### Factors

The aim of this chapter is first to describe the process of value investing and provide an explanation of the reasons for the existence of value premium. The different macroeconomic risk factors will also be explained and this will include inflation, economic growth, and volatility. Furthermore, volatility risk mitigation methods in a portfolio will be assessed. The chapter will describe the arising challenges in the course of volatility risk management.

The usage of dynamic factors in a multifactor model in a multifactor asset returns’ model will be explained. The explanation will be based on the Fama-French model as an example. Finally, we will compare the strategies of momentum investment, including their risk and return profiles.

# Value Investing

Relative to their net worth, value stocks have low prices: the book value has to be taken to account for the prices to be measured. For growth stocks, as compared to the book value, they are relatively costly. Money is sometimes lost in value investing, despite its generally good performance.

To compensate investors for losses incurred in bad times, premiums are offered by risk factors. The two known types of factors are (1) macro factors and (2) fundamental-based factors.

## Investment-style Factors

Both static and dynamic factors are included in investment factors. The market is a good example of a static factor that simply goes long to collect a risk premium.

## Macro Factors

In an economy, the slowing down of economic growth or high inflation affects all firms and investors, only at varying degrees. Since there is a high probability of being laid-off, high inflation or slow economic growth are highly disliked by most consumers. The affordability of the same basket of commodities and services in real terms also becomes lessened.

Slow growth and high inflation are beneficial to only some select few investors like debt collectors and large oil producers. The average investor’s bad times can be generally defined by bad outcomes of macro factors.

In comparison to a factor shock, the factor level does not matter in most cases. For most macroeconomic factors, persistence is a feature. This implies that the unexpected changes in the macro factors are the ones to be closely monitored.

The response of asset prices to these factors is contemporaneous. The onset of bad times and falling prices is usually preceded by increased inflation or unexpected adverse inflation. Investors get compensated for incurred losses by the risk premium in the long run, since the theory states that bad times of high inflation occur only in the short run.

Growth, volatility, and inflation are the three most crucial macro factors.

## Economic Growth

The volatility of risky assets is generally high in times of reduced economic growth, thereby making the assets to perform poorly. The only exception to this poor performance is government bonds which, in general, tend to do well during these times.

An investor should hold more bonds if he/she cannot bear large losses during recessions. This is the case for retired workers who need a constant stream of cash flow. During recessions, there may be a possibility of his/her portfolio to do much better, but terribly over the long run. It is often the case that stock returns fall in times of recessions.

## Inflation

Both stock and bonds experience turbulent times during high inflation periods. This time is often marked by a poor performance of all assets. The value of bonds also gets hurt by high inflation since their value gets lowered in real terms. Surprisingly, stocks generally perform poorly in periods of high inflation. Equities and bonds are usually affected negatively by high inflation.

## Volatility

This is a very crucial risk factor which is often measured using the VIX index, representing volatility in the equity market. In addition to measuring volatility, the VIX index also captures uncertainty. This happens since investors were not aware of the policy responses undertaken by the government during the market crisis.

In fact, uncertainty risk has recently been shown, in recent research, to be a separate risk factor for volatility risk, despite their high correlation. There can be quite severe losses when volatility spikes are high. Most of the time, volatility exhibits periods of calm punctuated by turbulent periods.

Apart from stocks, the return of many assets and strategies are also negatively associated increased volatility. In times of high volatility, the poor fairing of currency strategies is usually commonplace.

Volatility protection can also be bought by investors who dislike volatility risk. Volatility protection can be bought or sold in the option’s markets. However, derivatives contracts can also be held by traders. Large downward movements and assets that pay off in times of high volatility often accompany periods of high volatility.

Volatility, as a factor, usually has a negative price risk. Selling of volatility protection is a necessity to collect a volatility premium. The average trade in the VIX index is often above observed volatilities in actual stocks. For investors to collect the volatility premiums for options, which are usually quite expensive, they have to short volatility. For fixed income, currency, and commodities market, the volatility risk usually has a negative price.

During stable times, high and steady payoffs can be produced by selling volatility. Volatility protection should be sold through derivatives markets only by investors who can tolerate periods of very high volatility.

One short volatility strategy is the rebalancing strategy, through which a long-run volatility risk premium will be repeatedly captured. An average investor simply owning 100% of the market loses the long-run volatility risk premium. For a long-run investor, the likelihood of fat, left-hand tail losses is usually the most common risk.

However, volatility risk is not traded directly by rebalancing over assets; an additional volatility risk premium is brought by trading volatility. In this regard, as compared to simple rebalancing strategies, there are potentially much steeper losses in trading volatility in the derivatives markets.

Furthermore, the trading of pure volatility in derivatives can happen to absent any stances taken on expected returns via delta-hedging. To earn underlying factor risk premiums, rebalancing over the fundamental asset or strategy positions is usually done.

Due to the time-varying relationship between volatility and expected returns, challenges are often experienced in the construction of valuation models with volatility risk. The following equation represents an estimation of the return-volatility trade-off:

$$E\left( { r }_{ m } \right) -{ r }_{ f }=\bar { \gamma } { \sigma }_{ m }^{ 2 }$$

Where the market risk premium is given by $$E\left( { r }_{ m } \right) -{ r }_{ f }$$ , the variance of the market return is $${ \sigma }_{ m }^{ 2 }$$, and $$\bar { \gamma }$$ represents the average investor’s risk aversion, based on the CAPM theory.

# Other Macro Factors

There has been an extensive investigation of several other macro factors deserving attention from asset owners.

## Productivity Risk

The movements of macro variables and asset prices across the business cycle are explained by a class of real business cycle models that are developed in macroeconomics. There is a variation of macro variables and asset prices in these models across the business cycle, as a rational response of firms and agents adjusting to real shocks.

A neutral inflation that has no real effects is also another prevalent factor for real business cycle models. Since they involve optimizing companies that produce physical goods, the companies are subjected to shocks that affect their output. Productivity shock is one such shock that affects the output of a company.

The models designed to work at business cycle frequencies are less relevant to investors with short horizons. However, the productivity factor should be considered for long-horizon investors. The long-run productivity risk is usually mirrored in asset returns.

The new generation of dynamic stochastic generated equilibrium (DSGE) macro models has productivity as one of its sources of shocks. The economy is dynamic in DSGE models, and changes in economic variables are attributed to the actions of agents, technologies, and institutions or markets.

The setting of asset prices happens from the complex interaction of all these players and technologies. With DSGE models, we can think about the transmission of shocks from these factor risks across the economy. The action of policy players is a crucial part of DSGE models.

The fluctuations of business cycles are well described in the DSGE models since asset returns vary over the business cycle.

## Demographic Risk

Demographic risk is another crucial risk for a very long-term investor. The same way a productivity shock is a shock to firm production, demographic risk can be interpreted as a shock to labor output. In economic overlapping generations (OLG), demography – a slow-moving variable – is a factor. A life-cycle model is followed by a given individual.

Expected returns are affected by the demographic composition, as predicted by several OLG models. For this to occur, the following two main avenues are suggested by theory:

1. In the OLG framework, the life-cycle smoothing requires that the demand for consumption by a relatively large cohort should be in excess when the middle-aged to young population is small.
2. A change in the average risk characteristics of the economy is often accompanied by a change in asset prices. This can be linked to the fact that different cohorts have different risk characteristics. Demography can, therefore, predict stock returns. As people age, risk aversion increases and the equity premium should increase due to this rise in the average age of the population.

## Political Risk

The political or sovereign risk is the last macro risk that should be considered by an asset owner. In emerging markets, this kind of risk has always been important. Higher risk premiums are necessary for the compensation of the investors bearing it if the political risk is great.

Until the onset of the financial crisis, political risk was considered to be of concern to emerging markets only. We have now realized that developed economies are also exposed to this type of risk.

# Dynamic Factors

The market portfolio is the CAPM factor and the market factor is tradable with low-cost index funds, exchange-traded funds, and stock features. The macro risks are reflected by these factors and, at some levels, the economy’s underlying fundamental risk should also be reflected.

The trading of macro factors is not usually pragmatic, but some dynamic factors have a big advantage in that they can be easily implemented in the portfolios of investors.

## Fama and French (1993) Model

Asset returns are explained in this model with three factors – the traditional CAPM market factor and two other traditional factors that capture a size effect and a value/growth effect:

$$E\left( { r }_{ i } \right) ={ r }_{ f }+{ \beta }_{ i,MKT }E\left( { r }_{ m }-{ r }_{ f } \right) +{ \beta }_{ i,SMB }E\left( SMB \right) +{ \beta }_{ i,HML }E\left( HML \right) \quad \quad \quad \quad \left( i \right)$$

With a poorly performing market, the exposure of stocks to market factors is usually high and thus they tend to do badly. CAPM predicts that, over the long-run, stocks with high betas will have average returns that are high as compared to the market portfolio, for compensating investors for losses during bad times.

In equation ($$i$$), in addition to the market factor, the first factor is the SMB (Small Minus Big), which refers to the small stocks’ differential returns as compared to big stocks. The market capitalization of the stocks gives rise to the smaller and larger stocks. The outperformance of small companies is to be captured by the SMB factor, in relation to the large companies.

The HML factor stands for the returns of a portfolio of high-book-to-market stocks less the one whose book-to-market ratios are low. For the book-to-market ratio, we divide the book value by the market capitalization of the stock. The phenomenon of growth stocks being outperformed by value stocks on average is called the value effect.

SMB and HML factors of Eugene Fama and Kenneth French are constructed to capture the premiums of size and value respectively and apply the diversification concept for factors to capture the impacts of size and value by averaging many stocks. Since every stock can’t be large and every stock can’t be small, the average stock has market exposure.

The betas of SMB and HML in the Fama-French model are centered around zero, with the value and size of the market being neutral. A beta stock’s average in the CAPM is equal to 1, which also happens to be the market’s beta.

A very crucial assumption in the CAPM and Fama-French models is constant betas.

## Size Factors

The size effects refer to the fact that, after adjusting for their betas, small stocks used to perform better as compared to larger ones. The disappearance of the size effect can be explained by the following two responses:

1. The size premium’s original discovery could have just been data mining; and
2. The size effect was actually there, and the price of small cap stocks was bid up until the removal of the effect, with the actions of rational, active investors, who acted on news of the finding.

On average, the returns of small stocks are often higher than their large counterparts. Furthermore, other factors like value and momentum usually have stronger impacts in small stocks. There is also the tendency of small stocks to be less liquid than the larger ones.

## Value Factors

The value premium is robust in comparison to size. For the past 50 years, gains have been produced by value firms, apart from some several notable periods where they have lost money. Although value outperforms over the long-run, growth stocks can be underperformed by value stocks during certain periods, thereby posing a risk to the value strategy.

## Rational Theories of the Value Premium

After controlling for market exposure, the movement of value stocks is, together with other value stocks, in the rational story of value. This implies that all value stocks either do well together or perform badly at the same time.

Value is also risky, with the riskiness being shared by all value stocks to a greater or lesser degree. Creation of stocks’ portfolios ensures the diversification of some value risk. However, it is impossible to diversify away from a large number of value movements.

In the formulation of pricing kernel, the compensation for losing money during bad times is the reason why any risk premium exists. Bad times for value rarely line up with economic bad times.

The following are some factors to explain the value premium: investment growth, labor income risk, non-durable or luxury consumption, and housing risk. The betas of value stocks increase during some of the bad times, exposing value firms to risk.

## Firm Investment Risk

Berk, Green, and Naik built on real options literature, in 1999, by stating that the role of a manager is exercising real investment options to create value for shareholders. In this context, a company is made up of assets already in place and a set of investment options chosen by the manager to exercise.

The CAPM, which is a non-linear model, does not work fully when there are optional features. When the market returns are low, managers optimally exercise investment options, which are dynamically linked to book-to-market features, hence giving rise to a premium.

The flexibility of the firms with regards to their size and rates of response to shocks are the differentiating features between value firms and growth firms. Value firms become risky during bad times because they become burdened with more unproductive capital.

## Behavioral Theories of the Value Premium

Overextrapolation or overreaction to recent news is the center for most behavioral theories. Past growth rates often get extrapolated into the future by investors. Generally, high growth rates are often witnessed in growth firms. These companies’ prices are bid up to new highs, reflecting excessive optimism.

Since their growth prospects are usually underestimated by investors, value stocks are cheap. On the other hand, the growth prospects of growth firms are usually overestimated by investors, thus making them very costly.

Investors with other psychological biases also produce the value effect. The two psychological biases employed by Barberries and Huang are:

1. Loss aversion mental accounting: Each stock is looked at individually by agents rather than the overall gains and losses on their portfolio; and
2. A high book-to-market ratio stock is one that has achieved its relatively low price due to some bad prior performance.

## The Value in Other Asset Classes

Essentially, value purchases assets with high yields and sells assets whose yields are low. This strategy is referred to as value-growth investing, in equities, but goes by different names in other asset classes, e.g., riding the yield curve in fixed income strategy, roll-return in commodities, and carry in foreign exchange.

The carry returns of a foreign currency can be captured using the following equation:

$$\left( FX{ E }_{ i } \right) ={ \beta }_{ i,FX }E\left( HM{ L }_{ FX } \right) ,$$

A country $$i$$’s foreign carry return is given by $${ FX }_{ i }$$, and the currency $$i$$’s with regard to the carry factor $$HM{ L }_{ FX }$$ is given by $${ \beta }_{ i,FX }$$.

For small investors, low-cost index products are available for value strategies in equity, fixed income, and currency markets.

## Momentum

Momentum is another standard investment factor that was introduced by Jagadeesh and Titman during the same period Fama and French captured the size and value factors.

## Momentum Investing

In this strategy, stocks that have gone up over the past six months or so will be purchased and those that have been experiencing the lowest returns over a similar period will be sold.

The phenomenon that winner stocks will continue to win and losers continue to lose is referred to as the momentum effect. The momentum factor WML is called for the past Winners Less past Losers.

Momentum can also be observed in all asset classes, i.e., international equities, commodities, government bonds, corporate bonds, and real estate. Momentum is also referred to as trend investing and is synonymous with commodities trading advisory funds.

As a positive feedback strategy, momentum ensures that stocks with high past returns are attractive and momentum investors will continue purchasing them, making them continue going up.

Usually, momentum is applied as an investment factor that is added into the Fama-French model:

$$E\left( { r }_{ i } \right) ={ r }_{ f }+{ \beta }_{ i,MKT }E\left( { r }_{ m }-{ r }_{ f } \right) +{ \beta }_{ i,SMB }E\left( SMB \right) +{ \beta }_{ i,HML }E\left( HML \right) +{ \beta }_{ i,WML }E\left( WML \right)$$

Where $${ \beta }_{ i,WML }$$ is a momentum beta that is centered around zero. A similar intuition is applicable as with the Fama-French model.

## Value Investing Redux

Bad times are presented by factor risks to investors. The two main factors are (1) macro factors and (2) investment factors. The exposure of assets to factor risks is such that increased exposure for a factor with a positive risk premium implies that the expected return of the asset will also be higher.

# Practice Questions

1) John Salsborough, a fund manager, is holding a large amount of U.S. T-bills in its portfolio. In comparison, most other fund managers are attracted by value stocks and investment-grade corporate bonds. Salsborough’s fund will most likely outperform other funds in an economic environment where there is:

1. High inflation, high economic growth, and high volatility.
2. Low inflation, high economic growth, and low volatility.
3. High inflation, low economic growth, and high volatility.
4. Low inflation, low economic growth, and low volatility.