Principles of Managerial Finance Brief Edition

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Principles of Managerial FinanceBrief Edition

• Chapter 7

Risk and Return
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Learning Objectives

• Understand the meaning and fundamentals of risk,
  return, and risk aversion.
• Describe the procedures for assessing 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.

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Learning Objectives

• 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).

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Introduction

• If everyone knew ahead of time how much a stock
  would sell for some time in the future, investing
  would be 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.

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Risk Defined

• In the contest 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.

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Return Defined

• Return represents the total gain or loss on an
  investment.
• The most basic way to calculate return is as
  follows

kt Pt - Pt-1 Ct Pt-1

• Where kt is the actual, required or expected
  return during period t, Pt is the current price,
  Pt-1 is the price during the previous time
  period, and Ct is any cash flow accruing from the
  investment

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Chapter Example
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Single Financial Assets
Historical Return

• Arithmetic Average
• The historical average (also called arithmetic
  average or mean) return is simple to calculate.
• The 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 EXCEL.

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Single Financial Assets
Historical Return
Arithmetic Average
What you type
What you see
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Single Financial Assets
Historical Risk

• Variance
• Historical risk can be measured by the
  variability of its returns in relation to its
  average.
• Variance is computed by summing squared
  deviations and dividing by 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.

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Single Financial Assets
Historical Risk
Variance
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Single Financial Assets
Historical Risk
Variance
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Single Financial Assets
Historical Risk
Variance
What you type
What you see
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Single Financial Assets
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.

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Single Financial Assets
Historical Risk
Standard Deviation
What you type
What you see
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Single Financial Assets
Historical Risk
Normal Distribution
R-2?
R-1?
R2?
R1?
R
68
95
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Single Financial Assets
Expected Return 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 would occur.

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Single Financial Assets
Expected Return Risk
Expected Return E(R) ? piRi, where pi
probability of the ith scenario, and Ri the
forecasted return in the ith scenario.
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Single Financial Assets
Expected Return Risk
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Single Financial Assets
Expected Return Risk
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Single Financial Assets
Expected Return Risk
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Single Financial Assets
Expected Return Risk
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Single Financial Assets
Coefficient of Variation

• 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.

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Single Financial Assets
Coefficient of Variation
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Portfolios 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 hold a portfolio rather than a single
  asset.
• 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
  portfolio.

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Portfolios 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 7.3 and 7.4.

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Portfolios of Assets
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Portfolios of Assets
Recall Stocks A and B
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Portfolios of Assets
Portfolio AB (50 in A, 50 in B)
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Portfolios of Assets
Portfolio AB (50 in A, 50 in B)
Where the contents of cell B12 and B13 50 in
this case.
Here are cells B12 and B13
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Portfolios of Assets
Portfolio AB (50 in A, 50 in B)
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Portfolios of Assets
Portfolio AB (40 in A, 60 in B)
Changing the weights
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Portfolios of Assets
Portfolio AB (20 in A, 80 in B)
And Again
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Portfolios of Assets
Portfolio Risk Return
Summarizing changes in risk and return as the
composition of the portfolio changes.
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Portfolios of Assets
Portfolio Risk Return (Perfect Negative
Correlation)
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Portfolios of Assets
Portfolio Risk Return (Perfect Negative
Correlation)
Notice that if we weight the portfolio just right
(50/50 in this case), we can completely eliminate
risk.
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Portfolios of Assets
Portfolio Risk (Adding Assets to a Portfolio)
Portfolio Risk (SD)
Unsystematic (diversifiable) Risk
SDM
Systematic (non-diversifiable) Risk
of Stocks
0
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Portfolios of Assets
Portfolio Risk (Adding Assets to a Portfolio)
Portfolio Risk (SD)
Portfolio of Domestic Assets Only
Portfolio of both Domestic and International
Assets
SDM
of Stocks
0
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Portfolios of Assets
Capital Asset Pricing Model (CAPM)

• If you notice in the last slide, a good part of
  a portfolios risk (the standard deviation of
  returns) can be eliminated simply by holding a
  bunch of stocks.
• The risk you cant 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.

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Portfolios of Assets
Capital Asset Pricing Model (CAPM)

• Then 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 figured 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.

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Portfolios of Assets
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 assets systematic (non-diversifiable)
  risk.
• In general, cyclical companies like auto
  companies have high betas while relatively
  stable companies, like public utilities,have
  low betas.
• Lets look at an example to see how this works.

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Portfolios of Assets
Capital Asset Pricing Model (CAPM)

• The text goes through a fairly long calculation
  to arrive at beta.
• We will demonstrate the calculation using the
  regression analysis feature in EXCEL.
• By the way, its a whole lot faster.

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Portfolios of Assets
Capital Asset Pricing Model (CAPM)
This slide is the result of a regression using
the Excel. The slope of the regression (beta) in
this case is 1.92. Apparently, this stock has a
considerable amount of systematic risk.
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Portfolios of Assets
Capital Asset Pricing Model (CAPM)
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Portfolios of Assets
Capital Asset Pricing Model (CAPM)
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Portfolios of Assets
Capital Asset Pricing Model (CAPM)
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Portfolios of Assets
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 US T-bills
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Portfolios of Assets
Capital Asset Pricing Model (CAPM)

• 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 stocks return to
  changes in market conditions.

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Portfolios of Assets
Capital Asset Pricing Model (CAPM)

• After estimating beta, which measures a specific
  assets systematic risk, relatively easy to
  estimate variables may be obtained to calculate
  an assets required return..

E(Ri) RFR b E(Rm) - RFR, where E(Ri) an
assets expected or required return, RFR the
risk free rate of return, b an asset or
portfolios beta E(Rm) the expected return on
the market portfolio.
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Portfolios of Assets
Capital Asset Pricing Model (CAPM)
Example Calculate the required return for Federal
Express assuming it has a beta of 1.25, the rate
on US T-bills is 5.07, and the expected return
for the SP 500 is 15.
E(Ri) 5.07 1.25 15 - 5.07 E(Ri) 17.48
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Portfolios of Assets
Capital Asset Pricing Model (CAPM)
Graphically
E(Ri)
17.48
15.0
RFR 5.07
beta
1.25
1.0
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Portfolios of Assets
Capital Asset Pricing Model (CAPM)
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Portfolios of Assets
Capital Asset Pricing Model (CAPM)
SML
k
20
15
10
5
B
1
2
MSFT
FPL
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Portfolios of Assets
Capital Asset Pricing Model (CAPM)
SML1
k
20
SML2
15
Shift due to change in market return from 15 to
12
10
5
B
1
2
FPL
MSFT
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Portfolios of Assets
Capital Asset Pricing Model (CAPM)
SML2
SML1
k
20
15
Shift due to change in risk-free rate from 5 to
8. Note that all returns will increase by 3
10
5
B
1
2
MSFT
FPL