Chapter 8 Risks and Rate of Return

Investment Risk

The possibility that an investment will fail to pay the expected return or fail to pay a return at all

Investment risk is related to the probability of earning a low or negative actual return.

The greater the chance of lower than expected, or negative returns, theriskier the investment

the higher the investment risk the higher the required return to induce investors to purchase the asset

stand-alone risk

the risk an investor would face if he or she held only one asset

market risk + diversifiable risk

No investment should be undertaken unless its expected rate of return is high enough to compensate for its perceived risk

Portfolio Risk

total risk associated with owning a portfolio; sum of systematic and unsystematic risk

A portfolio's risk will be less than the average of all the stocks standard•deviations

The risk in a portfolio will increase. If less stocks are negatively correlated•with other stocks in the portfolio

Probability distributions

A listing of all possible outcomes, and the probability of each occurrence.

• Can be shown graphically

the tighter the assets probability distribution, the lower its risk. Three useful measures of stand-alone risk are standard deviation, coefficient of variation, and the Sharpe ratio. Standard deviation is a statistical measure of the variability of a set of observations as shown below:

T-Bill

A short-term debt obligation backed by the U.S. government with a maturity of less than one year.

T-bills will return the promised 3.0%, regardless of the economy.

• No, T-bills do not provide a completely risk-free return, as they are still exposed to inflation.

Although, very little unexpected inflation is likely to occur over such a short period of time.

• T-bills are also risky in terms of reinvestment risk.

• T-bills are risk-free in the default sense of the word

high tech

Moves with the economy, and has a positive correlation.This is typical

collection

Is countercyclical with the economy, and has a negative correlation. This is unusual.

Calculating the expected return

R=

standard deviation

Standard deviation (σi) measures total, or stand-alone, risk.

• The larger σi is, the lower the probability that actual returns will be close to expected returns.

• Larger σi is associated with a wider probability distribution of returns.

coefficient of variation (CV)

A standardized measure of dispersion about the expected value, that shows the risk per unit of return

is a better measure of stand-alone risk than standard deviation because it is a standardized measure of risk per unit;

The coefficient of variation shows the risk per unit of return, so it provides a more meaningful risk measure when the expected returns on two alternatives are not identical

risk premium

the difference between the return on a risky asset and a riskless asset,

return on a risky asset and a riskless asset, which serves as compensation for investors which serves as compensation for investors to hold riskier securities

represents the additional compensation investors require for bearing risk; it is the difference between the expected rate of return on a given risky asset and that on a less risky asset. An asset's risk can be considered in two ways: On a stand-alone basis and in a portfolio context.

risk aversion

assumes investors dislike risk and require higher rates of return to and require higher rates of return to encourage them to hold riskier securities.encourage them to hold riskier securities

calculating portfolio expected return

portfolio risk measures

Most stocks are positively (though not perfectly) correlated with the market (i.e., ρ between 0 and 1)

.• Combining stocks in a portfolio generally lowers risk.

creating a portfolio

σp decreases as stocks are added, because they would not be perfectlycorrelated with the existing portfolio.

• Expected return of the portfolio would remain relatively constant.

• Eventually the diversification benefits of adding more stocks dissipates(after about 40 stocks), and for large stock portfolios, σp tends to converge to about 20%.

market risk

portion of a security's stand-alone risk that cannot be eliminated through diversification.

Measured by beta.

is the risk that remains in a portfolio after diversification has eliminated all company-specific risk. Standard deviation is not a good measure of risk when a stock is held in a portfolio. A stock's relevant risk is the risk that remains once a stock is in a diversified portfolio. Its contribution to the portfolio's market risk is measured by a stock's beta coefficient

The market risk component of a total portfolio's risk cannot be reduced by•randomly adding/diversifying the portfolio

diversifiable risk

portion of a security's stand-alone risk that can be eliminated through proper diversification.

unsystematic

that part of a security's risk associated with random events. It can be eliminated by proper diversification and is also known as company-specific risk.

failure to diversify

If an investor chooses to hold a one-stock portfolio (doesn't diversify),would the investor be compensated for the extra risk they bear?

-NO!

-Stand-alone risk is not important to a well-diversified investor.

-Rational, risk-averse investors are concerned with σp, which is based upon market risk.

-There can be only one price (the market return) for a given security.

-No compensation should be earned for holding unnecessary,

diversifiable risk.

Capital Asset Pricing Model (CAPM)

Model linking risk and required returns. CAPM suggests that there is aSecurity Market Line (SML) that states that a stock's required return equals the risk-free return plus a risk premium that reflects the stock's risk after diversification.

a risk-free component and a risk premium

The risk-free component is approximated using Treasury securities and therisk premium is a function of beta for the security and the risk premium onthe market (Rm - Rf)

Primary conclusion: The relevant riskiness of a stock is its contribution to theriskiness of a well-diversified portfolio

primary conclusion

The relevant riskiness of a stock is its contribution to the riskiness of a well-diversified portfolio.

beta

Measures a stock's market risk, and shows a stock's volatility relative tothe market

.• Indicates how risky a stock is if the stock is held in a well-diversified portfolio.

which shows the extent to which a given stock's returns move up and down with the stock market.

Measures a stock's market risk, and shows a stock's volatility relative tothe market (ex. S&P 500 index)• Indicates how risky a stock is if the stock is held in a well-diversifiedportfolio

High beta stocks are most affected by changes in risk-aversion

comments on Btea

can the beta of a security be negative

yes, if the correlation between stock i and the market is negative

If the correlation is negative, the regression line would slope downward, and the beta would be negative.

• However, a negative beta is highly unlikely

calculating betas

Well-diversified investors are primarily concerned with how a stock is expected to move relative to the market in the future.

• Without a crystal ball to predict the future, analysts are forced to rely on historical data. A typical approach to estimate beta is to run a regression of the security's past returns against the past returns of the market

.• The slope of the regression line is defined as the beta coefficient for thesecurity.

market risk premium

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

• Its size depends on the perceived risk of the stock market and investors' degree of risk aversion.

• Varies from year to year, but most estimates suggest that it ranges

between 4% and 8% per year.

Verifying the CAPM Empirically

-The CAPM has not been verified completely.

-Statistical tests have problems that make verification almost impossible.

-Some argue that there are additional risk factors, other than the market risk premium, that must be considered.

Security Market Line (SML)

graphical representation of the expected return-beta relationship of the CAPM

The Security Market Line (SML) is the graphical representation of CAPM. If there is an increase in inflation (and everything else remains constant), the entire SML will shift upward but remain parallel to the existing line.

If there is an increase in investor risk aversion (and everything else remains constant), the slopeof the SML will get steeper, but the Rf rate will remain the same.

required rates of return 2

Expected return on the market

required rates of return

market risk premium

Beta for the market is

Beta for the market (as measured by the S&P 500) = 1.0Beta for the risk-free rate (as measured by the T-bill rate) = 0

Beta for risk free rate

Beta for the risk-free rate (as measured by the T-bill rate) = 0

investors are

risk averse

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

Rational investors should only be compensated for systematic/undiversifiable risk

• Rational investors should hold a diversified portfolio

expected rate of return

The expected rate of return is the return expected to be realized from an investment; it is calculated as the weighted average of the probability distribution of possible results

CAPM model

The capital asset pricing model (CAPM) explains how risk should be considered when stocks and other assets are held in portfolios

The CAPM states that any stock's required rate of return is equal to the the risk-free rate of return plus a risk premium that reflects only the risk remaining after diversification.

Most individuals hold stocks in portfolios. The risk of a stock held in a portfolio is typically lower than the stock's risk when it is held alone. Therefore, the risk and return of an individual stock should be analyzed in terms of how the security affects the risk and return of the portfolio in which it is held.

expected rate of return in a portfolio

The expected rate of return on a portfolio equals the weighted average of the expected returns on the assets held in the portfolio. A portfolio's risk IS NOT calculated as the weighted average of the individual stocks' standard deviations; the portfolio's risk is generally smaller because diversification lowers the portfolios risk

correlation

Correlation is the tendency of two variables to move together, while correlation coefficient is a measure of the degree of relationship between two variables. If a portfolio consists of two stocks that are perfectly

negatively correlated

then the portfolio is riskless because the stocks' returns move countercyclically to each other. If the returns of the stocks are perfectly

positively correlated

correlated then the stocks' returns would move up and down together and the portfolio would be exactly as risky as the individual stocks.

in this case diversification is useless for reducing risk

SML

Security Market Line, a graphical representation of the CAPM.

The security market line (SML) is an equation that shows the relationship between risk as measured by beta and the required rates of return on individual securities.

If a stock's expected return plots on or above the SML, then the stock's return is SUFFICIENT

to compensate the investor for risk. If a stock's expected return plots below the SML, the stock's return is INSUFFICIENT to compensate the investor for risk

The SML line can change due to expected inflation and risk aversion. If inflation changes, then the SML plotted on a graph will shift up or down parallel to the old SML. If risk aversion changes, then the SML plotted on a graph will rotate up or down becoming more or less steep if investors become more or less risk averse. A firm can influence market risk (hence its beta coefficient) through changes in the composition of its assets and through changes in the amount of debt it uses.

stock is above/below market line

above: Undervalued

below: Overvalued

Positively correlated stocks: their prices go up and down together

systematic risk

market risk

undiversifable

unsystematic risk

can be reduced by adding negatively correlated stocks

•(diversifying)