INTERNATIONAL CORPORATE FINANCE – 2025
PART I: FOREIGN EXCHANGE MARKETS
Stock markets
Expectations are really important in financial markets, in the stock market we see expected future
cash flows. We don’t know what will happen in the future, we can only make predictions. The
people providing cash flows are financial intermediaries or financial analysts, they help managers
and investors predict what future earnings and cash flows of companies will be, they make the
good or bad weather on the market. The key information that is provided, is EPS (Earnings Per
Share). This expected EPS is what investors look at from financial analysts, this is the benchmark
with respect to what future earnings will be.
Post Earnings Announcement Drift (PEAD)
Every 3 months companies issue an EPS, and the market compares them with the benchmark set
by financial analysts. When there is bad news the stock collapses, when there is good news it
goes up. The question is how bad or good the news really is. Investors can under- or overreact.
Let’s say there is good news and the company issues number that are higher than expected, the
stock will go up. In the market, investors rarely overreact, we almost always see an underreaction.
For the stock price to completely incorporate the information of the EPS being higher than
expected, it takes about 9 months on average. Larger stocks will go faster, and the other way
around. You should buy fast because it will go up every day. These 9 months are called Post
Earnings Announcement Drift.
EXAM: PEAD
- Stock market inefficiency, it is inefficient because the information doesn’t go into the stock
price right away. If the market is efficient, it processes the information and puts it into the
stock price, but here it takes forever.
- Underreaction.
- Better or worse EPS than expected, provided by financial analysts.
- Period of 9 months for the information to kick in the stock price (possibilities for profit).
The CEO of the company knows in advance that the EPS will go down and wants to change the
expectations to make sure the stock doesn’t collapse and shareholders don’t replace him. The
ones responsible for predictions are the financial analysts, so you give out information to them to
change their expectations. Analysts are paid based on their forecasts, if they don’t have
information they can’t forecast. It benefits both the CEO and the analyst. By the end of the year
the expectations walk down and become slightly pessimistic compared to what was expected at
the beginning of the year. As a company you push down the expectation to beat the forecast.
Another approach is to change the EPS (earnings management), you push it up a little bit to beat
the benchmark. CEO’s have a lot of pressure on them and on their reputation, coming from MBE
(Meeting or Beating Expectations). Setting accurate expectations is key. The incentive to do so
usually is their salary.
1
,Often totally fake information is given out to push the EPS over the benchmark, but regardless that
we know it is fake the stock still goes up. This gives it even more strength to do it. Not only numbers
are manipulated, but even words are manipulated when the earnings announcements are around
the corner. The market is being manipulated into EPS. As an investor you always need to be careful
with what information you will use and what the incentive of that specific information is.
Spot markets for foreign currency
There is always going to be a home currency (HC) and a foreign currency (FC). The HC/FC is always
based on the fact that we want to buy 1 foreign currency. For example, if we have the EUR
compared to the USD (EUR/USD), we want to know how many EUR we would need to buy one
USD. If the home currency goes up, the foreign currency appreciates (becomes more expensive).
When the home currency goes down, the foreign currency depreciates (becomes cheaper).
When you look at an exchange currency, there are always two numbers: the bid and ask price,
together called the bid-ask spread. In the case that you want to buy foreign currency, you should
look at the ask price which will always be the highest. The other way around, when you want to
sell foreign currency, you will get the bid price or lower price. The difference between the two
would be your profit. There are different institutions with different rates, because of those different
rates there is a possibility to make a profit. Of course, at our level, unless you have a million to put
down, you won’t make huge profits.
Cross-rates
There are two types of rates: primary rates (against the USD) and cross-rates (between two non-
USD currencies). Not for every currency there is a market, for a lot of markets there isn’t enough
liquidity. This is the reason we sometimes need multiple transactions to get to a certain currency.
For example, if you want GBP and you have EUR, you first have to buy USD and then sell that USD
for the eventual GBP.
𝐄𝐔𝐑⁄ 𝐄𝐔𝐑⁄ 𝐔𝐒𝐃⁄
𝐆𝐁𝐏 = 𝐔𝐒𝐃 𝐱 𝐆𝐁𝐏
If there is a mismatch between those two parts, you go into it because then there is a way to take
home some profits.
Inverted exchange rates
The bid of a certain currency equals 1 divided by the ask of the inverse of that currency. When you
get the bid-ask between two currencies, you can get the bid-ask of the inverse by using these:
𝐂𝐀𝐃⁄
𝐔𝐒𝐃
𝟏
𝐒𝐁𝐢𝐝 = 𝐔𝐒𝐃⁄
𝐒𝐀𝐬𝐤 𝐂𝐀𝐃
𝐂𝐀𝐃⁄
𝐔𝐒𝐃
𝟏
𝐒𝐀𝐬𝐤 = 𝐔𝐒𝐃⁄
𝐒𝐁𝐢𝐝 𝐂𝐀𝐃
Suppose a US bank quotes USD/GBP 1.7019-36, and USD/EUR 0.9850-67. What would the cross-
rate be for EUR/GBP in Frankfurt? In Frankfurt, the dealer will buy GBP at the lower rate and sell
GBP at a higher rate (in terms of EUR), the cross rate will reflect this.
𝐄𝐔𝐑⁄ 𝐔𝐒𝐃⁄ 𝐄𝐔𝐑⁄
𝐆𝐁𝐏 = 𝐆𝐁𝐏 𝐱 𝐔𝐒𝐃
2
,We will need to inverse the USD/EUR to get to the cross rate for EUR and GBP, how do we do this?
- Bid: you take the bid of the first rate (USD/GBP: 1.7019) times the bid of the second rate
(EUR/USD). For the second rate, we first need to take the inverse: 𝐒𝐁𝐢𝐝𝐄𝐔𝐑/𝐔𝐒𝐃
= 𝟎.𝟗𝟖𝟔𝟕. After
𝟏
doing this we can calculate the cross-rate bid: 𝟏.𝟕𝟎𝟏𝟗
𝟎.𝟗𝟖𝟔𝟕
= 𝟏. 𝟕𝟐𝟓𝟎 (EUR/GBP).
- Ask: you take the ask of the first rate (USD/GBP: 1.7036) times the ask of the second rate
(EUR/USD). For the second rate, we first need to take the inverse: 𝐒𝐀𝐬𝐤𝐄𝐔𝐑/𝐔𝐒𝐃
= 𝟎.𝟗𝟖𝟓𝟎. After
𝟏
doing this we can calculate the cross-rate ask: 𝟏.𝟕𝟎𝟑𝟔
𝟎.𝟗𝟖𝟓𝟎
= 𝟏. 𝟕𝟐𝟗𝟓 (EUR/GBP).
We now have the following bid-ask spread for the cross rate: EUR/GBP 1.7250-95. A questions like
this will most certainly come on the exam too.
EXAM:
Suppose you read the following quote on the Reuters screen: USD/CAD 1.000-05.
- What is the bank’s buying and selling rate for CAD?
➔ The bank’s buying rate for CAD is USD 1.000, and its selling rate is USD 1.005. You as a
person sell CAD at USD 1.000 and buy CAD at USD 1.005.
- What are the bank’s buying and selling rates for USD?
➔ The bank’s buying rate or bid for USD is 𝟏.𝟎𝟎𝟓
𝟏
or 0.9950, and the selling rate or ask is 𝟏.𝟎𝟎𝟎
𝟏
or 1.000. When you wear your Canadian hat, you sell USD at CAD 0.9950, and you buy
USD at CAD 1.000.
Potential profits in the market
The first thing we do is making sure that the two lines don’t overlap, if
they do there is no potential for making profits. In this example you
would buy at 58 and sell at 60. Always make sure that there is space
left to make potential profits. You need a lot of money to be able to
enjoy opportunities like this. Unless you have millions, you won’t be
able to make significant profits like this. Possibilities to arbitrage.
EXAM:
A NY bank is quoting AUD/USD 1.8885-90 and a bank in Sydney is giving the quote
USD/AUD 0.5275-80. Is there a profit or not?
To know if there are any chances at making profits, you should first take the inverse of the
quoting of the NY bank: 𝟏⁄𝟏. 𝟖𝟖𝟖𝟓 = 𝟎. 𝟓𝟐𝟗𝟓 and 𝟏⁄𝟏. 𝟖𝟖𝟗𝟎 = 𝟎. 𝟓𝟐𝟗𝟒. This gives us the quote
USD/AUD 0.5294-50. Because of the fact that the ranges of the one quote lie outside of the
ranges of the other, there is a possibility to make profit. There is no overlap between the
different quotes. You could also do it the other way around with the Sydney bank quoting:
𝟎. 𝟓𝟐𝟕𝟓 = 𝟏. 𝟖𝟗𝟓𝟕 and ⁄𝟎. 𝟓𝟐𝟖𝟎 = 𝟏. 𝟖𝟗𝟑𝟗. Which gives us AUD/USD 1.8939-57, there is no
𝟏⁄ 𝟏
overlap. In both cases you buy at the cheapest ask rate, and you sell at the highest bid.
Another way of checking for profit is buying 20 mil. AUD against USD from Sydney bank
(0.58895), which costs you 10,560,000 USD. You can sell 20 mil. AUD to the NY bank.
When the NY bank buys AUD (sells USD, 1.8890), you get 20,000,000/1.8890 USD or
10,587,612 USD. Your net profit is a little over 27,000 USD with no risk.
3
,It is also possible to have transactions between three different currencies, which is called
triangular arbitrage. We want to check whether it is better to buy another currency directly, or it is
better to first go by another third currency. In order to do this, you first have to create a synthetic
contract, to simplify things. You will combine two of the three currencies in one currency, and you
end up with two.
EXAM:
Suppose we have the following quotes: GBP/USD 1.6545-52 and IEP/USD 1.3655-65. We
first want to combine them and create a synthetic quote.
➔ (𝑮𝑩𝑷⁄𝑰𝑬𝑷)𝑩𝒊𝒅 = 𝟏. 𝟔𝟓𝟒𝟓 𝒙 𝟏⁄
𝟏. 𝟑𝟔𝟔𝟓 = 𝟏. 𝟐𝟏𝟎𝟖
➔ (𝑮𝑩𝑷⁄𝑰𝑬𝑷)𝑨𝒔𝒌 = 𝟏. 𝟔𝟓𝟓𝟐 𝒙 𝟏⁄
𝟏. 𝟑𝟔𝟓𝟓 = 𝟏. 𝟐𝟏𝟐𝟐
This gives us the following synthetic quote: GBP/IEP 1.2108-22. If there is another bank
giving you the following quote: 1.2095-105, can you then make a profit? Yes, in this case
you would make profit if you buy IEP at 1.2105 and you sell it again at 1.2108.
Do we know what makes forex markets tick?
Over the short term, exchange rates are unpredictable. However, over a few months from now
there will be starting to be indications of patterns and mean reversion.
The first thing we do with exchange rates is taking the logarithm of them. We do this to get rid of
outliers and cut extreme values down to reduce their influence. The logarithm can only be taken
of strictly positive values. Often you get better results when getting rid of the outliers. When it is
not significant, you take the log.
There are three statistics to know if we can predict exchange rates on the short term.
First-order autocorrelation
This is the relationship between the same things over time. Here we would look at the correlation
of the logarithm of the exchange rate over time.
Box-Ljung statistic
Another commonly used name for this test is the ‘Portmanteau test’, we call it like this because it
looks like a cloth hanger when you put it on a graph. This test looks at the significance of the
autocorrelation over time (the previous test measures it). The significance will fade away over
time, day by day.
- H0: the data are independently distributed (low values of Q).
- Ha: the data are not independently distributed, they exhibit serial correlation.
Augmented Dickey-Fuller (ADF) test
This is a test for the unit root in a time series sample. When
you’re dealing with time series analysis, the unit root is
what you really need to know. Having a unit root in your data
means that you’re not able to tell what the average is. You
have different averages depending on where you are. We
want one average of the whole time series. If you have a unit
4
, root in your data, you pause because when there is a unit root you cannot interpret the moments.
Like in the first graph, if you give someone the average of the graph, there is nothing that person
can do with it. When you have a unit root in your data, you can do one thing.
You have to take the returns, the first differences. Prices are unit root, you can’t predict for
example the stock price. This is why we always talk about returns, not prices. In the second graph
we see a situation that looks like a graph when we take the returns. We observe mean reversion,
or also called stationary time series, it reverts back to the average.
- H0: there is a unit root. - Ha: there is no unit root.
If you reject H0, you take the first difference. You can do this multiple times, we don’t want unit
root. At the exam we will get the following table, and the first thing you look at is the ADF. You need
to compare the table
with the critical value
for ADF. Let’s say we
take 3.41 as a critical
value, we see that for
example at 1.82 it is not
significant because the
number is lower than
the critical value. If the
test you obtain from the
table is lower than the
critical value, it is not
statistically significant because you can’t reject H0. There is unit root. We can’t interpret the
moment (averages, medians, standard deviations, …). The currencies are unpredictable.
This table is the second table we get at the exam, where we look at the first differences of
exchange rates. The first thing we look at is again ADF, here the values are much bigger which
means we can reject H0.
There is no unit root, we
can analyse the
moment. The second
thing we look at now is
autocorrelation, and
the third one would be
the Box-Ljung statistic.
For example, when we
look at GBP, DEM and
JPY we see that the
autocorrelation is close
to 0, whereas it was 1 before (first table). According to Q, having a critical value around 11, the first
one is significant and the others not. Even here the statistical significance of the autocorrelation
factor of the GBP is pretty low (3%). We can’t do much with 3%, despite it being statistically
significant. It isn’t enough to be economically significant too. We can conclude that the currencies
are unpredictable over the short term.
5
PART I: FOREIGN EXCHANGE MARKETS
Stock markets
Expectations are really important in financial markets, in the stock market we see expected future
cash flows. We don’t know what will happen in the future, we can only make predictions. The
people providing cash flows are financial intermediaries or financial analysts, they help managers
and investors predict what future earnings and cash flows of companies will be, they make the
good or bad weather on the market. The key information that is provided, is EPS (Earnings Per
Share). This expected EPS is what investors look at from financial analysts, this is the benchmark
with respect to what future earnings will be.
Post Earnings Announcement Drift (PEAD)
Every 3 months companies issue an EPS, and the market compares them with the benchmark set
by financial analysts. When there is bad news the stock collapses, when there is good news it
goes up. The question is how bad or good the news really is. Investors can under- or overreact.
Let’s say there is good news and the company issues number that are higher than expected, the
stock will go up. In the market, investors rarely overreact, we almost always see an underreaction.
For the stock price to completely incorporate the information of the EPS being higher than
expected, it takes about 9 months on average. Larger stocks will go faster, and the other way
around. You should buy fast because it will go up every day. These 9 months are called Post
Earnings Announcement Drift.
EXAM: PEAD
- Stock market inefficiency, it is inefficient because the information doesn’t go into the stock
price right away. If the market is efficient, it processes the information and puts it into the
stock price, but here it takes forever.
- Underreaction.
- Better or worse EPS than expected, provided by financial analysts.
- Period of 9 months for the information to kick in the stock price (possibilities for profit).
The CEO of the company knows in advance that the EPS will go down and wants to change the
expectations to make sure the stock doesn’t collapse and shareholders don’t replace him. The
ones responsible for predictions are the financial analysts, so you give out information to them to
change their expectations. Analysts are paid based on their forecasts, if they don’t have
information they can’t forecast. It benefits both the CEO and the analyst. By the end of the year
the expectations walk down and become slightly pessimistic compared to what was expected at
the beginning of the year. As a company you push down the expectation to beat the forecast.
Another approach is to change the EPS (earnings management), you push it up a little bit to beat
the benchmark. CEO’s have a lot of pressure on them and on their reputation, coming from MBE
(Meeting or Beating Expectations). Setting accurate expectations is key. The incentive to do so
usually is their salary.
1
,Often totally fake information is given out to push the EPS over the benchmark, but regardless that
we know it is fake the stock still goes up. This gives it even more strength to do it. Not only numbers
are manipulated, but even words are manipulated when the earnings announcements are around
the corner. The market is being manipulated into EPS. As an investor you always need to be careful
with what information you will use and what the incentive of that specific information is.
Spot markets for foreign currency
There is always going to be a home currency (HC) and a foreign currency (FC). The HC/FC is always
based on the fact that we want to buy 1 foreign currency. For example, if we have the EUR
compared to the USD (EUR/USD), we want to know how many EUR we would need to buy one
USD. If the home currency goes up, the foreign currency appreciates (becomes more expensive).
When the home currency goes down, the foreign currency depreciates (becomes cheaper).
When you look at an exchange currency, there are always two numbers: the bid and ask price,
together called the bid-ask spread. In the case that you want to buy foreign currency, you should
look at the ask price which will always be the highest. The other way around, when you want to
sell foreign currency, you will get the bid price or lower price. The difference between the two
would be your profit. There are different institutions with different rates, because of those different
rates there is a possibility to make a profit. Of course, at our level, unless you have a million to put
down, you won’t make huge profits.
Cross-rates
There are two types of rates: primary rates (against the USD) and cross-rates (between two non-
USD currencies). Not for every currency there is a market, for a lot of markets there isn’t enough
liquidity. This is the reason we sometimes need multiple transactions to get to a certain currency.
For example, if you want GBP and you have EUR, you first have to buy USD and then sell that USD
for the eventual GBP.
𝐄𝐔𝐑⁄ 𝐄𝐔𝐑⁄ 𝐔𝐒𝐃⁄
𝐆𝐁𝐏 = 𝐔𝐒𝐃 𝐱 𝐆𝐁𝐏
If there is a mismatch between those two parts, you go into it because then there is a way to take
home some profits.
Inverted exchange rates
The bid of a certain currency equals 1 divided by the ask of the inverse of that currency. When you
get the bid-ask between two currencies, you can get the bid-ask of the inverse by using these:
𝐂𝐀𝐃⁄
𝐔𝐒𝐃
𝟏
𝐒𝐁𝐢𝐝 = 𝐔𝐒𝐃⁄
𝐒𝐀𝐬𝐤 𝐂𝐀𝐃
𝐂𝐀𝐃⁄
𝐔𝐒𝐃
𝟏
𝐒𝐀𝐬𝐤 = 𝐔𝐒𝐃⁄
𝐒𝐁𝐢𝐝 𝐂𝐀𝐃
Suppose a US bank quotes USD/GBP 1.7019-36, and USD/EUR 0.9850-67. What would the cross-
rate be for EUR/GBP in Frankfurt? In Frankfurt, the dealer will buy GBP at the lower rate and sell
GBP at a higher rate (in terms of EUR), the cross rate will reflect this.
𝐄𝐔𝐑⁄ 𝐔𝐒𝐃⁄ 𝐄𝐔𝐑⁄
𝐆𝐁𝐏 = 𝐆𝐁𝐏 𝐱 𝐔𝐒𝐃
2
,We will need to inverse the USD/EUR to get to the cross rate for EUR and GBP, how do we do this?
- Bid: you take the bid of the first rate (USD/GBP: 1.7019) times the bid of the second rate
(EUR/USD). For the second rate, we first need to take the inverse: 𝐒𝐁𝐢𝐝𝐄𝐔𝐑/𝐔𝐒𝐃
= 𝟎.𝟗𝟖𝟔𝟕. After
𝟏
doing this we can calculate the cross-rate bid: 𝟏.𝟕𝟎𝟏𝟗
𝟎.𝟗𝟖𝟔𝟕
= 𝟏. 𝟕𝟐𝟓𝟎 (EUR/GBP).
- Ask: you take the ask of the first rate (USD/GBP: 1.7036) times the ask of the second rate
(EUR/USD). For the second rate, we first need to take the inverse: 𝐒𝐀𝐬𝐤𝐄𝐔𝐑/𝐔𝐒𝐃
= 𝟎.𝟗𝟖𝟓𝟎. After
𝟏
doing this we can calculate the cross-rate ask: 𝟏.𝟕𝟎𝟑𝟔
𝟎.𝟗𝟖𝟓𝟎
= 𝟏. 𝟕𝟐𝟗𝟓 (EUR/GBP).
We now have the following bid-ask spread for the cross rate: EUR/GBP 1.7250-95. A questions like
this will most certainly come on the exam too.
EXAM:
Suppose you read the following quote on the Reuters screen: USD/CAD 1.000-05.
- What is the bank’s buying and selling rate for CAD?
➔ The bank’s buying rate for CAD is USD 1.000, and its selling rate is USD 1.005. You as a
person sell CAD at USD 1.000 and buy CAD at USD 1.005.
- What are the bank’s buying and selling rates for USD?
➔ The bank’s buying rate or bid for USD is 𝟏.𝟎𝟎𝟓
𝟏
or 0.9950, and the selling rate or ask is 𝟏.𝟎𝟎𝟎
𝟏
or 1.000. When you wear your Canadian hat, you sell USD at CAD 0.9950, and you buy
USD at CAD 1.000.
Potential profits in the market
The first thing we do is making sure that the two lines don’t overlap, if
they do there is no potential for making profits. In this example you
would buy at 58 and sell at 60. Always make sure that there is space
left to make potential profits. You need a lot of money to be able to
enjoy opportunities like this. Unless you have millions, you won’t be
able to make significant profits like this. Possibilities to arbitrage.
EXAM:
A NY bank is quoting AUD/USD 1.8885-90 and a bank in Sydney is giving the quote
USD/AUD 0.5275-80. Is there a profit or not?
To know if there are any chances at making profits, you should first take the inverse of the
quoting of the NY bank: 𝟏⁄𝟏. 𝟖𝟖𝟖𝟓 = 𝟎. 𝟓𝟐𝟗𝟓 and 𝟏⁄𝟏. 𝟖𝟖𝟗𝟎 = 𝟎. 𝟓𝟐𝟗𝟒. This gives us the quote
USD/AUD 0.5294-50. Because of the fact that the ranges of the one quote lie outside of the
ranges of the other, there is a possibility to make profit. There is no overlap between the
different quotes. You could also do it the other way around with the Sydney bank quoting:
𝟎. 𝟓𝟐𝟕𝟓 = 𝟏. 𝟖𝟗𝟓𝟕 and ⁄𝟎. 𝟓𝟐𝟖𝟎 = 𝟏. 𝟖𝟗𝟑𝟗. Which gives us AUD/USD 1.8939-57, there is no
𝟏⁄ 𝟏
overlap. In both cases you buy at the cheapest ask rate, and you sell at the highest bid.
Another way of checking for profit is buying 20 mil. AUD against USD from Sydney bank
(0.58895), which costs you 10,560,000 USD. You can sell 20 mil. AUD to the NY bank.
When the NY bank buys AUD (sells USD, 1.8890), you get 20,000,000/1.8890 USD or
10,587,612 USD. Your net profit is a little over 27,000 USD with no risk.
3
,It is also possible to have transactions between three different currencies, which is called
triangular arbitrage. We want to check whether it is better to buy another currency directly, or it is
better to first go by another third currency. In order to do this, you first have to create a synthetic
contract, to simplify things. You will combine two of the three currencies in one currency, and you
end up with two.
EXAM:
Suppose we have the following quotes: GBP/USD 1.6545-52 and IEP/USD 1.3655-65. We
first want to combine them and create a synthetic quote.
➔ (𝑮𝑩𝑷⁄𝑰𝑬𝑷)𝑩𝒊𝒅 = 𝟏. 𝟔𝟓𝟒𝟓 𝒙 𝟏⁄
𝟏. 𝟑𝟔𝟔𝟓 = 𝟏. 𝟐𝟏𝟎𝟖
➔ (𝑮𝑩𝑷⁄𝑰𝑬𝑷)𝑨𝒔𝒌 = 𝟏. 𝟔𝟓𝟓𝟐 𝒙 𝟏⁄
𝟏. 𝟑𝟔𝟓𝟓 = 𝟏. 𝟐𝟏𝟐𝟐
This gives us the following synthetic quote: GBP/IEP 1.2108-22. If there is another bank
giving you the following quote: 1.2095-105, can you then make a profit? Yes, in this case
you would make profit if you buy IEP at 1.2105 and you sell it again at 1.2108.
Do we know what makes forex markets tick?
Over the short term, exchange rates are unpredictable. However, over a few months from now
there will be starting to be indications of patterns and mean reversion.
The first thing we do with exchange rates is taking the logarithm of them. We do this to get rid of
outliers and cut extreme values down to reduce their influence. The logarithm can only be taken
of strictly positive values. Often you get better results when getting rid of the outliers. When it is
not significant, you take the log.
There are three statistics to know if we can predict exchange rates on the short term.
First-order autocorrelation
This is the relationship between the same things over time. Here we would look at the correlation
of the logarithm of the exchange rate over time.
Box-Ljung statistic
Another commonly used name for this test is the ‘Portmanteau test’, we call it like this because it
looks like a cloth hanger when you put it on a graph. This test looks at the significance of the
autocorrelation over time (the previous test measures it). The significance will fade away over
time, day by day.
- H0: the data are independently distributed (low values of Q).
- Ha: the data are not independently distributed, they exhibit serial correlation.
Augmented Dickey-Fuller (ADF) test
This is a test for the unit root in a time series sample. When
you’re dealing with time series analysis, the unit root is
what you really need to know. Having a unit root in your data
means that you’re not able to tell what the average is. You
have different averages depending on where you are. We
want one average of the whole time series. If you have a unit
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, root in your data, you pause because when there is a unit root you cannot interpret the moments.
Like in the first graph, if you give someone the average of the graph, there is nothing that person
can do with it. When you have a unit root in your data, you can do one thing.
You have to take the returns, the first differences. Prices are unit root, you can’t predict for
example the stock price. This is why we always talk about returns, not prices. In the second graph
we see a situation that looks like a graph when we take the returns. We observe mean reversion,
or also called stationary time series, it reverts back to the average.
- H0: there is a unit root. - Ha: there is no unit root.
If you reject H0, you take the first difference. You can do this multiple times, we don’t want unit
root. At the exam we will get the following table, and the first thing you look at is the ADF. You need
to compare the table
with the critical value
for ADF. Let’s say we
take 3.41 as a critical
value, we see that for
example at 1.82 it is not
significant because the
number is lower than
the critical value. If the
test you obtain from the
table is lower than the
critical value, it is not
statistically significant because you can’t reject H0. There is unit root. We can’t interpret the
moment (averages, medians, standard deviations, …). The currencies are unpredictable.
This table is the second table we get at the exam, where we look at the first differences of
exchange rates. The first thing we look at is again ADF, here the values are much bigger which
means we can reject H0.
There is no unit root, we
can analyse the
moment. The second
thing we look at now is
autocorrelation, and
the third one would be
the Box-Ljung statistic.
For example, when we
look at GBP, DEM and
JPY we see that the
autocorrelation is close
to 0, whereas it was 1 before (first table). According to Q, having a critical value around 11, the first
one is significant and the others not. Even here the statistical significance of the autocorrelation
factor of the GBP is pretty low (3%). We can’t do much with 3%, despite it being statistically
significant. It isn’t enough to be economically significant too. We can conclude that the currencies
are unpredictable over the short term.
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