Finance 3220 Chapter 8

What is the coefficient of variation of the expected dollar returns given the following distribution of returns? 0.4 30 0.5 25 0.1 -20

0.6383 Use the given probability distribution of returns to calculate the expected value, variance, standard deviation, and coefficient of variation. Use the standard deviation and the expected return to calculate the coefficient of variation: $14.3614/$22.5 = 0.6383

A stock has a required return of 12%. The risk-free rate is 6% and the market risk premium is 5%. What is the stock's beta coefficient?

1.20 r = rRF + (rM - rRF)b 12% = 6% + (5%)b 6% = 5%b b = 1.20

If rRF = 5%, rM = 11%, and b = 1.3 for Stock X, what is rX, the required rate of return for Stock X?

12.8% rX = rRF + (rM - rRF)bX = 5% + (11% - 5%)1.3 = 12.8%

If rRF = 5%, rM = 11%, and b = 1.3 for Stock X, what would rX be if investors expected the inflation rate to increase by 2 percentage points? Assume that investors' risk aversion has not changed.

14.8% rX = rRF + (rM - rRF)bX = 7% + (13% - 7%)1.3 = 14.8%. A change in the inflation premium does not change the market risk premium (rM rRF) since both rM and rRF are affected. Changes in the market risk premium reflect changes in investors' risk aversion

Stock A has a beta of 1.2, Stock B has a beta of 0.6, the expected rate of return on an average stock is 12%, and the risk-free rate of return is 7%. By how much does the required return on the riskier stock exceed the required return on the less risky stock?

3.00% ri = rRF + (rM - rRF)bi = 7% + (12% - 7%)bi rA = 7% + 5%(1.20) = 13.0% rB = 7% + 5%(0.60) = 10.0% rA - rB = 13% - 10% = 3%.

Dothan Inc.'s stock has a 25% chance of producing a 30% return, a 50% chance of producing a 12% return, and a 25% chance of producing a −18% return. What is the firm's expected rate of return?

9.00%

You have been managing a $3 million portfolio. The portfolio has a beta of 1.10 and a required rate of return of 10%. The current risk-free rate is 5.6%. Assume that you receive another $600,000. If you invest the money in a stock that has a beta of 0.60, what will be the required return on your $3.6 million portfolio?

9.67%

Taggart Inc.'s stock has a 50% chance of producing a 25% return, a 30% chance of producing a 10% return, and a 20% chance of producing a −28% return. What is the firm's expected rate of return?

9.90%

Generally, investors would prefer to invest in assets that have:

A higher-than-average expected rate of return given its perceived risk.

Sharpe ratio

A measure of stand-alone risk that compares the asset's realized excess return to its standard deviation over a specified period. An investment with a higher ratio has performed better than one with a lower ratio.

correlation coefficient, p

A measure of the degree of relationship between two variables.

beta coefficient, b

A metric that shows the extent to which a given stock's returns move up and down with the stock market. Beta measures market risk.

capital asset pricing model

A model based on the proposition that any stock's required rate of return is equal to the risk-free rate of return plus a risk premium that reflects only the risk remaining after diversification.

A financial planner is examining the portfolios held by several of her clients. Which of the following portfolios is likely to have the smallest standard deviation?

A portfolio consisting of about 30 randomly selected stocks.

market portfolio

A portfolio consisting of all stocks.

standard deviation, σ

A statistical measure of the variability of a set of observations.

security market line (SML) equation

An equation that shows the relationship between risk as measured by beta and the required rates of return on individual securities.

Which of the following statements is correct?

Both the SML and a company's position on it change over time due to changes in interest rates, investors' aversion to risk, and individual companies' betas.

If a stock has a beta of zero, it will be riskless when held in isolation.

False

The market risk component of the total portfolio risk can be reduced by randomly adding stocks to the portfolio.

False

The risk in a portfolio will increase if more stocks that are negatively correlated with other stocks are added to the portfolio.

False

probability distributions

Listings of possible outcomes or events with a probability (chance of occurrence) assigned to each outcome.

Mikkelson Corporation's stock had a required return of 11.75% last year, when the risk-free rate was 5.50% and the market risk premium was 4.75%. Then an increase in investor risk aversion caused the market risk premium to rise by 2%. The risk-free rate and the firm's beta remain unchanged. What is the company's new required rate of return?

Old market risk premium 4.75% Old required return 11.75% b = (old return - rRF)/old RPM 1.32 New market risk premium 6.75% New required return = rRF + b(RPM) 14.38%

realized rates of return

Returns that were actually earned during some past period. Actual returns usually turn out to be different from expected returns except for riskless assets.

Suppose you observe the following situations: Security ABC Corp. DEF Inc. Beta 1.35 0.80 Expected Return 13.2% 10.1% Assume these securities are correctly priced. Based on the CAPM, what is the expected return on the market? What is the risk-free rate?

Rf + 1.35(RPM) = 13.2% Rf + .8(RPM) = 10.1% RPM = Market Risk Premium i.e. Rm - Rf Subtract two formulas above: .55(RPM) = .031 RPM = 5.636% Rf + 1.35(5.636) = 13.2% Rf = 5.59% Rm - 5.59% = 5.636% Rm = 11.23%

risk aversion

Risk-averse investors dislike risk and require higher rates of return as an inducement to buy riskier securities.

You invest $100,000 in only one stock. To which kind of risk will you primarily be exposed?

Stand-alone risk

how to calculate the required rate of return?

Subtract the risk-free rate of return from the market rate of return. Take that result and multiply it by the beta of the security. Add the result to the current risk-free rate of return to determine the required rate of return.

diversifiable risk

That part of a security's risk associated with random events; it can be eliminated by proper diversification. This risk is also known as companyspecific, or unsystematic, risk.

If investors expected inflation to increase in the future, and they also became more risk averse, what could be said about the change in the Security Market Line (SML)?

The SML would shift up and the slope would increase.

market risk premium, RPm

The additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk.

You want to create a portfolio equally as risky as the market, and you have $1,000,000 to invest. Given this information, fill in the rest of the following table: Asset Stock A Stock B Stock C Risk-free asset Investment $210,000 $320,000 Beta 0.85 1.20 1.35 1.35 Risk-free Asset

The beta of a portfolio is the weighted average of the betas of the assets. The beta of the risk-free asset is zero. 1.0=.21(.85)+.32(1.2)+wc(1.35)+(wrf)(0) Solve for wc=.324074 or $324,074 Risk-free investment = 1M - 210K-320K-324,074=$145,926.

In a portfolio of three different stocks, which of the following could not be true?

The beta of the portfolio is less than the beta of each of the individual stocks.

Based on your understanding of P/E ratios, in which of the following situations would the average trailing P/E ratio (current price divided by earnings per share over the previous 12 months) of the S&P 500 Index be higher?

The outlook for the economy and the markets is for an improvement.

expected rate of return

The rate of return on a common stock that a stockholder expects to receive in the future.

stand-alone risk

The risk an asset would have if it were a firm's only asset and if investors owned only one stock. It is measured by the variability of the asset's expected returns.

market risk

The risk that remains in a portfolio after diversification has eliminated all company-specific risk. This risk is also known as nondiversifiable or systematic or beta risk.

relevant risk

The risk that remains once a stock is in a diversified portfolio is its contribution to the portfolio's market risk. It is measured by the extent to which the stock moves up or down with the market.

coefficient of variation (CV)

The standardized measure of the risk per unit of return; calculated as the standard deviation divided by the expected return.

correlation

The tendency of two variables to move together.

expected return on a portfolio, r-hat p

The weighted average of the expected returns on the assets held in the portfolio.

A portfolio's risk is not equal to the weighted average of the individual stocks' standard deviations.

True

When returns on Stock A increase, returns on Stock B also increase. In general, this would mean that Stocks A and B are positively correlated.

True

A stock is in equilibrium if its required return ________ its expected return. In general, assume that markets and stocks are in equilibrium (or fairly valued), but sometimes investors have different opinions about a stock's prospects and may think that a stock is out of equilibrium (either undervalued or overvalued). Based on the analyst's expected return estimates, stock INO is _________ , stock AIL is in equilibrium, and stock DET is ___________ .

equals; undervalued; overvalued

The SML helps determine the risk-aversion level among investors. The steeper the slope of the SML, the _______ the level of risk aversion.

higher

The manager of The Growth Fund averages a 19% return each year, with a beta of 1.25. The manager of The Value Fund averages a 16% return each year with a beta of 1.0. If T-bills paid 6% and the expected market return was 14%, which advisor would be the superior stock selector?

r-hat G=6+1.25(14-6)=16% r-hat V=6+1(14-6)=14% Alpha is a measure of return in excess of CAPM expected return. Alpha (Growth Fund)=19%-16%=3% Alpha (Value Fund) = 16%-14%=2% Growth fund manager is superior because she beat the expected return, as defined by CAPM, by a larger amount.=6+1.25(14-6)=16% =6+1(14-6)=14%