The low volatility factor is a well known effect that goes against many common assumptions that investors would have. A natural prior assumption would be that stocks with higher volatility compared to stocks with lower volatility should all else being equal, 

. This is based on the common assumption that higher risk should generate higher returns, 

Counterintuitively, it is the stable lower volatility stocks that produced better risk-adjusted returns. Many investors and academics have termed this the 

This had led to the construction and classification of the low-volatility factor. This  factor has been shown to be:

The classification of this phenomenon as a factor therefore seems plausible and this has been actively harvested by the quantitative community for years. 

Reasons for the existence of the low-volatility factor  

Given the anomaly exists, the theory of why it exists has been explored and a few hypotheses have arisen, which are mostly behavioural in nature:

, investors have an urge to buy stocks that exhibit lottery-like distribution. This means they purchase stocks with high-volatility at premiums to their fair price and thus allow low-volatility stocks to benefit from higher future returns.

Various fund managers, via their structure and rules, may not be allowed to employ leverage to enhance their returns. They instead resort to investing in stocks with higher beta (to hopefully generate extra returns) and again pay premium prices for such stocks.

Some can argue that incentivization plays a role whereby fund managers who are benchmarked are only rewarded for beating the benchmark. They therefore again skew their investment decisions towards stocks with higher beta and pay price premiums for such stocks.

Potential behavioural explanation where investors tend to gravitate towards news-worthy or attention-grabbing stocks, which tend to be higher beta stocks, and therefore overpay again for these stocks.

In what periods does low-volatility do well ?

Low volatility is known as a defensive factor and has been shown to help overall portfolio performance during large market drawdowns as the low-volatility stocks help buffer the overall negative performance.

Low-volatility has also done very well since the global financial crisis, which has only helped increase the allure of the strategy. It is not surprising that during an era of quantitative easing and steady, consistent asset price growth that low-volatility strategies have done well.

This is a post concerning the low volatility factor and why it's important for quantitative equity portfolio investing.



7. Low-Volatility Factor

Style factors investing, commonly shortened to factor investing, is a rules-based approach that groups stocks together where each of the stocks share a set of common properties. These properties can be 

related by common fundamental balance sheet items

historical performance and statistical properties of stock returns

Style factors group stocks together into portfolios based on the above characteristics. It has been shown through history that investing in these portfolios can give investors a source of consistently high risk-adjusted returns and offers diversification rather than investing in the overall market or a simple index tracker. 

This is not an exhaustive list and there are indeed other well-known factors, such as reversion, short interest, seasonality and earnings yield but the ones listed are probably the most common and widely used. 

Additionally, style factors tend to be large-scale and are based on fundamental or price data and so can be applied across the entire universe of active securities each day. This means that style factors have large 

 and both large fund managers and small investors can invest in these strategies very easily. It is very positive that style factors can cope with this investment capacity and still deliver excess returns. 

For a factor to be embraced by the investing community as being a proper 

, then it should have the following properties:

occur in different geographical regions and markets

make economic or behavioural sense and can be backed up by academic published papers

If the efficient market hypothesis was to be believed then the current price of the stock would be fair and contain all the information available. However, due to behavioural biases and investment and benchmark criteria, factor premiums have been shown to consistently exist and investors aim to systematically harvest that premium via quantitative strategies. Factor premiums represent the extra return investors obtain by investing in a factor.

Different style factors perform differently during various stages of the economic cycle. There are no concrete rules but some generic principles can be inferred. A diversified portfolio most likely has a blended combination of various style factors at all times.

The original capital asset pricing model (capm) from the 1970s was the simplest model to explain a stocks return. It used a beta coefficient, that represented a correlation type measure between the stocks returns and the market returns, to model the stocks return. Alpha represents the extra return of the stock, that is not explained by its relationship to the market return. The capm model using alpha and beta, was given by

Advances to this model came from the work of Professors Fama and French who introduced a 3-factor model, where they modelled stock returns by introducing two new explanatory factors to extend the capm. They added 

 factor. This model represents a stocks return by saying some of its return comes from the market, some from the size factor and some from the value factor with a new alpha representing what is left over.

Prof Fama and French provide the return data on their website 

https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html 

Style factors can be used for various goals. 

Small investors or retail investors might just love a certain set of stocks e.g some value investors just always want exposure to cheap stocks. Others might just always want to be with the crowd and buy recent winners (momentum).

Investors can construct or tilt their portfolios to focus on various style factors.

For risk mitigation, portfolios can be analysed in terms of their factor exposure and modifications made.

Hedge funds typically aim to construct strategies that have limited exposure to style factors.

This is a post describing what equity style factors are and how they are used by investors to create diversified quantitatively-built portfolios.




1. Style Factors

The use of style factors within a diversified investment portfolio is an efficient long-term strategy. Like all investing, there are positive periods and some negative periods but if investors trust factors for the long-term, then it has been proven to yield 

Investors who stick with their style factors for long periods of time are 

. By constantly being invested in factors, investors allow themselves the time to deal with any potential under performance whilst also continuing to benefit from the diversification that a set of low correlation strategies generates. Style factor investing is therefore not short-term trading and is instead part of an overall diversified, long-term portfolio. 

Just like investing in the overall market, it is essential to hold these factor portfolios for long periods of time to ride out some factor underperformance that can occur and which could last for a few years. It is impossible to tell ahead of time which factors will do better in the future and we can only use the historical performance as a guide. It is also recommended to hold a blended combination of factors, which benefits from the diversification of various uncorrelated strategies.   

. The idea that an investor has a maximum amount of risk they would like to take is an intuitive concept and for some investors is as, or even more, important than return. Therefore, there are lots of different strategies competing for this 

. If there are ways to use uncorrelated strategies that will lower your overall risk, this is a very powerful concept. 

Risk-adjusted returns scale the returns achieved by the risk taken to achieve those returns. A 20% annual return with a portfolio volatility of 40% annualised is not the same as a 20% annual return with a portfolio volatility of 10%. Scaling returns by the risk taken to generate those returns gives us a 

. If we work with daily returns and assume a risk-free interest rate the formula for the sharpe ratio is

Long Style Factor ETFs vs Market-Neutral Style Factors 

If investors want to use factors to quantitatively invest, they have a choice between

using the traditional construction of a long-short, market neutral portfolio which general has very low correlation to the overall market  

form a long-only portfolio (similar to a smart beta) to tilt their portfolios to the factor but maintain long market exposure. 

analysing the performance difference between a factor investment strategy that is the traditional long-short versus one that is long-only. This is quite an important research piece as it identifies the successfulness of long-only factors, which are the majority of retail focused investments. Long-only factors are also popular with institutional investors who are benchmarked to market indices. 

To create a more market neutral long-short portfolio, the paper also applies a natural 

 of selling an index ETF, such as the SPY, to create a short side to sit alongside their long factor portfolio. Therefore this allows the creation of an overall market-neutral factor if an investor so desires.

Whether an investor wants to employ a long-only factor strategy or a long-short strategy depends on various criteria. Investors who employ long-short strategies are mostly concerned with 

generating absolute return, e.g a diversified strategy that can generate return independent of the overall market direction 

the ability to apply leverage to their portfolios

are allowed to short by their broker and/or operate in countries with no short-selling constraints

Investors who focus on long-only factor investing are more numerous and widespread. They tend to focus on 

tilt their portfolios to concepts or factors they believe in

where an investor wishes to significantly increase or reduce their exposure to a factor depending on how they think it will perform in the future. This can be employed via discretionary weighting schemes or they can employ a quantitative method to shift your factor weights according to some trusted model. 

Factor timing is a difficult thing to implement correctly, even though it has very natural appeal and makes sense - much like you weight stocks in your portfolio with different weights due to your conviction, the same can be said of factors. A recent paper by Gupta and Kelly at AQR entitled 

showed that by timing factors based on their recent performance, investors could earn higher sharpe ratios. 

Factor mean-reversion is one model that may offer a nice halfway house that avoids simply equal-weighting your factors and instead allows 

 tilting of your factor weights around some constant weighting. This can therefore allow factors that have performed poorly to be allocated less weight in your portfolio so less than the average weight but not zero weight. Alternatively, factors that are doing great are again weighted higher than the average but never allowed to grow to totally dominate your portfolio.  

Analysing the performance of style factors and how they are correlated to each other.




2. Style Factor performance and correlation

The concept of value is such a natural concept that the quantitative world of investing jumped onto this idea years ago. Various academic papers have started to provide structure and theoretical rigour to the properties that represent 

We can think of the value factor as a systematic method to identify and invest in stocks that appear to be 

priced cheaply compared to their fundamental balance sheets

. One simple example of this can be observed by looking at the 

If a company has a high book-to-market ratio it means the theoretical price of the equity of the company is higher than the stock price multiplied by the shares outstanding (market cap). This means that the market as a whole has priced this company at a theoretical value that is lower than the company equity. As a result, this means that the company is priced 

. Growth companies represent the opposite to value and therefore trade at prices that mean their book-to-market ratios are very low - as investors are banking on future increases in the company assets or equity and so buy the stock today which leads to very high prices.

 is often referred to as the spread between 

 with for example high book-to-market ratios, versus 

We have given one simple and explicit example of one value metric but there are many more such factors. In reality value strategies use more than one factor in their construction, some examples are

price to book value (terminology example: this is just the inverse of book-to-market)

Reasons for the existence of the value factor

Investors like to buy cheap things or feel like they are getting a bargain. If something can be bought for less than what it is arguably theoretically worth then it represents some 

. Cigar butt investing, made famous by Warren Buffet, is one such example where he attempts to invest in companies that might have one big run left in them to maximise return. 

Over the last 15 years though, value has been through a tough time as growth stocks and technology focused stocks have tested some of the logical reasons for value investing. Growth stocks, no matter what the price, have been accumulated by investors to the detriment of the value factor.

), as seen in the graph below, tends to historically have a lower rolling volatility than momentum. hml is constructed based on the book-to-market ratio that we previously discussed. The Fama-French hml portfolio goes long the highest (highest value/most cheap) 30% of stocks based on book-to-market and sells the bottom 30%. On average the long-short value factor has a 1y rolling volatility of less than 10% during the decade 2010-2020. However, since covid began in 2020, the volatility of value has increased significantly and has essentially matched the volatility of the momentum factor. This increase in volatility has also been directional with the market, with values correlation to momentum increasing as the rebound from covid occurred in Q2 2020.

Correlation of the value factor to other style factors

The value factor tends to have some naturally intuitive properties due to the impact of price in its construction. By this we mean that value stocks heuristically can be viewed as cheap stocks to some degree and therefore their recent performance may not be that good or significantly lag its peers. Momentum on the other hand is purely based on recent performance so we would expect value and momentum to be negatively correlated.    

It is nice to see that the correlation graphs align with our thinking in terms of illustrating that value tends to be negatively correlated with quality and momentum.  

The long-short value factor had a miserable decade from 2010-2019 and there was widespread talk within the quantitative investment community, did the value factor exist anymore. Typically, and after peak pessimism, the long-short value factor since covid began in 2020 has had a stellar two years and has cumulatively returned over 30% since Jan 1st 2020. Long-only value stocks have also significantly outperformed the broader market. 

Value tends to do well coming out of a recession or during periods of inflation and can be focused on defensive sectors such as utilities and consumer staples. Value does not tend to do well during the mid-to-late stages of a bull market i.e periods of exuberance such as what the market experienced preceding the tech bubble and also after the financial crisis - these were periods where growth stocks really outperformed. 

Historical yearly path performance of the value factor 

Next we plot the Fama-French style value factor, which is long-short market neutral and based on a book-to-market metric, a very simple naive value metric. If we compare the return spread of yearly returns for value versus say for example quality it is evident that, during the last 15 years anyway, value has been significantly more volatile than quality. 

However, the doomsday forecasted for value seems to have abated for now as the decade of 2020 has started with a massive rebound for value, compared to 2010-2019. The value factor has been the best performing factor for the last two years and so far in 2022 the value factor has again matched the 2021 performance year-to-date and if this continues value could yet again return 20% during 2022.   

Given the returns from 2021 and 2022 have only recouped a small percentage of the lost 2010 decade, there is continued speculation that the renaissance of value has a lot more room to go and the performance could continue for the decade starting 2020. 

This is a post describing what the value factor is and why it is important.




3. Value Factor

The quality factor is quite a subjective factor with 

 in their implementation from an asset manager to a hedge fund. 

The quality factor broadly represents companies that have 

robust earnings growth and cost-efficiency metrics

 represents company strength and is illustrative of well-managed businesses

Considering ways to measure a companies quality, we can classify companies under some broad quality categories

 contain various sub-factors that are measured via balance sheet ratios and derived metrics. This is not an exhaustive set and researchers have also proposed various other categories. 

If we consider the listed categories above, we can imagine 

 category containing metrics that represent company leverage, bankruptcy risk or idiosyncratic beta or volatility. 

 category may contain earnings growth metrics and/or earnings volatility metrics. 

 category can store items such as gross margin, return-on-equity, cashflow metrics.

A robust quantitative strategy can be then built by constructing and weighting all of the sub-factors within each category and then weighting the categories together to obtain a final investable quantitatively-driven strategy. 

The idea behind this type of method is obviously to encapsulate a broad spectrum of quality sub-factors. By using this set of diverse sub-factors, it allows investors to then effectively rank all stocks in our universe, choosing the top 20 stocks for example. This allows an investor to obtain a well-balanced strategy that represents companies of the highest quality.

The quality factor, as shown in the graph below, tends to have a 

On average the long-short quality factor has a 1y rolling volatility of less than 10%. 

Correlation of the quality factor to other style factors

Due to the characteristics it possesses, the quality factor has more nuanced properties than some alternative style factors. 

 for example, can very easily be summarised as small market cap stocks earning a return premium over large cap stocks to compensate investors for taking on the larger risk small cap companies possess. 

 stocks being purely price-based can be summarised as recent winners continuing to outperform recent losers. 

 on the other hand is concerned with more complicated balance sheet items where the relationship needs to be analysed on a deeper level and the easiest summary for quality is that it represents stronger/larger, well-managed companies with robust balance sheets and growth.  

It is nice to see that the correlation graphs align with our thinking in terms of,

 quality being negatively correlated with size and value. 

 chart below reviews the quality factor over the period 2010-2022. The quality factor has had quite an average decade with the only real performance coming after 2017. However, in more recent years we have seen 

 than that of the other style factors. Again, some of this we may first put down to the size of companies within quality and by hypothesising that large companies are less volatile. However, the quality factor here is market-neutral and so it is the quality factor premium we are modelling. The plot does show us that 

 in terms of volatility. However, it is evident that value and momentum are more volatile. This also makes sense due to stock prices being involved in the construction of momentum and value, either directly or indirectly.  

Historical yearly path performance of the quality factor 

Next we plot the Fama-French quality factor yearly performance, where the factor is long-short market neutral based on profitability and investment sub-factors. So far in 2022, the quality factor has had a torrid time and has lived up to the reputation that quality is negatively associated with value (i.e value has had a great 2022 so far). 

This is a post describing what the quality factor is and why it is important.




4. Quality Factor

The momentum factor is one of the most hotly contested yet natural factors to exist. Momentum is a classic phenomenon for stocks - winners beget winners and losers can find it tough to recover losses. Trend-following is a popular technical approach favoured by many investors, both professional and retail and makes intuitive sense. 

Since the global financial crisis, Central Banks acted in a coordinated way and each embarked on large-scale quantitative easing (QE) campaigns. As a result, nearly all asset prices inflated over the course of a decade and a momentum-style 

strategy worked very well. Going long equities and long bonds, similar to the 

, was a very successful investment and both markets rallied. 

Momentum can also occur on a sector basis. The technology sector rally from 2010 onwards, whilst based on a fundamental shift in productivity and usage, can also be put down to this 

 as technology winners turned into bigger winners and the price action was a self-fulfilling prophecy.

Reasons for the existence of the momentum factor

Traditional stock investors are human and exhibit human traits and patterns. Quantitative investment firms were quick to develop and build trading signals around this behaviour and classify the momentum premium as a bona fide style factor. Some general reasons why the momentum factor can exist are given by

Power of the crowd: following others is a lot easier than being a contrarian

Investors do not want to miss out, it would be difficult to describe to upper management why you were not long the biggest and most publicised winners of the year etc

These types of patterns can most easily be quantified by using historical returns to analyse which stocks have performed the best - and this is exactly what academics and quantitative firms did in order to come up with a definition of the 

The momentum factor, as seen in the graph below, tends to historically have a higher rolling volatility than all other style factors. This is quite natural as it is arguably the closest style factor to the overall market index. On average the long-short momentum factor has a 1y rolling volatility of 13% since 2010. Since covid began in 2020, the volatility of momentum significantly increased, up to approximately35%, but then sharply retreated back to its average once the Fed turned on the stimulus. 

Correlation of the momentum factor to other style factors

 is negatively correlated to the value factor, which overall makes sense. The relationship with the 

 also intuitively infers a positive relationship. Strong companies should perform well and leverage that performance to build market share and keep performing strongly i.e increase momentum. However these relationships are 

 and can ebb and flow as we can see, currently momentum and quality have close to zero correlation and could go negative.   

The momentum factor overall has proved to be a consistent performer across time and geography. Momentum tends to do well in environments where there is a consistent theme and volatility is relatively contained - this makes it easier for the status quo to continue and past winners to keep doing well. 

Historical yearly path performance of the momentum factor 

We now plot the Fama-French style momentum factor, which is long-short market neutral and based on recent price performance. This is a very simple but useful trend measure. Momentum much like value, is a more volatile factor and we can see this clearly in the yearly performance plots. 

Is there a January effect with the momentum signal ?

Anecdotal evidence suggests that there is some kind of momentum factor reversion that occurs in January. This also comes from some industry intuition that factor performance over the year-end turn can revert as asset managers and investors start the new year by trying to invest in the underperformers of last year and sell the best performers of the prior year. 

Is momentum recognised in academia as a valid factor ? 

Momentum over the last two decades has become quite a well-respected and harvested alpha factor. There has been some resistance in the traditional academic world in accepting it as a bona fide factor but there is now ample evidence that momentum exists. Carhart in 1997 did indeed extend the Fama and French 3-factor model to include a fourth momentum factor. Momentum has been shown to have the following properties: 

is evident through time and is not a fleeting occurrence

similar momentum factors found in other asset classes such as commodities and fixed income

momentum properties now extending into factor momentum so has a 2nd order effect also

Regardless of these properties, the resistance in academia may be down to the more 

reasons for its existence and a lack of financial explanation. Fama and French for example when they extended their 3-factor model chose to include two quality metrics (

), rather than add a momentum factor, as their factors are easier to 

 by referencing financial and economic logic. 

This is a post describing what the momentum factor is and why it is important.




5. Momentum Factor

When it comes to the stocks, the concept of company size is a well understood concept. It literally relates to the market capitalization (market cap) of a company which is obtained by multiplying the company shares outstanding by the share price each day. In terms of mathematical formula, for stock i with market cap = m, price = p, shares outstanding = s, we have the following formula 

Size was one of the first explanatory factors used back when the 

 (CAPM) was expanded upon in the 1990s. This CAPM model that related a stocks return to some alpha plus beta times the market return was too simplistic. Professors Fama and French expanded upon this model by introducing a value factor and a size factor, which they called 

This model therefore represents a stocks return as some extra return alpha plus various beta weightings multiplied by the returns on the market, the value factor and the size factor. But what is the size factor itself ? 

Academic research has shown that consistent returns were possible if investors went long a basket of small-cap stocks and short a basket of large-cap stocks and this is called the 

This makes intuitive sense as small cap stocks are viewed as inherently more risky (higher volatility and mostly higher beta) than large-cap stocks and therefore capm says that the return should be higher for small-cap stocks to compensate for this extra risk. 

Reasons for the existence of the size factor

The size factor is intuitively one of the easiest factors to understand and some of the common reasons for its use are given by:

it is linked to price volatility and higher beta, indicating it is riskier

economic theory is easy and intuitive to understand

capm and Fama-French models provides theoretical backing

The size factor is a major part of the Fama-French model and so historically was treated as an alpha factor and quantitatively focused investors seeked to harvest this 

. Over time, this size factor alpha has eroded after the factor became very widespread due to its natural understandability. As a result, it has arguably ceased to become a significant alpha factor and is instead used primarily in investors risk models or for filtering and selecting their investable universe. 

We do not construct and invest in a size factor explicitly as an alpha, as highlighted above. We do however use it for universe filtering and also during construction of other quantitative investment strategies to augment those signals to account for some of the size effect.  

The volatility of the long-short market neutral size factor is very similar to the value factor, with an average rolling 1y volatility of 9%. As we would expect during covid, this volatility spiked especially as the factor is small-cap focused but like 

, this increase has reversed and is expected now to return to its single digit average.

Correlation of the size factor to other style factors

The size factor has really one natural partner in terms of correlation, or negative correlation, to be more precise. 

 companies as we have discussed previously tend to be long established, historically strong companies and on average these are larger cap companies as a result. Therefore it is natural to see a consistently negative correlation between size and quality, which averages around -40% on a rolling 2y basis.  

As has become popular in the investing world, size is now treated as a risk factor or used in universe generation more so than used as a proactive alpha generating strategy which consumes some 

. The size factor's recent overall historical performance is indicative of this, as it hugs and oscillates around the zero level with a lack of consistent performance, either positive or negative. 

The historical yearly path performance of the size factor also shows us quite nicely the tightly coupled nature of those returns over a 13y history. With the exception of 2020 and covid, there was just a single year where size delivered an absolute performance of greater than 10%. Otherwise it is quite evenly split between up years and down years, 1/3 to 2/3, with most yearly returns at the 5% level. 

This is a post describing what the size factor is and why it is important.




6. Size Factor

The general concept of reversion implies that a trend comes to an end and reverses to some degree. This kind of price action can sometimes occur after recent strong performance - as there are always investors who want to 

 some profits and so sell their investments. 

If this type of profit-taking price action starts to accumulate and other investors follow suit, this can lead to reversion. If for example there is no new fundamental news out to help support the stock, then this profit-taking can cause the stock to fall quite quickly as others panic and sell, as they fear they have missed their 

 and therefore is not based or backed up by balance sheet data like for example value or quality. Reversion is a price-based signal and construction methods for it differ from user to user. 

The Fama and French market neutral short-term reversion factor is gross of transaction costs and therefore presents a very optimistic set of results. Reversion in practice is also notorious for being difficult to capture the theoretical results - this is due to missed fills, slippage and trading impact playing a large role. These can be difficult to capture fully in a backtest.  

Historical yearly path performance of the reversion factor 

If we look at the years in isolation the picture becomes even more rosy and over-optimistic for Fama-French's reversion factor. Apart from the massive drop in performance of the reversion factor after the Fed stimulus package took effect and the bull market returned, the short-term reversion factor has apparently delivered flat to 15% annual returns every year since 2010. Too good to be true it must be said. 

This is a post describing what the reversion factor is and why it is important.




8. Reversion Factor

Improve your understanding of what equity factors are and why they are used. 

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Low-Volatility Factor

Style Factors

Style Factor performance and correlation

Value Factor

Quality Factor

Momentum Factor

Size Factor

Reversion Factor