Page 1The University of Sydney
ECMT2130
Financial Econometrics:
TUT 02
Eric & Grace
The University of Sydney
Page 2The University of Sydney
What will we learn in lectures / tutorials?
Statistics and
Finance
Foundation
Regression
The Capital
Asset Pricing
Model (CAPM)
Arbitrage Pricing
Theory (APT)
Time Series
Exponential
Smoothing
Moving Average
(MA)
Autoregressive
Integrated
Moving Average
(ARIMA)
Autoregressive
Model (AR) Autoregressive
Conditional
Heteroscedasticity
(ARCH)
Generalised
Autoregressive
Conditional
Heteroscedasticity
(GARCH)
Deep Learning
Neural
Networks
(NN)
Long
Short-Term
Memory
(LSTM)
Complexity
Page 3The University of Sydney
Outline – Tutorial 02
(Quickly) Review - the Lecture 01
- See the mind map
Sample Questions
Python –Pandas
- Install and import pandas
- Calculation
- Index
Q&A
Page 4The University of Sydney
(Quickly) Review 1
Introduction to
Financial
Econometrics
Efficient
Market
Efficient Market
Hypothesis
Major Asset
Markets
Securities
Markets
Foreign exchange
markets
Derivatives
markets
Money
markets
Commodity
markets
Physical asset
markets
Allocative efficiency
Operational efficiency
Informational efficiency
Portfolio efficiency
Weak-form efficiency
Semi-strong-form efficiency
Strong-form efficiency
Random Walk
Prices in the
financial markets evolve
randomly.
Page 5The University of Sydney
(Quickly) Review 2
• The arithmetic net return is
!"# = !"# − 1 = !"# + !"# − !!
• If we assume the stock does not pay
dividend, then!"# = $!"#$! and !"# = !"# − 1 = $!"#%$!$!
• The log return is defined as
!"#& = ln !"# = ln !"#! = !"# − !
• Note that !"#& = ln !"# = ln 1 + !"# ≈ !"#
when !"# is small.
• Therefore, the log return is approximately
net return, when the net return is “small”.
Page 6The University of Sydney
(Quickly) Review 3
The Random Walk Model
• Depending on the dependence structure in ! , we have different
versions of random walk models. The most restrictive one is to assume ! is an i.i.d. sequence. The least restrictive one is to assume ! is a
white noise. While the most famous one is to assume ! is a “martingale
difference sequence” (m.d.s.),(!"#|ℱ!) = 0, ∀
• In this case, the log price sequence ! is called a “martingale”. This
model is consistent with the Efficient Market Hypothesis, as(!"#|ℱ!) = (!"# − !|ℱ!) = !"# ℱ!) − ! = 0 !"# ℱ!) = !
• The best forecast of tomorrow’s price is today’s price.
Page 7The University of Sydney
The Random Walk Model
• Depending on the dependence structure in ! , we have different
versions of random walk models. The most restrictive one is to assume ! is an i.i.d. sequence. The least restrictive one is to assume ! is a
white noise. While the most famous one is to assume ! is a “martingale
difference sequence” (m.d.s.),(!"#|ℱ!) = 0, ∀
• In this case, the log price sequence ! is called a “martingale”. This
model is consistent with the Efficient Market Hypothesis, as(!"#|ℱ!) = (!"# − !|ℱ!) = !"# ℱ!) − ! = 0 !"# ℱ!) = !
• The best forecast of tomorrow’s price is today’s price.
Page 8The University of Sydney
(Quickly) Review 4
• Suppose Sinan deposits $100 into the bank, and the interest rate of the
deposit is 5% per annum.
• If the bank pays interest annually, the end-of-year value of the deposit is $100×(1 + 5%) = $105.
• If the bank pays interest semi-annually, then the end-of-year value of the
deposit is $100× 1 + $%& & = $105.0625.
• In general, if the bank pays interest n times a year, then the end-of-year
value of the deposit is $100× 1 + $%' '
• What is the end-of-year value of the deposit if the 5% annual interest
rate is paid continuously, when → ∞? lim'→)$100× 1 + 5% ' = $100×$%
• The continuous compounding will yield the end-of-year value $105.1271
Compound Interest
Page 9The University of Sydney
(Quickly) Review 5
Expectatio
n Operator
• =
• + = +
• =
• + = +
• + = + ()
• + = + ()
Variance
Operator
• = 0
• + =
• = &
• + = &
• + = + + 2(, )
• + = & +& + 2(, )
'( = , = − − = − []
'( = , = (, )'(
Page 10The University of Sydney
Sample Questions
1.0 The Random Walk Model
The well- known Gaussian Random Walk (GRW) model is defined as! = !*# + !
Where ! ~ i.i.d. N(0, &)
Where ! is the log stock price, ln(!)
Show that the GRW model implies that the corresponding log returns series, !, are i.i.d. N(0, &).
Page 13The University of Sydney
Sample Questions
2.0 Compound rate
Here are some common frequencies:
Daily - Every day or 365 times per year
Weekly - Every week or 52 times per year
Monthly - Every month or 12 times per year
Quarterly - Every quarter or 4 times per year
Semi-annually - Every 6 months or 2 times per year
Annually - Every year
Page 14The University of Sydney
Sample Questions
2.0 Compound rate
• Compare the interest earned on a deposit of $10,000 invested for one year
at 3% p.a. compounding: (a) annually, (b) semi-annually, (c) monthly, and (d)
daily.
Page 16The University of Sydney
Sample Questions
3.0 Expectation, Variance, Covariance and Correlation
X 20 30 40 50 60 70 80 90 100 110
Y 11 22 33 44 55 66 77 88 99 100
Show expectation and sample variance of X and Y respectively.
Show the sample covariance and correlation of X and Y.
Page 18The University of Sydney
Python –Pandas
Python –Pandas
- Install and import pandas
- Calculation
- Index
Page 19The University of Sydney
Python –Pandas
https://pandas.pydata.org/
Pandas is a fast, powerful, flexible and easy to use open source data analysis and
manipulation tool, built on top of the Python programming language.