R-B-Ch.8 CAPM - Points to Refresh

Reilly and Brown IAPM

Chapter 8 - An Introduction to Asset Pricing Models

Capital Market Theory: An Overview

Capital market theory extends portfolio theory and develops a model for pricing all risky assets

Capital asset pricing model (CAPM) will allow you to determine the required rate of return for any risky asset

Assumptions of Capital Market Theory

1. All investors are Markowitz efficient investors who want to target points on the efficient frontier.
The exact location on the efficient frontier and, therefore, the specific portfolio selected, will depend on the individual investor’s risk-return utility function.

2. Investors can borrow or lend any amount of money at the risk-free rate of return (RFR).
Clearly it is always possible to lend money at the nominal risk-free rate by buying risk-free securities such as government T-bills. It is not always possible to borrow at this risk-free rate, but we will see that assuming a higher borrowing rate does not change the general results.

3. All investors have homogeneous expectations; that is, they estimate identical probability distributions for future rates of return.
Again, this assumption can be relaxed. As long as the differences in expectations are not vast, their effects are minor.

4. All investors have the same one-period time horizon such as one-month, six months, or one year.
The model will be developed for a single hypothetical period, and its results could be affected by a different assumption. A difference in the time horizon would require investors to derive risk measures and risk-free assets that are consistent with their time horizons.

5. All investments are infinitely divisible, which means that it is possible to buy or sell fractional shares of any asset or portfolio.
This assumption allows us to discuss investment alternatives as continuous curves. Changing it would have little impact on the theory.

6. There are no taxes or transaction costs involved in buying or selling assets.
This is a reasonable assumption in many instances. Neither pension funds nor religious groups have to pay taxes, and the transaction costs for most financial institutions are less than 1 percent on most financial instruments. Again, relaxing this assumption modifies the results, but does not change the basic thrust.

7. There is no inflation or any change in interest rates, or inflation is fully anticipated.
This is a reasonable initial assumption, and it can be modified.

8. Capital markets are in equilibrium.
This means that we begin with all investments properly priced in line with their risk levels.

Risk-Free Asset

An asset with zero standard deviation
Zero correlation with all other risky assets
Provides the risk-free rate of return (RFR)
Will lie on the vertical axis of a portfolio graph


Combining a Risk-Free Asset with a Risky Portfolio

Since both the expected return and the standard deviation of return for such a portfolio are linear combinations, a graph of possible portfolio returns and risks looks like a straight line between the two assets.

The Market Portfolio

Because portfolio M lies at the point of tangency, it has the highest portfolio possibility line
Everybody will want to invest in Portfolio M and borrow or lend to be somewhere on the CML
Therefore this portfolio must include ALL RISKY ASSETS

Because the market is in equilibrium, all assets are included in this portfolio in proportion to their market value

Because it contains all risky assets, it is a completely diversified portfolio, which means that all the unique risk of individual assets (unsystematic risk) is diversified away

Systematic Risk

Only systematic risk remains in the market portfolio
Systematic risk is the variability in all risky assets caused by macroeconomic variables
Systematic risk can be measured by the standard deviation of returns of the market portfolio and can change over time

Examples of Macroeconomic Factors Affecting Systematic Risk



The Capital Market Line (CML) and the Separation Theorem

The CML leads all investors to invest in the M portfolio
Individual investors should differ in position on the CML depending on risk preferences
How an investor gets to a point on the CML is based on financing decisions
Risk averse investors will lend part of the portfolio at the risk-free rate and invest the remainder in the market portfolio
Investors preferring more risk might borrow funds at the RFR and invest everything in the market portfolio

The decision to borrow or lend to obtain a point on the CML is a separate decision based on risk preferences (financing decision)

The Capital Asset Pricing Model: Expected Return and Risk

The existence of a risk-free asset resulted in deriving a capital market line (CML) that became the relevant frontier
An asset’s covariance with the market portfolio is the relevant risk measure
This can be used to determine an appropriate expected rate of return on a risky asset - the capital asset pricing model (CAPM)
CAPM indicates what should be the expected or required rates of return on risky assets
This helps to value an asset by providing an appropriate discount rate to use in dividend valuation models
You can compare an estimated rate of return to the required rate of return implied by CAPM - over/under valued

The Security Market Line (SML)

The relevant risk measure for an individual risky asset is its covariance with the market portfolio (Covi,m)
This is shown as the risk measure
The return for the market portfolio should be consistent with its own risk, which is the covariance of the market with itself - or its variance:

Determining the Expected Rate of Return for a Risky Asset

Ri = RFR + βi(Rm-RFR)

The expected rate of return of a risk asset is determined by the RFR plus a risk premium for the individual asset
The risk premium is determined by the systematic risk of the asset (beta) and the prevailing market risk premium (RM-RFR)

Using Security Market Line for Trading decisions

In equilibrium, all assets and all portfolios of assets should plot on the SML

Any security with an estimated return that plots above the SML is underpriced

Any security with an estimated return that plots below the SML is overpriced

An investor who derives value and return estimates for assets that are consistently superior to the consensus market evaluation (equilibrium returns) will earn better risk-adjusted rates of return than the average investor.

Independent estimates of return for the securities provide price and dividend outlooks

Beta estimation - Time intervals

Number of observations and time interval used in regression vary
Value Line Investment Services (VL) uses weekly rates of return over five years
Merrill Lynch, Pierce, Fenner & Smith (ML) uses monthly return over five years
There is no “correct” interval for analysis
Weak relationship between VL & ML betas due to difference in intervals used
The return time interval makes a difference, and its impact increases as the firm’s size declines

The Effect of the Market Proxy (Index used as market portfolio)

The market portfolio of all risky assets must be represented in computing an asset’s characteristic line
Standard & Poor’s 500 Composite Index is most often used
Large proportion of the total market value of U.S. stocks
Value weighted series
Includes only U.S. stocks
The theoretical market portfolio should include U.S. and non-U.S. stocks and bonds, real estate, coins, stamps, art, antiques, and any other marketable risky asset from around the world