Chapter 8. Risk and Rates of Return

An asset's risk can be analyzed in two ways:

(1) on a stand-alone basis, where the asset is considered by itself and (2) on a portfolio basis, where the asset is held as one of a number of assets in a portfolio

nominal, or quoted, risk-free rate, rRF

(1)a real inflation free rate of return, r* and (2)an inflation premium, IP, equal to the anticipated rate of inflation.

Slope Graphs notes:

-A steeper line suggests that an investor is very averse to taking on risk, whereas a flatter line would suggest that the investor is more comfortable bearing risk. -investors who are less comfortable bearing risk tend to gravitate toward lower-risk investments, while investors with a greater risk appetite tend to put more of their money into higher-risk, higher-return investments

market portfolio

-a portfolio consisting of ALL stocks in the market. It has low transactions costs and fees.

standard deviation (to Measure Risk)

-is a measure of how far the actual return is likely to deviate from the expected return. -use the standard deviation (σ, pronounced "sigma") to quantify the tightness of the probability distribution. The smaller the standard deviation, the tighter the probability distribution and, accordingly, the lower the risk.

three potential problems with historical risk premiums.

-what is the proper number of years over which to compute the average -historical premiums are likely to be misleading at times when the market risk premium is changing. -is that historical estimates may be biased upward because they include only the returns of firms that have survived—they do not reflect the losses incurred on investments in failed firms

In a portfolio context, a stock's risk can be divided into

1. diversifiable risk, which can be diversified away and is thus of little concern to diversified investors, and 2. market risk, which reflects the risk of a general stock market decline and cannot be eliminated by diversification

Sharpe Ratio

A measure of standalone 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.

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, or CAPM

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.

Risk analysis can be confusing, but it will help if you keep the following points in mind:

All business assets are expected to produce cash flows, and the riskiness of an asset is based on the riskiness of its cash flows. The riskier the cash flows, the riskier the asset. Assets can be categorized as financial assets, especially stocks and bonds, and as real assets, such as trucks, machines, and whole businesses. In theory, risk analysis for all types of assets is similar, and the same fundamental concepts apply to all assets.

5. Important-Past v Future Stocks

Although the past gives us insights into the risk and returns on various investments, there is no guarantee that the future will repeat the past. Stocks that have performed well in recent years might tumble, while stocks that have struggled may rebound. The same thing may hold true for the stock market as a whole.

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.

Using Historical Data to Measure Risk

Because past results are often repeated in the future, the historical s is often used as an estimate of future risk

A Bond's riskiness

Bonds offer relatively low returns, but with relatively little risk—at least if you stick to Treasury and high-grade corporate bonds.

average stock's beta

By definition, bA=1 because an average-risk stock is one that tends to move up and down in step with the general market.

diversifiable risk (unsystematic risk)

Diversifiable risk is caused by such random, unsystematic events as lawsuits, strikes, successful and unsuccessful marketing and R&D programs, the winning or losing of a major contract, and other events that are unique to the particular firm. Because these events are random, their effects on a portfolio can be eliminated by diversification—bad events for one firm will be offset by good events for another

2. Important- diversification

Diversification is crucial. By diversifying wisely, investors can dramatically reduce risk without reducing their expected returns. Don't put all of your money in one or two stocks or in one or two industries. A huge mistake that many people make is to invest a high percentage of their funds in their employer's stock. If the company goes bankrupt, they not only lose their job but also their invested capital. Although no stock is completely riskless, you can smooth out the bumps by holding a well-diversified portfolio.

How graphs would change

If we carefully selected the stocks included in the portfolio rather than adding them randomly, the graph would change. In particular, if we chose stocks with low correlations with one another and with low stand-alone risk, the portfolio's risk would decline faster than if random stocks were added

Averse to Risk

Investors in general are averse to risk, so they will not buy risky assets unless they are compensated with high expected returns.

flight to quality

Investors rapidly moved away from riskier investments and instead flocked toward safer investments such as Treasury securities and money market funds.

probability distribution

Listings of possible outcomes or events with a probability (chance of occurrence) assigned to each outcome. the tighter the probability distribution, the lower the risk.

Stats items

Probability distributions Expected rates of return, ("r hat") Historical, or past realized, rates of return, ("r bar") Standard deviation, σ (sigma) Coefficient of variation (CV) Sharpe ratio

3. Important- Real Returns

Real returns are what matters. All investors should understand the difference between nominal and real returns. When assessing performance, the real return (what remains after inflation) is what matters. It follows that as expected inflation increases, investors need to receive higher nominal returns

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.

risk aversion

Risk-averse investors dislike risk and require higher rates of return as an inducement to buy riskier securities. If you choose the less risky investment

A stock's riskiness

Stocks offer the chance of higher returns, but stocks are generally riskier than bonds. If you invest in speculative stocks (or, really, any stock), you are taking a significant risk in the hope of making an appreciable return.

Market Risk Premium (RPm)

The additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk. is hard to measure because it is impossible to obtain a precise estimate of the expected future return of the market,

Risk

The chance that some unfavorable event will occur.

risk premium (RP)

The difference between the expected rate of return on a given risky asset and that on a less risky asset.

Trade off between risk and return

The pattern of higher risk assets offering higher average annual returns on investment than lower risk assets. To entice investors to take on more risk, you have to provide them with higher expected returns.

expected rate of return

The rate of return expected to be realized from an investment; the weighted average of the probability distribution of possible results.

stand-alone risk

The risk an investor would face if he or she held only one asset. stand-alone risk is important to the owners of small businesses and in our examination of physical assets

4. Important- Investment Risk

The risk of an investment often depends on how long you plan to hold the investment. Common stocks, for example, can be extremely risky for short-term investors. However, over the long haul, the bumps tend to even out; thus, stocks are less risky when held as part of a long-term portfolio.

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

correlation and correlation coefficient

The tendency of two variables to move together. A measure of the degree of relationship between two variables.(p pronounced rho)

Risk Defined

The tighter the probability distribution of expected future returns, the smaller the risk of a given investment

1. Important- trade off

There is a trade-off between risk and return. The average investor likes higher returns but dislikes risk. It follows that higher-risk investments need to offer investors higher expected returns. Put another way—if you are seeking higher returns, you must be willing to assume higher risks.

Have there been any studies that question the validity of the CAPM? Explain.

a study by Eugene Fama of the University of Chicago and Kenneth French of Dartmouth found no historical relationship between stocks' returns and their market betas, confirming a position long held by some professors and stock market analysts

A stock's risk can be considered in two ways:

a. on a stand-alone, or single-stock, basis, or b. in a portfolio context, where a number of stocks are combined and their consolidated cash flows are analyzed.

in the CAPM theory

beta is the most appropriate measure of a stock's relevant risk

A stock's risk has two components,

diversifiable risk and market risk.

The portfolio's total risk can be divided into two parts

diversifiable risk and market risk. Diversifiable risk is the risk that is eliminated by adding stocks. Market risk is the risk that remains even if the portfolio holds every stock in the market

A company's beta can also change as a result of

external factors such as increased competition in its industry and expiration of basic patents

risk-free rate of return

is generally measured by the return on U.S. Treasury securities. Some analysts recommend that short-term T-bills be used; others recommend long-term T-bonds. We generally use T-bonds because their maturity is closer to the average investor's holding period for stocks.

Portfolio risk declines as

on average, portfolio risk declines as the number of stocks in a portfolio increases. The portfolio's risk declines as stocks are added, but at a decreasing rate; once 40 to 50 stocks are in the portfolio, additional stocks do little to reduce risk.

What are the implications of risk aversion for security prices and rates of return?

other things held constant, the higher a security's risk, the higher its required return, and if this situation does not hold, prices will change to bring about the required condition

Most stocks are ____ correlated with the market

positively

Ri

required rate of return on the ith stock. Note that if is less than , the typical investor will not purchase this stock or will sell it if he or she owns it. If is greater than , the investor will purchase the stock because it looks like a bargain. Investors will be indifferent if . Buying and selling by investors tends to force the expected return to equal the required return, although the two can differ from time to time before the adjustment is completed.

Sharpe Ratio Formula

sharpe ratio=(return-risk free rate)/ σ

Market Risk

stems from factors that systematically affect most firms: war, inflation, recessions, high interest rates, and other macro factors. Because most stocks are affected by macro factors, market risk cannot be eliminated by diversification.

Portfolio- risk

the risk of a stock held in a portfolio is typically lower than the stock's risk when it is held alone. Because investors dislike risk and because risk can be reduced by holding portfolios, most stocks are held in portfolios. Banks, pension funds, insurance companies, mutual funds, and other financial institutions are required by law to hold diversified portfolios.

expected return on a portfolio

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