Temp_store

LO 64.1: Describe and evaluate the low-risk anomaly of asset returns.
The capital asset pricing model (CAPM) from traditional finance states that there should be a positive relationship between risk and return. Higher risk, as measured by beta, should have a higher return. The low-risk anomaly appears to suggest the exact opposite. This anomaly finds that firms with lower betas and lower volatility have higher returns over time. For example, over a five-year period from 20112016, the cumulative return for a low volatility fund (iShares Edge MSCI Minimum Volatility USA ETF) was 68.75% relative to the cumulative return of 65.27% for the S&P 500 Index ETF.
Al p h a , Tr a c k in g Er r o r , t h e In f o r m a t io n Ra t io , a n d t h e Sh a r pe Ra t io

LO 63.5: Compare value and momentum investment strategies, including their risk and return profiles.
The fact that small stocks tend to outperform big stocks, after adjusting for the firms beta, was discovered by Banz (1981 )3 and similarly by Reinganum (1981).4 Following the publication of this finding, the effect disappeared. In other words, if you examine the returns to an SMB strategy from 1965 to 2011, returns to the strategy peak in the early 1980s, with no evidence of a small stock premium in subsequent years. The two possible explanations for the disappearing size effect are as follows: Data mining. Fischer Black (1993)5 suggested data mining following the publication of

the Fama and French study. If a finding is discovered with in-sample data (i.e., in the data used in the original study) but is not substantiated in further studies using out-of-sample data, then data mining provides a possible explanation for the result. Investor actions. Upon the publication of the Banz and Reinganum studies, investors, acting rationally, bid up the prices of small-cap stocks until the SMB effect was removed. This is consistent with the efficient market hypothesis (EMF1) in which investors exploit anomalies until they can no longer profit from them. If this is true, then size should be removed as a risk factor in the Fama-French model.
Note that small stocks do tend to have higher returns (i.e., weak size effect), partially because they are less liquid than large-cap stocks. Also, the value and momentum effects, discussed next, are stronger for small stocks. Flowever, the ability to capture small-cap excess returns over the market (on a risk-adj usted basis) is no longer present.
Value Investing
Unlike the disappearing size premium, the value risk premium has provided investors with higher risk-adjusted returns for more than 50 years. Value strategies have suffered periods of loss, including the 1990s recession, the dot com bull market of the late 1990s, and the 20072009 financial crisis. The notion of value investing dates back to when Graham and Dodd (1934)6 published Security Analysis with a focus on finding stocks that had prices lower than their fundamental values.
There are generally two explanations for the value premium, one rational and the other behavioral.
Rational Theories o f the Value Premium
Value stocks move with each other and co-vary with growth stocks in the rational story about the reason a value premium exists. They perform well together and poorly together.
3. Rolf W. Banz, The Relationship Between Return and Market Value of Common Stocks,
Journal o f Financial Economics 9 (1981): 3-18.
4. Marc R. Reinganum, Misspecification of Capital Asset Pricing: Empirical Anomalies Based on
EarningsYields and Market Values, Journal of Financial Economics 9, no. 1 (1981): 19-46. 5. Fischer Black, Beta and Return, Journal ofPorfolio Management 20, no. 1 (1993): 8-18. 6. Benjamin Graham and David Dodd, Security Analysis (New York: McGraw-Hill, 1934).
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Value is risky and, as such, value stocks sometimes perform poorly. The value premium is compensation for these periods of poor performance, for losing money during bad times. Value did perform poorly during the bull market in the late 1990s. This means rational stories must define bad times and that value earns a premium on average, not all of the time. Also, not all value risk can be diversified away. The remaining value risk is captured in the value premium.
Labor income risk, investment growth, luxury consumption, long-run consumption risk, and housing risk are factors that have been used to explain the value premium. Value stock betas often increase during bad times defined by these risks, causing value stocks to be particularly risky. Macro-based and CAPM risk factors turn out to be the same factors that affect value firms.
Consider the difference between growth and value firms. Growth firms are more adaptable and can adjust when times change because the bulk of their capital is human capital. Value firms are more old school with capital in the form of fixed assets that cannot be redeployed when times change. Thus, value firms have high and asymmetric adjustment costs. This makes value stocks fundamentally more risky than growth stocks.
The average investor holds the market portfolio. Some investors choose a value tilt and others a growth tilt. The decision boils down to how well the investor can withstand bad times. Given the factors defined previously as bad for value (i.e., labor income risk, investment growth, etc.), the investor must ask himself, Are these times bad for me (versus bad in general)? If, for example, an investor can manage well during times of low investment growth, that is not a bad time for that investor relative to the average investor. The investor, who has a comparative advantage in holding value stocks, can bear value risk and, therefore, can earn the value premium.
Behavioral Theories o f the Value Premium
Behavioral theories of the value premium revolve around two basic ideas: (1) overextrapolation and overreaction and (2) loss aversion and mental accounting.
Overextrapolation and overreaction. Investors have a tendency to assume that past growth rates will continue in the future. This is called overextrapolation. For example, a technology company may have a period of tremendous growth as it developed new products that are in high demand. Many investors may assume that this company will continue this growth into the fixture. Investors often bid up the prices of growth stocks beyond their intrinsic values due to unwarranted optimism. Prices fall when the high expected growth doesnt materialize, leading to lower returns than those earned on value stocks.
Loss aversion and mental accounting. Investors dislike losses more than they like gains (i.e., loss aversion), and they tend to view investment gains and losses on a case-by-case basis rather than on a portfolio basis (known as mental accounting). Barberis and Huang (2001)7 use this notion to explain the value premium. They argue that the reason value stocks have high book-to-market values is that they have undergone a period of very poor
Nicholas Barberis and Ming Huang, Mental Accounting, Loss Aversion, and Individual Stock Return s ) Journal o f Finance 56, no. 4 (2001): 1247-92.
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performance. Loss-averse investors view the stock as risker and, therefore, require a higher rate of return.
Professors Note: The extrapolation/overreaction behavioral explanation o f the value premium is different from the rational one in that in the behavioral explanation, value stocks are not riskier, they are just cheap relative to growth stocks. Investors tend to underestimate the growth prospects o f value stocks and overestimate the growth prospects o f growth stocks. This bids up the prices o f growth stocks and bids down the prices o f value stocks, allowing value stocks to outperform on average. Investors must determine i f they tend to overextrapolate or not. Investors who act like other average, non-over or under-reacting investors should hold the market por folio. Investors who overextrapolate will lean toward growth stocks, and those who underreact will lean toward value stocks.
Why are there not enough value investors in the market to push up prices and remove the value premium, as described in the section on the small-cap effect? Maybe investors find value investing difficult, although it is easy to sort stocks on a book-to-market basis using internet screening tools. Perhaps investment horizons must be too long to engage in value investing. The book-to-market value effect described here requires at least a three month to six month horizon. It is possible that not enough institutions have a long enough investment horizon to adopt a value investing approach.
Value investing exists in all asset classes. Strategies include: Riding the yield curve in fixed income (i.e., capturing the duration premium). Roll return in commodities (i.e., an upward or downward sloping futures curve
determines the sign of the return).
Carry in foreign exchange (e.g., long positions in currencies with high interest rates and short positions in currencies with low interest rates). In this case, high yields are akin to low prices in equity value strategies.
Retail investors can implement value strategies via low-cost index products. Large, institutional investors can, at least theoretically, cheaply implement value strategies across markets.
Momentum Investing
In 1993, the same year Fama and French captured the size and value/growth effects, Jagadeesh and Titman8 identified a momentum effect. Momentum strategies (also called trend investing) consist of buying stocks that have gone up over a period (e.g., six months or so) and short stocks that have fallen over the same period (i.e., buy past winners and sell past losers). The momentum factor, WML, stands for winners minus losers. It is also sometimes denoted UMD for up minus down, buying stocks that have gone up in price and selling stocks that have gone down in price. A momentum premium is observed in fixed income (government and corporate bonds), international equities, commodities, real estate, and specific industries and sectors.
Narasimhan Jegadeesh and Sheridan Titman, Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, Journal o f Finance 48, no. 1 (1993): 65-91.
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The returns to momentum investing exceed size and value investing premiums by a wide margin. Figure 2 illustrates the differences in returns across the three strategies. One dollar invested in the WML premium in January 1963 reached a high of more than $60 before following precipitously (below $30) during the 20072009 financial crisis. Correlation between the value premium and the momentum premium was only approximately 0.16 during this period. This means that value returns are not opposite momentum returns.
Figure 2: Returns for SMB, HML, and WML strategies
Year
Value and momentum strategies are, however, opposite each other in the following sense. Value investing is inherently stabilizing. It is a negative feedback strategy where stocks that have fallen in value eventually are priced low enough to become value investments, pushing prices back up. Momentum is inherently destabilizing. It is a positive feedback strategy where stocks that have been increasing in value are attractive to investors, so investors buy them, and prices increase even more. Momentum investing can lead to crashes (e.g., the more than 30% drop during the 20072009 financial crisis). Notice that value and growth returns did not fall in quite so dramatic a fashion. An investor following a momentum strategy should still rebalance his portfolio.
Momentum is often added to the Fama-French model as follows:
E(Ri) Rp + (3ijMKT x E(Rm Rf ) + Pi,SMB x E(SMB) + Pi5HML x E(HML)
+ Pi,WML x E(WML)
As mentioned, momentum can be riskier than value or size investing in that it is more prone to crashes. There have been 11 momentum crashes on record: seven during the 1930s Great Depression, three during the financial crisis starting in 2007, and one in 2001. During the 20072009 crisis, financial stocks were hit hard. Losers tend to keep losing, and they likely would have, but the government bailout put a floor on stock prices. Momentum
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investors were short these stocks. When the government bailed out financial firms and other firms that were hit hard, momentum investors experienced large losses as the market rebounded. During the Great Depression, policymakers also influenced asset prices, causing losses to momentum investors.
Momentum risk includes: Tendency toward crashes. Monetary policy and government risk (i.e., the government gets in the way of the natural
progression of asset prices).
Macro factors such as the business cycle, the state of the stock market, and liquidity risk. Behavioral explanations suggest that investor biases explain momentum. Investors overreact (a delayed overreaction) to good news about firms. This causes prices to drift upward. Alternatively, investors may underreact to good news, causing prices to increase less than they should have given the good news. As investors acquire more information, prices go up in the next period. Thus, behavioral explanations for the momentum premium fall into two, difficult-to-distinguish camps: 1. Overreaction to good news. In some cases overconfident, informed investors, like retail
investors and hedge fund managers, observe positive signals in stock performance. They attribute the performance to their own skill. The overconfidence leads to overreaction, pushing prices up above their fundamental values.
2. Underreaction to good news. In this case, news watchers ignore information in the
history of stock prices and other investors trade only on history (i.e., past price signals) and ignore fundamental information about the firm. In both cases, information is only partially incorporated into stock prices, causing an underreaction.
Whether there is momentum that results from overreaction or from underreaction, prices eventually revert to their fundamental values over the long run. An investor considering momentum investing must assess whether he leans toward overreaction or underreaction. Also, the investor must know that he can tolerate large losses during crash periods, historically concentrated around periods when policymakers (e.g., central banks) interrupt momentum, changing the course that asset prices would naturally take. In sum, assets are exposed to factor risks like value and momentum. Factor premiums compensate investors for losses during bad times.
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Ke y Co n c e pt s
LO 63.1 A value-growth investment strategy is long value stocks and short growth stocks. Value stocks have high book-to-market ratios, and growth stocks have low book-to-market ratios. Historically, value stocks have significantly outperformed growth stocks.
Risk premiums, including a value premium, exist to compensate investors for losses experienced during bad times. There are rational and behavioral explanations for why a value premium may exist. Value stocks are risky, thus the value premium compensates investors for losses during bad times (rational explanation). Investors undervalue the growth prospects of value stocks and overextrapolate past growth into future prospects, overvaluing growth stocks. Value stocks are underpriced relative to their fundamental values, and growth stocks are overvalued, leading to a value premium (behavioral explanation).
LO 63.2 Macroeconomic factors, like inflation and economic growth, affect all investors to varying degrees. Economic growth, inflation, and volatility are the three most important macro factors that affect asset prices. It is unanticipated changes to a risk factor that affect asset prices, not the level of the factor. In other words, it is not the level of inflation, but an unanticipated increase or decrease in inflation that causes stock and bond prices to rise or fall. Risky assets generally perform poorly during periods of low economic growth.
Other macroeconomic factors, like shocks to productivity, demographic risks, and sovereign risks, also affect asset returns.
Stocks and bonds generally perform poorly in periods of high inflation. Stock returns drop when volatility (measured by the VIX) increases.
LO 63.3 Volatility increases in periods of economic stress. There are two basic approaches to mitigating volatility risk:
Invest in less-volatile assets like bonds. One challenge to managing volatility is that asset prices, including less volatile assets, tend to perform poorly during periods of economic stress (e.g., 20072009).
Buy volatility protection in the derivatives market (e.g., buy out-of-the-money put
options). Sellers of volatility protection (i.e., those selling put options) collect volatility premiums.
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LO 63.4 The Fama-French model explains asset returns based on three dynamic factors. The factors are: The traditional CAPM market risk factor. A factor that captures the size effect (SMB or small cap minus big cap), historically,
small-cap stocks outperform large-cap stocks. The strategy is long small-cap stocks and short large-cap stocks.
A factor that captures the value/growth effect (F1ML or high book-to-market value
minus low book-to-market value). Value stocks tend to outperform growth stocks. The value-growth strategy is long value stocks and short growth stocks.
LO 63.3 A value strategy is long value stocks and short growth stocks. A momentum strategy is long winners (i.e., stocks that have gone up in value over the last six months or so) and short losers (i.e., stocks that have gone down in value over the last six months or so). A momentum strategy has vastly outperformed both value-growth and size strategies since 1963. Flowever, momentum strategies are subject to crashes. Rational and behavioral explanations can be used to describe both value and momentum risk premiums.
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Co n c e pt Ch e c k e r s
1.
2.
3.
4.
3.
A low book-to-market value ratio is indicative of a: A. value stock. B. growth stock. C. small-cap stock. D. large-cap stock.
Which of the following asset classes has approximately the same returns in high economic growth periods and low economic growth periods? A. Small-cap stocks. B. Large-cap stocks. C. Government bonds. D. High-yield bonds.
Which of the following investment options provides a means of mitigating volatility risk? A. Buying put options. B. Selling put options. C. Buying equities. D. Buying call options.
Which of the following is not a factor in the Fama-French three-factor model? A. The capital asset pricing model market risk factor. B. The small capitalization minus big capitalization risk factor. C. The winners minus losers risk factor. D. The high book-to-market value minus low book-to-market value risk factor.
Which of the following investment strategies stabilizes asset prices? A. A value investment strategy. B. A momentum investment strategy. C. A size investment strategy. D. Value, momentum, and size strategies all stabilize asset prices.
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Co n c e pt Ch e c k e r An s w e r s
1. B A companys book value per share is equal to total assets minus total liabilities all divided by shares outstanding. It indicates, on a per-share basis, what a company would be worth if it liquidated its assets and paid off its liabilities. Value stocks have high book-to-market ratios while growth stocks have low book-to-market ratios.
2. D During periods of recession, government and investment-grade bonds outperform equities and high-yield bonds. During expansion periods, equities outperform bonds. High-yield bond returns appear indifferent to changes in economic growth, yielding 7.4% in recessions and 7.7% in expansions.
3. A There are two basic approaches to mitigating volatility risk. They are investing in less volatile assets like bonds (instead of stocks) or buying volatility protection in the derivatives market, such as buying out-of-the-money put options.
4. C The Fama-French model includes the following three risk factors: The traditional capital asset pricing model market risk factor.
A factor that captures the size effect (SMB). A factor that captures the value/growth effect (HML).
The winners minus losers (WML) momentum factor was discovered by Jagadeesh and Titman.
5. A Value and momentum are opposite each other in that value investing is inherently stabilizing.
It is a negative feedback strategy where stocks that have fallen in value eventually are priced low enough to become value investments, pushing prices back up. Momentum is inherently destabilizing. It is a positive feedback strategy where stocks that have been increasing in value are attractive to investors, so investors buy them, and prices increase even more.
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The following is a review of the Risk Management and Investment Management principles designed to address the learning objectives set forth by GARP. This topic is also covered in:
A l ph a (a n d t h e Lo w -Ri s k A n o m a l y )
Topic 64
Ex a m Fo c u s
Investors are interested in generating alpha, which is the return earned in excess of a benchmark. It was traditionally thought that higher risk produced higher returns. However, in practice, strategies focused on lower volatility have actually been found to produce higher returns than higher-volatility investments. For the exam, be able to explain the impact of benchmark section on alpha. Also, understand how to apply factor regression to construct a benchmark with multiple factors, and how to measure alpha against that benchmark. Finally, be familiar with the potential explanations for return anomalies with regard to low risk.
Lo w -Ris k An o m a l y

LO 63.4: Explain how dynamic risk factors can be used in a multifactor model of asset returns, using the Fama-French model as an example.
The capital asset pricing model (CAPM) is a single-factor model. In the CAPM, the single risk factor is market risk. Stocks that have high exposure to the CAPM market factor perform well when the market performs well and poorly when the market performs poorly. Over the long run, stocks with high betas (i.e., a high market risk factor) should have higher returns than the market return. Returns are higher for high beta stocks to compensate investors for losses during bad periods.
The market portfolio can be readily traded via low-cost index funds, stock futures, and exchange-traded funds (ETFs). In general, macro factors, like political, inflation, and growth risks, are not directly traded (volatility risk is the exception). As a result, dynamic factors can be easily employed in portfolios. The best known example of a tradeable multifactor model is called the Fama and French model, introduced in 1993.2
Eugene F. Fama and Kenneth R. French, Common Risk Factors in the Returns on Stocks and Bonds, Journal of Financial Economics 33 (1993): 3-56.
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Professors Note: In the academic finance literature style factors, investment factors, and dynamic factors are used interchangeably. Practitioners also refer to these factors as smart beta or alternative beta. Fama and French were the first to develop a multifactor model that captured these effects.
The Fama-French model (called the Fama-French three-factor model) explains asset returns based on three dynamic factors. The model includes: The traditional CAPM market risk factor (MKT). A factor that captures the size effect (SMB). A factor that captures the value/growth effect (HML). The Fama-French three-factor model is expressed as follows:
E(Ri) – RF + (3i>MKT x E(Rm R f ) + Pi,s mb x E(SMB) + P^h m l x E(HML)
Following the market factor, the second factor in the model is SMB. The SMB factor refers to the difference between the returns on small stocks (small market capitalization) versus big stocks (large market capitalization). In other words, the risk factor is small stock returns minus big stock returns, thus SMB. Historically, small-cap stocks have outperformed large- cap stocks. This factor captures the higher performance of small companies relative to large companies. Note, however, that the average stock only has market exposure. Every stock cannot be large, and every stock cannot be small.
The third factor in the model is HML. This factor captures the return differential of high book-to-market stocks versus low-book-to-market stocks. The ratios are calculated as book value divided by market capitalization. Recall that a value strategy consists of buying low- priced stocks (i.e., taking a long position in low-priced stocks) and selling high-priced stocks (i.e., shorting high-priced stocks), normalized by book value. Growth stocks have high stock prices relative to book values, and value stocks have low stock prices relative to book values. Historically, value stocks have outperformed growth stocks. Thus, the Fama- French factors are constructed to capture size (SMB) and value (HML) premiums (known as factor-mimicking portfolios).
A value investor, who buys stocks that are perceived as trading below their fundamental value, would have a positive HML beta. Relative to the CAPM expected return, the value investors return adjusts upward by (3j HML x E(HML). Thus, the overall risk premium increases above the single-factor CAPM risk premium. Likewise, the overall risk premium is adjusted down by HML x E(HML) for growth stocks. This is because growth stocks have negative HML betas, so expected returns are adjusted downward.
In the CAPM, both the average stock beta and the market beta equal one. In the Fama- French model, the HML and SMB betas are centered on zero. The average investor earns the market return as the average stock (or portfolio of stocks) does not have a value or size tilt. This means the investor must specifically choose a value play or a size play, to benefit from the HML and SMB factors. Also, the CAPM and Fama-French models assume betas are constant, but empirical research indicates they vary and increase during bad times.
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Va l u e a n d M o m e n t u m In v e s t m e n t St r a t e g ie s

LO 63.3: Assess methods of mitigating volatility risk in a portfolio, and describe challenges that arise when managing volatility risk.
Volatility can be mitigated by investing in less volatile assets. As one would expect, bond returns are less impacted by volatility in equity markets (than equity returns). However, bonds are not necessarily a safe haven. Correlation between changes in the VIX and bond returns was 0.12 (between 1986 and 2011). This means bonds perform better than stocks (with a correlation coefficient of 0.39) when the VIX is rising, but the relationship is not highly positively correlated. For example, during the recent financial crisis, volatility was a factor that caused risky assets, bonds and stocks included, to fall simultaneously. The VIX can also capture uncertainty. Some research indicates that uncertainty risk is different from volatility risk, but the two risks are highly correlated.
Other investment approaches also perform poorly in periods of increased volatility. A number of strategies have a large exposure to volatility risk. For example, currency strategies perform poorly during periods of high volatility. For investors who want to avoid volatility, they can buy put options (i.e., protection against volatility). Out-of-the-money puts, which pay off during periods of high volatility, provide hedges against volatility risk.
In sum, there are two basic approaches to mitigating volatility risk. They are:
Invest in less volatile assets like bonds, understanding that they too can perform poorly during extreme circumstances such as the 20072009 financial crisis.
Buy volatility protection in the derivatives market (e.g., buy out-of-the-money put
options).
Volatility Premiums
Typically, an investor buys an asset, like a stock, and the long position produces a positive expected return. In other words, on average, assets have positive premiums. However, volatility has a negative premium. To collect the volatility premium, one must sell volatility protection (e.g., sell out-of-the money put options). Realized volatilities are lower on average (by approximately 2%3%) than VIX implied volatilities. This means that, on average, options are expensive and investors can collect volatility premiums by shorting volatility strategies.
During normal economic periods, selling volatility provides high, stable payoffs. However, when there is a crash, like the 20072009 financial crisis, sellers of volatility suffer large, negative returns. A volatility (swap) index constructed by Merrill Lynch indicates steadily (with minor blips) increasing cumulative returns between January 1989 and December 2007, until the financial crisis. Between September and November 2008, losses were nearly 70%. Considering the data leading up to the crisis (through December 2007), selling volatility looked like easy money. Considering the whole sample period, including the crisis,
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the data indicates negative skewness of 8.26. Without the crisis (i.e., only considering the data up to December 2007) the negative skewness was a mere 0.37.
Professors Note: Selling volatility is like selling insurance. I f you sell auto insurance, you collect stable premiums over time but occasionally face a large payout due to a car accident. The same is true for selling out-ofth e-money put options. The seller collects option premiums for years, then a disaster happens, like the 20072009 financial crisis, and the seller faces massive losses. Option purchasers know in advance what they can lose, the option premium, but sellers do not. Thus, during a market crash, losses could be massive for volatility sellers. Only investors who can tolerate periods o f high volatility, which often coincide with losses (sometimes very large losses), should sell volatility.
Academics have estimated a relationship between the expected market risk premium [E(Rm) Rp] and volatility. The equation is shown as follows:
E ( R m ) ^ F T XcrM
is equal to the variance of the market return and where investors risk aversion. While the coefficient ^ is positive in theory, various studies have estimated it as either positive, negative, or zero. Again, though, whether positive or negative, only those investors who can withstand massive losses during periods of high volatility should sell volatility.
represents the average
D y n a m ic Ris k Fa c t o r s

LO 63.2: Explain how different macroeconomic risk factors, including economic growth, inflation, and volatility affect risk premiums and asset returns.
Macroeconomic factors, such as increasing inflation or slowing economic growth, affect all investors to varying degrees. Most, though not all, investors are hurt by rising inflation, slowing economic growth, or both. But it is not the level of the factor that matters, it is the shock (i.e., unanticipated changes) to a factor. For example, asset prices generally fall when inflation unexpectedly increases. Economic growth, inflation, and volatility are the three most important macro factors that affect asset prices.
Economic Growth
Risky assets like equities generally perform poorly during periods of low economic growth. Less-risky assets like bonds, and especially government bonds, tend to perform well during periods of slow growth. For the investor who can weather a downturn easily, she should invest in equities because returns will be greater over the long run. Periods of stronger growth generally last longer than downturns. For the investor who cannot bear large losses during a period of slow growth, she should invest in bonds. Fler portfolio will likely perform better during the downturn but worse in the long run.
Figure 1 reports the returns of large and small stocks, as well as government, investment grade, and junk (high-yield) bonds during expansions and retractions as defined by the National Bureau of Economic Research (NBER). Returns are from Ibbotson Morningstar and cover the period 1932 through 2011. During periods of recession, government and investment grade bonds outperform equities and high-yield bonds, yielding 12.3% and 12.6%, respectively. During expansion periods, equities outperform bonds with large stocks yielding 12.4% and small stocks yielding 16.8%. Fligh-yield bond returns appear indifferent to changes in economic growth, yielding 7.4% in recessions and 7.7% in expansions.
Figure 1 also reports returns based on quarter-on-quarter real GDP growth and quarter-on- quarter consumption growth (i.e., real personal consumption expenditures). The patterns are similar to those exhibited by NBER expansion/recession data. Equities outperform in periods of high real GDP growth and high consumption growth, while bonds outperform in periods of low real GDP growth and low consumption growth. High-yield bonds perform slightly better in high-growth periods.
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Figure 1: Investment Returns During Expansions and Recessions
Large Stocks
Small Stocks
Government
Bonds
Investment
Grade
High Yield
Corporate Bonds
Returns
Full Sample Business Cycles
Recessions Expansions
Real GDP
Low High
Consumption
Low High Lnflation
Low High
11.3%
5.6% 12.4%
8.8% 13.8%
5.6% 17.1%
14.7% 8.0%
15.3%
7.8% 16.8%
12.2% 18.4%
5.6% 25.0%
17.6% 13.0%
7.0%
12.3% 5.9%
10.0% 3.9%
9.6% 4.4%
8.6% 5.4%
7.0%
12.6% 6.0%
9.7% 4.4%
9.1% 5.0%
8.8% 5.3%
7.6%
7.4% 7.7%
7.0% 8.2%
7.1% 8.2%
9.2% 6.0%
In terms of volatility, both stocks and bonds are more volatile during downturns and periods of low growth. For example, large stock return volatility was 23.7% during recessions and 14.0% during expansions. Government bonds perform best during recessions but are also more volatile during these periods (13.3% volatility during recessions and 9.3% volatility during expansions).
Inflation
High inflation is generally bad for both stock and bond prices and returns. Figure 1 indicates that all categories perform better in low inflation versus high inflation periods. Volatilities are also higher in high inflation periods. Large and small stocks return 14.7% and 17.6%, respectively, during low inflation periods, and 8.0% and 13.0% during high inflation periods. Bond yields of 8.6%, 8.8%, and 9.2% (government, investment grade, and high-yield bonds, respectively) during low inflation periods exceeded returns during high inflation periods by approximately 3.0%. Bonds are fixed payment securities. As such, it is clear that bonds should perform poorly in high inflation times. Inflation lowers real bond returns. It is less clear that stocks perform poorly in high inflation times since they represent ownership of real, productive companies, not a claim to a stream of fixed cash flows.
Volatility
Volatility is an important risk factor for many asset classes. The CBOE Volatility Index (VIX) represents equity market volatility. The correlation between the VIX and stock returns has historically indicated a negative relationship (correlation coefficient of 0.39 between 1986 and 2011). This means that stock returns tend to drop when the VIX (equity volatility) increases.
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The financial leverage of companies increases during periods of increased volatility because debt stays approximately the same while the market value of equity falls. The negative relationship between stock returns and volatility is called the leverage effect. As financial leverage increases, equities become riskier and volatility increases. Additionally, higher volatility increases the required rates of return on equities, pushing stock prices down. Thus, there are two paths to lower stock returns resulting from higher volatility: 1. When market volatility increases, the leverage effect suggests a negative relationship
between stock returns and volatility.
2. When market volatility increases, discount rates increase and stock prices decline so that future stock returns can be higher (to compensate for the higher volatility). The capital asset pricing model (CAPM) supports this second path.
Other Macroeconomic Factors
Other macroeconomic factors, including productivity risk, demographic risk, and political risk, also affect asset returns. Productivity shocks affect firm output. In periods of falling productivity, stock prices fall (like in the 1960s and 1970s). In periods of improving productivity (like the 1980s and 1990s computer revolution) productivity shocks are positive and stock prices generally increase. The correlation between productivity shocks and stock returns is relatively high (approximately 30%).
New models, called dynamic stochastic general equilibrium (DSGE) macro models, indicate that economic variables change over time due to the actions of agents (i.e., consumers, firms, governments, and central banks), technologies (and their impact on how firms produce goods and services), and the way that agents interact (i.e., markets). A benchmark model created by Smets and Wouters (2007)1 specifies seven shocks that impact the business cycle. They are: (1) productivity, (2) investment, (3) preferences, (4) inflation, (3) monetary policy, (6) government spending, and (7) labor supply.
Like productivity shocks, demographic risk, which can be interpreted as a shock to labor output, is a shock to firm production. Economic overlapping generation (OLG) models include demographic risk as a factor affecting investor returns. In these models, generations overlap. Young, middle-age, and retired workers exist in a system. Workers earn income and save during the young and middle-age stages. Retired workers disinvest. As a cohort progresses through life, they join others already in the cohort but born at an earlier time. According to several OLG models, events that shock the composition of the cohort, like World Wars I and II, infectious diseases, like the Spanish Flu of 1918, and the baby boom, which followed World War II, impact returns. For example, one model predicts that stock prices will fall when baby boomers retire as they liquidate assets to fund consumption. This would occur if there are relatively fewer young and middle-age investors to offset the asset liquidation of retirees. If there are a greater number of young and middle-age workers, relative to retirees, the impact will be lessened (or even overcome). Another study shows that risk aversion increases with age and that as the average age of the population increases, the equity risk premium should also increase. Note that it is important to use cross-country data in demographic studies. 1
1. Frank Smets and Rafael Wouters, Shocks and Frictions in US Business Cycles: A Bayesian Dynamic Stochastic General Equilibrium Approach, American Economic Review 97, no. 3 (2007): 586-606.
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Political (or sovereign) risk, once thought only important in emerging markets, increases risk premiums. The financial crisis of 20072009 made clear that political risk affects both developed and undeveloped countries.
M a n a g in g Vo l a t il it y Ris k

LO 63.1: Describe the process of value investing, and explain reasons why a value premium may exist.
Risk premiums are driven by factors. Econo my-wide (i.e., fundamental-based) factors such as inflation, volatility, productivity, economic growth, and demographics drive risk premiums. Additionally, factors related to tradeable investment styles such as momentum investing, value investing, and investing based on firm size drive returns.
A companys book value (i.e., net worth) per share is equal to total assets minus total liabilities divided by shares outstanding. It indicates, on a per-share basis, what a company would be worth if it liquidated its assets and paid off its liabilities. Value stocks have high book-to-market ratios while growth stocks have low book-to-market ratios, where market indicates the companys stock price. An investment strategy that is long value stocks and short growth stocks is called a value-growth strategy.
Historically, value stocks have significantly outperformed growth stocks. One dollar invested in a value-growth strategy in 1963 would be worth more than $6 around 2012, with a peak value of nearly $8 in 2006 and 2007. During the more than 40-year period, value stock returns experienced a sharp downturn during the tech boom, during the late 1990s, during the financial crisis in 2007-2009, and again in 2011. Overall, however, value investing appears to work. Are returns higher than growth investing returns due to a systematic factor? Alternatively, is there a value risk premium? Risk factors offer premiums to investors to compensate them for bearing losses in bad times, like the late 1990s and 20072009. Rational and behavioral explanations for the value premium will be discussed in detail in LO 63.3.
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M a c r o e c o n o m ic Fa c t o r s

LO 62.6: Describe efficient market theory and explain how markets can be inefficient.
The APT was one of the earliest forms of the efficient market theory. The APT is a multifactor model where market participantsincluding active managers and arbitrageursmove an assets expected return toward a value that represents an equilibrium risk-return tradeoff. The APT uses systematic factors that cannot be removed through arbitrage. As a result, investors demand to be compensated for this risk in the form of a risk premium.
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.Another efficient market theory was developed by Sanford Grossman and Joseph Stiglitz (1980).1 In their theory, markets are near-efficient and information is costless. Market efficiency is in part caused by active managers searching for areas of inefficiency, making markets more efficient in the process. We can expect to find these areas of inefficiency in illiquid market segments where information does not move freely and where these inefficiencies make it difficult to earn large profits. Note, however, that the assumption of costless information creates a circular argument: if there is no cost to information and prices already reflect all information, there wouldnt be a need to collect information. However, if no one collects information, then it cannot be fully reflected in asset prices.
Market efficiency is also described in the efficient market hypothesis (EMH). The EMH implies that speculative trading is costly, and active managers cannot generally beat the market. The average investor, who holds the market portfolio, can beat the market simply by saving on transaction costs. Even if markets cannot be perfectly efficient, the EMH is still useful because it can help investors identify areas of market inefficiency that can be exploited through active management.
The EMH has been refined to improve upon the CAPMs shortcomings by allowing for imperfect information and various costs, including transaction, financing, and agency costs. Behavioral biases also represent inefficiencies, which have similar effects as frictions. Behavioral biases can be described either through a rational or behavioral explanation approach.
Under the rational explanation approach, losses during bad times are compensated by high returns. It is important to clearly define what bad times constitutes, and whether these bad times are actually bad for investors. For example, an investor who shorted the market would benefit, rather than incur losses, in a bad times scenario.
Under the behavioral explanation approach, it is agents reactions (under/overreaction) to news that generates high returns. Perfectly rational investors are not prone to these biases, and they provide their own capital to take advantage of mispricing caused by biases. However, the markets may have barriers to the entry of capital that make it difficult to take advantage of mispricings, including structural barriers (e.g., certain investors are unable to take advantage of an opportunity) and regulatory barriers (e.g., minimum credit rating requirement of asset holdings). Structural barriers allow for behavioral biases to persist for a long time.
Ultimately, it is not the type of bias that matters, but whether the investor is different from the average investor who is subject to both rational and behavioral constraints, and whether return opportunities are expected to persist. 1
1. Sanford J. Grossman and Joseph E. Stiglitz, On the Impossibility of Efficient Markets,
American Economic Review 70 (1980): 393-498.
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Ke y Co n c e pt s
LO 62.1 Exposure to different factor risks earns risk premiums. Underlying factors may include the market, interest rates, investing styles, inflation, and economic growth. Factor risks represent exposures to bad times, and this exposure must be compensated for with risk premiums. There are three important principles of factor risk: 1.
It is not exposure to the specific asset that matters, rather the exposure to the underlying risk factors.
2. Assets represent bundles of factors, and assets risk premiums reflect these risk factors.
3.
Investors each have different optimal exposures to risk factors, including volatility.
LO 62.2 The capital asset pricing model (CAPM) is a single-factor model that describes how an asset behaves in relation to other assets and to the market. The CAPM incorporates an assets covariance with the market portfolio, measured by the assets beta. In the CAPM world, the only relevant factor is the market portfolio, and risk premiums are determined solely by beta. * 1
LO 62.3 The CAPM has six important lessons: 1. Hold the factor, not the individual asset.
2.
Investors have their own optimal factor risk exposures.
3. The average investor is fully invested in the market.
4. Exposure to factor risk must be rewarded.
3. Risk is measured as beta exposure.
6. Valuable assets have low risk premiums.
The CAPM has six main shortcomings (i.e., unrealistic simplifying assumptions): 1.
Investors only have financial wealth.
2.
Investors have mean-variance utility.
3.
Investors have a single period investment horizon.
4.
Investors have homogeneous (identical) expectations.
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5. Markets are frictionless (no taxes or transaction costs).
6. All investors are price takers.
LO 62.4 There are six lessons from the multifactor models: 1. Diversification is beneficial.
2.
Investors have optimal exposures, to factor risks in multifactor models.
3. The average investor holds the market portfolio.
4. Exposure to factor risks must be rewarded through risk premiums.
3. Risk is measured by factor betas.
6. Valuable assets have low risk premiums.
LO 62.3 Multifactor models define bad times over multiple factors using a pricing kernel, also known as the stochastic discount factor (SDF). The SDF represents an index of bad times. The SDF is denoted as m in the multifactor model, representing a single variable that captures all bad times for any given a and b constants:
m = a + b x Rm
The SDF model can also be set up using multiple factor exposures where factors represent different bad times.
The SDF model can be used to predict an assets price, where SDF is the relevant factor m:
The assets risk premium can be modeled using beta.
The risk premium equation can be set up using multiple factor exposures where factors represent different macroeconomic factors, including inflation, economic growth, the market portfolio, or investment strategy.
LO 62.6 Arbitrage pricing theory (APT) uses systematic factors that cannot be removed through arbitrage, and for which investors must be compensated for through risk premiums.
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Another efficient market theory developed suggests that markets are near-efficient and information is costless. Active managers search for areas of inefficiency in illiquid market segments, making markets more efficient in the process.
The efficient market hypothesis (EMH) states that speculative trading is expensive, and active managers cannot beat the market on average. The EMH is useful because it helps investors identify areas of market inefficiency that active management can exploit. The EMH has been refined to allow for imperfect information, various costs (transaction, financing, and agency), and behavioral biases.
Under the rational explanation of behavioral biases, losses during bad times are compensated for by high returns. Under the behavioral explanation, it is agents under- or overreactions to news that generates high returns. Market barriers may make it difficult to take advantage of mispricings.
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Co n c e pt Ch e c k e r s
1.
2.
3.
4.
3.
Which of the following concepts would least likely meet the definition of a factor? A. Market. B. Volatility. C. Hedge funds. D. Momentum investing style.
Infinitely risk-tolerant investors. According to the capital asset pricing model (CAPM), in equilibrium, all investors hold the mean-variance efficient portfolio. Which of the following investor types is an exception to this assumption? A. Infinitely risk-averse investors. B. C. Investors who hold some of the risk-free asset. D. Investors who hold the market portfolio. Assets that have losses during periods of low market returns have: low betas and low risk premiums. A. B. high betas and low risk premiums. C. low betas and high risk premiums. D. high betas and high risk premiums.
Which of the following statements best describes the relationship between asset payoffs and bad times events (high inflation, low economic growth, or both)? A. The higher the expected payoff of an asset in bad times, the higher the assets
B. The higher the expected payoff of an asset in bad times, the lower the assets
expected return.
expected return.
C. The expected payoff of an asset in bad times is unrelated to the assets expected
return, because it depends on investor preferences.
D. The expected payoff of an asset in bad times is unrelated to the assets expected
return, because arbitrageurs eliminate any expected return potential.
Which of the following statements least likely represents a limitation of the capital asset pricing model (CAPM)? A. All investors are price takers. B. C. All investors have the same expectations. D. There are uniform taxes and transaction costs.
Information is costless to obtain.
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Co n c e pt Ch e c k e r An s w e r s
1. C Assets, including corporate bonds, private equity, and hedge funds, are not considered factors themselves, but contain many factors, such as equity risk, interest rate risk, volatility risk, and default risk.
Some assets, like equities and government bonds, can be thought of as factors themselves. Factors may also include the market (a tradable investment factor), interest rates, or investing styles (including value/growth, low volatility, or momentum).
2. A According to the CAPM, all investors hold a combination of the risky mean-variance
efficient market portfolio and the risk-free asset. All investors hold the same market portfolio (therefore the mean-variance efficient portfolio is the market portfolio), and it is only the quantity of holdings that differs among investors. The only exception to this assumption is an infinitely risk-averse investor, who would only hold the risk-free asset.
3. D Assets that have losses during periods of low market returns have high betas (high sensitivity to market movements), which indicates they are risky and, therefore, should have high risk premiums. Low beta assets have positive payoffs when the market performs poorly, making them valuable to investors. As a result, investors do not require high risk premiums to hold these assets.
4. B The higher the expected payoff of an asset in bad times, the lower the assets expected return.
Assets that have a positive payoff in bad times are valuable to hold, leading to high prices and, therefore, low expected returns.
5. D The CAPM does not assume uniform taxes and transaction costs; it assumes there are no taxes or transaction costs (i.e., frictionless markets). The other limiting assumptions of the CAPM include:
1.
Investors only have financial wealth.
2.
3.
4.
Investors have mean-variance utility.
Investors have a single period investment horizon.
Investors have homogeneous (identical) expectations.
5. All investors are price takers.
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The following is a review of the Risk Management and Investment Management principles designed to address the learning objectives set forth by GARP. This topic is also covered in:
Fa c t o r s
Ex a m Fo c u s
Topic 63
Macroeconomic factors have been linked to asset returns. The most important macro factors that affect returns are economic growth, inflation, and volatility. Volatility risk can be mitigated by investing in low-volatility assets or buying volatility protection in the derivatives market (e.g., buying put options). The capital asset pricing model (CAPM) is a single-factor model that relates asset returns to market risk. The Fama-French model is a multifactor model that adds a size factor and a value factor to the original CAPM market factor to explain stock returns. A momentum factor can also help explain asset returns. The momentum strategy far outpaces the size and value-growth strategies in terms of returns. Ffowever, momentum strategies are prone to crashes. For the exam, understand the risk and return profiles of each factor. Also, be aware of rational and behavioral explanations for each factor.
Va l u e In v e s t in g

LO 62.3: Explain how stochastic discount factors are created and apply them in the valuation of assets.
Multifactor models define bad times over multiple factors. They use the concept of a pricing kernel, also known as the stochastic discount factor (SDF), which represents a random variable used in pricing an asset. The SDF represents an index of bad times, where the bad times are indexed by a multitude of different factors and states. The SDF is denoted as m in the multifactor model, where m is a single variable that captures all bad times for any given a and b constants:
m = a + b x Rm
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The CAPM is a special case of this model, where m moves linearly with the market return. However, modeling returns as linear is a shortcoming of the CAPM, which can be improved upon by using the pricing kernel which allows for the assumption of nonlinearity.
We can expand this model to include various factor exposures {fv f 2> etc.) where SDF depends on a vector of these factors, where all the k factors represent different bad times:
m = a + bjfj + b2f2 +
+ bkfk
With multifactor pricing kernels, bad times can be defined as periods when an additional $ 1 income becomes very valuable. Looking at bad times this way interprets SDF as a marginal utility. Periods of high marginal utility could arise from the loss of a job (resulting in low income, where the value of an extra dollar is high), low GDP growth, low consumption (resulting in current consumption below past consumption), or generally low economic growth.
Pr ic in g Ke r n e l s v s . D is c o u n t Ra t e M o d e l s
In a traditional discount rate model, the price of an asset is determined by discounting its future cash flows at the appropriate discount rate:
P : = E
payoff^ l + E(Ri)
The discount rate is determined through the CAPM as:
E(Ri) = RF +(3i x[E(RM) – R F
The SDF model can also be used to predict an assets price, where we use the SDF as the relevant factor:
Pj = E mxpayoff^] This equation helps explain the name stochastic discount factor, since the payoffs are discounted using m as the relevant factor. The SDF is called a pricing kernel, using the term kernel from statistics where we estimate m using the kernel estimator. Because the kernel is used to derive asset pricing, it is called a pricing kernel.
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If we divide both sides of the equation by the assets current price, constant payoff formula, which we can then use to derive the risk-free asset:
the equation gives us a
E mx payoff^
P ;
P ; = E m x (l + R|)] 1 = E m x (l + R|)] + R 1 1 + R
E[m X l], when payoffs are constant
We can also model an assets risk premium similar to the CAPM, where [fy = cov(Rp m) / var(m)]:
E ( R i) – R F =
^
l ^
var(m)
) x
var(m)^ , E(m) ,
Pi,m X Xm
Beta is multiplied by the price of the bad times risk, determined as:
var(m) E(m)
This equation represents the inverse of factor risk (denoted by the negative sign). In short, assets that have a positive payoff in bad times are valuable to hold, leading to high prices and low expected returns.
The equation for expected return can also be modeled as having exposure to the risk-free rate and multiple betas in the SDF model. Each beta represents a different macroeconomic factor, such as inflation, economic growth, the market portfolio, or investment strategy:
E(Ri) Rp + (3^ x E (fj) + (3i 2 x E(f2) + … +
xE(fjc)
Ef f ic ie n t M a r k e t Th e o r y

LO 62.4: Describe multifactor models, and compare and contrast multifactor models to the CAPM.
As mentioned, the CAPM is a single-factor model that looks at the market as the only factor and defines bad times as low returns to the market portfolio. By contrast, multifactor models incorporate other risk factors, including low economic growth, low GDP growth, or low consumption. One of the earliest multifactor models was arbitrage pricing theory (APT), which describes expected returns as a linear function of exposures to common (i.e., macroeconomic) risk factors.
The lessons from multifactor models are similar to the lessons from the CAPM: 1. Diversification is beneficial. In the CAPM, the market removes (diversifies away) idiosyncratic risk. In multifactor models, it is the tradable version of a factor that removes this risk.
2.
Investors have optimal exposures. Each investor has an optimal exposure to the market portfolio (in the CAPM) or to factor risks (in multifactor models).
3. The average investor holds the market portfolio. This is true under both the CAPM and
multifactor models.
4. Exposure to factor risk must be rewarded. In the CAPM, the market factor is priced
in equilibrium. In multifactor models, each factor has a risk premium, assuming no arbitrage or equilibrium.
3. Risk is measured by a beta factor. In the CAPM, an assets risk is measured by its beta. In multifactor models, an assets risk is measured by its factor exposures (i.e., factor betas).
6. Valuable assets have low risk premiums. Assets that have a positive payoff in bad times are attractive, and, therefore, have low risk premiums. In the CAPM, bad times are explicitly defined as low market returns.
P r ic in g Ke r n e l s

LO 62.3: Explain implications of using the CAPM to value assets, including equilibrium and optimal holdings, exposure to factor risk, its treatment of diversification benefits, and shortcomings of the CAPM.
Implications of Using the CAPM
The CAPM holds six important lessons.
Lesson 1: Hold the factor, not the individual asset.
In a CAPM world, stocks are held in proportion to their market capitalization, where the sole factor is the market portfolio. The market portfolio can be constructed by holding many assets, which helps diversify away idiosyncratic (firm-specific) risk, leaving only systematic (market) risk. Individual stocks have risk premiums, which compensate investors for being exposed to the market factor. Market risk affects all investors exposed to the market portfolio.
According to the CAPM, investors do not wish to hold assets in isolation, because diversification improves the risk-return profile of a portfolio. The concept is simple: diversification helps ensure that bad returns from one asset will be offset by the returns of
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other assets that perform well. This also improves Sharpe ratios (i.e., risk premium divided by total risk). Investors continue to diversify until they are left with the market portfolio, which represents the optimal diversified portfolio.
Mean-variance efficient portfolio. Portfolio diversification and Sharpe ratios can be graphically represented by the mean-variance efficient frontier. When investors hold portfolios that combine the risky asset and the risk-free asset, the various risk-return combinations are represented by the capital allocation line (CAL). The risky asset in this case is the mean-variance efficient (MVE) market portfolio, which is efficient because it represents the maximum Sharpe ratio given investors preferences. The specific combination of the risk-free asset and MVE portfolio depends on investors risk aversions.
Figure 1: Capital Allocation Line
Equilibrium. In equilibrium, demand for an asset equals supply, and since under the CAPM all investors hold the risky MVE market portfolio, the market is the factor. For equilibrium to happen, someone must hold the MVE portfolio as the risky asset. If no investor held the risky asset, the risky asset must be overpriced, and its expected return must be too low. This situation cannot represent an equilibrium state. Since under CAPM the expected payoff of an asset remains constant, the assets expected return must increase as its price falls. In equilibrium, the risk factor is the market, and it has a risk premium. The market factor is a function of investor risk aversions and utilities, and risk premiums will not disappear since investors cannot use arbitrage to remove systematic risk.
Lesson 2: Investors have their own optimal factor risk exposures.
Every investor holds the same risky MVE market portfolio, but the proportion in which they hold it differs. Investors hold different combinations of the risk-free asset and the risky portfolio, representing various positions along the CAL.
Lesson 3: The average investor is fully invested in the market.
An investor with an average risk aversion would hold 100% of the risky MVE market portfolio, which represents the tangency point of the MVE frontier and the CAL. The average investors risk aversion is, therefore, the risk aversion of the market.
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Lesson 4: Exposure to factor risk must be rewarded.
When all investors invest in the same risky MVE portfolio, the CAL for an investor is called the capital market line (CML) in equilibrium. The risk premium of the CML depends on an investors risk aversion and the volatility of the market portfolio:
E(Rm ) – R f = ‘fXCT^1
where E(RM) Rp is the market risk premium, 1 is the average investors risk aversion, and cr^ is the market portfolios variance. During volatile market times (e.g., the 20072009 financial crisis), equity prices typically fall and expected returns increase. In the CAPM world, the risk premium is proportional to the market variance. Because market variance removes all idiosyncratic risk, the remaining systematic risk should be rewarded through the risk premium. When the average investors risk aversion increases, the market risk premium should also increase.
Lesson 5: Risk is measured as beta exposure.
An individual assets risk is measured as factor exposure to the asset, and higher factor exposures to the asset indicate higher expected returns (assuming the risk premium is positive). The risk premium of an individual asset is derived under the CAPM formula using beta pricing to construct the security market line (SML). The formula states that:
E(Ri)-RF
= S ^ m ) x [E(Rm ) – R f ] var(RM)

Pi x [E(Rm ) ~ ^ f
where Ri is the individual stocks return, Rp is the risk-free rate, and beta is a function of the market variance and the assets co-movement with the market: [pi = cov(Rj, RM) / var(RM)]. Higher co-movements denote higher betas, which correspond to higher risk premiums. Whereas previously we looked at systematic risk and diversification, beta looks at idiosyncratic risk and the lack of diversification.
Higher betas imply lower diversification benefits. Investors tend to find high betas (high sensitivities to market returns) unattractive, and, therefore, want to be compensated with higher expected returns. On the other hand, low beta assets are valuable because they do comparatively well when markets perform poorly, offering significant diversification benefits. During the financial crisis, certain assets (safe havens like gold and government bonds) became so attractive that they had negative expected returns. This meant investors actually paid to hold these assets!
Lesson 6: Valuable assets have low risk premiums.
The CAPM risk premium represents the reward investors receive for holding the asset in bad times. Since the market portfolio is the risk factor, bad times indicate low market returns. Assets that have losses during periods of low market returns have high betas, which
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indicates they are risky and, therefore, should have high risk premiums. Low beta assets have positive payoffs when the market performs poorly, making them valuable to investors. As a result, investors do not require high risk premiums to hold these assets.
Shortcomings of the CAPM
The CAPM makes several simplifying assumptions that are necessary to make the model work; however, many of these assumptions are considered overly simplistic or not reflective of the real world. The assumptions of the CAPM break down especially in illiquid, inefficient markets where information may be costly and not available to all investors. We look at seven of these assumptions: 1.
Investors only have financial wealth. Investors have unique income streams and liabilities. Liabilities are often denominated in real terms, and income streams are risky because incomes decline during periods of low economic growth. As a result, both inflation and income growth are important factors. In general, investors have many factors that contribute to wealth, including human capital (or labor income risk).
2.
3.
4.
Investors have mean-variance utility. Mean-variance utility assumes a symmetric treatment of risk. In reality, investors have an asymmetric view of risk, disliking losses more than they like gains, which deviates from the CAPM assumptions. Therefore, in the real world, stocks exhibit different levels of downside risks. Those with higher downside risks should offer higher returns.
Investors have a single period investment horizon. While not a main assumption of the CAPM, a single period restriction does not hold in the real world. In the CAPM, all investors hold the market portfolio, which does not require rebalancing. However, the optimal strategy for long-term investors is to rebalance, which is a multi-period strategy.
Investors have homogeneous (identical) expectations. The assumption that all investors share the same expectations is not realistic in the real world, because investors have heterogeneous (differing) expectations. This can produce significant departures from the CAPM.
3. Markets are frictionless (no taxes or transaction costs). We all know that taxes and
transaction costs affect investor returns; therefore, the CAPM assumption of frictionless markets does not hold in the real world. For illiquid securities, transaction costs can be very high, further heightening the deviations from the CAPM. In addition, investors have heterogeneous beliefs, but they may not be able to fully act on differing expectations if there are trading restrictions (e.g., a prohibition on short selling). When this happens, stock prices reflect only the expectations of those who believe stock prices will rise, causing asymmetries in the market. This is a deviation from the CAPM.
6. All investors are price takers. In the real world, investors are often price setters and not price takers. Large (institutional) investors frequently trade on special knowledge, and large trades will often move the market.
7.
Information is free and available to everyone. In reality, information itself can be a factor. Information is often costly and unavailable to certain investors, which is a deviation from the CAPM.
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M u l t if a c t o r M o d e l s