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### FINANCE IN A CANADIAN SETTINGSixth Canadian Edition

Lusztig, Cleary, Schwab

CHAPTER EIGHT

CAPITAL MARKET THEORY

Learning Objectives

1. Explain the role of risk-free assets in an efficient portfolio.

2. Define the capital market line (CML), and explain what its slope indicates.

3. Compare and contrast systematic and non-systematic risk, and discuss the role of each in establishing the security market line (SML).

Learning Objectives

4. Define beta measure, and explain why it is more stable for large portfolios than for small ones than for individual stocks.

5. Identify some of the weaknesses in the capital asset pricing model (CAPM), and discuss alternative theories.

Building Efficient Portfolios

- Use approach based on portfolio theory developed by Harry Markowitz
- Portfolio theory is a normative meaning that tells investors how they should act to diversify optimally, which is based on the following assumptions:
- A single investment period
- Liquidity of positions
- Investors preference based only ona portfolio’s expected return and risk
- Homogenous expectations among investors regarding expected return and risk

The Efficient Set of Portfolios

- According to Markowitz’s approach, investors should evaluate portfolios based on their return and risk as measured by the standard deviation
- Efficient portfolio – a portfolio that has the smallest portfolio risk for a given level of expected return or the largest expected return for a given level of risk

The Efficient Set of Portfolios

- The construction of efficient portfolios of financial assets requires identification of optimal risk-expected return combinations attainable from the set of risky assets available
- Efficient portfolios can be identified by specifying an expected portfolio return and minimizing the portfolio risk at this level of return

The Efficient Set of Portfolios

The Attainable Set and the Efficient Set of Portfolios

The Efficient Set of Portfolios

- Risk averse investors should only be interested in portfolios with the lowest possible risk for any given level of return
- Efficient set (frontier) – is the segment of the minimum variance frontier above the global minimum variance portfolio that offers the best risk-expected return combinations available to investors
- Portfolios along the efficient frontier are equally “good”

Borrowing and Lending Possibilities

- Investors have the option of buying risk-free assets
- Investors can invest part of their wealth in risk-free asset and the rest in risky assets resulting in a new efficient frontier

Borrowing and Lending Possibilities

The Markowitz Efficient Frontier and the Possibilities Resulting from Introducing a Risk-Free Asset

Risk-Free Lending

- The expected return on a combined portfolio of risk-free and risky assets would be:
- Since the of risk-free assets is equal to 0 than the of the portfolio would be:

Risk-Free Lending

- Through a combination of risk-free investing and investing in a portfolio of risky assets, investors can improve the opportunity set available from the efficient frontier

Borrowing Possibilities

- Investors are no longer restricted to their initial wealth when investing in risky assets.
- Investors can:
- Buy stock on margin
- Borrow at the risk-free rate
- Borrowing additional funds for investment purposes allows investors to seek higher expected returns while assuming more risk

Borrowing Possibilities

The Efficient Frontier when Lending and Borrowing Possibilities Are Allowed

Borrowing Possibilities

- The proportion to be invested in the alternatives are stated as a percentage of an investor’s total investable funds with the different combinations adding up to 1.0

The Capital Asset Pricing Model (CAPM)

- Capital market theory is concerned with equilibrium security prices and returns and how they are related to the risk-expected return trade-off that investors face
- It measures the relative risk of an individual security and the relationship between risk and the returns expected from investing

Capital Market Line (CML)

- Depicts the equilibrium conditions that prevail in the market for efficient portfolios consisting of the optimal portfolio of risk-free and risky assets
- All combinations of assets are bound by the CML and at equilibrium all investors end up with efficient portfolios

Capital Market Line (CML)

- Slope of the CML is the market price of risk for efficient portfolios
- Slope of the CML =
- The CML is always upward sloping because the price of risk is always positive

Capital Market Line (CML)

The CML and the Components of Its Slope

The Security Market Line (SML)

- The SML is the key contribution of the CAPM to asset pricing theory
- The SML equation is:
- The SML represents the trade-off between systematic (as measured by beta) and expected returns for all assets

The Security Market Line (SML)

- It is depicted as the line from RF-Z in Figure 8.6

Beta

- Beta – the measure of the systematic risk of a security that cannot be avoided through diversification
- Beta measures a security’s volatility in price relative to a benchmark
- Beta – risk-free asset = 0

– market portfolio = 1.0

- Stocks - betas are higher risk securities

betas are lower risk securities

Portfolio Betas

- Are weighted averages of the betas for individual securities in the portfolio
- The equation is:

Over- and Undervalued Securities

- Securities plotted above the SML are undervalued because they offer more expected return given its beta
- Securities plotted below the SML are overvalued because they offer less expected return given its beta

Summary

1. An efficient portfolio has the highest expected return for a given level of risk or the lowest level of risk for a given level of expected return.

2. Capital market theory, based on the concept of efficient diversification, describes the pricing of capital assets in the market place. The new efficient frontier is called the capital market line (CML), and its slope indicates the equilibrium price of risk in the market.

Summary

3. Based on the separation of risk into its systematic and non-systematic components, the security market line (SML) can be constructed for individual securities (and portfolios).

4. Beta is a relative measure of risk, which indicates the volatility of a stock relative to a market index. While all betas change through time, betas for large portfolios are much more stable than those for individuals stocks

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