Intro to Finance: Chapter 8

Setting those concerns aside, the important question is whether the CAPM works in a practical sense. Do securities with higher betas earn higher returns over time? There is mixed evidence on that question. Many studies have supported the CAPM's main prediction, that stocks with higher betas should have higher returns on average, but the link between beta and expected returns seems:

"flatter" than the CAPM predicts. Investments with higher betas tend to earn higher returns, but not to the degree that the CAPM predicts.

The two green dotted line segments in Figure 8.5 illustrates what happens in the opposite extreme case when the correlation between two assets is:

-1

For stocks that are perfectly negatively correlated, the correlation coefficient equals:

-1, and a plot of the returns on those stocks would show that they fall exactly on a downward sloping line

The notion that risk is somehow connected to uncertainty is intuitive. The more uncertain you are about how an investment will perform...

... the riskier that investment seems.

The return of a stock that is half as responsive as the market should change (on average) by:

0.5% for each 1% change in the return of the market portfolio.

For example, when the market return increases by 10%, a portfolio with a beta of 0.75 will tend to experience a ___ increase in its return a portfolio with a beta of 1.25 will ___.

7.5% experience a 12.5% increase in its return. Clearly, a portfolio containing mostly low-beta assets will have a low beta, and one containing mostly high-beta assets will have a high beta.

What is a normal probability distribution?

A normal probability distribution, depicted in Figure 8.3, resembles a symmetrical "bell-shaped" curve. The symmetry of the curve means that half the probability is associated with the values to the left of the peak and half with the values to the right. As noted on the figure, for normal probability distributions, 68% of possible outcomes will lie between standard deviation from the expected return, 95% of all outcomes will lie between standard deviations from the expected return, and 99.7% of all outcomes will lie between standard deviations from the expected return.

Why is gambling risk seeking?

By design, the average person who buys a lottery ticket or gambles in a casino loses money. After all, state governments and casinos make money from these endeavors, which implies that individuals lose on average and the expected return is negative. People nonetheless buy lottery tickets and visit casinos, and in doing so they exhibit risk-seeking behavior.

What is correlation?

Correlation is a statistical measure of the relationship between any two series of numbers. The numbers may represent data of any kind, from investment returns to test scores.

What does scenario analysis do?

Scenario analysis provides a simple way to quantify that intuition, and probability distributions offer a more sophisticated method for analyzing the risk of an investment.

Describe what scenario analysis uses in order to benefit the investor.

Scenario analysis uses several possible alternative outcomes (scenarios) to obtain a sense of the variability of returns. One common method involves considering pessimistic (worst), most likely (expected), and optimistic (best) outcomes and the returns associated with them.

What is the coefficient of variation?

The coefficient of variation, CV, is a measure of relative dispersion that is useful in comparing assets with different standard deviations and different average, or expected, returns.

Explain probability.

The probability of a given outcome is its chance of occurring. We would expect that an outcome with an 80% probability would occur eight out of 10 times. An outcome with a probability of 100% is certain to occur. Outcomes with a probability of zero will never occur.

What is the range?

The range is the difference between the return provided by the optimistic and pessimistic scenarios. Intuitively, an asset with a greater range of possible returns seems more risky.

Explain risk averse.

The third category of behavior with respect to risk, and the one that describes the behavior of most people most of the time, is risk aversion.

What is the total rate of return?

The total rate of return (sometimes called the holding period return) is the total gain or loss experienced on an investment over a given period expressed as a percentage of the investment's value at the beginning of the period.

Changes in risk aversion and the slope of the SML result from changing preferences of investors, which generally stem from economic, political, or social events. Examples of events that increase risk aversion include:

a stock market crash or recession, assassination of a key political leader, and the outbreak of war

Because in practice the correlation between two investments is almost never , then we can repeat a lesson from before—the standard deviation of a portfolio is:

almost never equal to a weighted average of the standard deviations of the assets in the portfolio. Instead, the portfolio's standard deviation is almost always less than the simple weighted average.

A higher coefficient of variation means that:

an investment has more volatility relative to its expected return. Because investors prefer higher returns and less risk, one might intuitively expect investors to gravitate toward investments with a low coefficient of variation.

Fourth, we add up these terms over time...

and divide by n − 1

f we had many more data points for Google and Coca-Cola monthly stock returns, the histograms in Figure 8.2 would begin to look more and more like smooth curves representing a:

continuous probability distribution.

As part of that analysis, we will look at the statistical concept of _____, which underlies the process of diversification used to develop an efficient portfolio.

correlation

Most large firms rely on the CAPM to estimate their

cost of capital, which in turn has a major impact on the investments the firm chooses to undertake.

Earlier in this chapter we said that investors tend to be risk averse, which means they require compensation for bearing risk. However, diversifiable risk is:

costless to eliminate. An investor can completely eliminate diversifiable risk simply by holding a portfolio of assets from many different industries.

The variance measures the...

dispersion or volatility of an investment's return about its average return.

Figure 8.7 shows that:

diversifiable risk gradually disappears as the number of stocks in the portfolio increases.

To reduce portfolio risk, it is best to:

diversify by combining, or adding to the portfolio, assets that have the lowest possible correlation.

The CAPM makes several predictions. First among those is that stocks with higher betas tend to:

earn higher returns.

Investors want to create an _____, one that provides the maximum return for a given level of risk. We therefore need a way to measure the return and the standard deviation of a portfolio of assets

efficient portfolio

The terms are called portfolio weights because they indicate the fraction of a portfolio's total value invested in each asset. To account for 100% of the portfolio's assets, the sum of these weights must:

equal 1.

The key takeaway from Part C of Table 8.6 is that the standard deviation of a portfolio is almost never:

equal to a simple weighted average of the standard deviations of the assets in the portfolio.

For stocks that are uncorrelated, the correlation coefficient:

equals 0, which means there is no relation between the returns on the two stocks. A graph of uncorrelated stock returns would look like a random cloud of points, and a trendline drawn through those points would have a slope of zero.

Coca-Cola's monthly return was between 0% and 5% much more often, about 44% of the time over that same period. Google's returns were far more likely to be very high or low than were Coca-Cola's. For example, Google stock achieved a monthly return of between 15% and 20% about 4% of the time, whereas Coca-Cola stock never performed that well in a single month during this period. In principle, we could use these historical frequencies to:

form estimates of the probabilities of different return outcomes for Google and Coca-Cola on a forward-looking basis.

The slope of the security market line reflects the:

general risk preferences of investors in the marketplace

Most investments have more than two or three possible outcomes, and in most cases the probability of each outcome is unknown. One way to deal with such problems is to create a:

histogram using historical data on actual returns.

With perfect positive correlation, an investor still might prefer to:

hold some combination of both stocks rather than one, but the benefit of diversification is not as great as when the correlation coefficient is less than +1.

We have already seen that the average return on a portfolio depends on the average returns of the stocks in the portfolio, but a portfolio's standard deviation is more complex. .t depends not only on the standard deviations of the stocks in the portfolio but also on

how those stocks are correlated with each other.

Combining assets that have a low correlation with each other can sometimes simultaneously:

increase a portfolio's return while decreasing its standard deviation.

Think of the risk and return curve. We can make the very strong statement that it would be irrational for an investor to hold any portfolio that lies along the portion of the blue arc in Figure 8.5 that slopes up and to the left. Any portfolio on that portion of the curve is:

inefficient, meaning that there is another portfolio that invests more in JPMorgan (look at Figure 8.5 in the book) and provides a higher return for the same standard deviation. Only portfolios that lie along the portion of the blue arc that slopes up and to the right are efficient. (think of quantiative methods, it's dominating that one alternative)

Stated another way, when choosing between two investments, a risk-averse investor will not make the riskier investment unless...

it offers a higher expected return to compensate the investor for bearing the additional risk.

Investors who are risk averse prefer:

less risky over more risky investments, holding the expected rate of return fixed.

The ____ between these two stocks is what causes the arc to bend back and to the left before turning to the right.

low correlation

First the square of the weight invested in each stock (w1 and w2) is important. Second, the variance ( o^2 1 and o^2 2) and standard deviation (o1 and o2) of each stock have an impact on a portfolio's standard deviation. Third, and perhaps most important, the correlation coefficient (p12) between stocks 1 and 2 plays a key role. The lower is the correlation between the two stocks, the:

lower will be the portfolio's standard deviation.

Because Bank of America's stock returns are very sensitive to changing market returns, it has:

more exposure to nondiversifiable risk and is therefore a riskier stock than PepsiCo.

In Figure 8.7, nondiversifiable risk is represented by the horizontal black line below which the blue curve can never go...

no matter how diversified the portfolio becomes.

The capital asset pricing model (CAPM) links:

nondiversifiable risk to expected returns.

The red dotted line in Figure 8.5 shows what the average return and standard deviation of portfolios of JPMorgan and Medtronic would look like if the two stocks were:

perfectly positively correlated.

Because our goal in this section is to quantify the link between risk and return, and because there is no link between diversifiable risk and return, our attention must shift to:

quantifying nondiversifiable risk. It is the only risk that is relevant to understanding the tradeoff between risk and return in the market.

The (rm - Rf) portion of the risk premium is called the market risk premium because it:

represents the premium that the investor expects for taking the average amount of risk associated with holding the market portfolio of assets.

That relationship reflects risk aversion by market participants, who:

require higher returns as compensation for greater risk.

Despite its limitations, the CAPM sees widespread application in corporations that use the model to assess the:

required returns their shareholders demand (and therefore the returns the firms' managers need to achieve when they invest shareholders' money

Another central prediction of the CAPM is that beta is the only thing that explains why some stocks earn higher returns than others. According to the theory, no other factor is systematically related to returns. However, since the CAPM was developed:

researchers have uncovered other characteristics that appear to influence returns. Over time, small firms, for example, tend to earn higher returns than large firms do even after taking into account that smaller firms often have higher betas.

Most important business decisions entail two key financial considerations:

risk and return. Typically there is a tradeoff between them.

Different people react to risk in different ways. Economists use three categories to describe how investors respond to risk. What are they?

risk seeking risk neutral risk averse

One investor, observing in Table 8.1 that stocks pay an average annual return that is 6.1% higher than the average return on bonds, might decide that a risk premium of that magnitude is more than enough justification for investing in stocks. Another person might prefer to invest in bonds, even though they offer much lower returns, because they are not as risky as stocks. Both investors are risk averse, but they differ in terms of their:

risk tolerance.

In equilibrium, stocks must pay higher returns (on average) than bonds; otherwise,

risk-averse investors would not buy stocks.

Fundamentally, expected returns are driven by risk in the sense that...

riskier investments tend to produce higher returns

If we depict the capital asset pricing model (Equation 8.12) graphically, it is called the:

security market line (SML). The SML is a straight line that shows how an investment's expected return depends on its beta.

These histograms group monthly returns into bins or ranges and...

show the relative frequency with which returns fell into each bin historically.

The straight line indicates that the standard deviation of a portfolio in this special case (when the correlation coefficient is) is a:

simple weighted average of the standard deviations of the two stocks.

Analysts use different methods to quantify risk, depending on whether they are looking at:

single investment or a portfolio—a collection or group of assets.

The most common statistical measure used to describe an investment's risk is its:

standard deviation.

As discussed earlier, most investors are risk averse, which means they require increased returns for increased risk. If investors become more risk averse, then the slope of the SML becomes:

steeper because when investors are more risk averse, they demand a higher return for any risk level. This also means that risk premiums increase with greater risk aversion.

To estimate a stock's beta, analysts generally use historical data. The estimated beta may or may not actually indicate:

stock's future nondiversifiable risk. Therefore, the required returns specified by the model are only approximations. Users of betas commonly make subjective adjustments to the historically determined betas to reflect their expectations of the future.

Mathematically, an investment's total return is the...

sum of any cash distributions (e.g., dividends or interest payments) plus the change in the investment's price, divided by the beginning-of-period price, as expressed in the following equation.

Perhaps counterintuitively, the standard deviation of a portfolio is almost always less than a simple weighted average of the standard deviations of the assets in the portfolio. The key to understanding why that's true is:

the concept of correlation.

In general, the lower the correlation between asset returns:

the greater the risk reduction that investors can achieve by diversifying.

It's important to emphasize that the beta describes a general tendency:

the movement of one stock relative to the market on average

The trendline's negative slope suggests that when one stock performs well...

the other tends to perform poorly.

With perfect negative correlation, the ups and downs of one stock are exactly offset by the downs and ups of the other stock, so:

the portfolio return remains constant.

Nondiversifiable risk (also called systematic risk or market risk) is:

the portion of an asset's risk that is attributable to market factors that affect most if not all firms; diversification cannot eliminate this type of risk because it affects so many firms simultaneously. Factors such as war, inflation, pandemics, the macroeconomic cycle, international trade disputes, and political events are examples of nondiversifiable risk.

Diversifiable risk (sometimes called unsystematic risk, idiosyncratic risk, unique risk, or firm-specific risk) represents:

the portion of an asset's risk that is unique to that asset and can be eliminated through diversification. It is attributable to firm-specific events, such as strikes, lawsuits, management turnover, or the loss of key accounts

Second, for each of the n historical periods (e.g., each month or year),

we calculate the difference between each stock's return and its average return and divide that by the standard deviation. This is the "standardized" return.

It is likely we would find that larger cars cost more than smaller ones, so we would say that among new cars:

weight and price are positively correlated.

The return on a portfolio () is a:

weighted average of the returns on the individual assets from which it is formed.

Investors with a high risk tolerance:

will invest in riskier assets for a much lower risk premium.

In the graph, we plot nondiversifiable risk as measured by beta on the __ axis, and we plot expected returns, r, on the ___ axis.

x y

Equation 8.12 shows that the CAPM has two parts:

(1) the risk-free rate of return, Rf, which is the required return on a risk-free asset, typically a U.S. Treasury bill (T-bill), a short-term IOU issued by the U.S. Treasury; and (2) the risk premium.

For stocks that are perfectly positively correlated, the correlation coefficient equals:

+1 and a plot of the returns on these stocks would show that they lie exactly along an upward sloping line.

The beta coefficient for the entire market (and the average beta across all stocks) equals:

1.0.

The characteristic lines tell us that the betas for Bank of America and PepsiCo are 1.73 and 0.66 respectively. This means that there is a tendency for the return on Bank of America (PepsiCo) stock to move:

1.73% (0.66%) for each 1% move in the market's return.

A stock that is twice as responsive as the market should (on average) experience a:

2% change in its return for each 1% change in the return of the market portfolio.

Investments whose returns are more uncertain are generally riskier. Give an example:

A $1,000 government bill that guarantees its holder $5 interest after 90 days has no risk because there is no uncertainty associated with the return. A $1,000 investment in stock is very risky because the stock's value may change substantially over the same 90 days.

What is a discrete probability distribution?

A discrete probability distribution lists every possible value of some random variable along with the probability of that outcome.

What is risk?

In the most basic sense, risk is a measure of the uncertainty surrounding the return that an investment will earn.

It should be evident from the figure that Google stock returns have much greater dispersion than the distribution for Coca-Cola.

Intuitively, Google seems more risky than Coca-Cola.

Explain this relationship.

Investments with higher returns have higher standard deviations. For example, stocks have the highest average return at 11.5%, which is more than three times the average return on Treasury bills. At the same time, stocks are much more volatile, with a standard deviation of 19.7%, nearly seven times greater than the 2.9% standard deviation of Treasury bills. If we accept the idea that the standard deviation is a valid way to quantify an investment's risk, the historical data confirm the existence of a positive relationship between risk and return.

Explain risk neutral.

Investors who are risk neutral choose investments based solely on their expected returns, disregarding the risks. When choosing between two investments, risk-neutral investors will always select the investment with the higher expected return regardless of its risk.

What does risk seeking mean?

Investors who are risk seeking prefer investments with higher risk, so much so that they may choose investments with very low expected returns for the thrill of taking extra risk. ex: gambling

Should we look at range as our main method of analysis?

It's not unusual for financial managers to think about the best and worst possible outcomes when they are in the early stages of analyzing a new investment project. No matter how great the intuitive appeal of this approach, looking at the range of outcomes that an investment might produce is a highly unsophisticated way of measuring its risk. More refined methods require some basic statistical tools.

What is one simple way to quantify risk?

Measure the range of possible outcomes.

Risk-averse investors merely require ____ to induce them to purchase riskier assets

Risk-averse investors merely require compensation (in the form of a higher return

If you know the beta of any asset, you can use the ____ to find that asset's expected or required return.

SML

What is expected return?

When corporate financial managers are making investment decisions, they need a way to estimate the expected returns their investment opportunities might earn. As the name implies, an asset's expected return is the return that the asset is expected to generate in some future time period, and it is composed of a risk-free rate plus a risk premium.

A visual representation of such a distribution is:

a bar chart.

A portfolio is...

a collection or group of assets.

Probability distributions provide:

a more quantitative insight into an asset's risk.

If risk is related to the uncertainty surrounding an investment's return, we must be certain we know how to measure...

an investment's return.

The concept of correlation is essential to developing a portfolio that provides the highest possible return for:

any level of risk (i.e., an efficient portfolio)

Analysts use an asset's historical returns to estimate the:

asset's beta coefficient.

First, if we know all the different returns that an investment might generate, along with their associated probabilities, we define the....

average return, as follows:

Investment returns vary both over time and between different types of investments. By ____ historical returns over a long period, we can focus on the returns that different kinds of investments tend to generate.

averaging

Because eliminating diversifiable risk is so easy and inexpensive, the market does not reward investors who:

bear it with a higher return. Higher returns serve as compensation for bearing nondiversifiable risk and only that risk

By use of statistical techniques, the "characteristic line" that best explains the relationship between the asset return and the market return coordinates is fit to the data points. The slope of this line is:

beta.

The classic theory that links risk and return for all assets is the:

capital asset pricing model (CAPM).

Bills and bonds are both issued by the U.S. government and are therefore relatively safe investments. They differ in that bills have maturities of one year or less, whereas bonds ____.

have maturities ranging up to 30 years

The correlation coefficient measures:

he degree of correlation and takes values between and

If JPMorgan and Medtronic were perfectly negatively correlated, portfolios of them would have an average return and a standard deviation lying along one of these line segments. With perfect negative correlation the potential for risk reduction through diversification is at its greatest. In this case, it is always possible to find some combination of the two stocks that produces a portfolio that is entirely free of risk, a situation known as:

hedging.

To calculate the correlation coefficient for a pair of stocks, we need:

historical returns for each stock.

Portfolio betas have the same interpretation as the betas of individual assets. They indicate the degree of responsiveness of the

portfolio's return to changes in the market return.

Asset betas may be positive or negative, but:

positive betas are the norm. The majority of beta coefficients fall between 0.5 and 2.0.

. If two series tend to vary in the same direction, they are _____ correlated. If the series vary in opposite directions, they are ___ correlated.

positively negatively

The upward sloping line indicates that these two stocks are:

positively correlated.

The beta coefficient, β, is:

relative measure of nondiversifiable risk. It is an index of the degree of movement of an asset's return in response to a change in the market return.

A close relationship is evident between:

the investment returns and the standard deviations.

A risk-averse investor who believes that two different investments have the same expected return will choose:

the investment whose returns are more certain.

The market return is:

the return on the market portfolio of all traded securities. Analysts often use the Standard & Poor's 500 Stock Composite Index or some similar stock index as the market return.

Third, in each period we multiply the standardized return for one stock times...

the standardized return for the other.

the standard deviation is the square root of:

variance.

Investors with a low risk tolerance (or a high degree of risk aversion) require a:

very large risk premium to induce them to hold riskier assets.