Understanding Capital Asset Pricing Model (CAPM), the formula for CAPM with examples.
The capital asset pricing model (CAPM) is a financial model used to calculate the relationship between expected returns as well as the risk of investing in specific stocks or securities. The idea behind the CAPM is that investors demand an additional expected return (also known as risk premium) when asked to accept additional risk above that found in a risk-free asset (for example, T-bills). The CAPM originated from the Nobel Prize-winning studies of Harry Markowitz, James Tobin, and William Sharpe.
Capital Asset Pricing Model or CAPM is based on the premise that equity investors need to be compensated for their assumption of systematic risk in the form of a risk premium, or the amount of market return in excess of a stated risk-free rate. A proper assessment of the capital asset pricing model require a clear understanding of both systematic and unsystematic risk.
Systematic risk is the risk related to the overall market, which is also known as non-diversifiable risk. A company’s level of systematic risk depends on the covariance of its share price with movements in the overall market, as measured by its beta (β).
Unsystematic or “specific” risk is the company- or sector-specific and can be avoided through diversification. Hence, equity investors are not compensated for it (in the form of a premium). As a general rule, the smaller the company and the more specified its product offering, the higher its unsystematic risk.
The CAPM formula is:
K_{e} = R_{f} + ß * (R_{m} – R_{f})
Where:
Example
From the assumptions given below, calculate the required rate of return (K_{e}) on ABC Co’s common stocks:
Answer
The required rate of return ABC Co’s common stocks:
K_{e} of ABC Co = 2.93% + 1.10 x (8.35%-2.83%) = 8.89%
The CAPM formula with the company-specific risk premium- alpha (α) is given below
K_{e} = R_{f} + ß * (R_{m} – R_{f}) + α
Where:
Example
From the assumptions given below, calculate the required rate of return (K_{e}) on ABC Co’s common stocks:
Answer
K_{e} of ABC Co = 2.93% + 1.10 x (8.35%-2.83%) + 5% = 13.89%
The risk-free rate (R_{f}) is the expected rate of return obtained by investing in a “riskless” security. U.S. government securities such as T-bills, T-notes, and T-bonds are accepted by the market as “risk-free” because they are backed by the full faith of the U.S. federal government. Interpolated yields¹ for government securities can be located on Bloomberg 18 as well as the U.S. Department of Treasury website, among others.
The market risk premium (Rm – Rf) is the spread of the expected market return over the risk-free rate. Finance professionals, as well as academics, often differ over which historical time period is most relevant for observing the market risk premium. Some believe that more recent periods, such as the last ten years or the post-World War II era are more appropriate, while others prefer to examine the pre-Great Depression era to the present.
Beta (ß) is a measure of the market risk, or the systematic risk, of a security. A security with a large beta will have large swings in its price in relation to the changes in the market index. This will lead to a higher standard deviation in the returns of the security, which will indicate a greater uncertainty about the future performance of the security.
Beta is a measure of the covariance between the rate of return on a company’s stock and the overall market return (systematic risk), with the S&P 500 traditionally used as a proxy for the market. As the S&P 500 has a beta of 1.0, a stock with a beta of 1.0 should have an expected return equal to that of the market. A stock with a beta of less than 1.0 has a lower systematic risk than the market, and a stock with a beta greater than 1.0 has a higher systematic risk. Mathematically, this is captured in the CAPM, with a higher beta stock exhibiting a higher cost of equity; and vice versa for lower beta stocks.
Draw a diagram with the β of various securities along the X-axis and their expected return along the Y-axis. It was already noticed that β is a linear measure of risk. If we assume that a linear relationship exists between the risk and return, then only two points are sufficient to draw a straight line in this diagram. The line, representing the relationship between risk and expected return, is called the security market line. Under equilibrium conditions, all other securities will also lie along this line. Higher β securities will have a correspondingly higher expected return.
A public company’s historical beta may be sourced from financial information resources such as Bloomberg via function: BETA<GO>. Recent historical equity returns (i.e., over the previous two to five years), however, may not be a reliable indicator of future returns. Therefore, many bankers prefer to use a predicted beta such as the Bloomberg “Adjusted Beta” whenever possible as it is meant to be forward-looking.
The exercise of calculating WACC for a private company involves deriving beta from a group of publicly traded peer companies that may or may not have similar capital structures to one another or the target. To neutralize the effects of different capital structures (i.e., remove the influence of leverage), the banker must unlever the beta for each company in the peer group to achieve the asset beta (“unlevered beta”).
After calculating the unlevered beta for each company, the banker determines the average unlevered beta for the peer group. This average unlevered beta is then relevered using the company’s target capital structure and marginal tax rate.
The concept of a size premium is based on empirical evidence suggesting that smaller-sized companies are riskier and, therefore, should have a higher cost of equity. This phenomenon, which to some degree contradicts the CAPM, relies on the notion that smaller companies’ risk is not entirely captured in their betas given the limited trading volumes of their stock, making covariance calculations inexact. Therefore, the banker may choose to add a size premium to the CAPM formula for smaller companies to account for the perceived higher risk and, therefore, expected higher return. Ibbotson provides size premia for companies based on their market capitalization, tiered in deciles.
CAPM formula adjusted for Size Premium
K_{e} = R_{f} + ß * (R_{m} – R_{f}) + SP
Where: SP = Size premium
The Capital Asset Pricing Model is a fundamental contribution to our understanding of the determinants of asset prices. The CAPM tells us that ownership of assets by diversified investors lowers their expected returns and raises their prices. Moreover, investors who hold undiversified portfolios are likely to be taking risks for which they are not being rewarded.
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