The CAPM

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Project 5: A Simple Model in Asset Pricing

Jonathan K. Ramani

Overview

This project introduces and explains the Capital Asset Pricing Model (CAPM) — a fundamental framework in financial economics used to understand the relationship between risk and expected return. CAPM provides a simple but powerful formula to price risky securities and is widely used by investors and financial analysts.

What is CAPM?

The Capital Asset Pricing Model states that the expected return of a security is equal to the risk-free rate plus a risk premium:

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

Where:

  • $E(R_i)$: Expected return of asset i
  • $R_f$: Risk-free rate
  • $\beta_i$: Beta of the asset
  • $E(R_m)$: Expected return of the market portfolio

CAPM Expected Return (Julia)

function capm_expected_return(Rf::Float64, Rm::Float64, beta::Float64)
    return Rf + beta * (Rm - Rf)
end

Rf = 0.03
Rm = 0.09
betas = [0.8, 1.0, 1.2, 1.5]

expected_returns = [capm_expected_return(Rf, Rm, b) for b in betas]
println(expected_returns)

Estimating Beta (OLS)

using CSV, DataFrames, GLM

df = CSV.read("returns.csv", DataFrame)
df.asset_excess = df.asset_return .- df.rf
df.market_excess = df.market_return .- df.rf

model = lm(@formula(asset_excess ~ market_excess), df)
println(coef(model))

Last updated: June 2025

References