Chapter 12-13 Slides PDF

Chapter 12/13 Lessons from Market History, Risk and Return In these chapters… Chapter 12 Understand returns Understand risk Risk/return relationship and market efficiency Chapter 13 Types of risk: systematic versus unsystematic Portfolio management and diversification  Chapte...

Chapter 12/13 Lessons from Market History, Risk and Return In these chapters… Chapter 12 Understand returns Understand risk Risk/return relationship and market efficiency Chapter 13 Types of risk: systematic versus unsystematic Portfolio management and diversification  Chapter 12 Some Lessons from Capital Market History Returns The total return on your investment comes in two forms: 1. Capital gain – price change of the asset 2. Income – cash distributions in the form of dividends The trillion dollar question is how can we predict stock returns? A good starting point is establishing whether there exists a positive relationship between risk and return. If so, then the risk of the asset will reflect its expected return. Overview Return-based concepts: Dollar return ($, per year) Percentage return (%, per year) Holding period return (%, multiple years) Calculating average returns: arithmetic vs geometric “Expected” return (also called “required” return) Expected return = Risk-free rate + Risk premium Dollar returns Definition: The total dollar amount of return. It equals the rate of return multiplied by the dollar amount invested. E.g., a 10% return on a $100 investment equals a $10 dollar return. The 10% consists of capital gain and/or income components. E.g., a stock has an 8% capital gain and 2% dividend yield. On the $100 investment, the capital gain is $8 Example The investment amount is $37. This is the purchase price. The return comes in the form of both capital gain and income. The asset is sold for $40.33. The difference is $3.33 (=40.33-37). Plus, the dividend received was $1.85. That makes the total dollar return equal to $5.18. On a percentage basis, this amounts to 14% (=5.18/37 x 100%). Percentage return The total percentage return scales the dollar return by the beginning price Dividend yield = income received / beginning price Generally quoted on an annual basis. Can be based on past dividends paid or future dividend estimates Capital gains yield = (ending price – beginning price) / beginning price The percentage price change of the stock Example 1 Last year you bought a stock for $35. During the year, you received dividends of $1.25. Today, the stock is now selling for $40.  What is your dollar return? Dollar return = 1.25 + (40 – 35) = $6.25  What is your percentage return? Dividend yield = 1.25 / 35 = 3.57% Capital gains yield = (40 – 35) / 35 = 14.29% Total percentage return = 3.57% + 14.29% = 17.86% Example 2 Last year you bought 100 shares of stock for $45 per share, totaling $4500. Over the past year, you received dividends of $0.27 per share. The stock is now selling for $48.  What is your percentage return? Dividend yield = $0.27 / $45 = 0.60% Capital gains yield = ($48 – $45) / $45 = 6.67% Total percentage return = 0.60% + 6.67% = 7.27%  What is your dollar return? Dollar return = $27 + ($4800 – $4500) = $327 Dollar Return: $27 $327 gain $300 Time 0 1 Percentage Return: $327 –$4,500 7.3% = $4,500 Holding period return The holding period return is the return an investor would receive when holding an investment over a period over n years. The return in each year is specified as R1, R2, … HPR = (1 + R1) × (1 + R2) × …× (1 + Rn) – 1 Holding period return Suppose your investment provides the following returns over a four-year period: Your holding period return  (1 R1 ) (1 R2 ) (1 R3 ) (1 R4 )  1 (1.10) (.95) (1.20) (1.15)  1 .4421 44.21%  Average annual returns How do you compute the yearly average of a series of returns over multiple years? There are two approaches: 1. Arithmetic average Return earned in an average period (computed as the simple average) 2. Geometric average Compound return earned per period (representative of cumulative return) Average annual returns Suppose we have the following set of returns for years 1, 2, and 3: 5%, -3%, 12% Compute the arithmetic and geometric averages: Arithmetic average = (5 + (–3) + 12)/3 = 4.67% Geometric average = [(1+.05)*(1-.03)*(1+.12)]1/3 – 1 =.0449 = 4.49% Why are the different? Note that with the geometric average, each one builds on the last. It captures the cumulative effect. On a practical note The income portion of the return is realized immediately as dividends are paid. They must be reinvested (not necessarily in the same stock). Commonly used in retirement income. The capital gains portion is not realized until the investor sells the stock. Another practical note Financial markets play matchmaker: Investors seek to increase their wealth and companies need capital to fund their projects. The more that investors feel comfortable providing capital to financial markets, the more funds that are available for corporate investment. This is why corporate governance is important The more information that investors have about companies, the better and more informed decisions the investors can make. This is why disclosure requirements are important The return that investors receive for providing capital is the cost that companies incur for raising the capital. Investment Average Return Large Stocks 12.1% Small Stocks 16.9% Long-term Corporate 6.3% Bonds Long-term Government 5.9% Bonds U.S. Treasury Bills 3.5% Inflation 3.0% “In the short run, however, stock returns are very volatile, driven by changes in earnings, interest rates, risk, and uncertainty, as well as psychological factors, such as optimism and pessimism as well as fear and greed.” - Jeremy J. Siegel Source: Jeremy J Siegel, Stocks for the Long Run Expected return The return an investor is expected to receive. The expected return is theoretically positively related to risk. Investors require additional return to be enticed to buy riskier assets. Note: Developing a return expectation that aligns with realized returns is what many active investors try to achieve. For example, active portfolio managers seek to build portfolios that produce high returns over the long term. Risk premium The extra return earned for taking risk. Expected return = Risk-free rate + Risk premium Risk-free rate: Treasury bills (T-bills) are estimated to have zero risk and are commonly used as a baseline for other assets in the market.  Investment Average Return Risk Premium Large Stocks 12.1% 8.6% Small Stocks 16.9% 13.4% Long-term Corporate 6.3% 2.8% Bonds Long-term Government 5.9% 2.4% Bonds U.S. Treasury Bills 3.5% 0.0% The risk premium is found using this formula: Expected return = risk-free rate + risk premium Inflation Inflation = Loss of buying power To earn a positive real return, you must earn a rate of return that is greater than the rate of inflation. The T-bill rate loosely follows the inflation rate (compare the bottom graph to the top graph). Distribution of yearly stock market returns As of Aug 6, 2019 Year-by-year return on large stocks Year-by-year return on small stocks Notice that the returns on small stocks are more exaggerated. The ups are higher and the downs are lower. Explaining the risk premium: What does the data say? Various Dimensions of Expected Returns Market Equity premium—stocks vs. bonds Academic research has identified these equity and Company Size EQUITIES Small cap premium—small vs. large companies Relative Price1 fixed income dimensions, Value premium—value vs. growth companies which point to differences Profitability2 Profitability premium—high vs. low profitability companies in expected returns. Term These dimensions are Term premium—longer vs. shorter maturity bonds INCOME pervasive, persistent, and FIXED Credit Credit premium—lower vs. higher credit quality bonds robust and can be pursued in cost-effective portfolios. Thought-provoking questions Why don’t investors only buy small stocks since they provide the highest returns? Why even bother with the low returns of T-bills? Which asset class do you expect to perform the worst during a financial market downturn? How many years did the T-bill portfolio generate negative returns? What about the large and small stock portfolios? Estimating risk How do we measure risk? And how do we assign a risk premium? There are quantitative and qualitative approaches. We will discuss the most traditional method of using basic statistics, namely, the normal distribution. Risk = standard deviation In this context, risk is called volatility (σ) e normal distribution is defined by its mean and standard deviatio Which stock is riskier? Red or blue?  Stock Returns, 1990-2015: Coca-cola, Exxon-Mobil, and General Electric Is there a correlation between average return of an asset class and its standard deviation of returns? Yes, it is highly positive! This means that over the long-term investors can expect to earn higher returns when taking greater risk. The goal of portfolio managers is to construct a portfolio with the maximum amount of return given a particular Means and Standard Deviations of Annual Returns by Asset Class, 1926–2015 Average stock market risk premiums across countries Volatility in recent years: 08-09 financial crisis 2008 was one of the worst years for stock market investors in history  The S&P 500 plunged 37 percent  The index lost 17% in October alone From March ‘09 to Feb ‘11, the S&P 500 doubled in value Long-term Treasury bonds gained over 40 percent in 2008  They lost almost 26 percent in 2009 Volatility in recent years: Covid-19 2020 was an interesting year  The S&P 500 fell by more than 35% in roughly a month  The stock market decline was quicker than in 2008  Tech stocks proved to be the most resilient S&P 500 index in dark blue Nasdaq index in light blue Note: While the S&P 500 is diversified, the Nasdaq largely consists of tech- oriented companies Note on the dangers of assuming a normal distribution in stock returns Of interest to researchers lately is how to identify and address “fat tails” in distributions. If you assume returns are normally distributed, then you underestimate very large negative returns! Think of the red curve as your estimate and “Fat tails” in returns of various asset classes  CBOE VIX A forward-looking volatility measure http://www.cboe.com/vix Efficient markets What do we mean by efficient? Common interpretation: Markets are smart and generally get things right. Financial theory: How well does the market use all available information to price assets? Efficient markets “Asset prices fully incorporate all available information.” What does all mean? What does fully mean? Three forms of market efficiency: Weak, Semi-strong, and Strong Interesting questions about market efficiency 1. How quickly is new information captured? Speed of reaction 2. What information is captured? Simple versus complex 3. Is information incorporated correctly? Underreact or overreact 4. Does extraneous information affect prices? Noise Example Suppose the government announces that Boeing will get a large contract to build a fleet of expensive jets. How quickly does the market react? I.e., does it take a day or two for this news to get reflected in Boeing’s stock price? Can you quickly buy in before the stock price increases? Why does this matter? If markets get it right, then there’s no point in trying to “beat” the market. Trading on information events (like earnings announcements) will not be as profitable as you expect Searching for over- or undervalued stocks is a waste of time and money and will not lead to any extra return. Conundrum… How can markets get it right if no one is really trying? Major point: “Efficient markets” depend on competition among investors to outsmart one another. This competition pushes down the reward for being quicker and smarter. It may not be much, but we still expect investors still get compensated to some degree… In other words: Markets are “efficiently inefficient” Good luck trying to outsmart the market… US Equity Mutual Fund Performance The market's pricing power makes it difficult for investors who try to 42% outsmart other participants Survive through stock picking or 19% Outperform market timing. Prior 15 Years 2,711 funds at beginning As evidence, only 19% of US equity mutual funds have survived and outperformed their benchmarks over the past 15 years.  Investors like to chase past performance Do Outperforming US Equity Mutual Funds persist? Some investors select 25% Outperformed 682 funds 28% mutual funds based on past returns. However, funds that have outperformed in the past do 2000–2009 2010–2014 not always persist as 2,711 funds at beginning winners. Past performance alone provides little insight into a fund’s ability to outperform in the future. Question… If you can’t beat the market, can you still earn positive returns in the stock market? Yes! The positive risk-return relationship depends on assets being efficiently priced. Investors get compensated over the long-run for taking on risk. Just don’t expect a free lunch… Taking risk is not always fun. It hurts at the worst possible times. Free lunch: Diversification reduces portfolio risk while maintaining high returns Increasing the number of stocks in your portfolio will decrease the portfolio’s overall standard deviation. Why? Because their individual movements tend to offset and balance each other out. Behavioral finance Prospect Theory: When it comes to losses, people are willing to take much greater risks to avoid losses, even if those risks aren’t compensated by higher payoffs. Two psychology researchers, Kahneman and Tversky, were pioneers in the study of how humans process and assess risk. Behavioral finance Disposition Effect: People dislike losing more than they like winning. Investors hold losers too long and sell winners too quickly. Two finance researchers, Shefrin and Statman, identified this effect among investors. Behavioral finance Emotions related to financial gain versus loss are handled by different parts of the brain. For example: The amygdala processes fear (it takes over, we react even before we know we’re reacting, i.e., fight or flight). Dorsal anterior cingulate cortex and the insula process both physical pain and emotional pain Pleasure is related to the chemical compound Dopamine associated with food, sex, love, money, music, and beauty (addictive drugs also correspond to the release of dopamine) Behavioral finance Our brains have adapted to our environment over thousands of years. E.g., the amygdala is useful when we encounter a bear in the woods. But it may not be well-suited to for making smart financial decisions. E.g., similar to how a shark is an efficient predator in the ocean but very ineffective on land. Application: airplane pilot. Our minds are limited to the amount of information and data we can process. It is very difficult to multi-task! Emotions often drive our decision-making. The color red Stock market prediction Propensity to buy stocks Your emotions often work against you Reactive Investing in a Market Cycle Many people struggle to HIGHER PRICES separate their emotions from investing. Markets Elation go up and down. Reacting to current Optimism market conditions may Optimism Nervousness lead to making poor Fear investment decisions at the worst times. LOWER PRICES  Chapter 13 Risk, Return, and the Security Market Line Expected returns We think of future stock returns in terms of probabilities of possible outcomes. In this context, “expected” means average if the process if repeated many times. We compute our expectation like this: n E ( R )   p i Ri i 1 The “expected” return is a probability-weighted average return Example of probability-weighted averaging Imagine we play a game where you roll six-sided dice to win money: Roll a 1, and you win $1. Roll a 2, and you win $2. Roll a 3, and you win $3. Roll a 4, and you win $4. Roll a 5, and you win $5. Roll a 6, and you win $6. What is the most you would you pay to roll it? Example of probability-weighted averaging The probability of rolling any number is 1/6 We calculate the probability-weighted average: (1/6)x$1 + (1/6)x$2 + (1/6)x$3 + (1/6)x$4 + (1/6)x$5 + (1/6)x$6 = $3.50 You’re “expected” winnings per roll is $3.50. This doesn’t mean you expect to receive $3.50 on every individual roll. In fact, $3.50 isn’t even a single-roll option. It’s an average. Example: expected return Your boss has asked you to calculate the expected returns of AT&T and Verizon. To do this, you first estimate the probability of good and bad market states and then forecast the stock return in each market state. State Probability ATT VZ___ Boom 0.3 0.15 0.25 Normal 0.5 0.10 0.20 Recession 0.2 0.02 0.01 RATT =.3(15) +.5(10) +.2(2) = 9.9% RVZ =.3(25) +.5(20) +.2(1) = 17.7% Note that probabilities always add up to 1 Example: risk Now your boss has asked you to assess the risk of AT&T versus Verizon. To do this, you compute the variance and standard deviation. AT&T  2 =.3(0.15-0.099)2 +.5(0.10-0.099)2 +.2(0.02-0.099)2 = n 0.002029   = 4.50% 2 σ   p (R i 1 i i  E ( R )) 2 Verizon  2 =.3(0.25-0.177)2 +.5(0.20-0.177)2 +.2(0.01-0.177)2 = 0.007441 Try it on your own… Consider the following information: State Probability ABC, Inc. Return Boom.25 15% Normal.50 8% Slowdown.15 4% Recession.10 -3% What is the expected return? Try it on your own… Consider the following information: State Probability ABC, Inc. Return Boom.25 15% Normal.50 8% Slowdown.15 4% Recession.10 -3% What is the expected return? E(r) = 0.25(15%) + 0.5(8%) +.15(4%) +.1(-3%) = 8.05% Portfolio management A portfolio is a collection of assets (e.g., stocks, bonds, etc.). How do an individual asset’s risk and return affect the risk and return of the entire portfolio? Is the portfolio risk and return as simple as the sum of its parts? Let’s calculate portfolio-level return and portfolio-level risk. Calculating portfolio weights Suppose you have a $150,000 portfolio invested in four stocks. Taking a look at your account, you find the following amounts of each stock: $20,000 of stock C $30,000 of stock KO $40,000 of stock INTC $60,000 of stock BP Calculate the relative portfolio weights of the portfolio. Calculating portfolio weights C: 20/150 =.133 = 13.3% KO: 30/150 =.2 = 20% INTC: 40/150 =.267 = 26.7% BP: 60/150 =.4 = 40% Portfolio expected return The portfolio expected return is simply the weighted average expected return of the portfolio constituents. m E ( RP )  w j E ( R j ) j 1 wj = stock j weight in the portfolio E(Rj) = expected return of stock j Portfolio expected return Go back to the previous example and calculate the expected return of the portfolio. C: E(RC) = 19.69% KO: E(RKO) = 5.25% INTC: E(RINTC) = 16.65% BP: E(RBP) = 18.24% E(RP) =.133(19.69%) +.2(5.25%) +.267(16.65%) +.4(18.24%) = 15.41% Portfolio variance Computing the variance or volatility of the portfolio is not as straightforward, but here’s one approach: 1. Compute the portfolio’s expected return in each market state. E(RP) = w1R1 + w2R2 + … + wmRm n 2. Then compute the2 variance and standard deviation of the portfolio.  σ  p i ( R i  E ( R )) i 1 2 Example Suppose that we are equally invested in two stocks, A and B, and we’ve forecasted returns in boom and bust market states. State Probability RA RB RPortfolio Boom.4 30% -5% 12.5% Bust.6 -10% 25% 7.5% What is the expected return of the portfolio? What is the variance and standard deviation of the portfolio? Example Suppose that we are equally invested in two stocks, A and B, and we’ve forecasted returns in boom and bust market states. State Probability RA RB RPortfolio Boom.4 30% -5% 12.5% Bust.6 -10% 25% 7.5% What is the expected return of the portfolio? E(r) = 0.4(12.5%) + 0.6(7.5%) = 9.5% Example Now suppose that you are invested in stocks X and Z. The forecasts during up and down markets are as follows: State Probability X Z Boom.25 15% 10% Normal.60 10% 9% Recession.15 5% 10% What are the expected return and standard deviation for a portfolio with an investment of $6,000 in asset X and $4,000 in asset Z? Example State Prob. Portfolio expected return Boom 0.25 0.6*15% + 0.4*10% = 13% Normal 0.60 0.6*10% + 0.4*9% = 9.6% Recession 0.15 0.6*5% + 0.4*10% = 7% Portfolio expected return = 0.25*13% + 0.60*9.6% + 0.15*7% = 10.06% = 10.06% Portfolio variance = 0.25*(13% – 10.06%)2 + 0.60*(9.6% – 10.06%)2 + 0.15*(7%-10.06%)2 = 0.00036924 Standard deviation = sqrt(variance) = 0.0192156 = 1.92% Understanding portfolio risk Most investors hold a variety of stocks in their portfolio. The cool thing is that their individual movements may cancel each other out. But this depends on how each comoves with the others. The Correlation coefficient measures the relationship between two variables. Correlation can range from -1 to 1, where positive indicates they move in the same direction and negative in opposite directions.  Correlation, positive or negative portfolio combination do you think will have the lowest volat Correlation and portfolio decisions How does this factor into portfolio management decisions? You can reduce portfolio risk by combining assets with the lowest possible correlations!  Example: Combining assets with perfectly positive (X,Z) and negative correlation (X,Y)  Portfolio consisting of US and International stocks Standard deviation of monthly returns 4.8 4.6 4.4 4.2 4 3.8 3.6 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Percentage allocation to International stocks (0% = only US stocks, 100% = only Int'l stocks)  Portfolio consisting of US stocks and Hedge funds originated as private stock momentum strategy investment groups that implement 6 strategies that “hedge” market risk. 5 One way to do this is Volatility of monthly returns by buying a group of 4 stocks you expect to perform well and 3 shorting another group of stocks you 2 expect to perform poorly. 1 Presented here is a 0 generic “momentum” 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% strategy that purchases stocks that Percentage allocation to stock momentum strategy have done well while (0% = only US stocks, 100% = only stock momentum) shorting stocks that have done poorly. Diversification Combining assets with less-than-perfect positive correlation gives you diversification benefits in the form of lower portfolio risk! 1. The lower the correlation between assets, the greater are the diversification benefits. 2. The more assets added to the portfolio, the greater are the diversification benefits.  Diversification: Correlation The top shows the risk/return profile for securities A and B. The bottom shows the resulting overall portfolio standard deviation depending on the correlation between securities A and B. Notice that the lower the correlation between A and B, the lower is the portfolio standard deviation. Diversification: Number of securities As you add stocks to your portfolio, you can lower the standard deviation of your portfolio. IMPORTANT: You reduce the risk of the portfolio without reducing the expected return! Decomposing risk This naturally leads to a decomposition of risk into two types: Systematic Risk – the portion that is common to all stocks and therefore undiversifiable no matter how many securities you own Economy-wide: stock increases in value due to good economy Unsystematic Risk – the portion that is specific to the firm and therefore is diversifiable when you have enough securities in your portfolio Firm-specific: stock decreases in value because of inefficient management  Note that there is a maximum benefit, which The “diversifiable” risk is firm- occurs at around 30 stocks specific and goes away as you add (on average, selecting more firms to your portfolio. stocks at random) The “non-diversifiable” risk is common to all stocks in the economy, so it cannot be diversified away Decomposing risk Total risk = Systematic risk + Unsystematic risk The observed standard deviation of an individual security is a reflection of its total risk. The observed standard deviation of a well-diversified portfolio is a reflection of systematic risk. Fluctuations of the market index reflect systematic risk Decomposing risk Total risk = Systematic risk + Unsystematic risk Observed Economic Firm-specific stock fluctuations Managerial return Business cycle inefficiencies volatility Interest rate risk Product recalls Employee strikes R&D, innovation Which risk matters? Investors are enticed to take additional risk with additional return (a risk premium). To diversified investors, the only risk that matters and gets compensated is systematic risk. Therefore, expected return depends only on systematic risk.  Quantifying this idea with… The Capital Asset Pricing Model (CAPM) The amount of extra return (positive or Expected return on the negative) earned individual security i “Beta”, security i’s regardless of risk-level, sensitivity to the overall this contributes to total market, measure of volatility systematic risk The risk-free rate, i.e., The market return the return on an asset minus the risk-free rate, with zero risk (the CAPM called the “equity risk baseline) premium”, and is common to all firms Understanding What does beta tell us? The firm’s sensitivity to the overall market.  A beta = 1 implies the asset has the same systematic risk as the overall market  A beta < 1 implies the asset has less systematic risk than the overall market  A beta > 1 implies the asset has more systematic risk than the overall market A steeper slope (beta) implies greater sensitivity to the market return. E.g., if the market rises by 10%, by how much do we expect Asset S or Asset R to rise? Quick guide to interpreting beta Identifying total and systematic risk Standard Deviation Beta Security C: 20% 1.25 Security K: 30% 0.95 Which has higher systematic risk? Which has higher total risk? Which security has the higher expected return (according to the CAPM)? Calculating portfolio beta Suppose you own the following stocks: Security Weight Beta C.133 2.685 KO.2 0.195 INTC.267 2.161 BP.4 2.434 What is the portfolio beta? It is the weighted average of the portfolio constituents..133(2.685) +.2(.195) +.267(2.161) +.4(2.434) = 1.947 Which portfolio has greater risk? An investor is considering two allocation alternatives and needs to assess the risk-level of each one. Which one has greater risk? Which portfolio has greater risk? Compute the weighted average portfolio beta for each one: bv = (0.10  1.65) + (0.30  1.00) + (0.20  1.30) + (0.20  1.10) + (0.20  1.25) = 0.165 + 0.300 +0.260 + 0.220 + 0.250 = Portfolio v has a 1.195 ≈ 1.20 higher beta and bw = (0.10 .80) + (0.10  1.00) + (0.20 .65) + therefore greater (0.10 .75) + systematic risk (0.50  1.05) = 0.080 + 0.100 + 0.130 +0.075 + 0.525 = 0.91 Historical risk premiums Treasury bonds Stocks  Security Market Line Estimating a stock’s required return using the CAPM  Security Market Line Estimating a stock’s required return using the CAPM The greater is the beta, the larger will be Asset Z’s risk premium 1.5 x 4% = 6% Computing expected return Given the following betas, risk-free rate of 4.15%, and equity risk premium of 8.5%, compute each security’s expected return. Security Beta Expected Return C 2.685 4.15 + 2.685(8.5) = 26.97% KO 0.195 4.15 + 0.195(8.5) = 5.81% INTC 2.161 4.15 + 2.161(8.5) = 22.52% BP 2.434 4.15 + 2.434(8.5) = 24.84% Quiz yourself Benjamin Corporation, a growing computer software developer, wishes to determine the required return on asset Z, which has a beta of 1.5. The risk-free rate of return is 7%; the return on the market portfolio of assets is 11%. What is the required return for asset Z? Quiz yourself Benjamin Corporation, a growing computer software developer, wishes to determine the required return on asset Z, which has a beta of 1.5. The risk-free rate of return is 7%; the return on the market portfolio of assets is 11%. What is the required return for asset Z? Substituting bZ = 1.5, RF = 7%, and rm = 11% into the CAPM yields a return of: rZ = 7% + [1.5  (11% – 7%)] = 7% + 6% = 13% Empirical evidence of the CAPM The EMH and CAPM were developed in the late 1960s before computers were around to perform complex statistical analysis. It wasn’t until the 1980s that researchers could analyze large complex datasets, and by this time EMH and CAPM had taken hold in industry. In general, researchers found only weak evidence that a stock’s beta is related to realized returns. Furthermore, firm characteristics like size, valuation ratios, profitability, and momentum have explanatory power for future returns above and beyond the stock’s beta. Empirical evidence of the CAPM Reconciling theoretical and empirical factors help us understand what types of risk are compensated Theoretical = risks we expect to get compensated Empirical = risks we observe get compensated E.g., CAPM is strong theoretically but weak empirically Eviden Theory ce Research-based investment decisions What has become popular today is “factor-based investing”, which is evidence-based or research-based Factor-based investing helps an investor avoid taking risk that is not compensated E.g., had you invested $100 in the least volatile stocks in 1970, you would have over $1800 today. However, had you invested $100 in the most volatile stocks, you would have less than $5 today!!! It helps investors identify true risk factors as well as take advantage of mispriced stocks and market mistakes MSCI stock market “factors” The End!