The following articles are intended to provide a simple introduction to the most widespread and most frequently used factor models in practice. The aim is to explain the theoretical foundations of these approaches, to illustrate their relevance using examples of portfolio construction and thus to create an understanding of quantitative equity valuation and make it accessible to everyone. I welcome criticism and additions!
Sources are given for those who like to read up.
Motivation
Why is it relevant to deal with factor models at all? In practice, most institutional asset managers use factors to structure their portfolios. This is based on the realization that a considerable part of the cross-sectional variation of stock returns can be explained by systematic risk factors (cf. Fama & French, 1993; Carhart, 1997). This means two things for active managers: firstly, factor models are indispensable for correctly measuring their own value creation in relation to the market. Secondly, robust portfolios can be constructed on the basis of established factors, which can develop stable sources of return in the long term.
This is because a well-founded valuation is only possible in relative comparison to a suitable peer group. A multiple considered in isolation is not meaningful without a reference. In concrete terms, this means A price/earnings ratio (P/E ratio) of 40 cannot be clearly classified as 'expensive' or 'cheap' as long as there is no basis for comparison. If the peer group has a P/E ratio of 100, a value of 40 appears attractive; if it is 20, on the other hand, the same value would be more expensive than average. This logic applies analogously to all other valuation multiples.
The use of quantitative valuation models therefore provides clear added value. Factors are not the result of data mining, but can be at least partially justified by risk premiums or investor behavior. They are therefore not only empirically robust, but also theoretically plausible and well-founded. Each factor must therefore be replicable in a market-neutral manner, i.e. on both the long and the short side.
Practical relevance and challenges
Critics in the literature often point to the risk of "crowding", i.e. the potential loss of returns due to excessive capital inflows in factor-based strategies. Nevertheless, empirical evidence shows that factors are still capable of delivering systematic excess returns, even if the return premiums vary over time (Asness et al., 2022). The key challenge lies not so much in the question of whether factors have become obsolete, but rather in the correct implementation and ongoing development of the model construction.
So far, no established factor has been declared completely invalid by research. However, the methodology of construction has evolved, for example through the combination of several key figures (composite scores), sector- and size-neutral implementation or the integration of additional risk and robustness criteria.
1. the value factor
The value factor is one of the oldest and at the same time most controversial risk premiums. In recent years, it has often been criticized, particularly due to weak relative results. Historically, however, value is considered one of the fundamental pillars of quantitative capital market research and is still used today as an essential benchmark for assessing relative equity, bond and other asset class valuations (Asness, Moskowitz & Pedersen, 2013). Expectations of future cash flows are reflected in the market price. A value investor compares this with his own assessment of how well a company can generate future cash flows and derives the intrinsic value from this. He assumes that the market price will approach this intrinsic value in the long term. This assessment is based on the company's value creation potential. This includes an analysis of the products and services offered, the competitive position in the market, the potential for future growth, possible changes in margins and capital requirements and the choice of financing required to realize this growth.
The origins of value investing go back to Benjamin Graham and David Dodd (1934, Security Analysis). Their paradigm consisted of identifying undervalued companies on the basis of fundamental indicators. Classic indicators were a discount of the market price to the book value, high dividend yields or low multiples such as the price/earnings ratio (P/E) and the price/book ratio (P/B). The underlying assumption is that in an efficient market (Fama, 1970) securities are fairly in an efficient market (Fama, 1970), securities should be fairly valued, but in practice systematic mispricings occur that can be exploited by the value approach.
1.1 Modern operationalization of value
In the empirical asset pricing literature, value is usually measured using simple valuation ratios.
The most common construction, introduced by Fama and French (1992), uses the price-to-book ratio (P/B) as a proxy for value and forms a portfolio consisting of long positions in stocks with a high P/B and short positions in stocks with a low P/B. A high P/B indicates a favorable valuation (or high risk, from an efficient asset pricing perspective). A high B/P indicates a favorable valuation (or high risk, from the perspective of the efficient market hypothesis) and is associated with a high expected return, while a low B/P signals the opposite. In the classic implementation, the factor is updated once a year on June 30, based on book value and price data from the previous December 31. These values, and thus also the portfolio composition, remain constant until the next adjustment one year later. This means that the book and price data used for the portfolio are always between six and 18 months old. Fama and French (1992) made these conservative construction decisions to ensure that the book values used were actually available at the time of portfolio construction. They therefore chose price and book value from the same reference date, which seemed obvious at the time. Later research found these lags in accounting data to be suboptimal (Asness, C., & Frazzini, A. (2013)) and expanded this spectrum to include other multiples, such as:
- Price-earnings ratio (P/E)
- Price-to-book ratio (P/B)
- Price/sales ratio (P/S)
- Price/cash flow ratio (P/CF)
- PEG ratio (Price/Earnings-to-Growth)
- EV/EBITDA, CF/EV or EV/Sales
These ratios can be used individually or combined into composite scores to increase robustness and address balance sheet-specific weaknesses of individual industries (e.g. due to intangible assets in the carrying amount) (Asness, C., & Frazzini, A. (2020)).
1.2 Historical performance of the value factor
The empirical performance of the value factor by Fama and French (1992, 1993) shows a significant outperformance for value stocks, measured by the ratio of book to market value (HML factor). Over the period from 1926 to 2016, the classic long-short value factor in the USA achieved an annualized outperformance of around 1% p.a.. Comparable results can be observed for international markets, although the level of the premium varies from region to region.
More recent research has extended the original book-to-market measure and developed combined/multifactors that combine several valuation metrics. Asness, C., & Frazzini, A. (2020) show that a global combined value factor, constructed from a variety of fundamental multiples, delivers a robust premium in the mid-single-digit percentage range p.a. even after transaction costs. The authors also emphasize that the weak relative performance of value in the period 2010-2020 does not call into question the long-term existence of the premium, but can be explained by valuation differences between cheap and expensive stocks.
The work of Hanauer and Blitz (2021, Resurrecting the Value Premium). They show that an "enhanced value" approach, based on a broader set of key figures, would have generated an average long/short premium of around 5% p.a. in the US market and even over 8% p.a. in developed ex-US and emerging markets. In the more practically relevant long-only implementation, the excess return is reduced as expected, but is still well above the market at 3% p.a..
1.3 Theoretical justifications
The value premium can be explained from two perspectives:
1. Risk: Value stocks are often financially distressed or cyclically dependent and therefore carry higher systematic risks (cf. Chen & Zhang, 1998).
2. Behavior: Investors tend to overvalue growth companies and underestimate value stocks. The correction of these misvaluations is slow, which enables systematic excess returns for value strategies (cf. Lakonishok, Shleifer & Vishny, 1994).
1.4 Methodical implementation
The value factor is typically implemented by sorting all investable securities in a defined universe according to one or more valuation ratios. The relative position of each company within the cross-distribution is determined, often by percentile ranks.
Theoretically, the construction of each factor results from the fact that the cheapest 30 % of the stocks in a universe are defined as buy candidates, while the most expensive 30 % serve as sell positions.
Example: Assuming we look at four companies with P/E ratios of 10, 12, 14 and 20, the share with the lowest P/E ratio (10) is assigned to the top percentile (cheapest percentile), while the share with the highest P/E ratio (20) is assigned to the lowest percentile (1) (most expensive). Stocks with medium P/E ratios are placed in the intermediate ranks accordingly.
This ranking creates a relative valuation order within a peer group (e.g. market, region or sector). Based on this, portfolios can be systematically constructed, for example by buying the cheapest stocks (top quintile, decile or e.g. top 20 by value) and selling the most expensive (bottom quintile, decile or e.g. bottom 20 by value).
1.5 Practical implementation in EXCEL
In the next step, we will look at a practical example and discuss the role of data providers. This is precisely where the added value arises that portfolio managers and fund companies can offer through active management. For individual investors, such data sources are often difficult to access or involve high costs. In addition, the independent collection of data (data scraping) usually requires programming skills that are not available to every investor, despite modern tools such as ChatGPT. Further processing of the data is also a hurdle, as this usually requires advanced knowledge of Excel, VBA, R or Python. The following therefore shows a simple, concrete way of replicating a factor based on external data sources.
1. data import
As a starting point, we need a list of stock tickers. For free applications, it makes sense to use the holdings of exchange-traded funds (ETFs), as they have to publish their portfolio positions regularly.
In this example, we use the IUHC-ETF from BlackRock. (https://www.blackrock.com/de/privatanleger/produkt/280507/ishares-sp-500-health-care-sector-ucits-etf?switchLocale=y&siteEntryPassthrough=true )
After downloading the Excel or CSV file, we find the required tickers in column A. We copy these and paste them into a separate Excel file (column A). We then manually filter out non-stock-related positions (e.g. cash, index tickers or derivatives) so that only stocks remain in the universe.
2. data processing
In the next step, we select the tickers in column A and use the tab Data → Shares. This links the tickers with the corresponding fundamental data from the Microsoft data service.
Now we can call up the price/earnings ratio (P/E ratio) in column B. To do this, we enter in cell B1 the formula:
=A1.P/E RATIO
and drag it to the last line of the universe (e.g. line 60).
3. construction of the factor
In column C, we now create a ranking order based on the evaluation key figure. To do this, we use the QUANTILSRANG.INKL. function. In cell C1 the formula is:
=100-QUANTILSRANG.INKL($B$1:$B$60;B1)*100
Explanation of the steps:
- 100-... ensures that the cheapest companies receive the highest value (100), while the most expensive fall towards 0.
- QUANTILSRANG.INKL calculates the relative position within the distribution.
- $B$1:$B$60 is the universe that is ranked.
- B1 is the currently ranked stock.
- *100 transforms the result into. Percentage values.
This produces a percentile scale from 0 to 100, on which favorable companies are at the top and expensive companies at the bottom. These scores can then be used to construct a value portfolio (e.g. buy the top 30%, sell the bottom 30%).
Note for the theory nerds among you who have noticed the omitted topic of survivorship bias:
This aspect was deliberately omitted as its explanation would go beyond the scope and a correct implementation is hardly possible in practice without cost-intensive data providers.
