Risk and Return
Professor XXXXX
Course Name / Number
Introduction To Risk & Return
Valuing Risky Assets - Fundamental to Financial
Management
Three-Step Procedure for Valuing a Risky Asset
• Determine The Asset’s Expected Cash Flows
• Choose Discount Rate That Reflects Asset’s Risk
• Calculate Present Value (PV cash inflows - PV
outflows)
Trade-off Between Risk and Expected Return
2
Real Returns on U.S. Investments,
1900 - 2000
Mean
Return (%)
Asset
Standard
Deviation (%)
Highest
Year (%)
Lowest
Year (%)
Stocks
8.7
20.2
56.8
-38.0
Bonds
2.1
10.0
35.1
-19.3
Bills
1.0
4.7
20.0
-15.1
Inflation
3.3
5.0
20.4
-10.8
Source: Triumph of the Optimists: 101 Years of Global Investment Returns, by
Elroy Dimson, Paul Marsh, and Mike Staunton, Princeton University Press, 2002
Difference Between Average Return of Stocks and Bills = 7.7%
Difference Between Average Return of Bonds and Bills = 1.1%
Risk Premium - The Difference In Returns Between
Investments Having Different Risks
3
Real Return Approximately Equal to Nominal Return Minus Inflation
Rate
The Equity Risk Premium,
1900-2000
Country
4
Arithmetic
mean (%)
Geometric
mean (%)
Standard
deviation (%)
Australia
8.5
7.1
17.2
Canada
6.0
4.6
16.7
France
9.9
7.5
23.8
Germany
10.3
4.9
35.3
Italy
11.0
7.0
32.5
Japan
10.0
6.8
28.0
Netherlands
7.1
5.1
22.2
Switzerland
6.1
4.3
19.4
United Kingdom
6.5
4.7
19.9
United States
7.5
5.6
19.8
Risk Aversion
Risk Neutral
5
• 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
Financial Return
Return - The Total Gain or Loss Experienced on an
Investment Over a Given Period of Time.
Pt 1  Pt  Ct 1
Rt 1 
Pt
An example....
Investor Bought Utilyco
for $60/share
Dividend = $6/share
6
Sold for $66/share
$66 - $60 + $6
Rutil =
$60
$12

 20%
$60
Arithmetic Versus Geometric
Average Returns
Arithmetic Average is Generally Bigger Than
Geometric Average
An example....
7
Year
Return
2000
-10%
2001
+12%
2002
+15%
2003
+ 8%
AAR = 6.25%
GAR = 5.78%
The Difference Between Arithmetic Returns and Geometric Returns
Gets Bigger the More Volatile the Returns Are
Risk Of A Single Asset
How Do We Measure Risk?
• One Approach –Volatility of Asset’s 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
An example.…Immucell
Corp.
Monthly Returns for Jan
2000 – Dec 2002
8
Average Return =
0.838%
N
2
(
R

R
)
i
 it
2
(

26
.
96
%

0
.
838
%)
 2  t 1

N 1
35
(22.34%  0.838%) 2

 ......  4.4% 2
35
Historical vs. Expected Returns
Decisions Must Be Based On Expected Returns
There Are Many Ways to Estimate Expected Returns
Simple Way to Estimate Expected Return
9
Assume That Expected Return Going Forward
Equals the Average Return in the Past
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
E ( R p )  w1 E ( R1 )  w2 E ( R2 )  w3 E ( R3 )  ...  wN E ( RN )
10
Monthly Average Return and
Volatility For Three Stocks
• Use Monthly Returns for Period January 2000
– December 2002
Company
Average (mean)
monthly return, %
Standard deviation of
monthly return, %
WIRELESS TELECOM
GROUP INC
2.03
29.16
REINSURANCE GROUP
OF AMERICA INC
IMMUCELL CORP
0.68
12.31
0.83
20.98
Use The Average Returns as Estimates of
Expected Returns on Each Stock
11
Portfolio Expected Return
Average Return and Volatility For
Portfolios
0.025
0.020
50% WIRELESS + 50%
REINSURANCE
100% WIRELESS
TELECOM GROUP
0.015
50% WIRELESS + 50%
IMMUCELL
0.010
0.005
0.000
0.000
100% REINSURANCE
GROUP OF AMERICA
0.050
0.100
0.150
100% IMMUCELL CORP
0.200
0.250
0.300
Portfolio Standard Deviation
How Do Portfolios of These Stocks Perform?
12
0.350
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?
13
Expected Return For Portfolio
50% Wireless + 50% Immucell
E ( R p )  w1 E ( R1 )  w2 E ( R2 )
 0.52.03%  0.50.84%  1.43%
50% Wireless + 50% Reinsurance
E ( R p )  w1 E ( R1 )  w2 E ( R2 )
 0.52.03%  0.50.69%  1.36%
14
Expected Return of Portfolio Is The Average Of
Expected Returns Of The Two Stocks
Two-Asset Portfolio Standard
Deviation
 p  w1  1  w2  2  2w1 w2 12 1 2
2
2
2
2
2
Standard Deviation   p
2
Correlation Between Stocks Influences Portfolio
Volatility
15
What is Correlation Between Wireless and Immucell?
0.80
What is Correlation Between Wireless and Reinsurance Group?
-0.66
Correlation of Reinsurance Group,
Immucell, and Wireless
Relative Performance of Three Stocks
Stock Price Relative to Price in
January 2000
2.5
2
1.5
1
0.5
0
January 2000 - December 2002
Reinsurance Group
16
Immucell Corp.
Wireless Telecom
Wireless and Immucell Move Together; Wireless and Reinsurance
Move in Opposite Directions
When Stocks Move Together, Combining Them Doesn’t Reduce Risk
Much
Portfolio Expected Return
Average Return and Volatility For
Portfolios
0.025
0.020
50% WIRELESS – 50%
REINSURANCE
WIRELESS
TELECOM GROUP
0.015
50% WIRELESS – 50%
IMMUCELL
0.010
0.005
0.000
0.000
REINSURANCE GROUP
OF AMERICA
0.050
0.100
0.150
IMMUCELL CORP
0.200
0.250
Portfolio Standard Deviation
Wireless and Immucell Correlation: 0.80
17
Wireless and Reinsurance Group: -0.66
0.300
0.350
Expected Return on the Portfolio
Correlation Coefficients And Risk
Reduction For Two-Asset Portfolios
25%
-1.0 <  <1.0
20%
 is +1.0
15%
 is -1.0
10%
0%
5%
10%
15%
20%
25%
Standard Deviation of Portfolio Returns
18
Portfolios of More Than Two Assets
• Five-Asset Portfolio
E ( R p )  w1 E ( R1 )  w2 E ( R2 )  w3 E ( R3 )
 w4 E ( R4 )  w5 E ( R5 )
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?
19
Variance – Covariance Matrix
Asset
1
1
2
2
1 2
  1
5
2
1
   12
5
3
4
1
   13
5
2
1
   14
5
2
1
   15
5
2
1
   24
5
2
1
   25
5
2
1
   21
5
3
1
   31
5
2
1
   32
5
2
1 2
  3
5
2
1
   34
5
4
1
   41
5
2
1
   51
5
2
1
   42
5
2
1
   52
5
2
1
   43
5
2
1
   53
5
2
1 2
  4
5
2
1
   54
5
5
2
2
1
   23
5
1 2
  2
5
5
2
2
2
1
   35
5
2
2
1
   45
5
2
1 2
  5
5
2
Variance of Individual Assets Account Only for 1/25th of the
Portfolio Variance
20
The Covariance Terms Determine To A Large Extent The
Variance Of The Portfolio
What Is a Stock’s Beta?
Beta Is a Measure of Systematic Risk
 im
i  2
m
What If
Beta = 1?
21
What If
Beta > 1 or
Beta <1?
•
•
•
•
The Stock Moves 1% on Average When the
Market Moves 1%
An “Average” Level of Risk
The Stock Moves More Than 1% on Average
When the Market Moves 1% (Beta > 1)
The Stock Moves Less Than 1% on Average
When the Market Moves 1% (Beta < 1)
Diversifiable And Non-Diversifiable
Risk
• As Number of Assets Increases,
Diversification Reduces the Importance
of a Stock’s Own Variance
– Diversifiable risk, unsystematic risk
• Only an Asset’s Covariance With All Other
Assets Contributes Measurably to Overall
Portfolio Return Variance
– Non-diversifiable risk, systematic risk
22
How Risky Is an Individual Asset?
First Approach – Asset’s Variance or Standard
Deviation
What Really Matters Is Systematic Risk….How an
Asset Covaries With Everything Else
Use Asset’s Beta
23
Portfolio Risk, kp
The Impact Of Additional Assets
On The Risk Of A Portfolio
Diversifiable Risk
Total risk
Nondiversifiable Risk
1
5
10
15
20
25
Number of Securities (Assets) in Portfolio
24
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