There is so much assumed knowledge in the investing literature and posts online that sometimes it can be confusing. Users can treat this page as a dictionary-style reference page to refer back to at any point throughout the user journey on this topic.

This post could also be kept open in a separate page to refer back to easily while you are making your way through all the other articles in this topic. 

If there are any other items that users want added and explained, please email us at info@aikido.finance and we will be happy to update the page.

this term will be used everywhere on this site and elsewhere in social media etc. The 

has a broad definition and will depend on the end-user but you can think of it as the main stock index of that country e.g a US report states "the market was up 2% today" they most likely mean the S+P 500, which most people treat as the main US index, was up 2%. They could also mean that the average of the S+P 500, the Nasdaq and the Dow Jones was up 2%. If we switched the example to the UK, it is most likely the FTSE 100 the market was referring to or the EuroStoxx 50 for Europe.   

. Alpha measures the predictive power of a strategy or signal. It represents what returns the strategy is delivering to the investor, after accounting for the overall market performance - higher alpha means higher returns that are not explained by the market. If a manager or strategy is delivering no alpha then the strategy or manager is mostly 

 the performance of the market is referred to as beta and is essentially what any investor can achieve by simply investing in the overall market. Another use case for beta occurs when a strategy is referred to as 

. This means the strategy is delivering nothing in excess of what can be achieved by investing in the market directly. 

: this is the return of the market minus the risk-free rate i.e the premium an investor obtains by investing in the market instead of leaving money in a bank account

 the risk of the market in general that investors need to be compensated for in the form of a risk premium. This is also known as 

With any investment there is risk and there should be some expected return associated to that risk. This return should therefore be higher than the 

which is the rate an investor would receive for deposited cash in the bank and earn risk-free interest. 

non-systematic risk, idiosyncratic risk, specific risk 

This is the portion of risk that can be removed from a portfolio by ensuring that enough stocks are chosen to eliminate the unsystematic risk.

 no fixed definition but it generally refers to a metric that is risk-based that a person relies on to make decisions. This 

 is most likely a volatility-based metric where the user is concerned about how many ups and downs something has compared to the average price. The higher the volatility the higher the risk.  

 a framework by which you represent every single stock return by a strict model equation. Any coefficients in this model are most likely obtained from historical market data. The model's aim is to provide a clear representation to compare stocks against each other and to represent their returns via a simplified equation. We give an example in the capm model below.  

. It was the first factor model in academia where the returns of a stock are represented by a beta value (also called a coefficient) multiplied by the market return. It is an articulate way to represent a stocks excess return 

 this form of investing uses low-cost and mostly standardised products that aim to match the market, such as trackers or mutual funds. They can be limited in scope due to the indices they track and inflexible.

refers to the management of a portfolio mostly by a skilled investment/portfolio manager. The investment choices made are mostly hands-on and do not involve quantitative strategies. Their aim is to deliver superior returns to the market. However the fees are very expensive for such active management.

 tries to combine or mix the passive and active styles to create the best of both worlds, a slightly quantitative approach that aims to deliver better returns than the market. 

 this is a measure for the variation of data around its average value over a one-year horizon. It explains to the user how volatile an assets price is and the higher the volatility the riskier the asset. 

the process of ensuring that your portfolio is kept up to date with the strategy i.e stocks in your portfolio that are not in the strategy are sold and stocks in the strategy that are not in your portfolio are bought. Please refer to our 

 a method of historically testing how an investment strategy would have performed if you have invested in it back in time. It uses the investment to historically construct the portfolio you would have had using realistic execution prices to give you the set of portfolio returns you could have achieved. Please refer to our 

similar to the concept of a risk-adjusted return. The Sharpe ratio is calculated by first subtracting the risk-free rate from the average return of the strategy and dividing this by the volatility of the strategy returns. Essentially this scales any returns an investor gets by the volatility needed to generate the returns. As a heuristic, any sharpe ratio > 1 is a decent investment strategy. 

refers to continually moving your historical window used for your calculations. This is different to an expanding window that some people are familiar with. An expanding window takes 

 available for use in calculating statistics such as risk, return, sharpe ratio and so an expanding window grows with time. A rolling window in comparison ensures that only a fixed amount of data is used in any calculations of risk, return, sharpe ratio and when new data becomes available, that new data is included and other older historical data is removed. 

 a period of sustained negative performance is referred to as a drawdown. It represents in percentage terms how far your portfolio is from its previous highest value. Typically if your portfolio is not within 10-15% of its highest portfolio value, you are most likely classified as in a drawdown. However, serious drawdowns only occur when portfolios are around 20-25% or more below previous highs. Please refer to our 

 the length of a drawdown is a useful metric to consider when looking at a strategy. What investors do not want to see is a very large drawdown length, where this could indicate that the strategy in question does not have the alpha or predictive power to bounce back and breach the historical peak quickly and investors in that strategy suffer for a very long time. Short, sharp drawdowns can and do occur but if your drawdown length is short then investors are more likely to believe in the bounce-back nature of the strategy for the future. They believe it has enough alpha to perform again after a negative period. 

 industry term for a set of backtested results that indicate the efficacy of the strategy being analysed. It usually contains a strategy equity performance graph, risk and return and sharpe ratio statistics and a set of yearly returns so users can see how the strategy performed on a year-by-year basis. Please refer to our 

 this is the data used when your model is fitted and coefficients are estimated. Potentially the model is tweaked and changed multiple times during this training phase and so has the potential to overfit to this training data if care is not taken.

 this is data that your model does not see during its training. Once your model is fitted using the training data, it is then only ran against the test data. A nice property for your model to have is for the error to be the same when ran on the training data and the test data. This ensures that your model could potentially generalise well and produce good results when run in a live performing environment.

 bid-offer spreads mean you most often do not get the mid price 

this affects larger institutional clients more than smaller retail investors and also depends on the type of stock that is being bought. Market impact refers to the impact your own trades have on the price of the underlying stock during the execution phase of your order. 

 the fill price you received differs from what you assumed or expected you would get. For quantitative modelling, this can be important as backtested results assume you are filled with a price that you may not have achieved in real life. Slippage for example can be driven by:

 the order size being too large so the price move during execution

 time delay placing your order to the broker so the market moved 

stop-loss fill price differs from stop-loss order entered

 the volume-weighted average price is a price that is based on a weighted average summation of all order sizes and prices for that security over a specified period.

percentage-of-volume is another metric used by larger investment firms where there orders are executed via brokers 

 time-weighted average price that represents a similar concept to the vwap price. Twap refers to time-weighting so the execution algorithm fills your orders at a specific and consistent speed, it represents the security's 

. This is a lesser used fill method than both vwap and pov.

is an order to buy or sell an asset at a certain price. This order is not guaranteed to get filled.

is an order to buy or sell an asset immediately by executing at the best price available. Whilst it gives certainty to execution the slippage with this type of order can be more than an investor desires and is especially important for either large size market orders or orders executed for illiquid stocks.

 an order placed to ensure that an investor limits the losses on positions. It is an order to exit a losing position using a pre-defined price if the market drops to this price. Again, slippage can be a concern here because if the market is moving quickly the executing broker will use best efforts to fill the stop-loss order but may end up executing at a worse price. 

 this is an order and execution methodology where the order is placed on either the best bid price (if trying to buy) or best offer price (if trying to sell). If the price moves and the order is not filled, then the order updates with the price and again joins either the best bid or best offer side of the market. This simple form of a peg order can ensure that the investor does not cross the bid-offer spread and could end up getting filled at better rates than a market order. However the inverse is also true and by being passive with the execution, an investor may not get filled and instead have to purchase for example at a much higher price later in the day in order to execute. 

 the stock market provides two extra methods of filling orders, that have gained in popularity significantly over recent years. These are auction style events where client orders are entered alongside each other to come up with a composite price. Closing auctions in particular (are far more prevalent than opening auctions) now account for a significanly higher percentage of investors fills (upwards of 15% of the day's volume) as they provide a reliable and transparent method of achieving the closing price for the investors fills. 

this is an umbrella term that refers to company actions that change the corporate structure in terms of shares outstanding and price. These changes do not have any financial impact and there is no change to the market cap of the company. See stock splot and reverse split next for further explanation.

 a company increases the number of shares it has issued, with an accompanying pro-rate decrease in the stock price so the market cap remains unchanged. This is primarily executed by companies who share prices have grown too large so a single share costs too much, especially for retail focused investors. By splitting their stock they ensure that the price decrease allows more users to buy shares. An example is a 10-for-1 split where the number of shares increases by 10-fold and the share price then effectively drops by 90%, no losses are incurred by current shareholders as they get 10 shares for every 1 share they previously owned.

 this is the opposite of a stock split. In a reverse split, a company decreases its outstanding shares and thus aritifically increases its share price. It may do this because it wants to increase it's stock price, maybe due to potential delisting risk. Another reason for a reverse split may be to increase the chances of the stocks inclusion on an exchange or participate in an index or etf.

When a company takes a business unit and spins it out as a separate business with its own revenue stream.

only including companies that are alive today in your universe back through time and ignoring companies that delisted or went bankrupt. A quantitative investment companies data stack and backtester should be free of survivorship bias.  

another form of data bias where we allow our backtester, or strategy builder, to use data at a point in time that was only known in the future. This means all datasets in a companies data pipeline have to ensure that the data used was only data that was time-stamped and known from a particular day onwards, and not before.  

links closely with lookahead bias and means that we only use data at a 

 when the market and the participants would have received that data. 

Get to grips with some quantitative investing lingo and jargon.

1. Glossary: Learn some lingo 

You have the money to invest and now you need to decide what to invest in. Once you have identified the type of investments (cash, bonds, crypto, currency etc) you will next need to decide what portion of your money to invest in each. This decision will be influenced by how much risk you are prepared to take. This is where a risk budget comes in.

In summary, a risk budget is a method of asset allocation that combines an investor's financial goals, with their risk tolerance alongside the choice of available investments.  

There are a few key steps to creating a risk budget:

Decide what your overall risk metric is
 eg. ‘annual volatility percentage’ 

Take a view of the available investments
eg. Cash, bonds, active equity investing, commodities, quantitative equity investment, etc

Calculate the risk of each, using the metric chosen in step 1

Determine the marginal contribution of each individual investment into the overall risk of your portfolio

Build your investment portfolio accordingly

Example of a risk budget for ‘Risk Averse’ investor

This investor might conservatively choose ‘5% annual volatility’ for their overall risk metric

They opt for just 2 investments; cash and a quantitative equity strategy.

Cash being riskless will have a volatility of 0%.

Let's assume there are 3 available quantitative strategies with historical annual volatilities of 5%, 10% and 20% respectively.

The investor can now come up with various strategies for portfolios combining  cash and quantitative that will satisfy their 5% target risk budget volatility.

The portfolio could be built in a few different ways

Decide not to invest in cash at all, and invest all your money in the 5% quant strategy

Split your investment half in cash and half in the 10% quant strategy

Invest most of your money in cash and just a quarter of your money in the 20% strategy

Other terminology ‘Risk target’ versus ‘Risk capacity’

These two terms are closely linked and the ideal scenario is that they are aligned with each other. When they are aligned, the investor has transparent financial goals which are linked to their financial investments.

Risk target is the amount of annual volatility the investor is comfortable to take

Risk capacity is the annual volatility the investor needs to achieve their financial goals (i.e their desired annual expected return)

What is a risk budget and why is it important. How does your risk budget affect your portfolio allocation and choice of strategy.

2. Getting started with your risk budget

Whether you are focussed purely on quantitative strategies or have diversified in other asset classes, once you have set up your investment portfolio you will have some ongoing maintenance to keep it in line with the metric in your 

get back to your original asset allocation

. When one asset class significantly outperforms another, your portfolio drifts from its starting allocation.

Read on as we explain the process of rebalancing various asset classes or click 

 to learn specifically how to rebalance an Aikido portfolio.

1: Rebalancing a stock and bond portfolio

A classic investor holding stocks and bonds, may have decided to hold 50% of their portfolio in stocks and 50% in bonds at all times. They could plan to rebalance the portfolio on a monthly basis.

In this scenario let's assume the stock market consistently increases while the bond market decreases each month. At the end of each month, the investor rebalances and sells 3% worth of his strongly performing stock portfolio and buys 3% of the underperforming bond portfolio. This ensures his overall portfolio allocation to stocks and bonds stays consistent at 50% and 50%.

 to the stock market would have significantly increased through the year until they ended up in December with a whopping 83% of their money in stocks.

2: Rebalancing in the quantitative investing world

The reason rebalancing is particularly crucial in a quantitative investing framework is that most of the strategies that users may invest in, were backtested with a specific rebalancing frequency.

A quantitative strategy by design will have a rebalance period that was used in the 

A quantitative strategy uses data, either price+volume or fundamental balance sheet data, to decide at any point in time which companies are the best to invest in. This 

, so this means the quantitative strategy needs to account for this and update the “buy recommendations”. Updating the buy recommendations is equivalent to a rebalance frequency as 

the strategy will give a new list of stocks to invest in 

at that rebalance date, using this new price or fundamental data.

 that are currently in your portfolio are 

 in the updated quantitative strategy list, then they 

 and the new ones from the list added to your portfolio. This is the rebalance.

When selecting a quantitative strategy an investor is relying on a set of backtested results in order to reap returns in the future. We highlighted in the previous section, how quantitative strategies and backtests need to use updated information and that dictates the need to rebalance. Otherwise, if there is no rebalancing frequency the strategy is just a 

strategy where the stocks you own on day one are still in your portfolio years later. 

For any investor, the rebalance period they use for their portfolio is their own decision and it should consider a few elements:

. The more frequently a user rebalances, the more transaction costs they incur, which can degrade performance and increases the chance of slippage (slippage means your executed price differs from what you expected)

. Does the investor have the time and resources to commit to execute the rebalance trades on time every rebalance period

. Take into consideration the rebalance period used in the design of the quantitative strategy, but don’t feel bound to it. A strategy may be based on a fortnightly rebalance but you may still prefer to rebalance at month end.

Rebalancing an equity portfolio has more similarities to our example of (2) quantitative rebalancing than our example of (1) stock and bond portfolio rebalancing.

This is because users of the Aikido Finance platform are most likely running a small number of equity portfolios only. These strategies were also built and backtested using a rebalance period as specified in the construction of the strategy. 

Here is an example using a sample 5 stock portfolio

At the end of January the strategy will indicate the list of 5 stocks that need to be in the portfolio for February. The investor will rebalance by selling their GOOG and AMZN positions and buying NFLX and META. 

At the end of February the list will be reviewed for the coming month again. The rebalance will require the investor to sell their TSLA position and buy NVDA at the start of March.

Portfolio rebalancing is a crucial part of any long-term investment strategy. This post provides a high-level overview of rebalances.

3. What is portfolio rebalancing

When equity literature refers to factors and investing, they are really referring to 

. Factors are portfolios that consist of a set of stocks where each of those stocks in the set share a certain set of common properties. These properties can be

related by common fundamental balance sheet items

Factors are a means of grouping together stocks into portfolios where, it has been shown through history that, investing in these portfolios would have given investors a source of consistent risk-adjusted returns.

Factors have risen to prominence since the early 2000s and especially since 2010 and the rise of some 

 type factor exposure. Factor investing has been growing at a 30% 

 growth rate since 2010, with large asset managers like Blackrock indicating that factor investing will be worth over US$3 trillion by 2023.

 than the overall market - this has been shown using historical data and a huge amount of academic studies. 

Factors are a collection of specific rules that group specific stocks together based on similar characteristics. Factors, if applied for the long term, can be used to capture the 

that has been shown to exist in the financial markets.  

If the efficient market hypothesis was to be believed, then stocks prices would contain all current information and be fairly price and factor premiums would not exist. However, due to 

stock returns have been shown to exhibit these factor premiums. If investors invest in factors for the long-term, then these factors can be harvested for superior returns.  

it must follow a rules-based approach, based on financial metrics or price returns

it makes economic sense and most likely has academic backing

it has shown itself to be robust through long periods of time

ideally it works in most, if not all, geographies of the world

Each investment provider will construct their factors slightly differently. The rules governing the construction of factors are mostly heuristic in nature and will result in quantitative and financial modelling decisions that each provider makes for themselves. Overall the factors will still represent the same concept but the backtested results may differ slightly amongst the providers.

The factors found to be consistently referenced in the historic literature are:

, which are also popular factors. All of these factors have strong behavioural or fundamental reasons for their existence. If we group value, quality, size and dividend yield together, these factors use company fundamentals to characterise investor preferences:

others prefer high-quality companies with strong earnings growth and stable management

investors look for high dividend stocks to give them some income

 buys stocks that are considered cheap based on fundamental ratios such as price-to-book, price-to-earnings or net operating income. Theoretically investors believe that the prices for these stocks are too low and over time the market will adjust and investors will earn higher risk-adjusted returns as prices normalise.

 investors seek out companies that have shown strong management, robust earnings growth, strong margins, stable and manageable debt levels etc - all fundamental company metrics that indicate the company is strong, solid and well-managed.

 historically it has been shown in academic papers that small-cap companies outperform large-cap companies due to the risk-premium 

 factor that invests in stocks that have recently performed the best, based on the premise that this will continue in the future. This can be thought of as chasing recent winners, or fear-of-missing-out, as investors pile into positions in these so-called hot stocks, thus driving up their price in the future.  

 another price-based factor where it has been shown that stocks with historically lower than average volatility deliver higher risk-adjusted returns than stocks with historically high volatility. This is contrary to popular opinion, where it would seem natural that riskier stocks earn higher returns due to the extra risk the investor bears by holding them. The opposite is actually true and low-volatility has been referred to as an 

It has been shown to exist in numerous countries and also robust through time.

These factors are all expanded on in significant detail in our more advanced topic "Equity Style Factors".

What are factors and why are they used. We explain factors so their benefits are clearly understood and investors realise their power.

4. Factor investing explained

Reading media articles or posts online, a common term thrown around is 

 but do you know what that is? Well, mostly it's a pain metric for investors. In this article we want to explain this term for our users, explain how it is calculated and what a drawdown chart would look like. 

 the portfolio's highest performing level in history. If we take the 

 of the SPY ETF as an example first we plot the highest performing level, this is termed the Rolling Maximum and also referred to as High Watermark

Next we plot the cumulative or on-going performance.

Once our first graph has been completed, we can calculate the percentage difference between each line. We plot it on a new graph, and this is our Drawdown. This is what is regularly referred to in media articles and forums.

You will frequently see not only a  graphical depiction like ours above, but regularly it will be shown as a table. The tabular output is helpful to show deeper drawdown statistics, if for example you want to get a sense of the frequency and length of drawdowns. Other metrics that are commonly used in conjunction with drawdowns are

 and as such extra statistics like the above help investors judge what strategies to invest in. It helps provide a realistic expectation of what a user would have gone through emotionally if they had invested in that strategy in the past.

A quick code snippet for the python users out there who want to download some yahoo tickers for example, calculate returns and then show drawdowns. 

What are drawdowns and why are they important. How does drawdown analysis affect your portfolio allocation and choice of strategy.

5. Did someone say drawdown 

Tear-sheets are commonly used to represent graphical performance and summary statistics of a strategy. These can either be high-level sheets for an investment strategy or a deepdive with a granular low-level report. 

Keeping things concise can be very helpful and avoid any paralysis by analysis. We believe what most beginner investors care about are three things

what return should I hope to achieve with this strategy

 this strategy has suffered historically 

A set of results as shown below, can help a beginner investor quickly decide what strategy suits their needs. They can quickly see how much risk a strategy has historically had and also what was the worst portfolio performance they would have had to suffer through (the drawdown).  

In this case a very risk-averse investor might sacrifice a higher sharpe ratio strategy, "my momentum" with a sharpe of 0.8, for the lower performing strategy "deep-value" with a sharpe of 0.5. Why would someone do that ? The drawdown metric tells the story. An investor can ask themselves the question

Would I have really kept holding this strategy if I was down 40% and allowed my portfolio time to recover and enjoy the historical positive sharpe ratio of this strategy ?

This is the reason tear-sheets are helpful as it allows investors to choose strategies based on their own personal choice, financial goals and 

I'm a detail person, give me the granular tear-sheet

Quantitative investment professionals can dive as deep as they like into tear-sheets and produce very detailed reports. At Aikido Finance, we focus internally on two types of tear-sheets 

The first one is a strategy deep dive during the research phase, which helps identify strategy-specific properties. These may include items such as:

Analysis of how many stocks are investable through time in the strategy

Analysis of the predictive power of the strategy for long positions versus short positions

The more standard format for a tear-sheet output is found when used for backtested strategy performance. 

This tear-sheet is very detailed both graphically with tabular output and it covers everything from 

broken down into monthly seasonal returns

If we had to sum up what would be the go-to items on a tear-sheet, the table below would be a nice summary. It tells an investor the risk-adjusted return in various formats, the overall return and risk and drawdown statistics.

What are tear-sheets and why are they produced for investment strategies. We analyse the most important output metrics and explain their uses. 

6. Tear-sheets explained

Backtests are a crucial tool in quantitative finance. They are essentially a time-machine that allows you to measure how a systematic strategy built today 

 have performed if you had invested in that strategy in the past. 

use historical data in conjunction with your strategy to see what returns your strategy would have generated.

 The fundamental properties of a backtesting are

it is fundamentally sound representation of history

allows you to compare it to a benchmark if it is appropriate

it produces good results that satisfy your threshold for investment

allows the ability to analyse drawdowns and imagine how you would have coped

Backtests therefore allow for the delivery of a clear report back to the user that summarises the risk, return and drawdowns of the strategy, which is a very powerful tool to help investors make their capital allocation decisions.

What types of backtest engines are there  

There tends to be two types of backtest engines that are used in the industry

For-loop backtesters are built using the classic coding loop iteration, where each day for example is an iteration of the backtest. Analysing a daily rebalanced strategy for example from 2012 to 2022 therefore involves simulating, on a daily basis, how your strategy would have entered, exited positions, the fill prices used  and the returns of the strategy. It is a very structured form of backtesting and simpler to code.

Event-driven backtesters are built based on a more complicated codebase and involve events being logged by the backtest engine and then these events being executed in a queue system. These events can be items like 

Event-driven backtest engines are more difficult to code but can be re-used more easily in live trading so there is one codebase operating for backtesting and live trading, which is a robust method.

With any testing system, there are advantages and disadvantages. The advantages are clear to see as seeing backtest results gives the user confidence in their strategy. Backtest results can then be used to decide if an investor wants to allocate real capital to the investment strategy.    

The one big disadvantage of backtests is they typically over-inflate performance metrics so a prudent thing to do is treat them as an upper bound. It is probably less common for a strategy to have actually outperform the backtested results than to have underperformed. 

For a backtest engine to be very accurate, it needs to incorporate accurate transaction costs as well as market impact costs. Market impact is a difficult topic but it relates to the concept of attempting to model how your trades would have affected the fill prices and strategy performance 

the trades had occurred in history. Given the strategy being tested is new and was 

executed in reality back in time, your backtest engine needs to account for the impact that would have occurred. This is less of an issue for retail investors than large firms, given their investment sizes and market-moving impact.

There are some crucial things to ensure your backtest engine accounts for and has accurately modelled. We provide a list below 

 ensure all companies, even if they are now bankrupt, exist in your backtest engine and your strategy was allowed to hold those positions historically as it would have.

 make sure that all your data on a given day is accurate and was known at that point-in-time. Your backtest engine can only use information that was available to the whole market. 

 ensure that the fills your strategy received were achievable and modelled correctly.

 ensure that you have realistic commissions and fees built into the backtest engine.

 have an impact model in your backtest engine that accounts for both temporary and permanent impact, as highlighted in the previous section. 

The last point to mention for advanced users of backtests, is that a user can create an environment where they try to avoid as much as possible overfitting and in-sample testing. By this we mean that you can split out backtesting data into training and test data and hold-out this test data for a 2nd pass test. The temptation for tweaking a strategy to achieve the best backtest results on training data is very high. Having a test dataset means 

 your final strategy is chosen, you can then analyse how your strategy performed on the unseen test data. 

Once your backtest engine is built, the graphical and statistical output can be fully incorporated so a user gets a full standardised report on each strategy that was executed by the backtester. We give some examples of useful performance output below.

Get to grips with what backtests are and how they are built.

7. Backtests. Back to the future

Learn about quantitative investing and portfolio management.  

2. Tutorials on investing and portfolios