Upload
junior-lang
View
216
Download
0
Embed Size (px)
Citation preview
Investments: Analysis and Behavior
Chapter 4- Risk and Return
©2008 McGraw-Hill/Irwin
4-2
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.
4-3
Components of Return
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
PremiumRisk Required Inflation Expected Rate free-Risk
PremiumRisk Required Rate free-Risk NominalReturn Required
4-4
Annual Rates of Return on Common Stocks Approximate a Normal Distribution, 1950-present
0
2
4
6
8
10
12
Less t
han -
20%
-20%
to -
10%
-10%
to 0
%
0%
to 1
0%
10%
to 2
0%
20%
to 3
0%
30%
to 4
0%
40%
to 5
0%
More
than 5
0%
Annual Rates of Return
Fre
qu
en
cy
4-5
Computing Returns Arithmetic average return
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
Example 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%
N
N
tt
1
Return return average Arithmetic
1)100
Return1( return mean Geometric
1
1
NN
t
t
4-6
4-7
Risk Variation, or volatility of return
Most investors probably are more interested the chance of losing money
Standard deviation
Example 1: {[(0.10-0.0467)2 + (0.08-0.0467)2 + (-0.04-0.0467)2] / (3-1) }1/2 = 0.0757 or 7.57%
1N
Return AverageReturn Deviation Standard
N
1t
2t
4-8
Risk and Return Risk/Return relationship
The greater the risk, the more return should be demanded.
Coefficient of Variation
CoV = 7.57% / 4.67% = 1.62
Return Average
Deviation Standard Variation oft Coefficien
4-9
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%
Coefficent of variation 1.30 1.64 0.55 0.77
4-10
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
4-11
Figure 4.1 Cumulative Investment Value of $10,000 Investment inStocks and Bonds, 1950-present
$0
$1,000,000
$2,000,000
$3,000,000
$4,000,000
$5,000,000
$6,000,000
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Year
Cu
mu
lati
ve V
alu
e of
S
tock
s
$0$100,000$200,000$300,000$400,000$500,000$600,000$700,000$800,000$900,000$1,000,000
Cu
mu
lati
ve V
alu
e of
B
ond
s an
d I
nfl
atio
n
Common Stocks
Inflation
Treasury Bonds
Treasury Bills
4-12
Impact of Taxes
Capital Gains Only realized gains are taxed Short-term (less than one year)
taxed at marginal income tax rate
Long-term (over one year) Taxed at 20%
Dividends Taxed at 15%
Interest Income Taxed at marginal income tax rate
4-13
The tax man cometh
After-tax value of a $4,000 investment per year
Number earning 12% with annual income taxes paid at a rate of
of Years 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
4-14
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.
4-15
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:
However, the standardized measure of correlation is more popular:
Between -1 and 1
N
Return AverageReturnReturn AverageReturnCovariance
N
1tjjtiit
ij
ji
ijijij Dev. Std.Dev. Std.
CovariancenCorrelatio
4-16
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 / (7.576.6) = -0.47
A negative correlation means that stocks and gold tend to move in opposite directions.
4-17
Correlations in Total Returns for Stocks,
Bonds, Bills and Inflation, 1950-present
Stocks Bonds Bills Inflation
Stocks 1.00
Bonds 0.11 1.00
Bills -0.06 0.30 1.00
Inflation -0.23 -0.17 0.64 1.00
4-18
Portfolio Risk and Return Expected Portfolio Return
Standard Deviation of Portfolio Returns
N
1iiiP REWRE
N
i
N
iji
N
ijj
jiiiP RRCOVWWRVARWRSD1 1 1
2
4-19
4-20
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)
4-21
4-22
4-23
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%
Mean 4.62% 4.50% 4.56%
S.D. 11.81% 9.43% 9.61%
Covariance 0.66%
4-24
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%
4-25
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.
4-26
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?
4-27
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.
4-28
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.