Chapter 15 Portfolio Theory 15.1 Introduction to Portfolio Theory 15.2 The Capital Asset Pricing Model

Introduction to Portfolio Theory The return from any asset is the total gain or loss for a given time period Risk is the amount of variation in possible returns. Investors are risk averse; they dislike risk and demand higher rates of return on riskier investments. See example pg. 500

Risk and Return The risk premium is the extra return demanded by investors for accepting higher levels of risk. If one investment is riskier than another, investors will demand a higher level of return in order to invest in it.

Types of Risk Unsystematic risk is due to factors specific to particular firms, stocks or industries such as regional conditions, management or competition. Systematic risk occurs due to factors outside the control of investors, such as Interest rates, wars or inflation.

Portfolio Diversification A portfolio is the entire collection of investments held by an investor. Diversification is holding a portfolio of securities that includes assets from a wide range of different industries. Through diversification the risks associated with particular industries or stocks can be eliminated. Unsystematic risk can be completely diversified away so that the portfolio is only subject to systematic (market) risk.

Correlation Correlation is a measure of the degree to which share prices move together or against each other. When share prices tend to move together they are positively correlated. When share prices move in opposite directions they are negatively correlated. Stocks in the same industry are usually positively correlated as they face similar risks. e.g.: oil producers stock prices will all fall when world oil prices drop.

Correlation and Portfolio Diversification The most efficient portfolios are created with assets that have negative (or low positive) correlation. By having negatively correlated stocks in the same portfolio an investor can mitigate their risks. When an asset in a portfolio falls in value another negatively correlated asset in the portfolio will rise in value. See example pg. 506

Perfectly Positively Correlated

Perfectly Negatively Correlated

The Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) The area marked ‘all possible portfolios’ in the diagram shows the expected return and standard deviation (risk) of all feasible portfolios of risky assets. The darkened line at the top of the set of feasible portfolios is called the efficient frontier.

The Capital Asset Pricing Model (CAPM) The efficient frontier is the set of portfolios that offer the highest return for each level of risk. Rational investors will always attempt to choose a portfolio on the efficient frontier, as they will maximise their return for a given level of risk.

The Capital Market Line By adding a risk-free asset to an efficient portfolio we can create a new set of feasible portfolios. The capital market line is the line that runs from the risk-free asset, tangential to the efficient frontier. This line is the highest possible line that joins the efficient frontier to the risk-free asset.

The Capital Market Line

The Capital Market Line Any point on this line is an optimal portfolio as it will provide a higher return for a given level of risk than any other feasible portfolio. The slope of the capital market line represents the market price of risk. It shows the additional expected return that is required to compensate investors for an increase in risk.

The Capital Asset Pricing Model Equation The CAPM is based on the proposition that: Expected Rate of Return = Risk-free Rate + Risk Premium It can be expressed as the following equation: Eri = Rf + [(ERp – Rf) x ß] Where: Er = Expected return of security i Rf = Risk free interest rate ErP = Expected return on Portfolio β = Beta of the security

Beta (β) The Beta (β) of a stock is used to measure its systematic (non-diversifiable) risk. It indicates the degree of movement of an asset’s return in response to changes in the market return.

Beta (β) The formula to calculate beta is: β = Standard Deviation of Portfolio x Coefficient of Correlation Standard Deviation of Market See example pg. 510

The Security Market Line Shows the linear relationship between an individual security’s expected rate of return and its systematic risk as measured by beta. Graphical representation of the CAPM equation. Any security that does not lie on the SML is either under-priced or over-priced.

The Security Market Line