Chapter 6: Return and Risk

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Chapter 6: Return and Risk
Learning Goals
Understand the meaning and fundamentals of risk, return, and risk aversion.
Describe procedures for measuring the risk of a single asset.
Discuss the risk measurement for a single asset using the standard deviation
and coefficient of variation.
Understand the risk and return characteristics of a portfolio in terms of
correlation and diversification, and the impact of international assets on a
portfolio.
Review the two types of risk and the derivation and role of beta in measuring
the relevant risk of both an individual security and a portfolio.
Explain the capital asset pricing model (CAPM) and its relationship to the
security market line (SML).
Introduction

If everyone knew ahead of time how much a stock would sell for some time in
the future, investing would be a simple endeavor.

Unfortunately, it is difficult—if not impossible—to make such predictions with
any degree of certainty.

As a result, investors often use history as a basis for predicting the future.

We will begin this chapter by evaluating the risk and return characteristics of
individual assets, and end by looking at portfolios of assets.
Fundamental Concepts about Return and
Risk

In the context of business and finance, risk is defined as the chance of
suffering a financial loss.

Assets (real or financial) which have a greater chance of loss are considered
more risky than those with a lower chance of loss.

Risk may be used interchangeably with the term uncertainty to
refer to the variability of returns associated with a given asset.

Return represents the total gain or loss on an investment.

The most basic way to calculate return is as follows:

For example, compute the holding period return if you purchased a stock for
$100, received a $5 dividend, and sold the stock for $110.
Chapter Example Single Financial Assets
 Historical Return
 Arithmetic average
• The historical average (also called arithmetic average or mean) return is simple to
calculate.
• The accompanying text outlines how to calculate this and other measures of risk and
return.
• All of these calculations were discussed and taught in your introductory statistics
course.
• This slideshow will demonstrate the calculation of these statistics using Microsoft ®
Excel.
Historical Return
 Arithmetic Average
Single Financial Assets
 Historical Risk
 Variance
• Historical risk can be measured by the variability of an asset’s returns in relation to its
average.
• Variance is computed by summing squared deviations and dividing by the number of
observations minus one (n - 1).
• Squaring the differences ensures that both positive and negative deviations are given
equal consideration.
• The sum of the squared differences is then divided by the number of observations
minus one (n - 1).
 Historical Risk
 Standard deviation
• Squaring the deviations makes the variance difficult to interpret.
• In other words, by squaring percentages, the resulting deviations are in percent
squared terms.
• The standard deviation simplifies interpretation by taking the square root of the squared
percentages.
• In other words, standard deviation is in the same units as the computed average.
• If the average is 10%, the standard deviation might be 20%, whereas the variance
would be 20% squared.
 Expected Return and Risk
 Investors and analysts often look at historical returns as a starting point for
predicting the future.
 However, they are much more interested in what the returns on their
investments will be in the future.
 For this reason, we need a method for estimating future or “ex-ante”
returns.
 One way of doing this is to assign probabilities for future states of nature
and the returns that would be realized if a particular state of nature does
occur.
 Coefficient of Variation (CV)
 One problem with using standard deviation as a measure of risk is that we
cannot easily make risk comparisons between two assets.
 The coefficient of variation overcomes this problem by measuring the
amount of risk per unit of return.
 The higher the coefficient of variation, the more risk per return.
 Therefore, if given a choice, an investor would select the asset with the
lower coefficient of variation.
Portfolio of Assets
 An investment portfolio is any collection or combination of financial assets.
 If we assume all investors are rational and therefore risk averse, that investor will ALWAYS
choose to invest in portfolios rather than in single assets.
 Investors will hold portfolios because he or she will diversify away a portion of the risk that is
inherent in “putting all your eggs in one basket.”
 If an investor holds a single asset, he or she will fully suffer the consequences of poor
performance.
 This is not the case for an investor who owns a diversified portfolio of assets.
 Diversification is enhanced depending upon the extent to which the returns on assets “move”
together.
 This movement is typically measured by a statistic known as correlation as shown in Figure
6.3 below.
 Even if two assets are not perfectly negatively correlated, an investor can still realize
diversification benefits from combining them in a portfolio as shown in Figure 6.4 below.

Capital Asset Pricing Model (CAPM)
 If you notice in the last slide, a good part of a portfolio’s risk (the standard deviation of
returns) can be eliminated simply by holding a lot of stocks.
 The risk you can’t get rid of by adding stocks (systematic) cannot be eliminated through
diversification because that variability is caused by events that affect most stocks similarly.
 Examples would include changes in macroeconomic factors such interest rates, inflation,
and the business cycle.

Capital Asset Pricing Model (CAPM)
 In the early 1960s, researchers (Sharpe, Treynor, and Lintner) developed an asset pricing
model that measures only the amount of systematic risk a particular asset has.
 In other words, they noticed that most stocks go down when interest rates go up, but some
go down a whole lot more.
 They reasoned that if they could measure this variability—the systematic risk—then they
could develop a model to price assets using only this risk.
 The unsystematic (company-related) risk is irrelevant because it could easily be eliminated
simply by diversifying.

Capital Asset Pricing Model (CAPM)
 To measure the amount of systematic risk an asset has, they simply regressed the returns
for the “market portfolio”—the portfolio of ALL assets—against the returns for an individual
asset.
 The slope of the regression line—beta—measures an asset’s systematic (nondiversifiable) risk.
 In general, cyclical companies like auto companies have high betas while relatively stable
companies, like public utilities, have low betas.
 Let’s look at an example to see how this works.
 Capital Asset Pricing Model (CAPM)
 The required return for all assets is composed of two parts: the risk-free
rate and a risk premium.
 The risk premium is a function of both market conditions and the asset
itself.
 The risk-free rate (rf) is usually estimated from the return on U.S. T-Bills.
 The risk premium for a stock is composed of two parts:
• The market risk premium, which is the return required for investing in any risky asset
rather than the risk-free rate.
• Beta, a risk coefficient which measures the sensitivity of the particular stock’s return to
changes in market conditions.
 After estimating beta, which measures a specific asset’s systematic risk, relatively easy to
estimate variables may be obtained to calculate an asset’s required return.
 Example
• Calculate the required return for Federal Express assuming it has a beta of 1.25, the
rate on U.S. T-Bills is 5.07%, and the expected return for the S&P 500 is 15%.
 Some Comments on the CAPM
 The CAPM is based on an assumed efficient market with the following
characteristics:
• Many small investors each having the same information and expectations with respect
to securities
• Rational investors who are risk averse
• No restrictions on investment
• No taxes
• No transactions costs
 Because these assumptions do not strictly hold, the CAPM should only be
viewed as a useful conceptual framework for understanding the risk and
return on an investment.
 In addition, the data used to approximate the beta and other components of
the CAPM are historical.
 Because the CAPM is an expectational model, these variables may or may
not reflect the future variability of returns.
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