# Factors

Factors refer to systematic risks that explain at least partially movements in asset prices. Ross (1976) [1] defines the first multifactor model -- the famous arbitrage pricing theory (APT). The APT states that asset returns are simply linear combinations of factors plus a small idiosyncratic component. Returns of asset $i$ may then simply be expressed in the following way:

$r_i=\sum_k^K \beta_{k,i}f_k +\epsilon_i \tag{1}$

Unambiguously, all factors appearing in equation (1) are important in explaining return variation (covariance) and  from a practical perspective relevant particularly for risk management. However, not all factors are relevant for proxying the state of the economy (the asset pricing wording) or just simply bad times. Examples of these factors are: sectors, countries or commodities. On the other hand factors representing (or correlated with) these bad times are crucial in explaining differences in average returns, and are important in the asset pricing literature,  characterizing the ‘stochastic discount factor’. Differences in average returns are by this logic simply a result of risk compensation, hence, the factor theory gives rise to differences in expected returns. Classically, these systematic factors (also often called styles) are known as market, value, momentum, size, quality, carry, volatility, etc. and are widely used in the asset management industry to achieve higher returns.

Exposures of assets to these factors are typically measured in form of betas ($\beta$). Hence, it explains the meaning of the word "smart beta" in the investment industry as a representation for factor based investing. (“Smart” because of the positive past performance of these factors). Why is factor investing important from investors’ point of view? First, several factors provide positive risk-premia, which might be attractive if the risks involved can be tolerated. Second, many (expensive) active funds sell simple beta-strategies as alpha ($\alpha$) - for example a value fund being benchmarked against a market index, rather than against a simple value index. Investors should understand what exactly they are paying for.

The question whether these factors have delivered the positive (market neutral) returns in the past are indeed due to positive risk-premia associated with these (risk-) factors or whether they are due to behavioral biases, will not be answered here. We follow a similar strategy as the Nobel prize committee in 2013 and simply point to the both sides of the literature.
This section provides an introduction to widely used factors with references to selected literature. We also add a section about low volatility and low beta investing, which have recently gained increased attention. For a general and a more practitioner oriented overview, we can highly recommend Andrew Ang's recent book [2], which provides a great and detailed overview of factor based asset management. The more academically interested reader is referred to John Cochrane’s classic Asset Pricing book [3].

Market

Market is the most popular factor, both among practitioners and researchers. It  accounts for the systematic risk of investing into the whole stock universe. It is typically measured by an index, a highly diversified portfolio of stocks. Examples of such indices are,  the S&P 500 or the Russell 1000 for the US, and for the world, the most commonly used index is the MSCI World Developed. These indices are purely calculation based and not directly available as  investable assets, the closest investable proxies for the these stock market indices are ETFs, where the providers charge a small fee  (institutional investors would also consider the futures market as a good proxy). The market is also the most empirically studied factor with solid theoretical foundations --- the famous Capital Asset Pricing Model (CAPM), which links returns of individual assets to the market return, is the cornerstone of modern finance and factor theory. The model results in a simple yet powerful equation:

$\underbrace{E[R_i]-r_f}_{\text{Excess Return}} = \underbrace{\beta_i(E[R_M] - r_f)}_{\textbf{beta} \times \text{Market Risk Premium}} \tag{2}$

The CAPM predicts that return on an asset in excess of the risk-free rate $E[R_i]-r_f$ is determined by: (i) market risk premium $E[R_M] - r_f$ (market return in excess of the risk-free rate); (ii) how sensitive is this asset's return to the market risk premium. The sensitivity parameter, also known as beta, measures exposure to the market risk: high-beta securities depend more on market movements and offer higher expected returns in order to compensate investors for losses during market downturns. Low-beta assets, on the other hand, have low risk premia - such assets are attractive for investors, who buy them as an 'insurance' for losses in the distressed market, pushing their prices up, or equivalently, decreasing their expected returns. The key point here is that the exactly same reasoning applies to other factors such as value or size - returns are just combinations of different risk factors with different sensitivities (or exposures) to each of these factors. For more details, see Market.

Value

Value is buying relatively discounted stocks. Obviously, we cannot simply use prices and sort them from low to high to determine whether a stock is relatively cheap. Hence, we first scale prices by some measure of stock or company value. Classically, we scale market prices by book value (the value of all balance sheet assets minus the outstanding debt) to receive a ratio what is called book-to-market. However, any reasonable indication of value would return a similar result - for example, the price-to-earnings ratio. An investor buying a portfolio of relatively cheap stocks (i.e. those with high book-to-market ratios) and selling selling relatively expensive stocks (those with low book-to-market ratios) can earn a so called value premium. Empirically, the average return of such a strategy was positive over almost 100 years of history. Risk-based or rational explanations can justify the existence of a positive value premium as compensation for some systematic risk factor. Similar to the market factor, all value stocks share a common factor which cannot be diversified away, when investing into value. The premium can also be explained by behavioral theories. For more details, see Value.

Quality

Quality of an asset refers to a set of characteristics attractive to investors, so they are willing to buy such asset at a premium. The main point here is that quality, in contrast to many other factors, can be defined across several dimensions. First of all, it is an aspect of value investing - indeed, buying high quality assets at a fair price is similar in spirit to buying average quality assets cheaply. Second, in case of equity markets, high quality stocks are issued by firms which (relative to other firms): (i) are more profitable; (ii) whose profits grow faster; (iii) are safer in terms of default probability, leverage, volatility of stock returns and returns on equity; (iv) redistribute a greater fraction of their profits to shareholders. In practice, an asset manager can evaluate the characteristics above and then aggregate them into some score. This score can be used further either as a screening tool - ‘invest only in assets that score above some predefined threshold’ - or as an allocation tool - ‘buy the highest quality assets and sell the lowest quality assets’ - or both. Empirical evidence shows, that both long-only high-quality and long-short high-minus-low quality strategies generate positive and significant risk-adjusted returns. Moreover, taking quality into account helps to dramatically improve risk profile of pure value investing even in the universe of large-cap stocks. Note, that almost all quality measures are unrelated to the price information of a stock, in contrast to value and momentum. This is desirable from a diversification point of view, as it can be constructed independently from the information used in value and momentum strategies. For more details, see Quality.

References

1. The Arbitrage Theory of Capital Asset Pricing,
Ross, Stephen A.
, Journal of Economic Theory, Volume 13, p.341–360, (1976)
2. Asset Management: A Systematic Approach to Factor Investing,
Ang, Andrew
, (2014)
3. Asset Pricing,
Cochrane, John H.
, (2005)