Week 8

A U.S. Treasury bill has a beta of _____ while the overall market has a beta of _____.

0; 1

What is the beta of a portfolio with an expected return of 14% if Treasury bills yield 3.5% and the market risk premium is 7%?

1.50

Sibling Incorporated has a beta of 1.0. If the expected return on the market is 12%, what is the expected return on Sibling Incorporated's stock?

12%

A company you are researching has common stock with a beta of 1.8. Currently, Treasury bills yield 2.5%, and the market portfolio offers an expected return of 10%. What is the required return on this common stock?

16.00%

The risk free rate is 8% and the expected return on the market portfolio is 16%. A firm considers a project that is expected to have a beta of 1.3. What is the required rate of return on the project? If the expected IRR of the project is 19%, should it be accepted?

18.4%; Accepted

If you were told the risk free rate was 4%, the market return was 14% and the beta of a stock was .2, what is the expected (required) return on that stock?

6%

You are considering a new investment XYZ. The rate on T-bills is 3.3% and the return on the S&P 500 is 8.5%. You have measured the non-diversifiable risk of the XYZ investment you are considering to be .7. What rate of return will you require on the XYZ investment? Graph the SML and show the XYZ investment.

6.94%

What two components should the expected return on any investment come from?

A baseline risk-free rate of return that we would demand to compensate for inflation and the time value of money, even if there were no risk of losing our money. A risk premium that varies with the amount of systematic risk in the investment.

correlation

A measure of the degree to which returns share common risk. It is calculated as the covariance of the returns divided by the product of the standard deviations of each return.

value weighted

A portfolio in which each security is held in proportion to its market capitalization.

equally weighted portfolio

A portfolio in which the same amount of money is invested in each stock.

market proxy

A portfolio whose return should closely track the true market portfolio.

Capital Asset Pricing Model (CAPM)

An equilibrium model of the relationship between risk and return that characterizes a security's expected return based on its beta with the market portfolio.

What is the beta of a portfolio with E(Rp) = 18%, if rf = 6% and E(Rm) = 14%?

Beta = 1.5

The difference between beta and standard deviation is best described as:

Beta measures the risk investors are compensated for, while standard deviation measures both systematic and unsystematic risk.

What does beta tell us?

Beta measures the sensitivity of an investment to the fluctuations of the market portfolio. Beta tells us how much an investment's excess return is expected to change for each 1% change in the market portfolio's excess return.

What would you recommend to an investor who is considering an investment which, according to its beta, plots below the security market line (SML)?

Don't invest; risk is high relative to return.

Using Excel: Calculating a Stock's Beta

Enter or import the historical returns for the stock and the S&P 500 into Excel. Next, use the LINEST function in Excel. For the first series, highlight the stock's returns. For the second series, highlight the S&P 500's returns, as shown in the screenshot. Click Enter.

What do the weights in a portfolio tell us?

Portfolio weights tell us the fraction of the total investment in the portfolio held in each individual security.

Within the context of the CAPM, assume: Expected return on the market = 15% Risk free rate = 8% Expected rate of return on XYZ security = 17% Beta of XYZ security = 1.25 What is the required return on XYZ security according to the CAPM? Is XYZ fairly, over or under priced? If over or under priced, by how much?

Required return = 16.75%; Underpriced; Alpha = .25

When do stocks have more or less correlation?

Stocks that are in the same industry and stocks that are impacted by the same economic conditions are more positively correlated. For example, two airline companies would be more correlated than an airline company and a pharmaceutical company would be.

Summarize the CAPM and its use.

The CAPM is a powerful tool that is widely used to estimate the expected return on stocks and investments within companies. To summarize the model and its use: Investors require a risk premium proportional to the amount of systematic risk they are bearing. We can measure the systematic risk of an investment by its beta, which is the sensitivity of the investment's return to the market's return. For each 1% change in the market portfolio's return, the investment's return is expected to change by beta percent due to risks that it has in common with the market. The most common way to estimate a stock's beta is to regress its historical returns on the market's historical returns. The stock's beta is the slope of the line that best explains the relation between the market's return and the stock's return. The CAPM says that we can compute the expected, or required, return for any investment using the following equation: E[Ri] = rf + betai (E[R Mkt] - rf) which when graphed is called the security market line.

What does the CAPM say about the required return of a security?

The CAPM model says that the required return of a security equals the risk-free rate plus the security's amount of systematic risk (beta) times the market risk premium.

What is the security market line?

The Security Market Line (SML) is the line that goes through the risk-free investment (with a beta of 0) and the market (with a beta of 1). It shows the linear relation between the expected return and systematic risk, as measured by beta. The SML is a graphical representation of the CAPM.

What determines how much risk will be eliminated by combining stocks in a portfolio?

The amount of risk that will be eliminated by combining stocks in a portfolio depends on the correlation between the stocks. The higher the correlation between the stocks, the more the stocks move together, and the less the risk will be lowered by combining the stocks.

beta

The expected percentage change in the excess return of a security for a 1% change in the excess return of the market (or other benchmark) portfolio.

How is the expected return of a portfolio related to the expected returns of the stocks in the portfolio?

The expected return of a portfolio is the weighted average of the expected returns of the individual stocks in the portfolio.

Required return

The expected return of an investment that is necessary to compensate for the risk of undertaking the investment.

What will happen to the expected return on a stock with a beta of 1.5 and a market risk premium of 9% if the Treasury bill yield increases from 3% to 5%?

The expected return will increase by 2.0%.

portfolio weights

The fraction of the total investment in a portfolio held in each individual investment in the portfolio.

Market or equity risk premium

The historical average excess returns on the market portfolio.

What is the market portfolio?

The market portfolio is the portfolio of all risky investments, held in proportion to their market capitalization.

market index

The market value of a broad-based portfolio of securities.

You are considering a new investment which is expected to earn 12%. The beta of this new investment is 0.6. Treasury Bills are earning 3%, and the S&P 500 is expected to earn 10%. Which one of the following statements is correct?

The new investment is underpriced.

market portfolio

The portfolio of all risky investments, held in proportion to their value.

If the market portfolio is expected to offer returns of 16%, then what can be said about a portfolio expected to return 13%?

The portfolio's beta is less than 1.0.

Security market line (SML)

The pricing implication of the CAPM; it specifies a linear relation between the risk premium of a security and its beta with the market portfolio.

volatility of a portfolio

The total risk, measured as standard deviation, of a portfolio.

expected return of a portfolio

The weighted average of the expected returns of the investments in a portfolio, where the weights correspond to the portfolio weights.

A typical measure for the risk-free rate of return is the:

U.S. Treasury Bill rate.

An project you are evaluating has an IRR of 10%. The project's required return has been measured to be 16%. Therefore:

You should reject the project.

Which one of the following portfolios has the least amount of systematic risk?

a portfolio consisting of various U.S. Treasury bills

Investment projects that plot above the security market line would be considered to have:

a positive NPV.

Security Market Line

a positively sloped straight line displaying the relationship between expected return and beta

The amount of systematic risk present in a particular risky asset relative to that in an average risky asset (or the market in general) is called the:

beta coefficient.

Stock returns can be explained by the stock's _________ and the stock's __________.

beta; unique risk.

If the slope of the line measuring a stock's historic returns against the market's historic returns is positive, then the stock:

has a positive beta.has a positive beta.

The slope of the security market line equals:

the market risk premium.

market capitalization

the portfolio weight of each stock is proportional to the total market value of its outstanding shares