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Unformatted text preview: Chapter 10:
Risk and Return: Lessons
from Market History
Ken Seng Tan
Actsc 372
Fall 2011 Chapter Outline
Returns
HoldingPeriod Returns
Risk Statistics
Return Statistics
Risk Premium
Summary and Conclusions Actsc 372Chap. 10 Returns (Dollar vs Percentage)
Dividends Dollar Returns
= Dividend
+ Change in Market Value
Time 1 0 Percentage Return Initial
investment Ending
market value
dollar return
beginning market value dividend change in market value
beginning market value
dividend yield capital gains yield
Actsc 372Chap. 10 Returns: Example
Suppose you bought 100 shares of company X
at the beginning of the year at $25/share. Over
the past year, you received dividends
$0.20/share. At the end of the year, the stock
sells for $30/share. What is your return?
Initial investment = $25 × 100 = $2,500.
At the end of the year, you have stock worth
$3,000 and cash dividends of $20.
Return (in dollar)
= $520 = $20 + ($3,000 $2,500).
$520
Return (in percentage) = 20.8%
$2,500
Actsc 372Chap. 10 Holding Period Returns
The holding period return is the
return that an investor would get
when holding an investment over a
period of n years,
Suppose the return during year i is
given as ri:
holding period return
(1 r1 ) (1 r2 )
(1 rn ) 1
Actsc 372Chap. 10 Holding Period Return: Example
Year Return
1
10%
2
5%
3
20%
4
15% Holding period return
(1 r1 ) (1 r2 ) (1 r3 ) (1 r4 ) 1
(1.10) (.95) (1.20) (1.15) 1
.4421 44.21% Geometric average return:
(1 rg ) 4
rg (1 r1 ) (1 r2 ) (1 r3 ) (1 r4 ) .095844 9.58%
Arithmetic average return r1 r2 r3 r4
4 10% 5% 20% 15%
10%
4
Actsc 372Chap. 10 Arithmetic Average Return vs Geometric
Average Return
Example: A particular stock is bought for $100. The first
year it falls to $50. The second year it rises back to
$100. What is the average return on this investment?
Arithmetic Ave. Return =
Geometric Ave. Return =
Geometric average tells you what you earned per year
on average, compounded annually
Arithmetic average tells you what you earned per year in
a typical year.
Which return is higher ? Geometric vs Arithmetic Average Returns, 19572009 Capital Market Studies
A famous set of studies dealing with the rates of returns
on common stocks, bonds, and Treasury bills in the U.S.
was conducted by Roger Ibbotson and Rex Sinquefield.
James Hatch and Robert White examined Canadian
returns.
The text presents yearbyyear historical rates of return
starting in 1948 for the following five important types of
financial instruments:
LargeCompany Canadian Common Stocks
LargeCompany U.S. Common Stocks
SmallCompany Canadian Common Stocks
LongTerm Canadian Bonds
Canadian Treasury Bills Actsc 372Chap. 10 Returns to a $1 Investment, 19572009 1 R1957 1 R1958 1 R2009 112.63 for S&P/TSX Rates of Return 19572006
50 Common Stocks
Long Bonds
Tbills 40
30
20
10
0
10
20
30
1955 1965 1975 1985 1995 2005 Actsc 372Chap. 10 Risk Statistics
No universally agreedupon definition of risk.
Some common measures are:
Standard deviation (or variance)
The standard deviation is the standard statistical measure of
the spread of a sample, and it will be the measure we use
most of this time. Value at risk, VaR (or quantile risk measure)
Represents the maximum possible (in dollars) for a given
confidence VaR min Q : Pr L Q for a given loss r.v. L Conditional tail expectation (or Tail value at risk)
Actsc 372Chap. 10 Return Statistics
ˆ
Let ri , i 1,..., N be the observed (historical) rate of
return of a security in period i
Empirical average return (sample mean) ˆ
(r1 R ˆ
rN )
N Sample Variance: a measure of dispersion
Var R ER 1 2 N 1i N N 1 ˆ )2 ˆ
(ri N1 1 ˆ
ri 2 ˆ N ˆ2 ˆ2 i1 the standard deviation of those returns Std. Dev. VAR ˆ 1
N 1i N ˆ
(ri ˆ )2 1 the frequency distribution of the returns.
Actsc 372Chap. 10 Average Annual Returns, 19572009 Risk Premium
The Risk Premium is the additional return (over
and above the riskfree rate) resulting from
bearing risk.
One of the most significant observations of stock
and bond market data is this longrun excess of
security return over the riskfree return.
For the period 1957 through 2009, the average
excess return
from Canadian largecompany common stocks was
4.35% = 10.70% 6.35%
from Canadian longterm bonds was
2.17% = 8.52% 6.35%
Actsc 372Chap. 10 U.S. Stock Market Volatility
The volatility of stocks is not constant from year to year. 60
50
40
30
20
10 19
26
19
35
19
40
19
45
19
50
19
55
19
60
19
65
19
70
19
75
19
80
19
85
19
90
19
95
19
98 0 Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. Actsc 372Chap. 10 The RiskReturn Tradeoff (19572009)
12.00 Common Stocks 11.00 Annual Return Average 10.00
9.00 Long Bonds 8.00
7.00
6.00 TBills 5.00
4.00
3.00
2.00
0.00 5.00 10.00 15.00 20.00 25.00 Annual Return Standard Deviation
Actsc 372Chap. 10 Summary and Conclusions
This chapter presents returns for five asset
classes:
Canadian LargeCompany Common Stocks
U.S. LargeCompany Common Stocks
Canadian SmallCompany Common Stocks
Canadian LongTerm Bonds
Canadian Treasury Bills Stocks have outperformed bonds over most of
the twentieth century, although stocks have also
exhibited more risk.
The statistical measures in this chapter are
necessary building blocks for the material of the
next few chapters.
Actsc 372Chap. 10 ...
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This note was uploaded on 01/04/2012 for the course ACTSC 372 taught by Professor Maryhardy during the Fall '09 term at Waterloo.
 Fall '09
 MARYHARDY

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