Professor Megginson FIN 5043BAD 5283

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Chapter 5
Risk and Return
Professor MegginsonFIN 5043/BAD 5283
Spring 2006
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Risk and Return
The return earned on investments represents the
marginal benefit of investing.
Risk represents the marginal cost of investing.
A trade-off always arises between expected risk
and expected return.
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Risk and Return
Valuing risky assets - a task fundamental to
financial management
The three-step procedure is called discounted
cash flow (DCF) analysis.
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Financial Return
Return - The Total Gain or Loss Experienced on an
Investment Over a Given Period of Time.
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Value of 1 Invested in Equities, Treasury Bonds
Bills, 1900-2003
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Percentage Returns on Bills, Bonds, and Stocks,
1900 - 2003
Difference between average return of stocks and
bills 7.6 Difference between average return
of stocks and bonds 6.5
Risk premium the difference in returns offered
by a risky asset relative to the risk-free return
available
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Distribution of Historical Stock Returns, 1900 -
2003
Percent return in a given year
Probability distribution for future stock returns
is unknown. We can approximate the unknown
distribution by assuming a normal distribution.
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Volatility of Asset Returns
Asset classes with greater volatility pay higher
average returns.

• Average return on stocks is more than double the
  average return on bonds, but stocks are 2.5 times
  more volatile.

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The Equity Risk Premium Around The World,
1900-2004
Source Triumph of the Optimists 101 Years of
Global Investment Returns, by Elroy Dimson, Paul
Marsh, and Mike Staunton, Princeton University
Press, 2002. Updated by authors.
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Risk Aversion
Risk Neutral

• Investors Seek the Highest Return Without Regard
  to Risk

Risk Seeking

• Investors Have a Taste for Risk and Will Take
  Risk Even If They Cannot Expect a Reward for
  Doing So (Las Vegas)

Risk Averse

• Investors Do Not Like Risk and Must Be
  Compensated For Taking It

Historical Returns on Financial Assets Are
Consistent with a Population of Risk-Averse
Investors
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Two Assets With Same Expected Return But
Different Distributions
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Arithmetic Versus Geometric Returns

• Arithmetic return the simple average of annual
  returns best estimate of expected return each
  year.
• Geometric average return the compound annual
  return to an investor who bought and held a stock
  t years
• Geometric avg return(1R1)(1R2)(1R3).(1Rt)1/
  t 1

AAR (-10.2)(-12.5)(15.3)(8.9) ? 4
-10.212.515.38.9?4 0.375

• Year Return
• 2002 -10.2
• 2003 -12.5
• 2004 15.3
• 2005 8.9

GAR(1-0.102)(1-0.125)(10.153)(10.089)1/4 -1
(0.898)(0.875)(1.153)(1.089)0.25 -1
-0.33
The Difference Between Arithmetic Returns and
Geometric Returns Gets Bigger the More Volatile
the Returns Are
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Risk Of A Single Asset
How Do We Measure Risk?

• One Approach Volatility of Assets Returns
• Variance (?2) - The Expected Value of Squared
  Deviations From The Mean
• Units of Variance (-squared) - Hard to
  Interpret, So Calculate Standard Deviation,
  Square Root of ?2

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Historical vs. Expected Returns
Decisions Must Be Based On Expected Returns
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Expected Return For A Portfolio

• Most Investors Hold Multiple Asset Portfolios
• Key Insight of Portfolio Theory Asset Return
  Adds Linearly, But Risk Is (Almost Always)
  Reduced in a Portfolio

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Monthly Average Return and Volatility For Three
Stocks

• Use Monthly Returns for Period January 2000
  December 2002

Use The Average Returns as Estimates of Expected
Returns on Each Stock
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Average Return and Volatility For Portfolios
0.025
0.020
100 WIRELESS TELECOM GROUP
0.015
Portfolio Expected Return
0.010
0.005
100 IMMUCELL CORP
100 REINSURANCE GROUP OF AMERICA
0.000
0.000 0.050 0.100 0.150
0.200 0.250 0.300 0.350
Portfolio Standard Deviation
How Do Portfolios of These Stocks Perform?
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Average Return and Volatility For Portfolios
50 Wireless 50 Immucell Risk Increases With
Expected Return
50 Wireless 50 Reinsurance Risk Decreases at
First, Then Increases as Expected Return Rises
Why Do Portfolios of Different Stocks Behave
Differently?
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Expected Return For Portfolio
Expected Return of Portfolio Is The Average Of
Expected Returns Of The Two Stocks
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Two-Asset Portfolio Standard Deviation
Correlation Between Stocks Influences Portfolio
Volatility
What is Correlation Between Wireless and
Immucell? 0.80 What is Correlation Between
Wireless and Reinsurance Group? -0.66
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Correlation of Reinsurance Group, Immucell, and
Wireless
Wireless and Immucell Move Together Wireless and
Reinsurance Move in Opposite Directions When
Stocks Move Together, Combining Them Doesnt
Reduce Risk Much
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Average Return and Volatility For Portfolios
0.025
0.020
WIRELESS TELECOM GROUP
0.015
Portfolio Expected Return
50 WIRELESS 50 IMMUCELL
0.010
0.005
REINSURANCE GROUP OF AMERICA
IMMUCELL CORP
0.000
0.000 0.050 0.100 0.150
0.200 0.250 0.300 0.350
Portfolio Standard Deviation
Wireless and Immucell Correlation 0.80
Wireless and Reinsurance Group -0.66
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Correlation Coefficients And Risk Reduction For
Two-Asset Portfolios
25
20
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Expected Return on the Portfolio
10
0
5
10
15
20
25
Standard Deviation of Portfolio Returns
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Portfolios of More Than Two Assets

• Five-Asset Portfolio

Expected Return of Portfolio Is Still The Average
Of Expected Returns Of The Two Stocks
How Is The Variance of Portfolio Influenced By
Number Of Assets in Portfolio?
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Variance Covariance Matrix
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What Is a Stocks Beta?
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Diversifiable And Non-Diversifiable Risk

• As Number of Assets Increases, Diversification
  Reduces the Importance of a Stocks Own Variance
• Diversifiable risk, unsystematic risk
• Only an Assets Covariance With All Other Assets
  Contributes Measurably to Overall Portfolio
  Return Variance
• Non-diversifiable risk, systematic risk

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How Risky Is an Individual Asset?
First Approach Assets Variance or Standard
Deviation
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The Impact Of Additional Assets On The Risk Of A
Portfolio
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Risk and Return
Valuing Risky Assets Should Take Into Account
Expected Return and Risk Most Investors Risk
Averse Demand Compensation For Bearing
Risk Risk Can Be Defined In Many Ways Market
Should Reward Only Systematic Risk