CAPM Notes PDF

CAPM Describing the relationship between systematic (market) risk and the return for a given asset (typically a stock), the CAPM states that the expected return on an asset depends on two things only: the risk-free rate and a (beta-adjusted) market risk premium. The CAPM rests on a number of assumpt...

CAPM Describing the relationship between systematic (market) risk and the return for a given asset (typically a stock), the CAPM states that the expected return on an asset depends on two things only: the risk-free rate and a (beta-adjusted) market risk premium. The CAPM rests on a number of assumptions, perhaps the most important of which are: all investors share share the same input list of assets - i.e., they define the market in the same way investors are mean-variance efficient - i.e, they construct their portfolios to maximize the excess return per unit of risk. 𝑅f= is the risk-free rate of return ERM: the expected return on the market portfolio (or "the market return" for short) B equals the beta for asset i, when taken as a whole, equals the Market Risk Premium 1) Risk Free Rate The risk-free rate of return is just what it sounds like: it is the rate of return an investor will receive for investing in an asset whose returns are known with certainty. Strictly speaking, for an asset to be considered risk-free it must meet the following conditions: There can be no default risk There can be no uncertainty about reinvestment rates. (For instance, if the risk-free asset - typically a bond - pays a coupon, there can be no uncertainty about the rate at which those coupon payments are reinvested.) In practice however, satisfying the second condition would require using a different risk-free rate, and calculating a different expected return, for every reinvestment period. The Market Return The expected return on the market portfolio is perhaps the most subjective input required by the CAPM. In theory, because every investor has a different risk tolerance, the market risk premium - and, by extension, the expected return on the market portfolio - should be a weighted average of the risk premiums of all the market participants (where the weights are based on the amount each participant has invested in the market.) In practice, there is no perfect way to calculate such an average. For this reason, to estimate an expected return on the market portfolio we can use one of three approaches: Survey Premiums Here, the idea is to conduct a survey of (what one hopes) are especially knowledgeable market participants - i.e. Fund Managers, CFOs, academics, etc. The downside to this approach is its subjectivity; different groups will rarely report the same expectations. Historical Premiums This is the most common approach to estimating the expected return on the market portfolio. Here, the premium is taken to be the difference between the average return on stocks and the average return on a risk-free asset over an extended period of time. By taking this approach we implicitly assume: 1. The risk aversion of investors has not changed over time in any systematic way 2. The average riskiness of the portfolio has not changed in any systematic way. In addition, our answer will depend on a number of subjective decisions including the length of the time period used and our choice of a risk free asset. Implied Premiums The final approach is to calculate an implied premium - in essence, the present value of dividends paid by the market portfolio growing at a constant rate:  2) Beta In the simplest terms, it is a measure of a stock’s sensitivity to movements in the market. In the numerator we have the covariance between the return on stock and the returns on the market portfolio. On its own, this measure tells us nothing about how this stock compares to the riskiness of the average asset. To fix this, we standardize this value by dividing by the variance of the market portfolio Beta is also defined as the slope of the regression line when we regress the returns of the stock against the returns of the market portfolio. For this number to have meaning however, we need to be specific about what we mean by return and market. Specifically, we need to specify: a time span a sampling frequency a proxy for the market For instance, we could calculate a years' worth of daily returns, two years' worth of monthly returns, five years' worth of quarterly returns, etc. Defining The Market In theory, the market portfolio should include all tradable assets - stocks, bonds, real estate, etc. In practice, we typically limit ourselves to stocks, and even then, we only use a representative sample. We use this sample as our proxy for the market. Here we’ll be choosing from two different proxies: The S&P 500 The CRSP US Total Market Index - basically the whole stock market As seen above, there are several values of note produced when performing a regression: Alpha (𝛼) - Technically this is the y-intercept of the regression line. In finance, this is taken to be a measure of the stock’s performance, where the higher the alpha, the better the stock performs (at least when measured against the expectations of the CAPM). Beta (𝛽) - The slope of the regression line. R-Squared (𝑅2) - Statistically speaking, this is a measure of the goodness of fit. In Finance, we interpret this as the measure of risk (variance) that can be attributed to the market. The remainder is therefore firm-specific risk. Recall that beta measures the volatility of an individual stock in relation to the systematic risk of the entire market. To see what this means in practice, consider the following scenarios: 𝛽 = 1 - when beta equals 1 the stock is no more or less volatile than the market as a whole. 𝛽 > 1 - when beta is greater than 1, the stock is more volatile than the market as a whole. For instance, if the beta is 1.3, the stock is said to be 30% more volatile than the market. 𝛽 < 1 - when beta is less than 1 (but still greater than zero) the stock is less volatile than the market as a whole. For instance, if the beta is 0.5, the stock experiences only 50% of the market’s volatility. 𝛽= -1 - A beta of negative 1 means the stock is perfectly inversely correlated with the market; if the market goes up, the stock will go down by an equal amount. There are two other values to take note of:  By definition, the beta of the market portfolio itself is 1. The beta of a risk-free asset is 0. This makes sense because, again by definition, a risk-free asset has no relation at all to the volatility of the market. Excess return When stated in this form, the CAPM predicts the total return of the stock. We can also write the CAPM in terms of its excess return - the return predicted by the CAPM in excess of the risk free rate. Notice that, unlike the capital market line, the SML plots the return on a stock against its sensitivity to market risk, 𝛽, not it's total risk, 𝜎