Introduction

• Factors drive risk premiums.
• One set of factors describes fundamental, economy-wide variables like growth, inflation, volatility, productivity, and demographic risk.
• Another set consists of tradeable investment styles like the market portfolio, value-growth investing, and momentum investing.
• The economic theory behind factors can be
  • Rational, where the factors have high returns over the long run to compensate for their low returns during bad times, or
  • Behavioral, where factor risk premiums result from the behavior of agents that is not arbitraged away.

Value Investing

• Historically speaking, value stocks have beaten growth stocks. Value stocks have low prices in relation to their net worth, which can be measured by accounting book value. Growth stocks are relatively costly in comparison to book value.

Macro Factors

• Macro factors pervasively affect all investors and the prices of assets. When economic growth slows or inflation is high, all firms and investors in the economy are affected-it is just a question of degree.
• The level of the factor often does not matter as much as a shock to a factor.
• Asset prices respond to these factors contemporaneously. The risk premium over the long run compensates investors for the losses endured when bad times of high inflation occur in the short run.
• The three most important macro factors are growth, inflation, and volatility.

Economic Growth

• Risky assets generally perform poorly and are much more volatile during periods of low economic growth.
• However, government bonds tend to do well during these times.

Means Conditional On Factor Realizations

	Large Stocks	Small Stocks	Govt Bonds	Investment Grade	High Yield
Full Sample	11.3%	15.3%	7.0%	7.0%	7.6%
Business Cycles (1)
Recessions	5.6%	7.8%	12.3%	12.6%	7.4%
Expansions	12.4%	16.8%	5.9%	6.0%	7.7%
Real GDP (2)
Low	12.2%	8.8%	10.0%	9.7%	7.0%
High	13.8%	18.4%	3.9%	4.4%	8.2%
Consumption (3)
Low	5.6%	5.6%	9.6%	9.1%	7.1%
High	17.1%	25.0%	4.4%	5.0%	8.2%
Inflation
Low	14.7%	17.6%	8.6%	8.8%	9.2%
High	8.0%	13.0%	5.4%	5.3%	6.0%

Source:Table:2-1 2019 Financial Risk Manager Exam Part II: Risk Management and Investment Management Seventh Edition by Global Association of Risk Professionals

Volatilities Conditional On Factor Realizations

	Large Stocks	Small Stocks	Govt Bonds	Investment Grade	High Yield
Full Sample	16.0%	23.7%	10.6%	9.8%	9.5%
Business Cycles (1)
Recessions	23.7%	33.8%	15.5%	16.6%	18.1%
Expansions	14.0%	21.2%	9.3%	7.8%	6.8%
Real GDP (2)
Low	16.9%	23.7%	12.2%	11.8%	12.1%
High	14.9%	23.7%	8.5%	7.0%	6.0%
Consumption (3)
Low	17.5%	23.8%	11.9%	11.6%	11.8%
High	13.8%	22.7%	8.9%	7.4%	6.6%
Inflation
Low	15.5%	21.9%	9.6%	8.2%	7.7%
High	16.4%	25.4%	11.5%	11.1%	11.0%

Source: Table: 2-1 2019 Financial Risk Manager Exam Part II: Risk Management and Investment Management Seventh Edition by Global Association of Risk Professionals

Inflation

• High inflation tends to be bad for both stocks and bonds. During periods of high inflation, all assets tend to do poorly.
• It is no surprise that high inflation hurts the value of bonds: these are instruments with fixed payments, and high inflation lowers their value in real terms.
• It is more surprising that stocks-which are real in the sense that they represent ownership of real, productive firms-do poorly when inflation is high.
• Part of the long-run risk premiums for both equities and bonds represents compensation for doing badly when inflation is high.

Volatility

• Volatility is an extremely important risk factor. This table correlates changes in VIX with stock and bonds returns on a monthly frequency basis from March 1986 to December 2011:

	VIX Changes	Stock Returns	Bond Returns
VIX Changes	1.00	-0.39	0.12
Stock Returns	-0.39	1.00	-0.01
Bond Returns	0.12	-0.01	1.00

Source: Table: 2-2 2019 Financial Risk Manager Exam Part II: Risk Management Risk Management and Investment Management Seventh Edition by Global Association of Risk Professionals

• Stocks do badly when volatility is rising. The negative relation between volatility and returns is called the leverage effect. When stock returns drop, the financial leverage of firms increases since debt is approximately constant while the market value of equity has fallen. This makes equities riskier and increases their volatilities.
• Also, an increase in volatility raises the required return on equity demanded by investors, also leading to a decline in stock prices. This represents a time varying risk premium story and is the one that the basic CAPM advocates: as market volatility increases, discount rates increase and stock prices must decline today so that future stock returns can be high.
• Bonds offer some but not much respite during periods of high volatility, as the correlation between bond returns and 𝑉𝐼X changes is only 0.12. Thus, bonds are not always a safe haven when volatility shocks hit
• Volatility as measured by 𝑉𝐼X can also capture uncertainty-in the sense that investors did not know the policy responses that government would take during the financial crisis, whether markets would continue functioning, or whether their own models were the correct ones. Recent research posits uncertainty risk itself as a separate factor from volatility risk, but uncertainty risk and volatility risk are highly correlated.
• This Figure plots the 𝑉𝐼X index (left-hand side axis) in the dashed line and a one-year moving average of stock returns (on the right-hand side axis) in the solid line. Volatility tends to exhibit periods of calm, punctuated by periods of turbulence.
• The losses when volatility spikes to high levels can be quite severe.
• Stocks are not the only assets to do badly when volatility increases. Volatility is negatively linked to the returns of many assets and strategies. Currency strategies fare especially poorly in times of high volatility.

Source: Figure 2-2 2019 Financial Risk Manager Exam Part II. Risk Management Risk Management and Investment Management. Seventh Edition by Global Association of Risk Professionals

• Investors who dislike volatility risk can buy volatility protection (e.g., by buying put options). However, some investors can afford to take on volatility risk by selling volatility protection (again, e.g., in the form of selling put options). Buying or selling volatility protection can be done in option markets, but traders can also use other derivatives contracts, such as volatility swaps
• Volatility is a factor with a negative price of risk. To collect a volatility premium requires selling volatility protection, especially selling out-of-the-money put options.
• Options are expensive, on average, and investors can collect the volatility premium by short volatility strategies.
• Fixed income, currency, and commodity markets, like the aggregate equity market, have a negative price of volatility risk.
• Selling volatility is not a free lunch, however. It produces high and steady payoffs during stable times. Then, once every decade or so, there is a huge crash where sellers of volatility experience large, negative payoffs.

• Only investors who can tolerate periods of very high volatility-which tend to coincide with negative returns on most risky assets-should be selling volatility protection through derivatives markets. Selling volatility is like selling insurance. During normal times, a premium is collected for withstanding the inevitable large losses that occur every decade or so. The losses endured when volatility spikes represent insurance payouts to investors who purchased volatility protection.
• Rebalancing as a portfolio strategy is actually a short volatility strategy. There are two differences, however.
  • Rebalancing over assets does not directly trade volatility risk.
  • Pure volatility trading in derivatives can be done without taking any stances on expected returns through delta-hedging.
• A large literature has tried to estimate the return-volatility trade-off as here \(E(r_m) – r_f = \bar{\gamma} \sigma_m^2\)
• where
• E(R_m) – r_f, is the market risk premium, and \(\sigma_m^2\), is the variance of the market return.
• According to CAPM theory, \(\bar{\gamma}\) represents the risk aversion of the average investor.

Dynamic Factors

• The CAPM factor is the market portfolio, and, with low-cost index funds, exchange-traded funds, and stock futures, the market factor is tradeable. Other factors are tradeable too. These factors reflect macro risk and at some level should reflect the underlying fundamental risks of the economy. Macro factors like inflation and economic growth, however, are not usually directly traded (at least not in scale, with the exception of volatility), and so dynamic factors have a big advantage that they can be easily implemented in investors’ portfolios.
• The words “style factors,” “investment factors,” and “dynamic factors” can be used interchangeably. Sometimes these are also called “smart beta” or “alternative beta,” mostly by practitioners.
• The Fama-French (1993) model explains asset returns with three factors. There is the traditional CAPM market factor and there are two additional factors to capture a size effect and a value/growth effect:
• \(E(r_i) = r_f + \beta_{i, MKT}E(r_m – r_f) + \beta_{i, SMB}E(SMB) + \beta_{i, HML}E(HML) + \beta_{i, WML}E(WML)\)
• where two new factors, 𝑆𝑀𝐵 and 𝐻𝑀𝐿, appear alongside the regular CAPM market factor.

SMB Versus HML

Source: Figure 2-4 2019 Financial Risk Manager Exam Part II

Risk Management Risk Management and Investment Management

Seventh Edition by Global Association of Risk Professionals

Rational Theories Of The Value Premium

• In the rational story of value, value stocks move together with other value stocks after controlling for market exposure (and in fact covary negatively with growth stocks). All value stocks, therefore, tend to do well together or they do badly together.
• Value is risky, and the riskiness is shared to a greater or lesser degree by all value stocks. Some value risk can be diversified by creating portfolios of stocks, but a large amount of value movements cannot be diversified away. In the context of the APT, since not all risk can be diversified away, the remaining risk must be priced in equilibrium, leading to a value premium. The Fama-French model itself is silent on why value carries a premium.
• Some factors to explain the value premium include investment growth, labor income risk, nondurable or “luxury” consumption, and housing risk. A special type of “long-run” consumption risk might also be responsible for the value premium. During some of the bad times defined by these factors, the betas of value stocks increase causing value firms to be particularly risky.

Behavioral Theories Of The Value Premium

• Most behavioral theories of the value premium center around investor overreaction or overextrapolation of recent news. The standard story was first developed by Lakonishok, Shleifer, and Vishny (1994). Investors tend to over-extrapolate past growth rates into the future.
• The value effect can also be produced by investors with other psychological biases. Barberis and Huang (2001) generate a value effect by employing two psychological biases:
  • loss aversion, and
  • mental accounting
• The crucial question that behavioral models raise is: why don’t more investors buy value stocks and, in doing so, push up their prices and remove the value premium, just as investors appear to have done with the size premium ? Put another way, why aren’t there more value investors? It can’t be ignorance.
• Perhaps investors think value investing is too difficult. Yet simple strategies of academics sorting stocks on a book-to-market basis are available even to the smallest retail investor using stock screens freely available on the Internet.
• Perhaps it is the legacy of the efficient market theory developed in the 1970s but active managers have never believed in truly efficient markets, and now academics no longer believe in them either.
• Maybe not enough institutions have sufficiently long horizons to effectively practice value investing. The value effect documented here, though, is different from the “deep value” practiced by some investors, including Buffett. That requires five- to ten-year horizons. The book-to-market value effect described here is a three- to six-month effect. But perhaps even this horizon is too long for most “long-horizon” investors.

Value Of Other Asset Classes

• Value in essence buys assets with high yields (or low prices) and sells assets with low yields (or high prices). While in equities the strategy is called value-growth investing, the same strategy of buying high-yielding assets and selling low-yielding assets works in all asset classes but goes by different names. These different asset-class strategies are distinct, but they share many features.
  • In fixed income, the value strategy is called riding the yield curve and is a form of the duration premium.
  • In commodities it is called the roll return, and the sign of the return is related to whether the futures curve is upward- or downward-sloping.
  • In foreign exchange, the value strategy is called carry. This is a popular strategy that goes long currencies with high interest rates and shorts currencies with low interest rates.
• Value is a pervasive factor and theoretically can be implemented cheaply and in size by a large investor. For small investors, there are low-cost index products for value strategies in equity, fixed income, and currency markets as well. The pervasiveness of value across many different asset classes turns out to be something an asset owner should exploit in factor investing.

Momentum

• Another standard investment factor is momentum. Momentum is the strategy of buying stocks that have gone up over the past six (or so) months (winners) and shorting stocks with the lowest returns over the same period (losers), The momentum effect refers to the phenomenon that winner stocks continue to win and losers continue to lose. The momentum factor is called W𝑀𝐿, for past winners minus past losers. (It is also called 𝑈𝑀𝐷, for stocks that have gone up minus stocks that have gone gown.) The momentum strategy, like size and value, is a cross- sectional strategy, meaning that it compares one group of stocks (winners) against another group of stocks (losers) in the cross section, rather than looking at a single stock over time. Winners and losers are always relative stocks win or lose relative to each other, and the market as a whole can go up or down.
• Momentum returns blow size and value out of the water. Momentum is also observed in every asset class: international equities, commodities, government bonds, corporate bonds, industries and sectors, and real estate. In commodities, momentum is synonymous with commodities trading advisory funds. Momentum is also called “trend” investing, as in “the trend is your friend.
• There is one sense in which momentum is the opposite of value. Value is a negative feedback strategy, where stocks with declining prices eventually fall far enough that they become value stocks. Then value investors buy them when they have fallen enough to have attractive high expected returns. Value investing is inherently stabilizing. Momentum is a positive feedback strategy Stocks with high past returns are attractive, momentum investors continue buying them, and they continue to go up! Positive feedback strategies are ultimately destabilizing and are thus subject to periodic crashes.
• Momentum is primarily a cross-sectional strategy within an asset class: it looks at a particular group of stocks (those with past high returns) relative to another group of stocks (those with past low returns). Rebalancing, in contrast, should be done primarily at the asset class or strategy level because rebalancing requires the assets or strategies to exist over the long run while individual equities can disappear. Momentum manifests across asset classes, as does value. It can be part of a long-run investor’s opportunistic strategy (the Merton (1969) long-run hedging demand portfolio).

• Momentum is often used as an investment factor, added onto the Fama-French model:

\(E(r_i) = r_f + \beta_{i,\text{MKT}} E(r_m – r_f) + \beta_{i,\text{SMB}} E(\text{SMB}) + \beta_{i,\text{HML}} E(\text{HML}) + \beta_{i,\text{WML}} E(\text{WML})\)

The same intuition applies as with the Fama-French model. The momentum beta, \(\beta_{i,\text{WML}}\) is centered around zero. Winner stocks have positive momentum betas; their risk premiums are adjusted upward. Loser stocks have negative momentum betas; their risk premiums are adjusted downward. The market, neither a relative winner nor a relative loser, is simply the market.

Characterizing Momentum

• Characterizing Momentum Risk shows that despite the large return, on average, of momentum strategies, momentum is prone to periodic crashes. Some of these have lasted for extended periods. Loser stocks have a tendency to keep losing. Momentum seems to reflect monetary policy and government risk during extraordinary times. These have also been times of high volatility.
• At least some portion of momentum profits can be explained using rational theory by correlating it with macro factors. Momentum profits, for example, vary over the business cycle and depend on the state of the stock market, and there is a link with liquidity.
• The most widely cited theories are behavioral. In the main behavioral theories, momentum arises because of the biased way that investors interpret or act on information. Behavioral explanations, then, fall into two camps: momentum is an overreaction phenomenon, or it is an underreaction phenomenon. Distinguishing between these camps is difficult.
• The seminal overreaction models state that investors suffer from conservatism bias, which causes them to overreact to information because they stick doggedly to their prior beliefs. This causes momentum.
• Investors also have psychological biases giving rise to momentum. In this model, investors are overconfident and overestimate their abilities to forecast firms’ future cash flows. They also have biased self-attribution: when they are successful, it must be due to their skill, and when they are unsuccessful, it must be due to bad luck. Informed, overconfident investors (think of retail investors and overconfident hedge fund managers) observe positive signals about some stocks that perform well. These overconfident investors attribute the good performance to their own skill, leading to overconfidence. Based on increased confidence, they overreact and push up the prices of stocks above their fundamental values, generating momentum.
• The standard reference for the underreaction theory relies on “bounded rational” investors who have limited information. Momentum is caused by “news watchers” who receive signals of firm value but ignore information in the history of prices. Other investors trade only on past price signals and ignore fundamental information. The information received by the news watchers is received with delay and is only partially incorporated into prices when first revealed to the market. This causes underreaction.
• In both the underreaction and overreaction models, prices eventually reverse when they revert to fundamentals in the long run.