Download Investments: Analysis and Behavior

Investments: Analysis
and Behavior
Chapter 4- Risk and Return
©2008 McGraw-Hill/Irwin
Learning Objectives





Know the risk and return characteristics of different asset
classes.
Compute the impact of taxes on investment returns.
Be able to compute risk and return of a two-asset
portfolio.
Recognize optimal portfolios.
Learn how gains and losses affect investor perceptions
of risk.
4-2
Components of Return
Required Return  Nominal Risk - free Rate  Required Risk Premium
 Risk - free Rate  Expected Inflation  Required Risk Premium

Required Return
 The
return required to compensate for the amount of
risk expected.

Nominal risk-free rate
 Risk-free
rate
 Inflation

Required risk premium
 Return
that varies with the risk entailed
4-3
Annual Rates of Return on Common Stocks Approximate a Normal
Distribution, 1950-present
12
8
6
4
2
Annual Rates of Return
More than 50%
40% to 50%
30% to 40%
20% to 30%
10% to 20%
0% to 10%
-10% to 0%
-20% to -10%
0
Less than -20%
Frequency
10
4-4
Computing Returns

Arithmetic average return
N
Arithmetic average return 
 Return
t 1
t
N
 Example
1: (0.10+0.08-0.04)/3 = 0.0467 or 4.67%
 Example 2: (0.50-0.50)/2 = 0 or 0%

Geometric mean return
1
N

Return t 
Geometric mean return   (1 
)  1
100 
 t 1
N
1: (1.1×1.08×0.96)1/3 – 1 = 0.0448 or 4.48%
 Example 2: (1.5×0.5)1/2 – 1 = -0.134 or -13.4%
 Example
4-5
4-6
Risk

Variation, or volatility of return
 Most
investors probably are more interested
the chance of losing money
 Standard deviation
N
Standard Deviation 
 Return
t 1
t
 Average Return 
2
N 1
1: {[(0.10-0.0467)2 + (0.08-0.0467)2 + (-0.040.0467)2] / (3-1) }1/2 = 0.0757 or 7.57%
 Example
4-7
Risk and Return

Risk/Return relationship
 The
greater the risk, the more return should
be demanded.
 Coefficient
of Variation
Coefficien t of Variation 
Standard Deviation
Average Return
CoV = 7.57% / 4.67% = 1.62
4-8
Annual data, 1950 to 2005
Long-Term
Short-term
Common
Treasury
Treasury
Inflation
Stocks
Bonds
Bills
Rate
Arithmetic average
13.27%
6.39%
4.92%
3.89%
Median
15.40%
3.65%
4.85%
3.19%
Geometric mean
11.93%
5.92%
4.92%
3.85%
Standard deviation
17.24%
10.51%
2.71%
2.99%
1.30
1.64
0.55
0.77
Coefficent of variation
4-9
More Returns

Total Return
 Includes
dividends, interest, income, and
capital gains (losses)

Inflation
 Reduces
future buying power
 Nominal return

Return with inflation included
 Real return
 Return with inflation removed
 Return as a buying power measurement
4-10
$6,000,000
Common Stocks
$5,000,000
Inflation
$4,000,000
Treasury Bonds
$3,000,000
Treasury Bills
$1,000,000
$900,000
$800,000
$700,000
$600,000
$500,000
$400,000
$300,000
$200,000
$100,000
$0
$2,000,000
$1,000,000
$0
Cumulative Value of
Bonds and Inflation
Cumulative Value of
Stocks
Figure 4.1 Cumulative Investment Value of $10,000 Investment in
Stocks and Bonds, 1950-present
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Year
4-11
Impact of Taxes

Capital Gains
 Only
realized gains are taxed
 Short-term (less than one year)

taxed at marginal income tax rate
 Long-term


Taxed at 20%
Dividends
 Taxed

(over one year)
at 15%
Interest Income
 Taxed
at marginal income tax rate
4-12
The tax man cometh
After-tax value of a $4,000 investment per year
Number
of Years
earning 12% with annual income taxes paid at a rate of
0%
30%
40%
50%
1
$4,000
$2,800
$2,400
$2,000
5
25,411
16,558
13,857
11,274
10
70,195
41,341
33,474
26,362
15
149,119
78,435
61,247
46,552
20
288,210
133,955
100,565
73,571
25
533,335
217,053
156,227
109,729
30
965,331
341,430
235,029
158,116
4-13
Forming a Portfolio

Don’t put all your eggs in one basket!

The purpose of owning different types of
stocks and different asset classes is diversify.

The main goal of diversification is to reduce
overall investment risk.
4-14
Statistical Measures


The risk of a portfolio is determined by how the
individual securities co-move over time.
Covariance is a measure of that co-movement:
 Return
N
Covariance ij 

t 1
it
 Average Return i   Return
jt
 Average Return
j

N
However, the standardized measure of correlation
is more popular:
Covariance ij
Correlatio n ij   ij 
 Between
Std. Dev. i  Std. Dev. j
-1 and 1
4-15
Example:
The stock market earned the following returns; 10%, 8%, -4%. During the
same period, gold earned returns of 5%, -3%, 10%.
What is the covariance and correlation between the stock market and gold?





First compute the average and standard deviation for stocks and for
gold. The statistics for stocks were computed earlier (average=4.67,
standard deviation=7.57%).
Gold’s average return = (5-3+10)/3 = 4%. Standard
deviation=[(1/2)((5–4)2+(-3–4)2+(10–4)2)]1/2 = 6.6%
Covariance = (1/N)∑{(Stock Returnt – Stock Average)  (Gold Returnt –
Gold Average)}
= (1/3){(10-4.67)(5-4)+(8-4.67)(-3-4)+(-4-4.67)(10-4)} =
-23.33
Correlation = Covariance / (Standard Deviation Stock  Standard
Deviation Gold)
= -23.33 / (7.576.6) = -0.47
A negative correlation means that stocks and gold tend to move in
opposite directions.
4-16
Correlations in Total Returns for Stocks,
Bonds, Bills and Inflation, 1950-present
Stocks
Bonds
Bills
Stocks
1.00
Bonds
0.11
1.00
Bills
-0.06
0.30
1.00
Inflation
-0.23
-0.17
0.64
Inflation
1.00
4-17
Portfolio Risk and Return

Expected Portfolio Return
N
ER P    Wi ER i 
i 1

Standard Deviation of Portfolio Returns
SDRP  
N
W
i 1
i
 VARRi   Wi  W j  COV Ri R j 
N
2
N
i 1 j 1
j i
4-18
4-19
Combining these investments allows for the
possibility of risk reduction




The goal of the investor is to form a portfolio
the moves to the upper-left corner of the
risk/return graph.
The very highest level of return for each level
of risk desired is the efficient portfolio.
All the efficient portfolios make up the
efficient frontier.
The optimal portfolio for you is the one that
maximizes your utility (given your risk
aversion)
4-20
4-21
4-22
Combining similar assets don’t produce much risk reduction…
Month
GM
Ford
Portfolio A
November
0.0%
-2.0%
-1.0%
December
22.8%
2.3%
12.1%
January
11.7%
17.1%
14.4%
February
11.7%
1.1%
6.3%
March
6.2%
7.7%
6.9%
April
-7.7%
-5.6%
-6.6%
May
-7.3%
-2.5%
-4.9%
June
-16.7%
-8.7%
-12.8%
July
10.2%
23.0%
16.4%
August
21.3%
11.7%
16.4%
September
1.9%
4.1%
3.0%
October
8.8%
10%
9.6%
4.62%
4.50%
4.56%
11.81%
9.43%
9.61%
Mean
S.D.
Covariance
0.66%
4-23
Combining very different firms does provide risk reduction…
Month
Microsoft
Citigroup
Portfolio B
November
2.9%
-1.7%
0.6%
December
-7.4%
-6.6%
-7.0%
January
0.1%
-0.6%
-0.2%
February
6.4%
-3.8%
1.2%
March
-6.7%
-0.6%
-3.7%
April
-3.0%
5.2%
1.0%
May
3.9%
1.9%
2.9%
June
-2.3%
-0.3%
-1.3%
July
-4.5%
-5.2%
-4.8%
August
4.1%
6.2%
5.1%
September
4.1%
1.9%
3.0%
October
1.7%
-1.8%
0.0%
Mean
-0.16%
-0.52%
-0.34%
S.D.
4.64%
3.84%
3.49%
Covariance
0.06%
4-24


Investor Perceptions of Risk
Portfolio theory is based on the statistics of how
investment returns co-move over time.
Do people really view risk from this statistical
perspective?



No, people tend to see high returns as safe. When the
markets go up, people jump in.
Risk is felt after returns turn negative
Myopic view (short-term perspective)


After 3-years of losses, long-term investors become 3-year
investors—they want out!
House Money Effect

After experiencing a gain, or profit, gamblers become
willing to take more risk.
4-25
In Panel A, pick the retirement plan option for your pension
plan investment.
Panel A
Option A
Option B
Option C
Good Market Conditions (50% chance)
$900
$1,100
$1,260
Bad Market Conditions (50% chance)
$900
$800
$700
Panel B
Program 1
Program 2
Program 3
Good Market Conditions (50% chance)
$1,100
$1,260
$1,380
Bad Market Conditions (50% chance)
$800
$700
$600
Then, in Panel B, pick the retirement plan program for your
pension plan investment.
Who picked what?
4-26



Notice that Option C appears to be a “high” risk
investment in Panel A.
Program 2 is the same as Option C, but it
appears to be a “middle” risk investment.
In a study…
 People
seemed to prefer Option B over Option C
when choosing from Panel A.
 People seemed to prefer Option C over Option B
when they were shown in Panel B.

In short…
 People
don’t really know what level of risk they want
to take.
 People measure risk in relative, not absolute, terms.
4-27
Investor Risk Perceptions Make the Use of
Portfolio Theory Difficult for Real Investors

People mentally keep track of things in
separate mental “file folders,” called mental
accounting.



The profits, losses, return of each investment are
considered separately.
This makes thinking in terms of the interaction
between investments difficult.
The result, is that people frequently fail to
diversify.
4-28