What is a discount rate?

Equity Valuation in R

Cliff Ang

Senior Vice President, Compass Lexecon

Capital Asset Pricing Model (CAPM)

Mathematically, the CAPM is as follows:

$$ E(R_i) = R_f + \beta_i (R_m - R_f) $$

where

$E(R_i)$ is the return on stock i
$R_f$ is the risk-free rate of return
$R_m$ is the market return
$R_m - R_f$ is the equity risk premium (ERP)
$\beta_i$ is the sensitivity of stock i's return to the market return

Beta

Don't put your eggs in one basket
You should always try to reduce firm-specific risk
Investors are only compensated from taking on systematic risk (a/k/a market or undiversifiable risk)
Beta is a measure of systematic risk

Using Regression Analysis to Estimate Beta

Beta is typically estimated using a market model regression of the form:

$$ R_i = \alpha + \beta \times R_m $$

(unlike the CAPM, no risk-free rate in the market model!!!)

where

$\alpha$ and $\beta$ are coefficients generated by the regression
$R_i$ is the return on stock $i$
$R_m$ is the market return

Using Regression Analysis to Estimate Beta

The regression is typically performed using

2 to 5 year estimation period
Weekly or monthly returns

Estimating Beta

# Calculate stock return
rets <- Delt(prices$firm_ret)

# Calculate market return
rets$spy <- Delt(prices$spy)

# Rename first variable
names(rets)[1] <- "firm_ret"

# Remove first observation - NA
rets <- rets[-1, ]

# Run regression
reg <- lm(myl ~ spy, data = rets)

# Extract beta
beta <- summary(reg)$coeff[2]

Let's practice!

Equity Valuation in R