1-1 1 A Brief History of Risk and Return. 1-2 A Brief History of Risk and Return Two key...
-
Upload
candice-floyd -
Category
Documents
-
view
218 -
download
1
Transcript of 1-1 1 A Brief History of Risk and Return. 1-2 A Brief History of Risk and Return Two key...
1-2
A Brief History of Risk and Return
• Two key observations:
1. There is a substantial reward, on average, for bearing risk.
2. Greater risks accompany greater returns.
1-3
Dollar & Percent Returns
• Total dollar return = the return on an investment measured in dollars• $ return = dividends + capital gains
• Total percent return is the return on an investment measured as a percentage of the original investment.• % Return = $ return/$ invested• The total percent return is the return for each
dollar invested.
1-4
Percent Return
t
ttt
t
tt
t
t
P
PPD
CGYDY
P
PPCGY
P
DDY
11
1
1
Return %
Return %
Dividend Yield
Capital Gains Yield
1-5
Example: Calculating Total Dollar and Total Percent Returns
• You invest in a stock with a share price of $25. • After one year, the stock price per share is $35. • Each share paid a $2 dividend.
• What was your total return?
Dollars Percent
Dividend $2.00 $2/25 = 8%
Capital Gain $35 - $25 = $10 $10/25= 40 %
Total Return $2 + $10 = $12 $12/$25 = 48%
1-6
Annualized Returns
Effective Annual Rate (EAR)
1)HPR1(EAR M
Where:
HPR = Holding Period Return
M = Number of Holding Periods per year
1-7
Annualized Returns – Example 1
P0 = $20 P.33 = $22 t = “.33” since 4 months is 1/3 of a year
4-month HPR = 3 periods per year
Holding Period Return (HPR)
Annualized Return
(EAR)
%$
$$
.
1020
2022
P
PP
0
0330
%.
).(
133
1101 3
You buy a stock for $20 per share on January 1.
Four months later you sell for $22 per share.
No dividend has been paid yet this year.
1-8
Annualized Returns – Example 2
P0 = $20 P2 = $28
HPR = 2 years (t = 2)
HPR per year = ½ (0.50)
Holding Period Return
(HPR)
Annualized Return
(EAR)
%$
$$
4020
2028
P
PP
0
02
%.
).( .
3218
1401 500
Suppose the $20 stock you bought on January 1 is selling for $28 two years later
No dividends were paid in either year.
1-16
Historical Average Returns
• Historical Average Return = simple, or arithmetic average.
• Using the data in Table 1.1: • Sum the returns for large-company stocks from 1926
through 2006, you get about 984 percent.
• Divide by the number of years (80) = 12.3%.
• Your best guess about the size of the return for a year
selected at random is 12.3%.
n
return yearly Return AverageHistorical
n
1i
1-18
Average Returns: The First Lesson
• Risk-free rate:
• Rate of return on a riskless investment• Risk premium:
• Extra return on a risky asset over the risk-free rate
• Reward for bearing risk• The First Lesson: There is a reward, on
average, for bearing risk.
1-20
Risk Premiums
• Risk is measured by the dispersion or spread of returns
• Risk metrics:• Variance • Standard deviation
• The Second Lesson: The greater the potential reward, the greater the risk.
1-21
Return Variability Review and Concepts
• Variance (σ2)• Common measure of return dispersion • Also call variability
• Standard deviation (σ) • Square root of the variance• Sometimes called volatility• Same "units" as the average
1-22
Return Variability: The Statistical Tools for Historical Returns
• Return variance: (“N" =number of returns):
• Standard Deviation
1N
RR σ VAR(R)
N
1i
2
i2
VAR(R) σ SD(R)
1-23
Example: Calculating Historical Variance and Standard Deviation
• Using data from Table 1.1 for large-company stocks:(1) (2) (3) (4) (5)
Average Difference: Squared:Year Return Return: (2) - (3) (4) x (4)1926 11.14 11.48 -0.34 0.121927 37.13 11.48 25.65 657.821928 43.31 11.48 31.83 1013.021929 -8.91 11.48 -20.39 415.831930 -25.26 11.48 -36.74 1349.97
Sum: 57.41 Sum: 3436.77
Average: 11.48 Variance: 859.19
29.31Standard Deviation:
1-24
Return Variability Review and Concepts
• Normal distribution: • A symmetric, bell-shaped frequency
distribution (the bell-shaped curve)• Completely described with an average
and a standard deviation (mean and variance)
• Does a normal distribution describe asset returns?
1-28
Arithmetic Averages versusGeometric Averages
• The arithmetic average return answers the question: “What was your return in an average year over a particular period?”
• The geometric average return answers the question: “What was your average compound return per year over a particular period?”
1-29
Geometric Average Return: Formula
1R1(...)R1()R1(GAR /N1N)21
Where:
Ri = return in each period
N = number of periods
Equation 1.5
1-30
Geometric Average Return
1)R1(GARN/1N
1ii
Where:
Π = Product (like Σ for sum)
N = Number of periods in sample
Ri = Actual return in each period
1-31
Example: Calculating a Geometric Average Return• Using the large-company stock data from Table 1.1:
Percent One Plus CompoundedYear Return Return Return:1926 11.14 1.1114 1.11141927 37.13 1.3713 1.52411928 43.31 1.4331 2.18411929 -8.91 0.9109 1.98951930 -25.26 0.7474 1.4870
1.0826
8.26%
(1.4896)^(1/5):
Geometric Average Return:
1-32
Geometric Average Return
Year % Return $$ Invested1.0000$
1926 11.14 1.1114$ 1927 37.13 1.5241$ 1928 43.31 2.1841$ 1929 -8.91 1.9895$ 1930 -25.26 1.4870$
N 5I/Y CPT = 8.26%PV (1.0000)$
PMT 0FV 1.4870$
1-33
Arithmetic Averages versusGeometric Averages
• The arithmetic average tells you what you earned in a typical year.
• The geometric average tells you what you actually earned per year on average, compounded annually.
• “Average returns” generally means arithmetic average returns.
1-34
Geometric versus Arithmetic Averages
• For forecasting future returns:• Arithmetic average "too high" for long forecasts
• Geometric average "too low" for short forecasts
1-35
Blume’s Formula
• Form a “T” year average return forecast from arithmetic and geometric averages covering “N” years, N>T.
Average Arithmetic1-N
T-N AverageGeometric
1N
1TTR
)(
1-36
Check This 1.5aCompute the Average Returns
Year % Return $$ Invested1.0000$
1926 10 1.1000$ 1927 16 1.2760$ 1928 -5 1.2122$ 1929 -8 1.1152$ 1930 7 1.1933$
4.00
N 5I/Y CPT = 3.60%PV (1.0000)$
PMT 0FV 1.1933$
Arithmetic Average
Geometric Average
1-37
Check This 1.5b
BLUME'S FORMULA
Arithmetic Average 4.0%Geometric Average 3.6%
N 25
For T = 5
AverageArithmeticAverageGeometric N
TTR
1-N
T-N
1
1
)(
%...
%).)(.(%).)(.(
%)(%).(
%%.)(
9333332360010
04833306316670
424
2063
24
4
41-25
5-25 63
125
155
R
1-38
Check This 1.5bBLUME'S FORMULA
Arithmetic Average 4.0%Geometric Average 3.6%
N 25
For T = 10
AverageArithmeticAverageGeometric N
TTR
1-N
T-N
1
1
)(
%...
%).)(.(%).)(.(
%)(%).(
%%.)(
853502351
04625006337500
424
1563
24
9
41-25
10-25 63
125
11010
R
1-39
Risk and Return
• The risk-free rate represents compensation for the time value of money.
• First Lesson: • If we are willing to bear risk, then we can
expect to earn a risk premium, at least on average.
• Second Lesson: • The more risk we are willing to bear, the
greater the expected risk premium.