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2201AFE Corporate FinanceWeek 8:
Some Lessons from Capital Market History
Readings: Chapter 10
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Agenda
Last Lecture
Some Lessons from Capital Market History Key Concepts and Skills
Real World Application
The Non-Normal Fidelity Magellan Fund
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Last Lecture
Evaluation of NPV Estimates
Scenario Analysis
Sensitivity Analysis
Simulation Analysis
Break-even
Accounting Cash
Financial
Operating Leverage
Other consideration in Capital Budgeting
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Some Lessons from Capital Market History
Chapter 10
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1. Introduction & Financial
Statements
2. Time Value of Money
3. Valuing Shares & Bonds
7. Mid-semester Exam
8. Some Lessons from Capital
Market History
11. Financial Leverage & Capital
Structure Policy
13. Options & Revision
9. Return, Risk & the Security
Market Line
5. Making Capital Investment
Decisions & Project Analysis
12. Dividends & Dividend Policy
6. Revision for Mid-sem Exam
4. Net Present Value & Other
Investment Criteria
10. Cost of Capital
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Key Concepts and Skills
Returns
Holding period returns
Return statistics: Arithmetic Mean (AM) & Geometric Mean
(GM)
Risk
Variance (VAR or 2) & Standard Deviation (SD or) Historical risk and returns on various types of investments
Lessons from history
Efficient Market Hypothesis (EMH)
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The financial markets generally are unpredictable. So that
one has to have different scenarios. The idea that you can
actually predict what's going to happen contradicts my
way of looking at the market.
George Soros
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History of Australia Stock Exchange
Read more on: http://www.asxgroup.com.au/history.htm
http://globaltrendtraders.com/stock-market-analysis/stock-market-history-3-
ways-to-use-it-to-your-advantage/
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Returns
Dollar Returns (Investment Profit)
the sum of the cash received and
the change in value of the asset, indollars.
Percentage Returns
the cash received and the change
in value of the asset divided by theoriginal investment.
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Dividends
Ending market
value
Year 0 Year 1
Initial investment
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Returns
Dollar Return = Dividend + Change in Market Value
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yieldgainscapitalyielddividend
P
PP
P
C
P
)P(PCR
yieldgainscapitalyielddividend
valuemarketbeginning
valuemarketinchangedividend
valuemarketbeginning
returndollarReturnPercentage
1t
1tt
1t
t
1t
1tttt
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Example Calculating Returns
You bought a bond for $950 one year ago. You have
received two coupons of $30 each. You can sell the bond
for $975 today. What is your total dollar return?
Income = 30 + 30 = 60
Capital gain = 975 950 = 25
Total dollar return = 60 + 25 = $85
What is the percentage return?
Total dollar return / Beginning value
85 / 950 = 8.95%
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Example Calculating Returns
You bought a stock for $35 and you received dividends of
$1.25. The stock is now worth $40.
What is your dollar return?
Dollar return = 1.25 + (40 35) = $6.25
What is your percentage return?
Dividend yield = 1.25 / 35 = 3.57% Capital gains yield = (40 35) / 35 = 14.29%
Total percentage return = 3.57% + 14.29% = 17.86%
or Dollar return / Beginning price:
6.25 / 35 = 17.86% (unrealised) Nominal vs. Real
Realised vs. Unrealised
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Holding Period Return
The holding period return
The return that an investor would get when holding an
investment over a period ofn years
Holding Period Return
= (1+r1) (1+r
2) (1+r
n) 1
where r1, r2 ... rn are yearly returns
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Holding Period Return: Example
Suppose your investment provides the following returns
over a four-year period:
Your holding period return:
= (1+r1) (1+r2) (1+r3) (1+r4) 1
= (1.10) (0.95) (1.20) (1.15) 1
= 0.4421 = 44.21%
14
Year Return
1 10%
2 -5%
3 20%
4 15%
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Geometric Mean
An investor who held this investment would have earned an
annual average compound return of 9.58%:
Geometric Mean = GM = Rg = [1+R]1/t1
Rg = [(1+R1)(1+R2)(1+R3)(1+R4)]1/t 1 =
Rg = [(1.10)(0.95)(1.20)(1.15)]1/4 1 = 9.58%
So, our investor made 9.58% per year, for four years, earning a
holding period return of 44.21%
= (1.095844)4 = 1.4421 1
= 0.4421 = 44.21%
15
Year Return
1 10%
2 -5%
3 20%
4 15%
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Arithmetic Mean
Arithmetic Mean = AM = Ra
Our investor earned 10% return in an average year, over
the four year investment period.
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Year Return
1 10%
2 -5%
3 20%
4 15%
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Example: Calculating AM and GM
What is the arithmetic and geometric mean for the
following returns?
Year 1 5%
Year 2 -3%
Year 3 12%
AM = [0.05 + (0.03) + 0.12] / 3
= 0.0467 = 4.67%
GM = (1+0.05) (10.03) (1+0.12)]
1/3
1= 0.0449 = 4.49%
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Arithmetic vs. Geometric Mean
Arithmetic mean returns earned in an average period
over multiple periods (used as estimated return).
Geometric mean average compound returns per period
over multiple periods.
The geometric average will be less than the arithmetic
average unless all the returns are equal.
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Arithmetic vs. Geometric Mean
Which is better?
The arithmetic average is overly optimistic for long horizons
use over short term.
The geometric average is overly pessimistic for short
horizons use over long term.
15-20 years or less: use arithmetic mean.
20-40 years or so: split the difference between them.
40+ years: use geometric mean.
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Risk
Risk is the chance or possibility of loss (Concise Oxford).
Risk is the chance of things not turning out as expected
(Economist).
Risk is the uncertainty of future outcomes (Reilly & Brown).
Perhaps the most important
Reports that say that something hasn't happened are alwaysinteresting to me, because as we know, there are known knowns;
there are things we know we know. We also know there are
known unknowns; that is to say we know there are some things
we do not know. But there are also unknown unknowns -- the
ones we don't know we don'tknow(former US DefenseSecretary Donald Rumsfeld).
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Risk Measurements
Main Measures:
Variance (VAR)
Standard Deviation (SD)
Variance = the average of the squared differences between
the actual return and the average return.
Standard Deviation = square root of Variance.
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Example VAR and SD
22
Year
Actual
Return
R
Average
Return
Rmean
Deviation from
the Mean
R Rmean
Squared
Deviation
(R Rmean)2
1 0.15 0.105 0.045 0.002025
2 0.09 0.105 -0.015 0.000225
3 0.06 0.105 -0.045 0.002025
4 0.12 0.105 0.015 0.000225Total 0.42 0.00 = 0.0045
Average = 0.42 / 4 = 0.105
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Example Standard Deviation
SD = 3.87%
68% of possible outcomes will lie between 6.63% and 14.37%
(mean 1SD) = ( 1) = (10.50 3.87%).23
mean
6.63% 10.50% 14.37%
68%
95%
99%
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Historical Return Statistics
The history of capital market returns can be summarized by
describing:
The average return.
The standard deviation of those returns.
The frequency distribution of the returns.
Comparison is made on: Large-Company Common Stocks.
Small-company Common Stocks.
Long-term Bonds.
Short-term Bank Bills.
Inflation.
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FV f $1 i i 1979
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FV of $1 investment in 1979
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Hi t i l R t 1979 2009
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Historical Returns, 1979-2009
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L f C it l M k t Hi t
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Lessons from Capital Market History
Data reflects two features often observed in financial
markets.
There is a reward for bearing risk.
The larger the potential reward, the larger the risk.
This is called the risk-return trade-off.
There is a positive relationship between risk and return.
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Ri k P i
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Risk Premium
The extra return earned for taking on risk.
The risk premium is the return over and above the risk-free
rate.
Average Return Risk-free Rate = Risk Premium
What is a risk free rate?
Treasury bills are considered to be risk-free. Can use
Government bonds as well.
Considered risk free in terms of ability of pay interest
obligations.
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Average Annual Returns and Risk Premiums
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Average Annual Returns and Risk Premiums
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Efficient Capital Markets
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Efficient Capital Markets
Stock prices are in equilibrium or are fairly priced.
If this is true, then you should not be able to earnabnormal or excess returns.
Efficient markets DO NOTimply that investors cannot earn
a positive return in the stock market.
Efficient Market Hypothesis or EMH Eugene Fama 1970,
Journal of Finance.
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Why does it matter?
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Why does it matter?
If markets are efficient:
Prices reflect true value: Equilibrium value consistent with
information.
Cannot profit from present information that is available.
Price reaction can fluctuate but no observable trend.
No over-reaction or under-reaction.
No lags and also leads.
Price changes are independent and random.
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Market Efficiency Defined
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Market Efficiency Defined
Price Information
Fully (properly) New/surprise/unexpected
Instantaneously Relevant
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Efficient Market
Pr
ice
Event time t
Information is reflected in
share price instantaneously.
Key issues
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Key issues
What happens when something unanticipated occurs and how
quickly do asset prices adjust?
1. How does the market react if the market is efficient?
2. How does the market react if the market is inefficient?
What happens when something anticipated occurs?
1. How does an efficient market react to anticipated events?
2. How does an inefficient market react to anticipated events?
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Unanticipated Favourable Event
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Unanticipated Favourable Event
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Efficient Market
Price
Event time t
Inefficient Market
Price
Event time t
Efficient Market: Prices would
adjust up very quickly.
Inefficient Market: Prices would
drift upward for some timefollowing the event.
Anticipated Favourable Event
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Anticipated Favourable Event
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Efficient Market: Prices would
drift up for some time beforethe event and then stabilise.
Inefficient Market: Prices would
drift up for some time before theevent and continue up after.
Efficient Market
Price
Event time t
Inefficient Market
Price
Event time t
Stock Price Reaction
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Stock Price Reaction
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Why does it matter?
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Why does it matter?
If prices DOfully reflect all current information, it would
not be worth an investors time to use information to find
under-valued securities.
If prices DO NOT fully reflect information, FIND AND USE
THAT INFORMATION, and perhaps you will be able to make
a killing in the market.
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Semi-strong form efficiency
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g y
Prices reflect all publicly available information including
trading information, annual reports, press releases, etc.
If the market is semi-strong form efficient, then investors
cannot earn abnormal returns by trading on public
information.
Implies that fundamental analysis will not lead to abnormal
returns.
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Strong form efficiency
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g y
Prices reflect all information, including public and private.
If the market is strong form efficient, then investors couldnot earn abnormal returns regardless of the information
they possessed.
Empirical evidence indicates that markets are NOT strongform efficient and that insiders could earn abnormal
returns.
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Real World Application
The Non-Normal Fidelity Magellan Fund
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The Non-Normal Fidelity Magellan Fund
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Fidelity Magellan
One of the worlds most popularmutual funds, the Fidelity
Magellan fund is the largestactively managed mutual fund inthe world
The fund started on May 2, 1963.Peter Lynch became legendary as
the Magellan fund manager(retired in 1990)
FUM stands at US$47billion
Monthly data: April 1987through October 2007 (n = 247)
Just how normal are monthlyreturns from the fund?
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Histogram - Full Sample
Fidelity Magellan (1987-2007, monthly)
0%
3%
6%
9%
12%
15%
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
0%
20%
40%
60%
80%
100%
Return Distribution (Fidelity) CDF (Fidelity) CDF N(0,1) PDF N(0,1)
`
37.71Range
11.91 (Dec 91)Maximum return (%)
-25.80 (Oct 87)Minimum return (%)
7.63 vs N(0,1) = 3Kurtosis
-1.09 vs N(0,1) = 0Skewness
4.53Volatility (%)
+ 0.45Comparison to Average (+/-)
1.44 (Oct 07)This Month (%)
0.98Arithmetic Average (%)
37.71Range
11.91 (Dec 91)Maximum return (%)
-25.80 (Oct 87)Minimum return (%)
7.63 vs N(0,1) = 3Kurtosis
-1.09 vs N(0,1) = 0Skewness
4.53Volatility (%)
+ 0.45Comparison to Average (+/-)
1.44 (Oct 07)This Month (%)
0.98Arithmetic Average (%)
Non-Normal Monthly Returns
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Oct 87 Aug 98 Sep02 = 0.98
Aug90
Sep 01
Fidelity Return Distribution
0
5
10
15
20
-26% -22% -18% -14% -11% -7% -3% 1% 4% 8%
Monthly Return
0
0.2
0.4
0.6
0.8
1
7.63 vs N(0,1) = 3Kurtosis
-1.09 vs N(0,1) = 0Skewness
7.63 vs N(0,1) = 3Kurtosis
-1.09 vs N(0,1) = 0Skewness
Next Week
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Next week, we will look at returns, risk and the security
market line.
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