Transcript WHAT IS FINANCIAL ECONOMICS? Continue…

LECTURE NOTES : WEEK 1
WHAT IS FINANCIAL ECONOMICS?
 Financial economics is a branch of
Economics.
 Financial economics deals with the
financial markets.
 The prices of stock, commodities and
exchange rates are forever changing.
Tomorrow’s price is uncertain. This
uncertainty impact on the behavior of
investors and, ultimately, on market
prices.
WHAT IS FINANCIAL ECONOMICS?
Continue…

The very existence of financial
economics as a discipline is
predicted on uncertainty.
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In the absence of uncertainty,
financial economics reduce to
exercise in microeconomics.
Risk and Uncertainty
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The lender faces considerable uncertainty
relating the value of the money when it is
repaid, i.e. the future value of the money is
uncertain.
The quantification of the uncertainty is
known as risk.
Risk should be distinguished from
uncertainty. The distinction between these
terms was clarified by Knight(1921), who
viewed a risky situation as one in which some
probability can be attached to the future
value of a particular investment. If no
probabilities can be attached to these
outcomes, the future remain uncertain.
RISK
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What is risk: The chance that the actual
return on an investment will be different from
the expected return.
Factors contributing to risk
1. Competition
2. product innovation
3. the shift of commercial banking to capital markets
4.Increased market volatility
5.the disappearance of old barriers which limited the
scope of operations for various financial institution.
Types of Risk
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Total Risk= General Risk + Specific Risk
or
Total Risk= Systematic Risk + Nonsystematic
Risk
Systematic Risk (Market Risk): Actually all
securities have some systematic risk, whether
bonds or stocks, because systematic risk
directly encompasses interest rate, market
and inflation risk.
Type of Risk Continue…
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Non-Systematic Risk: The variability in a
security’s total returns not related to
overall market variability is called the
non-systematic risk. For example, the
company share prices may change due
to an exploration success, an important
research discovery, or change in
executive.
What is Financial Market?
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The function of financial markets is to
transfer funds from savers to
borrowers.
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The creation of financial assets and
liabilities, through lending and
borrowing, gives rise to financial
instruments.
What are Shares?
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A corporation is set up with an authorized
share capital of 2 million in the form of one
million shares .
Share price is $2
Ten (10) individual hold 100,000 shares each,
then each individual is said to have a 10%
ownership equity in the corporation
Shares may be bought and sold on the stock
exchange.
Shareholders are rewarded through the
payments of dividend and/or through the
appreciation of share prices when the
company is profitable.
Daily Returns
Direct statistical analysis of financial
prices is difficult, because consecutive
prices are highly correlated and the
variances of the prices increase with
time. Prices are not stationary (we will
discuss this topic later).
As the result changes in prices can be
used to give appropriate results for the
price.
Returns
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It is the reward for undertaking investments
Measurement of historical Return is important
to investors because;
1. The measurement of historical returns is
necessary for investors to assess how well
they have done or how well the investment
managers have done on their behalf.
2. The historical return plays a larger part in
estimating future, unknown returns.
Daily Returns Continue….
Three types of prices changes have been used
in previous research.
Rt: Daily Return
Rt= Pt - Pt-1 …………(1)
Rt= ((pt – pt-t)/ pt-1)……….(2)
Rt= (ln(Pt) – Ln(pt-1))……….(3)
Disadvantage of Using the First Equation
The first equation(1) is depends on the price
units, so the comparisons between series are
difficult.
Further disadvantage of using the first
equation(1) is that their variances are
proportional to the price level.
Percentage Point
-0.2
-0.4
-0.6
1966- 2000
Feb-99
Feb-96
Feb-93
Feb-90
Feb-87
Feb-84
Feb-81
Feb-78
Feb-75
Feb-72
Feb-69
Feb-66
Feb-63
Feb-60
Monthly Excess Log Aus Stock Return
0.2
0
Date
0.2
High Volatility due to Major Shocks
0.1
0.0
-0.1
-0.2
Low Volatility
Stock Market Crash
October 1987
-0.3
-0.4
60
65
70
75
80
85
ASX1
90
95
00
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Lowest Monthly Returns Over 1980 1990
1. 20th October -1987- Stock Market Crash (32.08%)
2. 29- October - 1987 Australian Dollar Loses 3%
3. 16th -October -1989 London Stock market
Crashes
4. 27th -October -1987 Australian Dollar falls below
US 70 cents
5. 23-October 1987 Iranian missile attack on Kuwait
6. 26-October 1987 Hong Kong market drops 33%
7. 4th November 1987 US dollar plunges due to
budget deficit problem
4th December 1987 Concern over the stabilty of the
Tokyo market.
Source: Corporate Finance: S.R.Bishop, H.R.Crapp,
R.W.Faff and G.J.Twite. (Page.194).
Measuring Return
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A correct return measure must incorporate
the two components of return
1. Yield and
2. Price changes
Bond Total Return
BOND TR =[ It + (Pt –Pt-1)]/Pt-1
It: the interest payment received during the
period
Pt and Pt-1 are the beginning and ending
prices respectively
Measuring Return
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Stock TR
Stock TR=[ Dt + (pt – pt-1)]/pt-1
Dt: the dividend paid during the period
Pt and Pt-1 are the beginning and ending
prices respectively
Example: 100 shares of XYZ company are
purchased at $32 and sold one year later at
$28 per share. A dividend of $2 per share is
paid.
Stock TR= 2 + (28 – 32)/32= - 0.0625
*100=-6.25%
Measuring Return
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Stock TR
Stock TR= Dt + (pt – pt-1)/pt-1
Dt: the dividend paid during the period
Pt and Pt-1 are the beginning and ending
prices respectively
Example: 100 shares of XYZ company are
purchased at $32 and sold one year later at
$28 per share. A dividend of $2 per share is
paid.
Stock TR=[ 2 + (28 – 32)]/32= - 0.0625
*100=-6.25%
Measuring Return
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Return Relative(RR): The total return for
an investment for a given period stated on
the basis of 1.0. When calculating the
geometric mean the negative return cannot
be used. The return relative solve the
problem.
Example: 100 shares of XYZ company are
purchased at $32 and sold one year later at
$28 per share. A dividend of $2 per share is
paid.
Stock TR=[ 2 + (28 – 32)]/32= - 0.0625
*100=-6.25%
Return Relative RR= 1 + (-0.0625)= 0.9375
Summary Statistics For Return
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Arithmetic Mean: The average value
Geometric Mean: The compound rate of
return over time.
 It is often used in investments and
finance to reflect the steady growth rate
of invested funds over some past period
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Arithmetic Mean Versus
Geometric Mean
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The arithmetic mean measures the
average performance. It is an expected
return for next period.
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The geometric mean measures the
change in wealth overtime. It shows
how the money grows over a specific
period.
Summary Statistics For Return
Continue..
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Geometric Mean
The geometric mean is defined as the nth
root of the product resulting from multiplying
a series of return relatives together
G=[(RR1)(RR2)(RR3)---(RR4)]1/n -1
Calculators with the power functions can be
used to calculate the roots.
An alternative method of calculating the
geometric mean is to find the log of each
return relative, sum them , divide by n, and
taking the antilog.
Calculation of the Arithmetic and
Geometric Mean
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Year
2000
2001
2002
2003
2004
XYZ Stock (%)
-2.25
13.26
-3.78
10.78
14.75
 Arithmetic
Return Relative
0.9775
1.1326
0.9622
1.1078
1.1475
Mean: [-2.25 + 13.263.78+10.78+14.75]/5= 6.52%
Calculation of the Arithmetic and
Geometric Mean Continue..
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Geometric Mean:
{(0.9975)(1.1326)(0.9622)(1.1078)(1.1475)}
1/5 -1 = 1.0625 – 1= 0.0625*100=6.25%
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Note that geometric average rate of return is
always lower than the arithmetic average
return because it reflects the variability of the
returns.
The spread between the two depends on the
dispersion of the distribution.
The greater the dispersion, the greater the
spread between the two means.
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Summary Statistics For Return
 Cumulative
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Wealth Index:
Cumulative wealth over time, given
an initial wealth and a series of
returns on some asset.
CWIn= WI0(RR1)(RR2)---(RRn)
CWIn: the cumulative wealth index as of the
end of the period n
WIo: the beginning index value, typically $1
Summary Statistics For Return
Continue..
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CWI2004=
1.00(0.9975)(1.1326)(0.9622)(1.1078)(1.1475)=1.38
$10,000 invested at the end of 1999 (the beginning of
2000) would have been worth 13,800 by the end of
2004.
Summary Statistics For Return
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Inflation-adjusted cumulative wealth
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CWI1A= CWI/CIINF
CWI1A= the cumulative wealth index value
for any asset on inflation-adjusted basis
CWI=the cumulative wealth index for any
asset on a nominal basis.
CIINF= the ending index value for inflation,
calculated as (1+geometric rate of inflation
)n, where n is the number of period
considered.
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Problems
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1. Calculate the arithmetic mean and
geometric mean
Year
XYZ stock Price Dividends
1999
84.32
$2.44
2000
66.79
$3.01
2001
77.85
$3.01
2002
56.78
$3.01
2003
79.89
$3.01
2004
100.31
$3.01
Problems Continue..
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1. Calculate the total return (TR)
2. Calculate the arithmetic mean and
geometric mean.
3. Determine the effects of reinvesting
returns.
Strategy A. Keep a fixed amount (say $1,000)
invested and do not reinvest return
Strategy B: reinvest return and allow
computing
Problems Continue..
4. Calculate the standard deviation
 5. Calculate the cumulative wealth
index and geometric mean.
 5.calculation of inflation –adjusted
return (rate of inflation is 2.1%)
 6.Analyzing the components of a
cumulative wealth index.
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A Review of Statistical Principles
Useful in Financial Data Analysis.
1.Mean
2. Median
3. Mode
4. Variance
5.Standard deviation
6. The Coefficient of Variation
8. Histogram
7. Coefficient of Skewness
8. Coefficient of Kurtosis
MEASURING RISK
STANDARD DEVIATION

T

1
Xt  X

N  1 t 1

2
VARIANCE- RISK
T

1
2
 
X

X

t
N  1 t 1

2
The Coefficient of Variation
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CV 

X
The coefficient of variation (CV) allows us to compare the relative
variability of the two data sets, because it adjusts for differences in the
magnitudes of the means of the data sets.
Risk Premiums
A risk premium is the additional return
investors expect to receive, or did
receive, by talking on increasing
amounts of risk.
 Equity risk premium: The difference
between the return on the stocks and a
risk free rate (proxied by the return on
treasury bill).
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Distribution of Returns
The Coefficient of Skewness
Positive Skewness
The distribution has a long tail to the right.
Mean Return > Median Return > Mode
Negative Skewness
The distribution has a long tail to the left.
Mean Return < Median Return < Mode.
Symmetrical Distribution
Mean = Median = mode
Skewness
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For distributions that are symmetric such as
the normal distribution, there is no skewness.
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Symmetric Distribution
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Skewness = 0
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For some distributions however, high (low)
values can be more common than low (high)
values. In this case the distribution is
skewed.
Skewness is computed as
1
S
N

X

T
t 1

3

X
/

t
3
Kurtosis
Kurtosis indicates the peakedness of the
distribution
Kurtosis
T

1
K   Xt  X
T t 1

4
/
4
Platykurtic
Distribution that are less peaked (flatter)
are referred to as platykurtic.
Leptokurtic
Distributions that are more peaked than
the normal distribution are referred to
as leptokurtic.
Mesokurtic
Distributions that resemble a normal
distribution as referred to as
mesokurtic.
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Distribution of Financial Time-series
Leptokurtosis
Leptokurtic distributions are found in asset
returns.It differs from normality in two
respects
 1..Fatness in the tails, which corresponds to
points in times where large movements in
financial series have been excessive relative
to the normal distribution.
 2..Sharp peaks, which corresponds to periods
when there is very little movement in the
financial series.
 Distributions which have these two properties
are known as leptokurtic.
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ASX(AUS Stock Price Index) Return
Leptokurtosis
60
Ser ies : RT
Sample 1981M02 2001M01
Obs erv ations 240
50
Mean
Median
Max imum
Minimum
Std. D ev .
Sk ew nes s
Kur tos is
40
30
20
10
J ar que-Ber a
Probability
0.008395
0.008532
0.154030
-0.424631
0.053812
-2.102938
19.44229
2880.383
0.000000
0
-0.4
-0.3
-0.2
-0.1
0.0
0.1
1.Fatness in the tails: Which corresponds to points in time where large movements in
financial series have been excessive relative to the normal distribution.
2.Sharp peaks: Which corresponds to periods when there is very little movement in
the financial series.
• Leptokurtic distributions are found in assets
returns when there are periodic jumps in asset
prices. Markets where there is discontinuous
trading, such as security markets that close
overnight or at weekends,are more likely to
exhibits jumps in asset prices.
• The reason is that information which has an
influence on asset prices but it published when the
market are closed will have an impact upon prices
when the market reopens, thus causing a jump
between the previous closing price and the
opening price.
• The jump in price, which is most notable in daily
or weekly data, will result in higher frequencies of
large negative or positive returns than would be
expected if the markets were to trade continuously.
•FTSE(UK Stock Price Index) Return
•Normal Distribution Plot
40
Series: RT
Sample 1981M02 2001M01
Observations 240
30
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
20
10
Jarque-Bera
Probability
0
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.010296
0.012761
0.094293
-0.219390
0.038330
-0.943359
7.638189
250.7251
0.000000
The Normal Distribution
The normal distribution of a random variable X with mean 
and a variance2, is denoted as N(,2) and is given by
f ( x) 
1
2
2
e
 ( x   ) 2 / 2 2
,  x  
 Distribution
of Financial Time-series
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The distribution of many financial series have
extreme observations in both tails of their distribution
which is not consistent with the assumption of
normality.
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This “fatness” in the tails of the distribution is known
as kurtosis.
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Testing for Normality
Clearly it is important to know if the
assumption of normality for example, is
consistent with the Financial data.
A simple way to test for normality is to
compare the computed skewness and kurtosis
coefficients with the theoretical values under
the assumption of normality; namely 0 and 3
respectively. Thus, test are
Null Hypothesis: Ho: Normal Distribution
Alternative Hypothesis: Ha: Not True
Testing for Normality
continue
Skewness Test
Kurtosis Test
Z Sk 
Z Kt 
S
6/T
K 3
24 / T
Kurtosis Test:
Both test statistics are distributed under the null
hypothesis of normality as N(0,1). Thus
“large” values of the test statistic, say greater
than 2, constitute rejection of the null
hypothesis of normality.
Jarque-Bera test
of normality.
JB  Z  Z
2
Sk
2
Kt
JB is distributed as chi-square distribution.
The null hypothesis Ho: Normal Distribution
The Alternative Hypothesis Ha: Not True
We reject Ho at the 5% level when the p-value is less (<) than 
= 0.05.
This test is commonly referred to as the Jarque-Bera test of
normality.
TEST OF NORMALITY
AUS/US EXCHANGE RATE OF RETURN
800
Series: RETURN
Sample 7/04/1983 6/07/1994
Observations 2710
600
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
400
200
Jarque-Bera
Probability
0
-0.025
0.000
0.025
P-value 0.000 is less (<) than 0.05.
Decision; Reject Ho. It is nonnormal
-8.77E-05
0.000149
0.030938
-0.045606
0.006321
-0.878176
8.916766
4301.323
0.000000
References
Bessis,J., 1998, Risk Management in
Banking,John Wiley & Sons.
 Jones, P.C., 2002, Investments analysis
and management, John Wiley & Sons
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