RSM332 Lesson 9

Beta

how much more or less risky an asset is compared to the market

(Beta) β = 0

If β = 0, the asset has no market-related risk; E(R) = Rf

Beta = 1

If β = 1, the asset has the same risk as the market and earns the market return. E(R) = E(Rm)

Beta > 1

If β > 1, the asset is more volatile than the market and should earn higher expected returns. E(R) > E(Rm)

Can beta be negative?

Yes. A negative beta means the asset moves opposite to the market and should earn a return BELOW Rf

Think of this as INSURANCE against risk. we PAY for this insurance (or demand less return in exchange for less risk)

Systematic Risk (Market Risk)

Risk that cannot be diversified away; driven by macroeconomic forces. Only this risk is rewarded in CAPM

Idiosyncratic Risk (Firm-Specific Risk)

Risk unique to a company that is uncorrelated with the market. It can be diversified away, so investors are not compensated for bearing it.

Orthogonality of Idiosyncratic Risk

Idiosyncratic risk is "orthogonal" to the market, meaning it doesnt move AT ALL with the market.

ie. Cov(εi, Rm) = 0.

It has NO effect on beta or expected return. Complete randomness

Market Risk Premium AND give formula

The additional return investors demand for holding the market portfolio:

E(RM) − Rf

Security Market Line (SML)

A graph of (E(R) on y-axis against BETA (assets risk) on x-axis.

All correctly priced assets lie on the SML.

Mispricing and Alpha

Alpha = Actual return − CAPM expected return. Assets above the SML have positive alpha (underpriced).

Why variance fails for single stocks

Individual variance mixes market risk and idiosyncratic noise. Only market risk affects expected return.

Why idiosyncratic risk is not rewarded

Investors can diversify it away at zero cost, so the market offers no premium for bearing it.

Perfect diversification

When a portfolio holds all risky assets (the market portfolio), idiosyncratic risk is eliminated.

Tangent Portfolio = Market Portfolio (Rm)

In equilibrium, the tangency portfolio becomes the market portfolio because everyone's optimal risky portfolio must equal supply of all risky assets.

Covariance as true risk contribution

Cov(Ri, RM) determines how adding asset i affects portfolio risk. Low or negative covariance provides better diversification.

Lower Correlation = Better Diversification

As correlation decreases, portfolio variance falls. At ρ = −1, perfect diversification is possible.

Beta as Sensitivity

Beta shows how sensitive a stock is to market movements: ΔRi ≈ β ΔRM.

CAPM Interpretation

Beta is the only determinant of required return because only systematic risk is priced.

Risk-Free Asset Role

Provides the intercept of the SML and allows creation of portfolios with any combination of market and risk-free asset.

Slope of SML

Equal to the market risk premium: E(RM) − Rf. Higher slope means higher return for taking market risk.

Why expected return depends only on beta

Expected return compensates investors only for unavoidable market risk; diversifiable risk does not affect pricing.

High SD but Beta = 0

Even with huge volatility (SD), if beta = 0, the asset earns Rf because all volatility is diversifiable and unpriced.

Negative Beta Assets

A negative beta asset hedges the market; investors accept a lower return (even below Rf) for its hedging benefits.

Regression Estimation of Beta

Beta is estimated as the slope in a regression of excess security returns on excess market returns.

R² in Beta Regression

R² shows how much of total risk is market-related. Low R² means most risk is idiosyncratic.

Portfolio Beta

Weighted average of individual betas. Determines portfolio expected return under CAPM.

SML vs. CML

The CML uses SD as a measure of risk and applies only to efficient portfolios; the SML uses beta as a measure of risk and applies to all assets

Roll's Critique

We cannot observe the true market portfolio, so CAPM cannot be empirically tested in a clean way.

Efficient Portfolio

Any portfolio that contains all risky assets in market proportions; lies on the CML and has no idiosyncratic risk.

Only systematic risk is rewarded in _________

CAPM

Idiosyncratic risk is NOT rewarded in _________

CAPM

In CAPM, only _________ determines required return

Beta

_____________ implies that every asset must be priced that it falls exactly on the SML

CAPM

difference between SML and CML

only portfolios containing Rf and M fall on the CML.

ALL assets and ALL portfolios fall on the SML

Stocks (or securities) that have a higher covariance with the market portfolio, will be considered _________ risky

MORE

Takeaway of CAPM

stocks (or individual securities) that have high covariance with mkt portfolio will be considered as MORE risky

What is the slope of the SML

Slope = Market Risk Premium (MRP)

CAPM use the _____________ portfolio as a reference portfolio or benchmark

reference portfolio

"market risk" is also called _______________ risk

systemic

Total risk formula

Total risk = market risk + idiosyncratic risk

If CoviM = VarM.... that means

asset has the same risk as the market

if CoviM > VarM.... that means

asset has more risk then the market

if CoviM < VarM.... that means

asset has less risk then the market

Security Market Line (SML) graphs __________ assets

RISKY

The y-int of the SML is the _____________

Rf (Risk-free rate)

Beta = 0

MRP formula

Slope = E(RM) - Rf

Under SML, Rf = MRP for all assets... but the only difference is ________

Beta

Higher Beta (B) is associated with higher ___________

return

CAPM is commonly used to estimate the cost of ________ used in DDM/DCF

equity

Returns that are difference from the CAPM expectation (ie. are not falling on the SML), are called _________

Alpha

Alpha measures...

how much a portfolio or asset outperformed (or underperformed) the return predicted by CAPM