasks that require high volumes of data and also allow them to have more accurate calculations of position sizes and risk management.</li><li>This computation power allows execution of certain types of strategies that would be impossible for humans to execute by themselves such as high-frequency trading strategies that triggers orders in less than one second using order book information.&nbsp;</li><li>All these things are not possible in a discretionary world where traders are unable to continuously compute risk and monitor the market.&nbsp;</li><li>The quantitative approach to trading also gets rid of emotions that can alter the course of transactions.</li></ul>



<h3>Disadvantages</h3>



Despite these advantages, the quantitative approach to trading also has some drawbacks.&nbsp;



<ul><li>The main constraint of quantitative trading is that it generally requires a far larger capital base than what is utilized in retail discretionary trading.&nbsp;</li><li>Another drawback is that there are many datasets that are expensive for the retail trader. Specifically intraday data feeds are costly.&nbsp;</li><li>In the cryptocurrency market, there are traders and algorithmic trading firms which locate servers in the same cloud, and using the same domain as the exchange. This practice allows them to send orders and match the exchange engine much faster than traditional traders. This also increases costs.</li></ul>



In the last few years, the quantitative trading field has grown significantly and there are many tools and open source platforms that allow the retail traders to build and backtest their quantitative strategies.&nbsp;&nbsp;

Quantitative Trading - Advantages and Disadvantages

There are different types of trading strategies which differ in terms of their time horizon, risk profiles, capital requirements, as well as liquidity and volatility needed for a correct execution. These algorithmic trading strategies can be classified into the following types:



<ul><li><a href="https://financetrain.com/momentum-strategies/">Momentum Strategies</a></li><li><a href="https://financetrain.com/mean-reversion-strategies/">Mean Reversion Strategies</a></li><li><a href="https://financetrain.com/market-making-strategies-and-day-trading-strategies/">Market Making Strategies</a></li><li>Intra-day Momentum or <a href="https://financetrain.com/market-making-strategies-and-day-trading-strategies/">Day Trading Strategies</a></li></ul>



Each of these strategies have different risk-reward ratios, and traders and investors should base their trading plan based on their own profile and preferences. For example, if a trader cannot stand overnight gaps and some drawdowns in the course of a position, their trading style would be more suitable for a Day Trading Strategy. In contrast, if a trader wants to ride trends they would prefer momentum strategies.&nbsp;



The objective of a momentum strategy is to capture the trend of a stock or other asset. So these strategies are best designed for traders with higher time horizon as they have to wait for a trending setup and decide accurate entry and exit points.&nbsp;



On the other hand, market making strategies are for the very short term, and traders wish to exploit inefficiencies in the order book that are produced in seconds or milliseconds.&nbsp;



In the following lessons, we will discuss these trading strategies in more detail.

Types of Quantitative Trading Strategies

Even though we classify momentum with a longer time frame than a day, it is necessary to point out that momentum can also exist within the day. Traders can find momentum during the day, as well as for longer time frames. The strategies that we analyze below have long-time horizon momentum.



A&nbsp;momentum strategy&nbsp;is based on identifying and following a price trend in the market. It is based on the premise that an asset price that is moving strongly in a direction will continue to move in that direction until the price trend loses strength. The momentum is determined based on the trading volume and rate of price change. Momentum can be classified into&nbsp;time-series momentum&nbsp;and&nbsp;cross-sectional momentum.&nbsp;



<h3>Time-series Momentum</h3>



Time series momentum means that past returns are correlated with future returns.



In order to design a&nbsp;time-series momentum strategy, researchers calculate the correlation coefficient of the returns using a statistical approach, where the null hypothesis represents no correlation between returns.&nbsp;



The correlation coefficient of returns can vary across lags and sometimes the most positive correlation is between returns of different lags. For example, we can find that the correlation coefficient of returns in one day is negative, and the correlation coefficient of returns in a twenty day window is positive. So, while using this approach, it is necessary to take into account the different timeframes of the returns correlations.&nbsp;



<h3>Cross-sectional Momentum</h3>



Cross-sectional momentum&nbsp;is based on the relative performance of two prices series, where one price series outperforms the other. The hypothesis in this type of strategy support is that if one price series outperforms the other in the present, it is likely to keep doing so in the future.



<h3>Working with Momentum Strategies</h3>



Momentum strategies can be based on&nbsp;technical indicators&nbsp;and&nbsp;breakouts. For example, it is possible to define an entry signal to buy when the price reaches a new N-day high, or when the price exceeds the upper Bollinger band, or when the price exceeds the N-day Moving Average or Exponential Moving Average.&nbsp;



Relative Strength Index&nbsp;(RSI) and&nbsp;Moving Average Convergence Divergence&nbsp;(MACD) are typical indicators used to find signals of oversold and overbought stocks that could lead to entry orders to go long or short.



Other classical momentum strategies generate signals to buy when the number of up days exceeds the number of down days in a moving period. A sophisticated approach would buy or sell the stock prior to the big movement by detecting chart patterns as well as&nbsp;resistance&nbsp;and&nbsp;support&nbsp;levels and make entries prior to the big move.



These types of strategies many times are supported by pipelines or screeners in order to find stocks that meet some criteria. For example, one pipeline could select stocks that are within 10% of their 52-week high and rank them from highest to lowest to this high. After getting this group of stocks, traders may wait for a pull back to enter into the market.



<h3>Risks</h3>



Momentum strategies&nbsp;involve a high level of risk because there is no guarantee that the price will continue to go higher in case of an uptrend or continue to go down in case of a downtrend. Statistics show that the number of winning trades in a momentum strategy are few compared to the number of losing trades. However, these types of strategies have a high reward/risk rate. So, a few winning trades can make the strategy profitable despite the big number of losing trades.



For this reason, these types of strategies require an integral trading plan with a strict definition of entry and exit points and knowledge about the current market regime. Usually traders set stop loss orders to exit position to prevent a big loss when the trend has a reversal and start to move in the opposite direction.



<h3>Profitability</h3>



The strategy metrics of a&nbsp;momentum strategy&nbsp;will differ from those of other types of strategies such as a&nbsp;mean reversion strategy. Usually in a&nbsp;momentum strategy, the ratio of winning trades over losing trades is lower than 1 as there are more losing trades than winning trades.&nbsp;&nbsp;Momentum strategies, therefore,&nbsp;&nbsp;rely on a small number of winning trades with a greater profit. In contrast, the number of winning trades for a&nbsp;mean reversion strategy&nbsp;is higher than the number of losing trades. Mean reversal strategies are profitable based on the amount of winning trades and not the reward/risk relation of each trade.

Momentum Strategies

Mean reversion strategies,&nbsp;also called pairs trading, tend to capture market anomalies or inefficiencies between prices of stocks, ETFs or commodities with similar behavior. These assets usually pertain to the same industry and are affected by the same supply and demand dynamics. So, in normal conditions, it is expected that both assets have a similar path.



In some occasions, the relative prices of a pair of assets can deviate from its mean and this generates trading opportunities in which one can buy the stock with the lower price and sell the stock with the higher price.&nbsp;



To take advantage of the differences that might arise between stocks with similar properties, a practical approach is to make a ratio between the assets returns and calculate a historical thresholds for this ratio such as one and two historical standard deviations.



The strategy executes orders when the ratio of the prices or the ratio of the returns moves beyond one or two standard deviation, going long on the cheaper asset and going short on the outperformer asset.&nbsp; There are statistical techniques that are suitable to find stocks with similar performance in the past that could be suitable for this type of strategy.



<h3>Identifying Assets Exhibiting Mean Reversion</h3>



Researchers and analyst can conduct co-integration test such as the&nbsp;Augmented Dickey Fuller (ADF) test&nbsp;between a lists of stocks to determine good picks for a&nbsp;mean reverting strategy. Also the&nbsp;Hurst Exponent&nbsp;and the&nbsp;Variance Ratio test&nbsp;are used as methods to identify stocks that have similar behavior.*



Similarly, it is also possible to design a&nbsp;mean reverting strategy&nbsp;for a single stock. We can use the&nbsp;Bollinger Band&nbsp;(BB) technical indicator to set up a mean reversion strategy. First, it is necessary to choose a market that is moving within a range (without trend), and then we can spot the Bollinger Band and make trading decisions. When the price touches the upper band of the Bollinger Band (sell trade) and when the price touches the lower band of the Bollinger Band (buy trade).



<h3>Additional Notes&nbsp;(Advanced / Optional)</h3>



It is possible to perform the CADF (Cointegrated Augmented Dickey Fuller) test between two stocks by using the residuals of a <a href="https://financetrain.com/introduction-to-linear-regression/">linear regression</a> model for the two asset prices. The CADF is performed with the residual series from the linear regression, and the null hypothesis states that there is a unit root between the two series* and the alternative hypothesis states that both series are stationarity.



If we have evidence to reject the null hypothesis of the presence of a unit root, we have evidence for a <a href="https://financetrain.com/stationary-process-in-time-series/">stationary series</a> (and cointegrated pair) and can create a stationary portfolio between the two assets in the framework of a mean reverting strategy.



* The pair ratio of the series will not recover to a certain "mean" because it follows a stochastic process.



Likewise the ADF can be used to determine if a single time series of an asset prices is stationary or not. Other useful tests for determining if a time series can be mean reverting are the Hurst Exponent and the variance ratio. The goal of the&nbsp;Hurst Exponent&nbsp;is to provide us with a scalar value that will help us to identify whether a series is mean reverting, random walking or trending. The output of this test is a coefficient between 0 and 1. A value lower than 0.5 implies that the series can be mean reverting for a certain period. Values equal to 0.5 are indicative of a random walk in the time series, and values higher than 0.5 are associated with a trending behaviour.



On the other hand the&nbsp;variance ratio&nbsp;test assesses the null hypothesis that a univariate time-series is a random walk. It gives the probability (p-value) that the null hypothesis of a random walk process of the variance of the price series is true or the Hurst Exponent is 0.5.



If the <a href="https://financetrain.com/understanding-hypothesis-testing-p-value/">p-value</a> of the variance ratio test is small (p-value &lt; 0.05) we can reject the null hypothesis of a <a href="https://financetrain.com/simulate-random-walk-rw-in-r/">random walk process</a>. This means that the variances between the different returns lags of the time series are not equal.



On the other hand, if the p-value is greater than 0.05, we cannot reject the null hypothesis of a random walk process. This means that the time series could be modeled by a random walk with the form P_t = P_{t-1} + µ + e_t, where µ is a constant and e_t is independent and identically distributed. A key implication of this model is that the variance of (P_t - P_s) is linear in the lag between t and s.

Mean Reversion Strategies

<h2 id="lecture_heading">Market Making Strategies</h2>



Market making strategies are called &nbsp;execution strategies&nbsp;or&nbsp;sell-side methods&nbsp;which are designed to capture spreads, otherwise known as the difference in price between buys and sells. Market makers provide liquidity to the order book of a certain asset and are constantly updating the price based on the supply and demand in the market.



In a&nbsp;market making strategy, signals can be generated by extracting information from the order book and real time transactions. One common signal in this type of strategy is the tick imbalance bar that has the goal of detecting how informed traders are playing in the market. The imbalance bar is produced when there is an imbalance between bid and ask ticks that exceed an expectation.&nbsp;



These strategies are based on high frequency data and demand high storage requirements, execution optimization and quantitative models to grasp market regime. Generally, algorithms designed for these strategies are fed with tick level transaction data and a real time copy of the order book of the exchange.&nbsp;&nbsp;



<h3>Day Trading Strategies or Intraday Momentum</h3>



A big advantage of&nbsp;day trading strategies, when compared to strategies with longer time periods, is that they do not suffer big drawdowns such as those occurring during a financial crisis event. They also have higher&nbsp;Sharpe ratios&nbsp;compared to&nbsp;inter-day momentum strategies. These strategies try to gain profits from short-term opportunities during the day.



A well-know&nbsp;day trading strategy&nbsp;is the&nbsp;Opening Gap Strategy. This setup is originated when a stock or an ETF starts the new trading session with an open price having a big gap compared to the previous market close. The gap can be in either direction.&nbsp;



Trading strategies can be automated in order to find stocks and ETFs that have great gaps between the previous close and current open and define entry points based on the price action within one hour after the markets open.&nbsp; Exit rules can also be defined by the algorithm.&nbsp;



In case the gap has bullish direction, and the price makes a new high after the up-gap, the stop loss can be placed at the close level of the previous day.



Other great sources for&nbsp;day trading strategies&nbsp;are&nbsp;news sentiments. Market news are momentum drivers which can extend along the whole trading session. An&nbsp;Earning Announcement&nbsp;and other corporate events will move stock prices, and this movement would persist for some time after the announcement. Many trading strategies have developed around&nbsp;Earnings Announcement&nbsp;in order to profit from stocks moves. This kind of strategy is called the&nbsp;Post Earnings Announcement Drift (PEAD). For an implementation and backtesting of this strategy, it is necessary to get the dates of the Earning Announcement and define rules to enter and exit the position.



Day traders also use&nbsp;scalping strategies&nbsp;to make profits from the market. These strategies run over the shortest time frames such as one and five minutes. A&nbsp;scalping strategy&nbsp;can be built around overbought and oversold signals generated by technical indicators such as the&nbsp;Relative Strength Index&nbsp;(RSI) and the&nbsp;Stochastic.&nbsp;

Market Making Strategies and Day Trading Strategies

As a <a href="https://financetrain.com/how-to-become-a-trader/">quantitative trader</a>, it is a good practice to establish a strategy pipeline that will provide with a stream of ongoing trading ideas. We can have a framework to backtest trading ideas that can be based on any open source projects such as quantstrat from R package.



<h3>Idea Sources</h3>



There are plenty of text-books, blog sites, forums, whitepapers and articles where we can find basic trading strategy ideas. We can start with these and then redefine them based on our own trading style and understanding of the market. It is very important to define our style before we start building a trading strategy. Some elements that require definitions are: what timeframe I would use to build a strategy, which assets I would trade, what is my risk/reward ratio, what is the maximum drawdown I can bear, etc.



<h3>Indicators</h3>



We can combine fundamental and technical indicators in designing a trading strategy. We can select stocks that meet some fundamental conditions in terms of Price to Earning (P/E), Price to Book (P/B), Earning per Share (EPS), Return on Equity (ROE), among others, and secondly use technical indicators for entering into the market.&nbsp;



<h3>Criteria</h3>



In the same way, we can select stocks that meet some criteria of volatility, or stocks that show an interesting trading pattern such as Inside Day Breakouts, Flags, Double Bottom, Double Root, Triangles among others. The volatility is related to the type of instruments for trading. The forex and cryptocurrency markets are more volatile than the stock markets for example.



<h3>Other Considerations</h3>



The choice of asset class should be based on other considerations too, such as trading capital constraints, brokerage fees and leverage capabilities.



Reading academic papers as well as books are wonderful sources to get with new trading and investment ideas.&nbsp; These are great sources to understand and go deeper with the risk management side, as many papers provide tools for rebalancing and optimizing portfolios seeking the minimum variance constraint.

How to Generate Trading Ideas

The first step in the process of designing a trading strategy is to choose which type of strategy will be used and a timeframe to trade.&nbsp; As stated earlier, the strategy can seek different goals and should be according to each person’s preferences and trading style. The different strategies are designed to take advantage of some market conditions or market inefficiencies.



Once the type of strategy is selected, the researcher should come with different ideas about the strategy by reading research papers, perform statistical analysis for a group of assets, evaluate technical indicators on stocks and conduct exploratory data analysis to get better insights about the assets.&nbsp;



A common workflow in generating a trading strategy after the research activities consists of:&nbsp;



<ol><li>Signal generation process of the strategy&nbsp;</li><li>Trade execution&nbsp;</li><li>Backtesting</li><li>Risk management</li></ol>



Let’s look at each of these in detail.



<h3>1. Signal Generation</h3>



A trade signal is a trigger for buying or selling a security. This forms the primary trading logic of a strategy. The process of generating the trading signals is at the heart of any trading strategy.



The analysis to generate these trading signals can be based on multiple disciplines such as technical analysis, fundamental analysis or quantitative analysis, as well as economics.



<ul><li>Signals can be generated based on technical indicators such as <a href="https://financetrain.com/what-is-relative-strength-index-rsi/">Relative Strength Index</a> (RSI), <a href="https://financetrain.com/predict-stock-trends-using-macd/">Moving Average Convergence Divergence</a> (MACD), Bollinger Bands (BB), Stochastic Lines and Moving Average Crossover. These are only a few examples as there are tons of technical indicators to create signals. </li><li>Signals can also be created based on resistance and support lines as well as chart patterns that lead to breakouts. These types of signals try to ride the volatility of stocks and are used in <a href="https://financetrain.com/momentum-strategies/">momentum strategies</a>.</li><li>Signals can also be based on statistical approaches as is the case in pairs trading or <a href="https://financetrain.com/mean-reversion-strategies/">mean reverting strategies</a>. For example, if the mean reverting strategy was built on two assets when the relative returns of both assets deviates one or two standard deviations from a certain threshold, a signal to go long and to go short is generated.  </li></ul>



So the first step is to find signals that would produce some alpha in the short or long term. Once we have the signals generated, we should analyze how the orders will be triggered and what would be our approach to risk management.



<h3 id="lecture_heading">2. Strategy Execution</h3>



Strategy execution&nbsp;is one of the key aspects in building a trading strategy. Transactions of the strategy are executed based on different&nbsp;order types.&nbsp;



<h4>Market Orders and Limit Orders</h4>



The most <a href="https://financetrain.com/equity-types-of-orders/">common order types</a> are the market orders and limit orders. Market orders trigger transactions immediately and the final price could be different from the order price.



On the contrary limit orders trigger transactions at a specific price, and the final price is identical to the order price.&nbsp;



<h4>Slippage</h4>



An important concept which arises while using market orders is called&nbsp;slippage.&nbsp;Slippage&nbsp;happens when trades get a different price than the price expected on an entry or exit from a trade.&nbsp;



Slippage&nbsp;increases when a fundamental news is coming such as an&nbsp;Earnings Report&nbsp;or a&nbsp;Federal Reserve Announcement.&nbsp;To avoid&nbsp;slippage,&nbsp;one can use limit orders to enter or exit a position.&nbsp;



<h4>Stop Orders and Stop Limit Orders</h4>



Traders also uses stop orders and stop limit orders. Stop orders can be used to enter or exit a position but are only processed if the price reaches a certain level. In case of a buy stop order, if the current price is at USD 15.50, the stop order would be placed at USD15.60, and it is only triggered if the current price reached the USD 15.60 level.



The stop order, also known as stop loss order, can also be affected by&nbsp;slippage. On the contrary, a stop limit order is a combination of a stop and a limit order and ensures that the trader gets the desired price. In this order type the stop and limit prices might be different.



If the current market price is at USD 15.75, a trader could place a stop limit order to exit position with a stop of USD 15.40 and a limit of USD 15.30. When the price reaches USD 15.40 the order becomes a live sell limit order and will be filled only at USD 15.30 or better price. As long as the price is above 15.30 which is the limit price, the trade will be fulfilled. Stop limit orders for exit are used because investors don’t want to sell below the limit price and wait for the price to rise back to the limit price.



<h4>Other Order Types</h4>



Finally there are more complex orders that brokers provide such as Immediate or Cancel (IOC), Market on Open, Market on Close, Good-till-Canceled (GTC), Good-till-Date/Time (GTD), Iceberg/Reserve&nbsp; that allow traders to create more complex executions models.

Designing A Trading Strategy For Profit

Backtesting a trading strategy refers to testing the strategy with historical data and observe their metrics, results and performance. Commonly, <a href="https://financetrain.com/backtesting-quantitative-trading-strategies/">backtesting</a> has some pitfalls that should be considered by any trader before they put a strategy in production. 



Data Scientist and developers should take into account issues such as&nbsp;Optimization Bias,&nbsp;Survivorship Bias&nbsp;and&nbsp;Market Impact&nbsp;when backtesting their trading strategies.&nbsp;



<h3>Optimization Bias</h3>



Optimization Bias&nbsp;takes place when a trading strategy was built based on a large number of parameters.&nbsp;



The excess of parameters can lead the strategy to outperform the market with sample data, but with live market data or out of sample data, the strategy might have poor performance. Therefore, a good practice is to keep the strategy simple with fewer parameters.&nbsp;



<h3>Survivorship Bias</h3>



Survivorship Bias&nbsp;means that the dataset used for backtesting doesn’t contain the full list of stocks at every point in time, but only consider those stocks that have “survived”.



If we use a dataset that only considers stocks that have overcome drawdowns periods, and not those stocks that were delisted, or stocks that got in bankruptcy, we are introducing&nbsp;Survivorship Bias&nbsp;and the strategy returns can increase artificially.&nbsp;



<h3>Market Impact</h3>



Market Impact&nbsp;could be important for large transactions that are executed to rebalance portfolios. This can cause price movements that are reflected by the difference between the transaction price and what the market price would have been in the absence of the transaction.



On the other hand, the&nbsp;market impact&nbsp;could increase the bid ask spread. More illiquid assets have large spreads (difference between the bid and ask price). Depending on the supply and demand dynamics of the stock and the exchange that is used to trade, the spread can vary and increase transaction costs.&nbsp;Market impact&nbsp;can be addressed by taking a conservative perspective about trade prices while backtesting.



When backtesting and sourcing trading ideas, it is a good practice to consider other insights beyond the strategy returns. These insights are the leverage, volatility required, capital requirements, and risk metrics such as maximum drawdown tolerance and Sharpe ratio.&nbsp;

Backtesting a Trading Strategy - Considerations

Lastly we should have rules to manage the risk of the strategy. Risk and money management are the most important aspect in a trading strategy. This field focuses on drawdowns, leverage and volatility. It is important that any trading plan contains a risk management approach to minimize drawdowns, by the use of stop loss or stop limit orders, as well as avoid days of higher volatility.&nbsp;&nbsp;



Traders and investors should have in their mind an integral plan to execute trades or enter into a new position. Within this plan, the risk management of transactions and positions is the most important feature in the long term. On many occasions, investors or traders earn great profits in bull markets but they lose all or almost all their portfolio value when a bear market starts.



<h3>Maximum Drawdown</h3>



One of the main concepts in analyzing the risk of a strategy is the&nbsp;Maximum Drawdown&nbsp;that the strategy has. The&nbsp;Maximum Drawdown&nbsp;is defined as the accumulated loss of buying an asset in their highest point and selling at their lowest point during a period of time. Drawdown in contrast, refers to the decline in value in the next period from a previous local maximum.



The&nbsp;Maximum Drawdown&nbsp;is a good measure for funds and portfolio managers to become aware of the maximum possible loss of a strategy in a certain period. The important property of the&nbsp;Maximum Drawdown&nbsp;is that its value was obtained from a real world financial series and is not originated from a model with some theoretical assumptions as many times happens.



Some risk metrics such as the <a href="https://financetrain.com/value-at-risk-of-a-portfolio/">Value at Risk</a><a href="https://financetrain.com/value-at-risk-of-a-portfolio/"> (VaR) of a portfolio </a>assume that the returns of the strategy are independently and normally distributed. In the real word, returns have fat tails and serial correlation, and their distribution differs from a normal distribution. The VaR doesn’t reflect the large losses during the history of the financial market.



The <a href="https://financetrain.com/calmar-ratio-definition-calculation-and-importance/">Calmar Ratio</a> is a risk metric that accounts for the Maximum Drawdown of a strategy. The Calmar Ratio is defined as the compounded annualized growth rate divided by the Maximum Drawdown over the same period. Unlike the <a href="https://financetrain.com/sharpe-ratio/">Sharpe Ratio</a>, the Calmar Ratio cannot be scaled to different time horizons, so portfolios that use the Calmar Ratio should have the same backtesting period.



In order to develop a more realistic approach of risk management, in the past few years, new measures of risk have been proposed that focus more on the drawdowns and&nbsp;Maximum Drawdowns&nbsp;rather than the volatility or&nbsp;VaR. This approach takes into account the&nbsp;drawdown distribution&nbsp;which uses the drawdown (magnitude and duration) to define the loss function.&nbsp;



There are other methods to achieve and appropriate risk management and control risk in trading strategies that are more related with strategies based on single or a few assets.&nbsp; One of these methods is the&nbsp;Constant Proportion Portfolio Insurance (CCPI), which has the rule of adjust the order size when the strategy has a drawdown.



In case of a drawdown, the CPPI will decrease order size faster making almost impossible that the account approach to the maximum drawdown. The method controls leverage with regards to the current drawdown. If the current drawdown increases, the leverage would decrease.&nbsp; A drawback of this method is that it doesn’t prevent for a big drawdown during an overnight gap.



<h3>Avoiding Losses</h3>



A common method to avoid losses is the usage of a&nbsp;Stop Loss. The common application of the&nbsp;Stop Loss&nbsp;is to exit an existing position whenever its unrealized P&amp;L drops below a threshold. The&nbsp;Stop Loss&nbsp;only works when the market is open. If the prices “gap” down or up when the market opens the&nbsp;Stop Loss&nbsp;order may be executed at a much lower/higher price.&nbsp;



Also, a&nbsp;Stop Loss&nbsp;is a safety tool either in a&nbsp;mean reversion&nbsp;or a&nbsp;momentum strategy. In case of a&nbsp;mean reversion strategy, a regime change from mean reversion to a trending behavior could cause great losses if the account doesn’t have a&nbsp;Stop Loss.&nbsp;Momentum strategies&nbsp;benefit from&nbsp;Stop Loss&nbsp;orders in cases of a reversion in price that could cause drawdowns in the strategy.



As we stated, the risk of a <a href="https://financetrain.com/mean-reversion-strategies/">mean reversion strategy</a> is different from the risk in a <a href="https://financetrain.com/momentum-strategies/">momentum strategy</a>. This means that the stop loss order is used differently in the two approaches.  In a momentum strategy the use of a Stop Loss is more straightforward as it prevents losses when prices reverse. In a mean reversion strategy the price is ranging and the Stop Loss should be greater than the maximum intraday drawdown.

Risk Management of a Trading Strategy

There are some risks indicators that traders and investors need to watch to avoid days with high volatility. These indicators are referred to as&nbsp;leading risk indicators. A good example of a risk indicator is the&nbsp;VIX&nbsp;index. This index tracks the implied volatility of the stocks that compose the S&amp;P 500 index.&nbsp; If VIX is higher than 35, the likelihood of a big gap in prices on market open and an increase in volatility becomes greater.&nbsp;



Besides&nbsp;VIX, another leading risk indicator is the&nbsp;TED&nbsp;spread. This is the difference between the three-month London Interbank Offered Rate (LIBOR) based in US dollars and the three-month T-bill interest rate.&nbsp;&nbsp;



The graphs for TED spread and VIX Volatility Index are shown below:



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/TED-Rplot-1024x621.png" alt="" class="wp-image-26347"/></figure></div>



<figure class="wp-block-image"><img src="https://financetrain.com/wp-content/uploads/VIX-Rplot-1024x621.png" alt="" class="wp-image-26348"/></figure>



In both graphs we see that VIX index and the TED spread have spikes, especially the VIX index (many times is greater than 20). To avoid extreme volatility a conservative approach to preserve capital in the long term should avoid these periods. The above two graphs for VIX index and TED spread were created in R and the data was tablen from FRED Economic data website. In the next article, you can learn about how to create the VIX index and TED spread charts in R.



To conclude, any individual strategy or portfolio investment need to be evaluated taking into account their potential risks and losses. In the long term, profitable strategies are those that can control and manage risk better than others. Using risk metrics such as Drawdowns, Max Drawdown Expectations, Calmar and Sharpe ratios, Stop Loss orders are a set of important tools to manage risks in trading strategies.

Risk Indicators - VIX Index and TED Spread

In this lesson, will will look at how to create the two graphs in R. Before you start, it is important to setup your basic environment:



<h3>Setup Environment</h3>



Open RStudio and ensure that you have the basic setup in place.



<ul><li>Create a new directory called ‘<code>quantative-trading-strategies-r</code>’ in your computer. We will use this director for all the exercises in this course.</li><li>Set this directory as your working directory using the&nbsp;<code>setwd()</code>&nbsp;command. You can also check the current working directory using the&nbsp;<code>getwd()</code>&nbsp;command in R console.</li><li>Use the command&nbsp;<code>CTRL+L</code>&nbsp;to clear the console (Use this whenever you feel the console is cluttered).</li><li>Create a new R script where we will be writing our R script.</li><li>Install and load the&nbsp;<code>ggplot2</code>&nbsp;package by typing the following commands in the console:</li></ul>



<pre class="wp-block-code"><code>#Install ggplot2
install.packages("ggplot2")
 
#Load ggplot2
library("ggplot2")</code></pre>



<h3>Plot the TED Spread</h3>



In order to plot the TED spread, you can follow the following instructions:



Step 1: Download Data



You can download the data for TED spread from the FRED® Economic Data website.



Get TED data from&nbsp;<a href="https://fred.stlouisfed.org/series/TEDRATE">https://fred.stlouisfed.org/series/TEDRATE</a>



For convenience, we have also provided the data files below.



You can download the data file and save it in your working directory.



Step 2: Load the data in your R Environment



To read a csv with R, the best way to do it is with the command&nbsp;<code>read.csv</code>.



<pre class="wp-block-code"><code>ted &lt;- read.csv("TEDRATE.csv",stringsAsFactors = FALSE)</code></pre>



Step 3: Transform Data



The read.csv function interpret both columns as factors columns, so we need to change to the appropriate columns data types.



We will convert character columns to numeric and date columns, and remove NA values with complete.cases.



The complete.cases function returns a logical vector specifying which observations/rows have no missing values across the entire sequence.



<pre class="wp-block-code"><code>ted$TEDRATE &lt;- as.numeric(ted$TEDRATE)
ted$DATE &lt;- as.Date(ted$DATE)
ted &lt;- ted[complete.cases(ted),]</code></pre>



Finally, we have ‘ted’ as a dataframe containing our prepared data.



Step 4: Plot the Graph



Now, we can use ggplot2 library to plot the graph.



<pre class="wp-block-code"><code>ggplot(ted, aes(DATE, TEDRATE)) + geom_line(color = "red") + xlab("") + ylab("Daily Prices")+ggtitle("TED Spread")</code></pre>



The complete script for creating the TED spread is provided below:



<pre class="wp-block-code"><code># Get TED data from https://fred.stlouisfed.org/series/TEDRATE
# Load the data using read.csv

ted &lt;- read.csv("TEDRATE.csv",stringsAsFactors = FALSE)

# The read.csv function interpret both columns as factors columns, so we need to change
# to the appropriate columns data types. Convert character columns to numeric and date
# columns, and remove NA values with complete.cases

ted$TEDRATE &lt;- as.numeric(ted$TEDRATE)
ted$DATE &lt;- as.Date(ted$DATE)
ted &lt;- ted[complete.cases(ted),]

# View the data
ted

# Plot the graph

ggplot(ted, aes(DATE, TEDRATE)) + geom_line(color = "red") + xlab("") + ylab("Daily Prices")+
 ggtitle("TED Spread")</code></pre>



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/TED-Rplot-1024x621.png" alt="" class="wp-image-26347"/></figure></div>



<h3>Plot the VIX Index</h3>



You can follow the exact same steps above to plot the VIX volatility index. The complete script for it is provided below:



<pre class="wp-block-code"><code># Get VIX data from https://fred.stlouisfed.org/series/VIXCLS
# Load the data using read.csv

VIX &lt;- read.csv("VIXCLS.csv",stringsAsFactors = FALSE)

# Convert character columns to numeric and date columns, and 
# remove NA values # with complete.cases

VIX$VIXCLS &lt;- as.numeric(VIX$VIXCLS)
VIX$DATE &lt;- as.Date(VIX$DATE)
VIX &lt;- VIX[complete.cases(VIX),]

# View the data
VIX

# Plot the graph

ggplot(VIX, aes(DATE, VIXCLS)) + geom_line(color = "blue") + xlab("") + ylab("Daily Prices")+
 ggtitle("VIX Prices")</code></pre>



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/VIX-Rplot-1024x621.png" alt="" class="wp-image-26348"/></figure></div>

Plotting the VIX Index and TED Spread in R

The&nbsp;quantmod&nbsp;package for R is designed to assist the quantitative traders in the development, testing, and deployment of statistics based trading models. Using&nbsp;quantmod, quant traders can quickly explore and build trading models.



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/quantmod.png" alt="" class="wp-image-26354"/></figure></div>



The important features of quantmod that we will use are divided into three categories: 1) downloading data, 2) charting, and 3) technical indicators and other functions.



<h3>Downloading Data</h3>



The Quantmod package provides useful tools for loading, and managing data in R. With Quantmod we can download data from public sources such as Yahoo, Oanda, Google, the Federal Reserve Economic Data(FRED), and also from&nbsp; SQL databases and CSV files.&nbsp;



<h3>Charting</h3>



The package has great capabilities for creating charts and we can plot different graphs types such as lines, bars and candlestick. Once we have the charts, we can add technical indicators into it to analyze signals, entry and exit points from a specific trading rules.



<h3>Technical Indicators and Trading Signals</h3>



Quantmod has a wide list of technical indicators (MACD, RSI, EMA, SMA, ROC, and ADX, among others) that we can plot together with the price series or price candlestick charts. Finally, it is possible to create trading signals with the indicators and plot them into the chart.



To start using the Quantmod library, you can install and load it in your R environment using the following commands in R console or R Studio (Preferred).



<pre class="wp-block-code"><code>install.packages('quantmod') 
library(quantmod) </code></pre>

Introduction to Quantmod in R

Once the quantmod package is installed and library is loaded, we can start using the library. We will start by showing some examples of how to download data from the web and load the data into the environment.



Quantmod provides a very powerful function for downloading financial data from the web. This function is called getSymbols. The&nbsp;getSymbols()&nbsp;method sends a request to download and manage data from public sources or local data. It is necessary to pass some parameters within this method to make the desired request. The first argument of this function is a character vector specifying the names of the symbols to be downloaded. Then you can specify the source from which you want to get the data.



The quantmod package is capable of downloading data from a variety of sources. The current supported sources are: yahoo, google, MySQL, FRED, csv, RData, and oanda. For example, FRED (Federal Reserve Economic Data), is a database of 20,070 U.S. economic time series (see&nbsp;<a href="http://research.stlouisfed.org/fred2/" target="_blank" rel="noreferrer noopener">http://research.stlouisfed.org/fred2/</a>).



<h3>Example: USD/EUR exchange rates from Oanda</h3>



For example, we can run the following command to get the data of the USD/EUR exchange rates from Oanda.



<pre class="wp-block-code"><code>getSymbols(Symbols = 'USD/EUR', src = "oanda")

# On success it will display the following and create USDEUR object
[1] "USD/EUR"
</code></pre>



Here we have loaded the data for USD/EUR from the Oanda API which provides free currency data. The&nbsp;getSymbols()&nbsp;method doesn’t return any output. Instead, it creates an internal object in the Global Environment which in this case is the USDEUR object. The data object is an “extensible time series” (xts) object.



To see the starting point of the data, type the following command. It fetches and displays the first 15 rows of the data.



<pre class="wp-block-code"><code>head(USDEUR,15) # You should see the following result.
 
 USD.EUR
2019-02-11 0.884834
2019-02-12 0.885164
2019-02-13 0.884514
2019-02-14 0.886430
2019-02-15 0.886331
2019-02-16 0.885238
2019-02-17 0.885267
2019-02-18 0.883885
2019-02-19 0.883780
2019-02-20 0.881384
2019-02-21 0.881816
2019-02-22 0.881970
2019-02-23 0.882340
2019-02-24 0.882317
2019-02-25 0.880924</code></pre>



<h3>Downloading Multiple Symbols</h3>



We can also make a request for multiple symbols. Suppose we want to request data for multiple ETFs, such as SPY, IVV, QQQ and IWF. We will first create a vector containing symbols of these ETFs. Let’s call this vector ‘etfs’. Once we have the vector, we will create two more variables defining the start date and end date for the period for which we want the data. Then we will use the&nbsp;getSymbols()&nbsp;command to actually request the data.



<pre class="wp-block-code"><code> 
#Lists of ETFs to load
 
etfs &lt;- c('SPY' # SPDR S&amp;P 500 ETF TRUST 
 ,'IVV',# iShares Core S&amp;P 500 ETF 
 'QQQ', # PowerShares QQQ Trust, Series 1
 'IWF' ) #iShares Russell 1000 Growth ETF
 
start_date &lt;- '2014-02-01'
 
end_date &lt;- '2019-08-06'
 
getSymbols(Symbols = etfs, src = "yahoo", index.class = "POSIXct", from =start_date, to = end_date)
 
[1] "SPY" "IVV" "QQQ" "IWF"
 </code></pre>



In this example the&nbsp;getSymbols&nbsp;function returns 4 objects that are “SPY”, “IVV”, “QQQ” and “IWF”. These objects are loaded in the Global Environment. Each object should be called separately and returns only its own information.



<pre class="wp-block-code"><code>head(SPY)
 
 SPY.Open SPY.High SPY.Low SPY.Close SPY.Volume SPY.Adjusted
2014-02-03 177.97 178.37 173.83 174.17 254837100 156.2863
2014-02-04 174.95 175.84 174.11 175.39 165012400 157.3810
2014-02-05 174.78 175.56 173.71 175.17 164230500 157.1836
2014-02-06 175.58 177.48 175.22 177.48 132877600 159.2564
2014-02-07 178.31 179.87 177.73 179.68 170787200 161.2306
2014-02-10 179.70 180.07 179.21 180.01 92218800 161.5267


head(IWF)
 
 IWF.Open IWF.High IWF.Low IWF.Close IWF.Volume IWF.Adjusted
2014-02-03 83.33 83.57 81.30 81.42 2564900 75.79685
2014-02-04 81.78 82.33 81.53 82.17 2604700 76.49506
2014-02-05 81.86 82.18 81.15 81.92 2871200 76.26232
2014-02-06 82.26 83.07 82.21 83.05 2421900 77.31428
2014-02-07 83.53 84.31 83.28 84.25 2575800 78.43140
2014-02-10 84.39 84.53 84.08 84.48 1538900 78.64553</code></pre>



Quantmod provides built-in functions to retrieve individual columns from the above data. In order to take separate columns for one of the above objects, we can use the following commands:



<pre class="wp-block-code"><code>Open &lt;- Op(IVV) # Get only the Open Price column of IVV ETF
High &lt;- Hi(IVV) # Get only the High price column of IVV ETF
Low &lt;- Lo(IVV) # Get only the Low price column of IVV ETF
Close&lt;- Cl(IVV) # Get only the Close Price column of IVV ETF
Volume &lt;- Vo(IVV) # Get only the Volume column of IVV ETF
AdjClose &lt;- Ad(IVV) # Get only the Adjusted close column of IVV ETF</code></pre>



<h3>Load Data from SQL Database</h3>



The&nbsp;getSymbols()&nbsp;function also allows loading data from a SQL database such as MySQL or Sqlite. To load data through MySQL, this function needs additional parameters such as database name, user, password and host. An example of this is described below:



<pre class="wp-block-code"><code>getSymbols(Symbols = etfs, src = "MySQL", dbname = db, user = user, password = password, host = host, index.class = "POSIXct", from = start_date, to = end_date)</code></pre>



<h3>Load Data from FRED Database</h3>



With&nbsp;getSymbols()&nbsp;we can get data from the&nbsp;FRED&nbsp;database which has thousands of datasets that cover financial, economic and production indexes, interest rates, macroeconomic indexes, monetary and international trade transactions.&nbsp;



﻿In the below example, we are downloading the&nbsp;Fed Fund Rate&nbsp;(shortest interest rate term settled by the Federal Reserve of United States) data:



<pre class="wp-block-code"><code>getSymbols(Symbols = 'FEDFUNDS', src = "FRED", adjust=TRUE)
 
tail(FEDFUNDS,15) # tail() gets us the last rows of the dataset
 
 FEDFUNDS
2018-07-01 1.91
2018-08-01 1.91
2018-09-01 1.95
2018-10-01 2.19
2018-11-01 2.20
2018-12-01 2.27
2019-01-01 2.40
2019-02-01 2.40
2019-03-01 2.41
2019-04-01 2.42
2019-05-01 2.39
2019-06-01 2.38
2019-07-01 2.40</code></pre>

Downloading Data Using Quantmod Package in R

Apart from loading data from external and local sources,&nbsp;Quantmod&nbsp;is also suitable for making beautiful charts. There are three types of charts: lines, bars and candlestick. We will learn how to create these charts to show historical data for SPY index.&nbsp;In Quantmod, the function to create charts is called&nbsp;chartSeries. With the&nbsp;type&nbsp;parameter we can change the chart type.



<pre class="wp-block-code"><code># Use the chartSeries() function to create charts. With the type parameter we can change the chart type.

chartSeries(SPY, type="line")</code></pre>



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/SPY-chart-1024x621.png" alt="" class="wp-image-26361"/></figure></div>



We can also subset the graph for a certain period using the&nbsp;subset&nbsp;parameter. The following command produces a candlestick chart only for the 2019 data.



<pre class="wp-block-code"><code>chartSeries(SPY, type="candlestick", subset='2019')</code></pre>



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/SPY-plot-candlestick-1024x621.png" alt="" class="wp-image-26362"/></figure></div>



<h3>Adding Technical Indicators with Quantmod</h3>



The&nbsp;Quantmod&nbsp;package provides built in technical indicators that can be included in the charts. We will now see how to calculate technical indicators with Quantmod for the SPY index and finally, create an R dataframe with the close prices and the technical indicators as columns.



<pre class="wp-block-code"><code>#### Calculates Indicators: EMA,RSI, ADX, STOCHASTIC, ATR
 
EMA &lt;- round(EMA(Cl(SPY),n=14),3)
RSI &lt;- round(RSI(Cl(SPY),n=14),3)
ADX &lt;- round(ADX(HLC(SPY),n=14),3)
ATR &lt;- round(ATR(HLC(SPY),n=14),3) 
STOCH &lt;- round(stoch(HLC(SPY)),3) * 100
 
# At this point it will be a good idea to explore these objects and view the data contained.
# You can use commands such as dim(), head(), and tail() to do this.

# Combine the required indicators into a single data table.
 
spyIndicators &lt;- data.frame(cbind(Cl(SPY),RSI,ADX$ADX,ATR$atr,STOCH$fastK,STOCH$fastD))
 
# Add custom column names for each column
 
colnames(spyIndicators) &lt;- c('SPY','RSI','ADX','ATR','KLine','DLine')
 
# View last 15 rows of the data to get a feel of the data
tail(spyIndicators,15) # shows the last 15 rows of the data
 
 SPY RSI ADX ATR KLine DLine
2019-05-15 285.06 44.151 26.221 3.617 34.2 21.1
2019-05-16 287.70 49.858 24.589 3.655 51.7 36.3
2019-05-17 285.84 46.270 22.850 3.642 39.3 41.7
2019-05-20 283.95 42.893 21.863 3.585 26.8 39.3
2019-05-21 286.51 48.388 20.588 3.542 45.7 37.3
2019-05-22 285.63 46.724 19.558 3.402 39.6 37.3
2019-05-23 282.14 40.739 19.917 3.521 16.5 33.9
2019-05-24 282.78 42.201 19.857 3.420 26.2 27.4
2019-05-28 280.15 38.047 20.298 3.463 2.3 15.0
2019-05-29 278.27 35.367 21.444 3.461 12.5 13.7
2019-05-30 279.03 37.290 22.225 3.373 18.6 11.1
2019-05-31 275.27 32.187 23.460 3.403 0.2 10.4
2019-06-03 274.57 31.328 24.981 3.407 9.2 9.3
2019-06-04 280.53 44.834 24.821 3.600 46.2 18.5
2019-06-05 282.96 49.220 23.937 3.534 61.2 38.9</code></pre>



<h3>Add Indicators to Charts </h3>



In order to add technical indicators in a chart, Quantmod provides the <code>add{IndicatorName)()</code> function. We will use this function for plotting the RSI and the MACD of SPY prices. Both indicators are plotted with the default parameters which are specified below:



<pre class="wp-block-code"><code>### Charting with Technical Indicators 

chartSeries(SPY,type="line")
addRSI(n=14,maType="EMA")
addMACD(fast=12,slow=26,signal=9,type='EMA',histogram = TRUE)</code></pre>



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/Technical-indicators-quantmod-1024x621.png" alt="" class="wp-image-26364"/></figure></div>

Creating Charts with Quantmod

We will perform some data analysis with the 4 ETF symbols that we have loaded into the environment. This analysis consists of comparing the returns of the four ETFs, observing their correlations, getting some statistics, and trying to answer some questions such as which of the ETFs has the best performance in the whole period. We will also perform a breakdown analysis of the returns of each ETF by year.



<h3>Create Dataframe of Adjusted Prices</h3>



To start with, we will create a data frame that contains the adjusted prices of all the four ETFs.



<pre class="wp-block-code"><code>adjustedPrices &lt;- data.frame(cbind(SPY$SPY.Adjusted,IVV$IVV.Adjusted,QQQ$QQQ.Adjusted,IWF$IWF.Adjusted))
 
head(adjustedPrices)

SPY.Adjusted IVV.Adjusted QQQ.Adjusted IWF.Adjusted
2014-02-03 156.2863 156.6725 79.55049 75.79685
2014-02-04 157.3810 157.7458 80.13563 76.49506
2014-02-05 157.1836 157.5401 79.92802 76.26232
2014-02-06 159.2564 159.6420 80.94727 77.31428
2014-02-07 161.2306 161.7259 82.39124 78.43140
2014-02-10 161.5267 161.9495 82.86315 78.64553
2014-02-11 163.2944 163.7383 83.80693 79.44613
2014-02-12 163.3752 163.8725 83.96736 79.60438
2014-02-13 164.2186 164.6685 84.59025 80.16293
2014-02-14 165.1249 165.5450 84.76012 80.33982
</code></pre>



<h3 id="lecture_heading">Calculate Daily Returns</h3>



Now we will use the&nbsp;dailyReturn&nbsp; function from Quantmod to calculate daily returns of each ETF. The results are expressed in percentages. We will also names the columns of the returns dataframe with the string symbols of each ETF and preview the data.



<pre class="wp-block-code"><code># Use the dailyReturn function from Quantmod to calculate daily returns of each ETF. The results are expressed in percentages.

returns &lt;- data.frame(round(dailyReturn(SPY)*100,4),
 round(dailyReturn(IVV)*100,4),round(dailyReturn(QQQ)*100,4),
 round(dailyReturn(IWF)*100,4))
 
# Names the columns of the returns dataframe with the string symbols of each ETF
 
colnames(returns) &lt;- etfs
 
head(returns,10)
 SPY IVV QQQ IWF
2014-02-03 -2.1352 -2.1233 -2.1136 -2.2921
2014-02-04 0.7005 0.6850 0.7356 0.9211
2014-02-05 -0.1254 -0.1304 -0.2591 -0.3042
2014-02-06 1.3187 1.3342 1.2752 1.3794
2014-02-07 1.2396 1.3054 1.7838 1.4449
2014-02-10 0.1837 0.1383 0.5727 0.2730
2014-02-11 1.0944 1.1045 1.1390 1.0180
2014-02-12 0.0495 0.0819 0.1914 0.1992
2014-02-13 0.5163 0.4858 0.7418 0.7017
2014-02-14 0.5519 0.5323 0.2008 0.2207</code></pre>



<h3 id="lecture_heading">Create Correlation Matrix</h3>



<pre class="wp-block-code"><code># Correlation matrix of the ETFs returns.
 
cor(returns)
 
 SPY IVV QQQ IWF
SPY 1.0000000 0.9937751 0.9240429 0.9699816
IVV 0.9937751 1.0000000 0.9214337 0.9724484
QQQ 0.9240429 0.9214337 1.0000000 0.9687469
IWF 0.9699816 0.9724484 0.9687469 1.0000000</code></pre>



The correlation matrix of the returns shows that all ETFs are highly correlated with each other during the period 2014-2019. The greatest correlation is between the IVV and SPY, and the lowest correlation is between IVV and QQQ.&nbsp;



Note: Since we’re directly executing the&nbsp;cor()&nbsp;function, it will just create and display the correlation matrix. It will not save the object in the Environment. If you want to load/save it in the environment as an object use something like&nbsp;corrMatrix &lt;- cor(returns). This will save the results in a variable called&nbsp;corrMatrix.



<h3>Calculate Various Statistics for ETFs</h3>



It will be interesting to observe some statistics of the returns of each ETF in the whole period. In the following code, we are calculating statistics such as mean, standard deviation, median, min, max of ETF returns.



<pre class="wp-block-code"><code>ETFStats &lt;- do.call(data.frame, 
 list(mean = round(apply(returns, 2, mean),4),
 sd = round(apply(returns, 2, sd),4),
 median = round(apply(returns, 2, median),4),
 min = round(apply(returns, 2, min),4),
 max = round(apply(returns, 2, max),4)))
 
t(ETFStats)
 
 SPY IVV QQQ IWF
mean 0.0372 0.0372 0.0591 0.0482
sd 0.8327 0.8356 1.0596 0.9033
median 0.0499 0.0512 0.1006 0.0830
min -4.2107 -4.1698 -4.5767 -4.0930
max 5.0525 4.9049 6.2439 5.6418</code></pre>



The QQQ ETF has the highest volatility in the period with a standard deviation of the returns of 1.06 between 2014-2019. Also QQQ has the highest value in the mean returns among the group. The maximum daily return was for QQQ too with 6.24%.&nbsp;



Notes:



<ul><li>This function allows you to call any R function, but instead of writing out the arguments one by one, you can use a list to hold the arguments of the function.&nbsp;</li><li>The apply function is useful for applying a function across either the rows or columns of a data matrix, that is, you may apply a function across each row or across each column. For example, in the above code, we have&nbsp;apply(returns, 2, mean).&nbsp;The first argument is the returns data, which contains returns for each ETF for a period of time. The rows represent returns for each date. Each column is for one ETF. The second argument specified the dimension over which to apply the function (1 for rows and 2 for columns). The third argument is the function we want to apply. In this case, we are applying the mean function over each column in the returns data matrix. Similarly, the apply function is used to calculate other statistics.</li><li>The&nbsp;t()&nbsp;function transposes a matrix or data.frame.</li></ul>



<h3 id="lecture_heading">Asking Exploratory Questions</h3>



We can also use R to find answers to exploratory questions while analyzing the data. For example, find the date of the highest returns for QQQ. With a good understanding of R functions, we can answer these kind of questions as shown below:



<pre class="wp-block-code"><code># Find the date of the highest return for QQQ. The ‘which’ command will return the index in the returns dataframe with the highest value of the QQQ returns.
 
max_ret &lt;- which(returns$QQQ == max(returns$QQQ))
 
# Once you have the index, you can retrieve the actual row from the dataframe.
 
returns[max_ret,]
 
 SPY IVV QQQ IWF
2018-12-26 5.0525 4.9049 6.2439 5.6418</code></pre>



The highest return value for QQQ was on 2018-12-26. It seems that this date has the highest returns value for the four ETF.&nbsp;

Data Analysis with Quantmod in R

We will now plot a graph to show the accumulated returns of the ETFs over a period of time.&nbsp; We can do so by following the following steps:



<ul><li>Build a dataframe with the 4 ETFs prices and a date column. Calculate daily returns and cumulative returns.&nbsp;The&nbsp;cumsum()&nbsp;function returns the cumulative sums (i.e. the sum of all values up to a certain position of a vector).</li><li>Change the format of the data from wide shape to long shape with the&nbsp;gather()&nbsp;function from&nbsp;dplyr&nbsp;package.</li><li>Use&nbsp;ggplot2&nbsp;to graph the ETFs performance in the whole period.</li></ul>



<hr class="wp-block-separator"/>



Step 1: Build a dataframe with the 4 ETFs prices and a date column. Calculate daily returns and cumulative returns.



<pre class="wp-block-code"><code># Make the cumRets dataframe with the cumulative returns for each of the ETFs using cumsum() function 
# The dailyReturn is a built in function from quantmod to get the daily returns.
 
cumRets &lt;- data.frame(date = index(SPY),
 cumsum(dailyReturn(SPY) * 100),
 cumsum(dailyReturn(IVV) * 100),
 cumsum(dailyReturn(QQQ)* 100),
 cumsum(dailyReturn(IWF))* 100)
 
# Add new names to the columns of cumRets dataframe
 
colnames(cumRets)[-1] &lt;- etfs
 
head(cumRets,10)
 
 date SPY IVV QQQ IWF
1 2014-02-03 -2.1352 -2.1233 -2.1136 -2.2921
2 2014-02-04 -1.4347 -1.4382 -1.3780 -1.3709
3 2014-02-05 -1.5602 -1.5686 -1.6371 -1.6752
4 2014-02-06 -0.2414 -0.2345 -0.3619 -0.2958
5 2014-02-07 0.9981 1.0709 1.4220 1.1491
6 2014-02-10 1.1818 1.2092 1.9947 1.4221
7 2014-02-11 2.2762 2.3137 3.1337 2.4401
8 2014-02-12 2.3256 2.3957 3.3251 2.6393
9 2014-02-13 2.8419 2.8814 4.0669 3.3410
10 2014-02-14 3.3938 3.4137 4.2677 3.5616</code></pre>



Step 2: Change the format of the data from wide shape to long shape with the gather function from dplyr package.



The data is currently wide-shaped because each date’s data is wide. For better analysis, We want the data to be long, where each date of data is in a separate observation.



<pre class="wp-block-code"><code># Make a tidy dataset called longCumRets which group the returns of each ETF in the same column. 
# The second and third parameter of the gather function are the new columns names in the tidy dataset.

# Note: You need to install the tidyr package to use the gather function. Use install.packages('tidyr') for installing and library(tidyr) to load it.
 
longCumRets &lt;- gather(cumRets,symbol,cumReturns,etfs)
 
head(longCumRets,10)
 
 date symbol cumReturns
1 2014-02-03 SPY -2.1352
2 2014-02-04 SPY -1.4347
3 2014-02-05 SPY -1.5602
4 2014-02-06 SPY -0.2414
5 2014-02-07 SPY 0.9981
6 2014-02-10 SPY 1.1818
7 2014-02-11 SPY 2.2762
8 2014-02-12 SPY 2.3256
9 2014-02-13 SPY 2.8419
10 2014-02-14 SPY 3.3938</code></pre>



Step 3: Use ggplot2 to graph the ETFs performance in the whole period.



<pre class="wp-block-code"><code># Plot the performance of the ETF's indexes
 
ggplot(longCumRets, aes(x=date,y=cumReturns,color = symbol)) + geom_line()+ ggtitle("ETF’s Accumulated Returns")</code></pre>



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/Etfs-accumulated-returns-1024x497.png" alt="" class="wp-image-26370"/></figure></div>



As we can observe in the graph, all ETFs are correlated, which means that they are affected by similar drivers. QQQ has the greatest performance in the whole period while SPY and IVV have the lowest performance. At the end of 2018 a big drawdown has affected all ETFs performance.



A note about reshaping data:



There are times when our data is considered unstacked and a common attribute of concern is spread out across columns. To reformat the data such that these common attributes are gathered together as a single variable, the gather() function will take multiple columns and collapse them into key-value pairs, duplicating all other columns as needed.



<h3>Measuring Overall ETFs Performance - Yearly Breakdown</h3>



To go deeper in analyzing ETFs performance during the period, we will make a breakdown about ETF performance by year. With this picture we can gain an insight into which ETF has the greater and poor performance by year. This can be achieved by following the following steps:



<ul><li>Step 1:&nbsp;Transform the&nbsp;returns&nbsp;dataframe from wide to long creating the&nbsp;longrets&nbsp;dataframe. With this shape, we would have two new columns that are symbol and returns, which store the daily returns for each symbol in long format.</li><li>Step 2:&nbsp;Make a new column in&nbsp;longrets&nbsp;with only the year from the index of returns.</li><li>Step 3:&nbsp;Calculate the mean of returns for each group, where the group is composed of a particular symbol-year.</li></ul>



<pre class="wp-block-code"><code># Transform the returns dataframe from wide to long creating the longrets dataframe.
 
longrets &lt;- gather(returns,symbol,returns,etfs)
 
head(longrets)
 
 symbol returns
1 SPY -2.1352
2 SPY 0.7005
3 SPY -0.1254
4 SPY 1.3187
5 SPY 1.2396
6 SPY 0.1837

 
# Take only the years from the index names of returns that have the dates
 
longrets$year &lt;- substr(rownames(returns),1,4)
 
head(longrets)
 
 symbol returns year
1 SPY -2.1352 2014
2 SPY 0.7005 2014
3 SPY -0.1254 2014
4 SPY 1.3187 2014
5 SPY 1.2396 2014
6 SPY 0.1837 2014
 
# The aggregate function can split a data frame columns by groups and then
# apply a function to these groups. In our case the column that we are 
# interested to split is the returns column and the groups are symbol and year.
# Finally we will apply the mean function to each of these groups.
 
groupedReturns &lt;- aggregate(longrets$returns, list(symbol=longrets$symbol,year=longrets$year), mean)
 
groupedReturns
 
 symbol year x
1 IVV 2014 0.065175325
2 IWF 2014 0.062363203
3 QQQ 2014 0.082309524
4 SPY 2014 0.064810823
5 IVV 2015 0.001005556
6 IWF 2015 0.020585714
7 QQQ 2015 0.038149603
8 SPY 2015 0.001565079
9 IVV 2016 0.040590079
10 IWF 2016 0.024551190
11 QQQ 2016 0.028030159
12 SPY 2016 0.039951587
13 IVV 2017 0.071888048
14 IWF 2017 0.100740637
15 QQQ 2017 0.111167729
16 SPY 2017 0.071519124
17 IVV 2018 -0.020522311
18 IWF 2018 -0.003539841
19 QQQ 2018 0.006568924
20 SPY 2018 -0.020306375
21 IVV 2019 0.088256376
22 IWF 2019 0.111604027
23 QQQ 2019 0.112140940
24 SPY 2019 0.088615436
 </code></pre>



The&nbsp;groupedReturns&nbsp;dataframe provides useful insights about the mean returns of each ETF by year. We can see that the best symbol-year was QQQ 2019 with mean returns of 11%, while the poor symbol-year performance was IVV 2018 with a mean return of -2%. It is very appealing to show these insights graphically.&nbsp;



<pre class="wp-block-code"><code>annReturnBars &lt;- ggplot(groupedReturns,aes(x=symbol,y=x)) +
 geom_bar(stat="identity",aes(fill=symbol))+
 facet_wrap(~year,ncol=2) +
 theme(legend.position = "right") + ggtitle("ETF mean returns by Year")

annReturnBars
</code></pre>



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/Annual-returns-perf-1024x621.png" alt="" class="wp-image-26371"/></figure></div>



In this bar plot chart we can observe that the QQQ ETF has the highest performance in all years, except for 2016 where the most performant was IVV ETF. Also we can observe that 2018 was the worst year of the period, where only QQQ has slightly positive returns. On the other hand, 2017 were a good year for all ETFs, and up to this moment 2019 is a good year too.



In the next section, we would start with the quantstrat package that provides an infrastructure to build, backtest and analyze trading strategies.

Measuring Overall ETFs Performance

Quantstrat Example in R - EMA Crossover Strategy

Once we have the strategy results, quantstrat provides many functions to analyze the strategy and observe important metrics of performance and risk. We would combine the&nbsp;quantstrat&nbsp;package with the&nbsp;PerformanceAnalytics&nbsp;package to show important performance and risk metrics in a trading strategy. We will look at the following:



<ul><li>Plot the Strategy Performance</li><li>Strategy Statistics and Stats per Trade</li><li>Portfolio Returns</li><li>Account Summary and Equity Curve</li><li>Portfolio Summary and Strategy Performance</li><li>Equity Return Distribution</li></ul>



<h3 id="lecture_heading">Plot the Strategy Performance</h3>



We can plot the performance using the&nbsp;chart.Posn(). The&nbsp;chart.Posn()&nbsp;takes two parameters that are portfolio name and the symbol string and return a chart with the symbol price series, the accumulated profit loss and the Drawdown charts. The trades of the strategy are marked in green and red on the price series chart.



<pre class="wp-block-code"><code># Chart Performance of the Strategy

chart.Posn(portfolioName, Symbol = symbolstring)
 </code></pre>



<h4>QQQ EMA Crossover Prices, Strategy P&amp;L and Drawdowns</h4>



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/chart-perf-ema-crossover-1024x686.png" alt="" class="wp-image-26378"/></figure></div>



<h3 id="lecture_heading">Strategy Statistics</h3>



tradeStats()&nbsp;function calculates statistics about the strategy. These statistics are related to measures about the strategy profits, risk metrics and general features of the strategy such as number of transactions, highest profitable trade, highest loser trade, average profit per trade among others.&nbsp; In our example, we have the following information:



<pre class="wp-block-code"><code>tstats &lt;- tradeStats(portfolioName)
 
tstats &lt;- data.frame(t(tstats))
 
colnames(tstats)
 
tstats
 
 QQQ
Portfolio FirstPortfolio
Symbol QQQ
Num.Txns 42
Num.Trades 21
Net.Trading.PL -3805
Avg.Trade.PL -171.1905
Med.Trade.PL -231.9994
Largest.Winner 1590
Largest.Loser -882.0001
Gross.Profits 2127.999
Gross.Losses -5722.998
Std.Dev.Trade.PL 485.9721
Std.Err.Trade.PL 106.0478
Percent.Positive 14.28571
Percent.Negative 85.71429
Profit.Factor 0.3718328
Avg.Win.Trade 709.3329
Med.Win.Trade 337.9996
Avg.Losing.Trade -317.9444
Med.Losing.Trade -243.4995
Avg.Daily.PL -171.1905
Med.Daily.PL -231.9994
Std.Dev.Daily.PL 485.9721
Std.Err.Daily.PL 106.0478
Ann.Sharpe -5.592018
Max.Drawdown -5822.998
Profit.To.Max.Draw -0.6534434
Avg.WinLoss.Ratio 2.230997
Med.WinLoss.Ratio 1.388092
Max.Equity 512.9992
Min.Equity -5309.999
End.Equity -380</code></pre>



The&nbsp;perTradeStats()&nbsp;function takes two arguments that are the portfolio name and the symbols strings and outputs the statistics and results by trade.&nbsp; The results contain information such as: the net profit for each trade, the start and end time of each trade, the percentage of profit of the trade, among other interesting variables. We will not show the output of this function, but feel free to try it in R Studio.



<h3>Portfolio Returns</h3>



The PortfReturns(account)&nbsp;show the daily returns for each symbol of the strategy. We would pass&nbsp; the output of the&nbsp;PortReturns()&nbsp;to the&nbsp;table.Arbitrary&nbsp;function of the&nbsp;PerformanceAnalytics&nbsp;package to condense and create fundamental metrics with the returns of the strategy.



<pre class="wp-block-code"><code># Store the returns of the strategy in an object called rets
 
rets &lt;- PortfReturns(Account = accountName)
 
rownames(rets) &lt;- NULL
 
tab.perf &lt;- table.Arbitrary(rets,
 metrics=c(
 "Return.cumulative",
 "Return.annualized",
 "SharpeRatio.annualized",
 "CalmarRatio"),
 metricsNames=c(
 "Cumulative Return",
 "Annualized Return",
 "Annualized Sharpe Ratio",
 "Calmar Ratio"))
 
tab.perf #displays the performance metrics
 
 QQQ.DailyEqPL
Cumulative Return -0.07613984
Annualized Return -0.01429584
Annualized Sharpe Ratio -0.42604174
Calmar Ratio -0.12881185
 
 
tab.risk &lt;- table.Arbitrary(rets,
 metrics=c(
 "StdDev.annualized",
 "maxDrawdown",
 "VaR",
 "ES"),
 metricsNames=c(
 "Annualized StdDev",
 "Max DrawDown",
 "Value-at-Risk",
 "Conditional VaR"))
 
tab.risk #displays the risk metrics
 
 QQQ.DailyEqPL
Annualized StdDev 0.03355503
Max DrawDown 0.11098234
Value-at-Risk -0.00248965
Conditional VaR -0.00248965
 </code></pre>



<h3 id="lecture_heading">Account Summary and Equity Curve</h3>



The&nbsp;getAccount(AccountName)&nbsp;function returns the account summary and equity curve of the strategy.



<pre class="wp-block-code"><code>a &lt;- getAccount(accountName)
 
equity &lt;- a$summary$End.Eq
 
plot(equity, main = "Equity Curve QQQ")</code></pre>



<h4>Equity Curve QQQ EMA Crossover Strategy</h4>



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/Equity-curve-1024x616.png" alt="" class="wp-image-26379"/></figure></div>



<h3 id="lecture_heading">Portfolio Summary and Strategy Performance</h3>



The&nbsp;getPortfolio(portfolioName)&nbsp;function returns the portfolio summary. With this function we can view how the portfolio object is updated on a daily basis every time we have new transactions.&nbsp;



<pre class="wp-block-code"><code>portfolio &lt;- getPortfolio(portfolioName) 
 
portfolioSummary &lt;- portfolio$summary
 
colnames(portfolio$summary)
 
"Long.Value" "Short.Value" "Net.Value" 
"Gross.Value" "Period.Realized.PL" "Period.Unrealized.PL"
"Gross.Trading.PL" "Txn.Fees" "Net.Trading.PL" </code></pre>



These are the columns of the portfolioSummary xts object. Every time we have a new transaction these columns would be updated.



<pre class="wp-block-code"><code>## Account Performance Summary
 
ret &lt;- Return.calculate(equity, method = "log")
 
ret
 
charts.PerformanceSummary(ret, colorset = bluefocus, 
 main = "Strategy Performance")</code></pre>



<h4>Cumulative Return, Daily Returns and Drawdown QQQ&nbsp; EMA Crossover Strategy</h4>



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/Strategy-perf-1024x698.png" alt="" class="wp-image-26380"/></figure></div>



<h3 id="lecture_heading">Equity Returns Distribution</h3>



We can also draw a boxplot with the daily equity returns distribution of the strategy.



<pre class="wp-block-code"><code>rets &lt;- PortfReturns(Account = accountName)

chart.Boxplot(rets, main = "QQQ Returns", colorset= rich10equal)
 </code></pre>



<h4>Daily Equity Returns Distribution</h4>



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/Equity-distribution-1024x698.png" alt="" class="wp-image-26381"/></figure></div>



As we observed, quantstrat provides many tools for the analysis of a trading strategy from multiple perspectives. With these tools we can get accurate information about strategy results and risks.&nbsp; In the next section, we will create a new strategy and with that explore some more features and functionality of quantstrat.

Quantstrat - EMA Crossover Strategy - Performance and Risk Metrics

Quantstrat Example in R - RSI Strategy

One of the main advantages of&nbsp;quantstrat&nbsp;package is that we can backtest strategies with multiple symbols as fast as with one symbol. The package provides fast computations for multiple symbols that allow analysts to get insights of strategies in an efficient approach.&nbsp;



In this case study we will build a strategy that works with 9 ETFs which are described below, and its signal is based on the three Exponential Moving Average (EMA) Crossover in order to run the trend. There are three EMAs that generate a crossover signal to buy when EMA4 &gt; EMA9 &gt; EMA18 and exit positions when EMA4 &lt; EMA9 &lt; EMA18.



In the performance analysis we will get the same info as we did before, but with the breakdown by symbol. This leads to an analysis by symbols where we can get an overview of the worst and best performing symbols. The steps are the same as before: Objects Initialization, Add Indicators, Add Signal, Add Rules, Apply the Strategy to the Portfolio, and Get Metrics.&nbsp;



Before proceeding, start a new R session and ensure that the&nbsp;quantstrat and ggplot2&nbsp;libraries is loaded.



Note: For convenience, the complete R file is attached below.



<div class="wp-block-file"><a href="https://financetrain.com/wp-content/uploads/multi-symbol-strategy.R.zip">multi-symbol-strategy.R</a><a href="https://financetrain.com/wp-content/uploads/multi-symbol-strategy.R.zip" class="wp-block-file__button" download>Download</a></div>



<h3>Initialize Currency and Instruments</h3>



<ul><li>Initialize current (USD)</li><li>Create symbol variable (we will use the Apple stock - AAPL)</li><li>Set timezone</li><li>Define the stock metadata using the stock() function</li></ul>



<pre class="wp-block-code"><code># Make sure quantstrat, dplyr and ggplot2 are loaded before starting. 
# library(quantstrat)
# library(dplyr)
# library(ggplot2)

# User search() to check what's loaded

# Initialize the currency. The accounting analytics back-end systems need to know what currency the prices are listed in

currency('USD') 

# Set the time to UTC, since that’s the time zone for a “Date” class object. Some orders need the time to be in UTC

Sys.setenv(TZ="UTC")

# Create a Symbols vector

Symbols &lt;- c('SPY',#
 'IWM', # iShares Russell 2000 ETF
 'QQQ', # PowerShares QQQ Trust, Series 1
 'IYR', # iShares U.S. Real Estate ETF
 'TLT', # iShares 20+ Year Treasury Bond ETF
 'EEM', # iShares MSCI Emerging Markets ETF
 'EFA', # iShares MSCI EAFE ETF
 'GLD', # SPDR Gold Trust
 'DBC' # Invesco DB Commodity Index 
)

# Define the stock metadata

stock(Symbols,currency='USD',multiplier=1)
</code></pre>



<h3>Define Dates and Load Historical Data</h3>



<pre class="wp-block-code"><code># The initDate is used in the initialization of the portfolio and orders objects, and should be less than the startDate, which is the date of the data.

initDate &lt;- '2013-01-10'

startDate &lt;- '2014-07-01'

startEquity &lt;- 100000

endDate &lt;- '2019-08-14'

tradeSize &lt;- startEquity/length(symbols)

# Fetch the data from tiingo api. This command require an api key that can be acquired in the tiingo site

token &lt;- token &lt;- 'your api key'
getSymbols(Symbols,from=startDate,to=endDate,adjust=TRUE,src='tiingo',api.key=token)
</code></pre>



<h3>Initialize Portfolio, Account and Order Objects</h3>



<pre class="wp-block-code"><code># Name the strategy, portfolio and account with the same name

portName &lt;- stratName &lt;- acctName &lt;- 'multipleSymbols'

# Remove objects associated with a strategy

rm.strat(stratName)

# Initialization of the Portfolio, Account and Orders objects with their required parameters. The startEquity value in the initEq parameter on the account initialization is added in order to compute returns.

initPortf(portName,symbols=Symbols,initDate = startDate)

initAcct(acctName,portfolios = portName,initDate = startDate,initEq = startEquity)

initOrders(portfolio=portName,startDate=startDate)
</code></pre>



<h3>Initialize and Store the Strategy</h3>



<pre class="wp-block-code"><code># Initialize and store the strategy 
 
strategy(stratName,store=TRUE)</code></pre>



<h3>Add Indicators</h3>



<pre class="wp-block-code"><code># Add Indicators

add.indicator(strategy=stratName, name="EMA", arguments=list(x = quote(Cl(mktdata)), n=4), label="EMA4")

add.indicator(strategy=stratName, name="EMA", arguments=list(x = quote(Cl(mktdata)), n=9), label="EMA9")

add.indicator(strategy=stratName, name="EMA", arguments=list(x = quote(Cl(mktdata)), n=18), label="EMA18")

# Test the indicators while building the strategy.
# This allows a user to see how the indicators will be appended to the mktdata object in the backtest. If the call to applyIndicators fails, it means that there most likely is an issue with labeling (column naming).

test &lt;- applyIndicators(stratName, mktdata=OHLC(QQQ))

tail(test,10)

 QQQ.Open QQQ.High QQQ.Low QQQ.Close EMA.EMA4 EMA.EMA9 EMA.EMA18
2019-08-01 191.51 194.98 189.23 190.15 191.8198 192.5779 192.0640
2019-08-02 188.82 188.99 186.21 187.35 190.0319 191.5323 191.5678
2019-08-05 183.51 183.51 179.20 180.73 186.3111 189.3718 190.4270
2019-08-06 182.38 183.80 181.07 183.26 185.0907 188.1495 189.6726
2019-08-07 181.32 184.51 179.89 184.25 184.7544 187.3696 189.1018
2019-08-08 185.15 188.32 184.57 188.26 186.1566 187.5477 189.0132
2019-08-09 187.32 188.00 185.03 186.49 186.2900 187.3361 188.7476
2019-08-12 185.34 185.90 183.50 184.35 185.5140 186.7389 188.2847
2019-08-13 184.27 189.68 184.02 188.39 186.6644 187.0691 188.2958
2019-08-14 185.31 185.95 182.42 182.76 185.1026 186.2073 187.7130
</code></pre>



<h3>Add Signals</h3>



<pre class="wp-block-code"><code># Add Signals
 
add.signal(strategy=stratName, name="sigCrossover", arguments = list(columns=c("EMA.EMA4","EMA.EMA9"),relationship="gt"),label="Up4X9")
 
add.signal(strategy=stratName, name="sigCrossover", arguments = list(columns=c("EMA.EMA9","EMA.EMA18"),relationship="gt"),label="Up9X18")
 
add.signal(strategy=stratName, name="sigCrossover", arguments = list(columns=c("EMA.EMA4","EMA.EMA9"),relationship="lt"),label="Down4X9")
 
add.signal(strategy=stratName, name="sigCrossover", arguments = list(columns=c("EMA.EMA9","EMA.EMA18"),relationship="lt"),label="Down9X18")
 
# We take the columns Up4X9 and Up9X18 to create the longEntry column in the mktdata object, which is True when EMA4 > EMA9 and EMA9 > EMA 18
 
add.signal(strategy=stratName, name="sigFormula", arguments = list(columns=c("Up4X9","Up9X18"),formula="Up4X9 &amp; Up9X18"),label="longEntry")
 
# Define the long exit
 
add.signal(strategy=stratName, name="sigFormula", arguments = list(columns=c("Down4X9","Down9X18"),formula=("Down4X9 &amp; Down9X18")),label="longExit")
 </code></pre>



<h3>Add Rules</h3>



<pre class="wp-block-code"><code># Rule to enter in a long position(type="enter")

add.rule(strategy = stratName,name='ruleSignal', 
 arguments = list(sigcol="longEntry",sigval=TRUE,
 orderqty= 100, ordertype="market", orderside="long",
 replace=FALSE, tradeSize = tradeSize, maxSize=tradeSize,threshold=NULL),
 label="longEnter", enabled=TRUE, type="enter")

# Rule to exit (type="exit") of a long position. When the column shortEntry is True, we should exit our long position

add.rule(strategy = stratName,name="ruleSignal",
 arguments = list(sigcol="longExit", sigval=TRUE, 
 orderqty= "all", ordertype="market", replace=FALSE,
 orderside="long"),label="longExit", enabled=TRUE, type="exit")
 </code></pre>



<h3 id="lecture_heading">Apply Strategy</h3>



We will now apply the strategy to portfolio and then update the portfolio, account and equity.



<pre class="wp-block-code"><code># Apply strategy to the portfolio
 
t1 &lt;- Sys.time()
 
results &lt;- applyStrategy(stratName,portfolios = portName,symbols = Symbols)
 
t2 &lt;- Sys.time()
 
print(t2-t1)
 
# Set up analytics. Update portfolio, account and equity
 
updatePortf(portName)
 
dateRange &lt;- time(getPortfolio(portName)$summary)[-1]
 
updateAcct(portName,dateRange)
 
updateEndEq(acctName)</code></pre>



<h3 id="lecture_heading">Plot Accumulated Equity Returns</h3>



<pre class="wp-block-code"><code># Plot the equity curve of the strategy
 
final_acct &lt;- getAccount(acctName)
 
options(width=70)
 
plot(final_acct$summary$End.Eq, main = "Multiple Symbols Portfolio Equity")</code></pre>



<h4>Multiple Symbols Portfolio Equity Triple EMA Crossover Strategy</h4>



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/multi-symbol-portfolio-equity-1024x675.png" alt="" class="wp-image-26392"/></figure></div>



<h3 id="lecture_heading">Portfolio Statistics</h3>



<pre class="wp-block-code"><code>tStats &lt;- tradeStats(Portfolios = portName, use="trades", inclZeroDays=FALSE)
 
# Get performance information for each symbol
 
tab.profit &lt;- tStats %>% 
 select(Net.Trading.PL, Gross.Profits, Gross.Losses, Profit.Factor)
 
# t: transpose
 
t(tab.profit)
 
 DBC EEM EFA GLD IWM IYR
Net.Trading.PL 266.4998 3713.685370 -629.807645 211.000000 9403.746347 4037.07263
Gross.Profits 266.4998 4862.953129 125.911927 2752.000000 11603.902733 4354.18955
Gross.Losses 0.0000 -1149.267759 -755.719572 -2541.000000 -2200.156385 -317.11692
Profit.Factor NA 4.231349 0.166612 1.083038 5.274126 13.73055
 QQQ SPY TLT
Net.Trading.PL 6569.62866 -708.0645 3222.506379
Gross.Profits 6890.56991 0.0000 3799.799792
Gross.Losses -320.94126 -708.0645 -577.293413
Profit.Factor 21.46988 0.0000 6.582094
 
# Average trade profit per symbol
 
tab.wins &lt;- tStats %>% 
 select(Avg.Trade.PL, Avg.Win.Trade, Avg.Losing.Trade, Avg.WinLoss.Ratio)
 
(t(tab.wins))
 
 DBC EEM EFA GLD IWM IYR
Avg.Trade.PL 266.4998 742.737074 -157.451911 52.750000 3134.58212 807.4145
Avg.Win.Trade 266.4998 2431.476565 62.955964 2752.000000 11603.90273 1451.3965
Avg.Losing.Trade Nan -383.089253 -377.859786 -847.000000 -1100.07819 -158.5585
Avg.WinLoss.Ratio NA 6.347024 0.166612 3.249115 10.54825 9.1537
 
 QQQ SPY TLT
Avg.Trade.PL 1313.92573 -236.0215 537.084397
Avg.Win.Trade 1722.64248 Nan 949.949948
Avg.Losing.Trade -320.94126 -236.0215 -288.646706
Avg.WinLoss.Ratio 5.36747 NaN 3.291047
 </code></pre>



<h3 id="lecture_heading">Cumulative Returns</h3>



<pre class="wp-block-code"><code># Returns on Equity(ROE) by Symbol
 
rets &lt;- PortfReturns(Account = acctName)
 
rownames(rets) &lt;- NULL
 
# Chart the cumulative returns for all the symbols
 
charts.PerformanceSummary(rets, colorset = bluefocus)
 </code></pre>



<h4>Cumulative Returns by ETF’s Triple EMA Cross Over Strategy</h4>



<div class="wp-block-image"><figure class="aligncenter"><img src="https://financetrain.com/wp-content/uploads/Multiple-symbol-cum-returns-1024x675.png" alt="" class="wp-image-26393"/></figure></div>



<h3>Performance Statistics for Each Symbol</h3>



<pre class="wp-block-code"><code># Performance Statistics and risk metrics for each symbol 
# Performance : annualized and cumulative returns s 
# Risk metrics : Sharpe and Calmar ratio 
 
tab.perf &lt;- table.Arbitrary(rets,
 metrics=c(
 "Return.cumulative",
 "Return.annualized",
 "SharpeRatio.annualized",
 "CalmarRatio"),
 metricsNames=c(
 "Cumulative Return",
 "Annualized Return",
 "Annualized Sharpe Ratio",
 "Calmar Ratio"))
 
round(tab.perf,5)
 
 DBC.DailyEqPL EEM.DailyEqPL EFA.DailyEqPL GLD.DailyEqPL
Cumulative Return 0.00266 0.03719 -0.00635 0.00190
Annualized Return 0.00052 0.00716 -0.00124 0.00037
Annualized Sharpe Ratio 0.24670 0.46053 -0.23570 0.04058
Calmar Ratio 0.10078 0.23305 -0.10153 0.01016
 IWM.DailyEqPL IYR.DailyEqPL QQQ.DailyEqPL SPY.DailyEqPL
Cumulative Return 0.09275 0.04061 0.06655 -0.00714
Annualized Return 0.01748 0.00781 0.01267 -0.00140
Annualized Sharpe Ratio 0.38301 0.52618 0.57011 -0.24452
Calmar Ratio 0.25103 0.38344 0.26922 -0.14163
 TLT.DailyEqPL
Cumulative Return 0.03236
Annualized Return 0.00624
Annualized Sharpe Ratio 0.56136
Calmar Ratio 0.32163
</code></pre>



<h3>Risk Statistics by Symbol</h3>



<pre class="wp-block-code"><code># Risk Statistics by Symbol
 
tab.risk &lt;- table.Arbitrary(rets,
 metrics=c(
 "StdDev.annualized",
 "maxDrawdown",
 "VaR",
 "ES"),
 metricsNames=c(
 "Annualized StdDev",
 "Max DrawDown",
 "Value-at-Risk",
 "Conditional VaR"))
 
round(tab.risk,5)
 
 
 DBC.DailyEqPL EEM.DailyEqPL EFA.DailyEqPL GLD.DailyEqPL IWM.DailyEqPL
Annualized StdDev 0.00210 0.01555 0.00528 0.00914 0.04565
Max DrawDown 0.00515 0.03072 0.01225 0.03649 0.06962
Value-at-Risk -0.00016 -0.00149 -0.00053 -0.00084 -0.00464
Conditional VaR -0.00016 -0.00342 -0.00110 -0.00115 -0.01233
 IYR.DailyEqPL QQQ.DailyEqPL SPY.DailyEqPL TLT.DailyEqPL
Annualized StdDev 0.01484 0.02223 0.00572 0.01114
Max DrawDown 0.02036 0.04705 0.00987 0.01944
Value-at-Risk -0.00144 -0.00230 -0.00044 -0.00065
Conditional VaR -0.00358 -0.00500 -0.00044 -0.00065</code></pre>



The results above show that the symbol IWM has the best performance among all ETFs in the portfolio. The annual returns for IWM was 1,75% and the cumulative return was 9,3%. In the second place comes the QQQ ETF which has an annual return in the whole period of 1,23% and cumulative returns of 6,65%.&nbsp;



The worst performance among the ETF’s in the portfolio was for SPY ETF with an annualized return of -0.14% and a cumulative return of -0,71% in the whole period. Regards, the ETF with the Maximum Drawdown level, we can observe that the IWM ETF has the Maximum Drawdown lever among the rest of the ETF’s with a 7% of Maximum Drawdown.



In terms of Sharpe and Calmar Ratio, the best level of&nbsp;Sharpe&nbsp;Ratio is observed for IWR ETF with a value of 0.38 and Calmar ratio of 0.25. Remember, when we define Calmar Ratio in the risk management section, we point out that this ratio takes into account the Maximum Drawdown level in its calculation. So for a conservative strategy this ratio is fundamental.



Finally the QQQ ETF has the higher Sharpe Ratio with a value of 0.57 which is followed by the TLT ETF with a Sharpe Ratio value of 0.56. Overall, this strategy has positive returns at the end of the period, but is affected by a significant drawdown at the end of 2018. The exit rule of this strategy given by&nbsp; triple EMA cross down is to exit the position when the market reverse.

Quantstrat Case Study - Multiple Symbol Portfolio

Quantitative Trading Strategies in R

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COURSE

Quantitative Trading Strategies in R

LESSONS