Capital Asset Pricing Model (CAPM)

Learning Outcomes

•Introduction to the Capital Asset Pricing Model (CAPM)

•CAPM Assumptions

•Capital allocation Line. Capital Market Line. Security Market Line

•Beta as a measure of risk

•Arbitrage Pricing Theory (APT)

• How do we calculate the expected return for a risky asset?

• We use the Capital Asset Pricing Model (CAPM).

• CAPM is used to price individual securities or a portfolio.

What is CAPM?

• Key assumptions:

1. There is a risk-free asset.

2. There are risky assets with expected returns, standard deviations of returns, and correlations of returns.

3. An investor can lend or borrow any amount at the risk-free rate.

4. An investor can buy any amount of a risky asset.

CAPM Model Assumptions

• Capital allocation in portfolio theory is how we apportion funds between risk-free and risky assets.

• Capital allocation line charts all combinations of the risk-free and risky asset.

Capital Allocation Line (CAL)

E(R)

Standard Deviation

Risk free Rate

• A portfolio is ‘efficient’ if it maximises the expected level of return for its level of risk.

• The efficient frontier maps all combinations of risky assets, without the risk-free asset.

• By combining a risk-free asset with a portfolio on the efficient frontier, it is possible to construct a super-efficient portfolio, whose risk–return profiles are superior to those of portfolios on the efficient frontier.

Capital Market Line (CML)

E(Rm)

Portfolio Risk

Risk free Rate

S.D.m

Borrowing

LendingEfficient frontier

Super-efficient portfolio

CML = Best possible CAL

Using the risk-free asset, investors who hold the super-efficient portfolio may:

• Leverage their position by shorting the risk-free asset and investing the proceeds in additional holdings in the super-efficient portfolio, or

• Selling some of their holdings in the super-efficient portfolio and investing the proceeds in the risk-free asset.

The resulting portfolios have risk-reward profiles which all fall on the capital market line.

Capital Market Line (CML)

E(Rm)

Portfolio Risk

Risk free Rate

S.D.m

Borrowing

LendingEfficient frontier

Super-efficient portfolio

CML = Best possible CAL

• The security market line (SML) is derived from the CML.

• The CML determines the risk or return for efficient portfolios.

• The SML demonstrates the risk or return for individual stocks.

• The SML considers only systematic risk (beta).

• The CML considers total risk – standard deviation (σ).

Securities Market Line

β1.0

x

Securities Market Line

E(Rm)

xalpha

Rf

Market Portfolio

•The Capital Market Line defines efficient portfolios.

•The Security Market Line defines both efficient and non-efficient portfolios.

•SML measures risk through beta which shows a security’s contribution to risk for a portfolio.

Security Market Line

β1.0

x

Securities Market Line

E(Rm)

xalpha

Rf

Market Portfolio

• The Capital Asset Pricing Model calculates the expected return for a risky asset.

Return = rf +β(rm-rf)

• rf – Returns from Risk free investments

• β – Proportion of funds invested in the market portfolio

• Rm – Expected returns from investing in the market portfolio

CAPM Model

Key takeaways: • Investments lying below the

SML - overvalued

• Investments lying above the SML - undervalued

• Investments on the line are correctly priced

• For higher return, must increase risk (β)

Security Market Line

β1.0

x

Securities Market Line

E(Rm)

xalpha

Rf

Market Portfolio

• Beta is a measure of sensitivity of an asset to a change in the market.

• The beta sign may be (+/-) depending on how the asset return moves in relation to the market.

Interpreting Beta

Interpreting Beta

β>1 • Investment moves in same direction as

market but to greater extent

β=1 • Investment moves in same direction as

market and to same extent

β=0 • Investment is uncorrelated with market

– risk free

β<0 • Investment moves in opposite direction

to market

σs = σiCorimSystematic risk is the correlation of total risk between asset and market

Beta is a proportion of market portfolio risk we are willing to invest

Beta is the covariance of the market and asset divided by the variance of the market

β = σs σm

σi σmCorim σ2m

Calculating Beta

If the risk-free rate is 6%, the market is expected to return 14%, what return would a diversified investor require from an investment with a β of:

A. 0 B. 0.5 C. 1.0 D. 1.5

Example: CAPM

•Investors are rational and risk averse

•Investors are fully diversified – only consider systematic risk

•Capital markets are in equilibrium and have perfect information

•No transaction costs

•Can borrow and lend at the risk free rate

•Rate of return is only valid as long as its inputs are valid

•Difficult to estimate beta

•Only considers fully diversified portfolios

Assumptions Limitations

Assumptions & Limitations of CAPM

•APT is an alternative pricing theory to CAPM that considers several factors when calculating expected return, not only risk premium (rm-rf) as in CAPM

CAPM: r = rf + βF

APT: r = rf + b1F1 + b2F2 + b3F3...

Arbitrage Pricing Theory (APT)

•Construct portfolios with selected sensitivities to certain of the factors.

•Manage the portfolio to its strengths, optimising sensitivity to the factors that we can predict.

•Protect the portfolio against unpredictable factors.

APT confers the ability to construct a new portfolio with any level of sensitivity to each of the factors.

Arbitrage Pricing Theory (APT)

• Investors are rational and risk averse

• Markets are efficient, no transaction costs to permit arbitrage

• Factors that are sensitive are uncorrelated

• APT does not specify the factors to use

• Need to determine beta of each factor and their stability

• May be difficult to construct a pure factor portfolio

LimitationsAssumptions

Arbitrage Pricing Theory (APT)

• The objective in portfolio management is to maximise expected return given a level of risk.

• The Capital Asset Pricing Model calculates the expected return for a risky asset.

• Beta is a measure of sensitivity of an asset to a change in the market.

• Arbitrage Pricing Theory looks at several factors instead of only risk premium in calculate expected return.

• CAPM and APT models of expected return incorporate a number of assumptions and limitations.

Recap