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Michael Brenndoerfer

Capital Market Theory - CAPM and the Efficient Frontier › The Security Market Line

Michael BrenndoerferDecember 14, 20255 min read

Quantitative FinanceAll chapters

Part 9 of 15Portfolio Theory and Investment Analysis

Chapter 47Capital Market Theory - CAPM and the Efficient Frontier › The Security Market Line

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While the Capital Market Line describes the risk-return relationship for efficient portfolios, the Security Market Line (SML) describes the relationship for all individual assets and portfolios, efficient or not. The difference is the set of investments each line describes. The CML tells us about portfolios that combine the risk-free asset with the market portfolio. The SML tells us about any asset, regardless of whether it is efficiently priced or part of an optimal portfolio.

Security Market Line

The Security Market Line shows the linear relationship between expected return and systematic risk (beta) for all assets in equilibrium. Its equation is the CAPM formula:

E[R_i] = R_f + \beta_i (E[R_M] - R_f)

where:

$E[R_i]$ : required/expected return on asset $i$
$R_f$ : risk-free rate of return
$\beta_i$ : systematic risk of asset $i$
$E[R_M]$ : expected return of the market portfolio
$E[R_M] - R_f$ : market risk premium

The key difference between the CML and SML lies in the risk measure used:

CML uses total risk (standard deviation $\sigma$ ) and applies only to efficient portfolios
SML uses systematic risk (beta $\beta$ ) and applies to all assets and portfolios

This difference reflects a fundamental insight. For efficient portfolios, which have no idiosyncratic risk, total risk and systematic risk are proportional. But for individual assets or inefficient portfolios, total risk includes both systematic and idiosyncratic components. Only the systematic component determines expected return, so beta is the appropriate risk measure for pricing individual securities.

The intuition behind the SML is powerful: since unsystematic risk can be diversified away at no cost, investors should not expect compensation for bearing it. The market only compensates investors for systematic risk exposure. An asset's expected return depends solely on its beta, not on its total volatility. Two assets with identical betas should have identical expected returns, even if one has much higher total volatility due to idiosyncratic risk.

The term $E[R_M] - R_f$ is called the market risk premium or equity risk premium. It represents the extra return investors demand for holding the risky market portfolio instead of the risk-free asset. Historical estimates for the U.S. market range from 4% to 8% annually, though this is subject to considerable debate. The market risk premium reflects our aggregate risk aversion, as a more risk-averse investor population would demand a higher premium for bearing market risk.

The SML equation provides a benchmark for evaluating any investment. If an asset's expected return exceeds the SML prediction given its beta, it offers more return than required for its risk level, making it attractive. If an asset's expected return falls below the SML prediction, it fails to compensate adequately for its systematic risk and should be avoided or sold.

In[12]:

Code

import numpy as np

# Create SML plot with assets
rf_sml = 0.03
market_premium = 0.06  # 6% market risk premium
market_return_sml = rf_sml + market_premium

# Generate hypothetical assets
np.random.seed(789)
n_assets_sml = 25
asset_betas = np.random.uniform(0, 2, n_assets_sml)
# True expected returns from CAPM
capm_expected = rf_sml + asset_betas * market_premium
# Actual returns with some noise (representing estimation error or mispricing)
actual_returns = capm_expected + np.random.normal(0, 0.015, n_assets_sml)

# SML line
sml_betas = np.linspace(0, 2.2, 100)
sml_returns = rf_sml + sml_betas * market_premium

The Security Market Line visualizes this relationship, helping us identify undervalued and overvalued assets.

Out[13]:

Visualization

Scatter plot of assets above and below the Security Market Line, with distinct markers for positive and negative alpha. — The Security Market Line (SML) displays the equilibrium relationship between systematic risk (beta) and expected return. Assets above the SML have positive alpha and returns above the level required for their risk; assets below it have negative alpha.

The chart visually distinguishes between properly priced, undervalued, and overvalued assets. Assets lying on the SML are in equilibrium, while those above the line offer returns superior to CAPM predictions (positive alpha), and those below fail to compensate adequately for their systematic risk. The vertical distance from each asset to the line represents the magnitude of its mispricing. You would seek to buy assets above the line and sell or avoid assets below it.