Lesson 4 Redux

What is CAPM and what does it show?

CAPM is a set of predictions concerning equilibrium expected returns on risky assets.

It shows the expected return investors should require for holding a risky asset, given its contribution to market risk.

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Who developed Modern Portfolio Theory, when, and what did it show?

Harry Markowitz developed Modern Portfolio Theory in 1952.

 

It showed that diversification can reduce overall portfolio risk and that efficient frontiers exist.

Who developed CAPM and when?

CAPM was developed by Sharpe, Lintner and Mossin in 1964.

What are the two categories of CAPM assumptions?

Individual behaviour assumptions

2. Market structure assumptions

List and explain the three individual behaviour assumptions of CAPM.

Investors are rational mean-variance optimisers.

They prefer higher expected return and lower variance.

 

2. Investors share a single-period planning horizon.

Everyone invests over the same time period.

 

3. Investors have homogeneous expectations.

They use the same information, expected returns, variances and covariances.

List and explain the four market structure assumptions of CAPM.

. All assets are publicly traded.

 

2. Investors can borrow, lend and short sell at a common risk-free rate.

 

3. There are no taxes.

 

4. There are no transaction costs.

Why are CAPM assumptions useful?

They simplify the model and allow a single market equilibrium to emerge.

What is meant by “all investors optimise their portfolios using the Markowitz model of efficient diversification”?

Each investor uses expected returns, variances and covariances to construct an efficient frontier.

 

They identify the optimal risky portfolio by drawing the tangent CAL to the efficient frontier.

 

Portfolio weights are therefore determined by the Markowitz optimisation process.

 

Why under CAPM do all investors choose the same optimal risky portfolio?

Because all investors have homogeneous expectations, the same investable universe and the same risk-free rate.

 

Therefore, they construct the same efficient frontier, draw the same CAL and identify the same optimal risky portfolio.

 

Why does the market portfolio exist under CAPM?

If all investors choose the same optimal risky portfolio, then the aggregate of all investors’ risky portfolios must also have those same weights.

 

This aggregate portfolio is the market portfolio.

What is the market portfolio?

The market portfolio is the value-weighted portfolio of all risky assets in the investable universe.

What are homogeneous expectations?

Homogeneous expectations mean that all investors have identical expectations about returns, variances and covariances.

Why does the CAL become the CML?

The CAL becomes the CML when the risky portfolio used in the CAL is the market portfolio.

 

Under CAPM, the optimal risky portfolio is the market portfolio, so the CAL based on it is the Capital Market Line.

What is the relationship between the Market Portfolio and the Optimal Risky Portfolio under CAPM?

Under CAPM, the optimal risky portfolio is the market portfolio.

 

Because all investors face identical expectations and the same risk-free rate, they all identify the same optimal risky portfolio.

 

What is meant by a value-weighted portfolio?

A value-weighted portfolio allocates weights according to the market value of each asset relative to the total value of all assets in the portfolio.

 

Larger companies therefore receive larger weights.

What is the key prediction of CAPM regarding investor portfolio choice?

All investors should hold the same risky portfolio (the market portfolio).

 

Differences between investors only affect how much they allocate to the market portfolio versus the risk-free asset.

What is the equation for the Market Risk Premium?

Market Risk Premium = E(rM) − rf

Where:

E(rM) = Expected return on the market portfolio

rf = Risk-free rate

What is the Market Risk Premium?

The Market Risk Premium is the additional return investors require for investing in the market portfolio instead of risk-free assets.

Calculate the Market Risk Premium.

Expected Market Return = 10%

Risk-Free Rate = 3%

Market Risk Premium

= 10% − 3%

= 7%

What is the equation for calculating the proportion allocated to the optimal portfolio M?

y = (E(rM) − rf) / (AσM²)

Where:

y = proportion invested in the market portfolio

A = risk aversion coefficient

σM² = variance of the market portfolio

What is the value of y for the average risky portfolio under CAPM?

y = 1

Because net borrowing and lending across all investors must equal zero.

What is the relationship between market risk premium and risk aversion under CAPM?

Because y = 1:

E(rM) − rf = AσM²

Therefore, the Market Risk Premium is directly proportional to:

• Risk aversion

• Market variance

Why does CAPM assume the appropriate risk premium on an asset is determined by its contribution to the risk of investors' overall portfolios?

Because CAPM assumes investors are already diversified.

Firm-specific risk is therefore irrelevant.

Only market risk matters.

How is risk measured under CAPM?

Risk is measured using Beta.

Beta measures sensitivity to movements in the market portfolio.

What is Beta?

Beta measures the sensitivity of an asset's return to movements in the market portfolio.

When does Beta increase?

Beta increases when covariance with the market increases.

What does Beta = 1 mean?

The asset moves one-for-one with the market.

What does Beta > 1 mean?

The asset is more sensitive to market movements than the market itself.

What does Beta < 1 mean?

The asset is less sensitive to market movements than the market.

What does Beta = 0 mean?

The asset has no systematic relationship with market movements.

What does a negative Beta mean?

The asset tends to move in the opposite direction to the market.

What is the equation for Portfolio Beta?

βP = Σ wiβi

Portfolio beta is the weighted average of the constituent asset betas.

Calculate Portfolio Beta.

Asset | Weight | Beta

A | 60% | 1.2

B | 40% | 0.8

βP

= 0.60(1.2) + 0.40(0.8)

= 1.04

What is the CAPM equation?

E(ri) = rf + βi[E(rM) − rf]

Calculate expected return using CAPM.

Risk-Free Rate = 3%

Expected Market Return = 11%

Beta = 1.5

E(ri)

= 3 + 1.5(11 − 3)

= 3 + 12

= 15%

A stock has an expected return of 14%.

Risk-Free Rate = 4%.

Expected Market Return = 9%.

Calculate Beta.

14 = 4 + β(9 − 4)

14 = 4 + 5β

10 = 5β

β = 2

Suppose the Market Risk Premium is 8%.

Toyota Beta = 1.10

Ford Beta = 1.25

A portfolio invests:

25% in Toyota

75% in Ford

Calculate the portfolio risk premium.

Portfolio Beta

= 0.25(1.10) + 0.75(1.25)

= 1.2125

Portfolio Risk Premium

= 1.2125 × 8%

= 9.7%

What is the Security Market Line (SML)?

The SML is the graphical representation of the CAPM equation.

What are the axes of the Security Market Line?

Y-axis = Expected Return

X-axis = Beta

What are the intercept and slope of the SML?

Intercept = Risk-Free Rate

Slope = Market Risk Premium

(E(rM) − rf)

What does it mean if an asset lies on the SML?

The asset is correctly priced.

What does it mean if an asset lies above the SML?

The asset is undervalued.

Expected return is higher than required by CAPM.

Positive alpha.

What does it mean if an asset lies below the SML?

The asset is overvalued.

Expected return is lower than required by CAPM.

Negative alpha.

What is Alpha?

Alpha is the difference between an asset's actual expected return and its CAPM required return.

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What is the equation for Alpha?

α = Actual Return − CAPM Return

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Calculate Alpha.

Actual Return = 16%

CAPM Return = 13%

α = 16% − 13%

α = +3%

Positive alpha indicates undervaluation.

What is meant by Positive Alpha?

The asset offers a higher return than CAPM predicts.

The asset is undervalued.

What is meant by Negative Alpha?

The asset offers a lower return than CAPM predicts.

The asset is overvalued.

What is the difference between the SML and the CML?

CML:

• Uses Standard Deviation as risk

• Uses efficient portfolios only

• Derived from Modern Portfolio Theory

SML:

• Uses Beta as risk

• Applies to any asset or portfolio

• Derived from CAPM

Draw and fully label the Security Market Line (SML).

Y-axis = Expected Return

X-axis = Beta

Labels:

• Risk-Free Rate

• Market Portfolio

• Security Market Line

The slope equals the Market Risk Premium.

Draw and explain an asset above the SML.

The asset lies above the Security Market Line.

Expected return exceeds CAPM required return.

Positive Alpha.

Undervalued.

Draw and explain an asset below the SML.

The asset lies below the Security Market Line.

Expected return is below CAPM required return.

Negative Alpha.

Overvalued.

What are three criticisms of CAPM?

CAPM relies on:

• Homogeneous expectations

• Frictionless markets

• Borrowing and lending at the risk-free rate

These assumptions may not hold in reality.

What is the main criticism of CAPM relating to Beta?

Beta alone may not fully explain expected returns.

This led to the development of multifactor models such as the Fama-French model.

What is the expected Beta of the market portfolio?

The Beta of the market portfolio is 1.

What is the expected return of an asset with Beta = 0 according to CAPM?

The expected return equals the risk-free rate.

A stock has Beta = 1.4.

The market risk premium is 6%.

Calculate the stock's risk premium.

Risk Premium

= Beta × Market Risk Premium

= 1.4 × 6%

= 8.4%