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PROSPECTIVE ANALYSIS
OF EXCHANGE RATE
IN THE ASPECT
OF HEDGING TRANSACTIONS
Marcin Jędrzejczyk
INTERNATIONAL
TRANSACTIONS
Exchange rate
differences
FINANCIAL
RISK
RISK AVOIDEMENT
STRATEGIES
FINANCE ENGINEERING
Risk – the possibility of not getting to the predicted
goals (not achieving success)
HEDGING
The income made in the transaction
should be higher or the loss lower
than without using hedging security
HEDGING
The activity which should lead to the security of
the company against the unexpected change in
the price of the financial instrument.
Therefore it is an activity that uses the futures
market transactions to limitate the risk
connected with unfavorable changes of the
price on the spot market.
HEDGING IN CONTRACT
APPROACH
HEDGING
PARTY WHICH
AVOIDS RISK
PARTY WHICH
BUYS RISK
TRADING
ER e.g. PLN/$
ERff
Financial futures price
LOSSES
t1
t
THE BASE
The average difference between
observed prices quoted on the spot
and financial futures market
b(t )  S (t )  F (t )
b(t) – the base
S(t) – exchange rate on the spot market
F(t) – er on the financial futures market
MAIN AIM
To find the correlation between the
profits made on exchange rate
differences
connected with the
change in prices on both markets
(spot and financial futures).
IMPORTANT NOTE:
Theoretical situation may appear when the
changes on both markets are equal what
implicates the fact of total elimination of risk
MAIN CLASSIFICATION OF HEDGING
Selling hedge
short hedge
Buying hedge
long hedge
Decision making
backgroung
The party tends to sell
the assets to the foreign
investor within the long
payment horizon using
the exchange rate from
the day of the future
payment
The investor tends to buy
the assets from the foreign
party within the long
payment horizon using the
exchange rate from the day
of the future payment
Type of the risk
avoidment
The risk of the
depreciation of the
exchange rate
The risk of the apreciation
of the exchange rate
CASE STUDY 1
Company value
(Euro)
1 mln
Profit (loss)
1,5 mln
Profit (loss)
0,5 mln
Profit (loss)
4 PLN:E 1
4,5 PLN:E 1
3,5 PLN:E 1
CASE STUDY 1
Company value
(Euro)
1 mln
Profit (loss)
1,5 mln
Profit (loss)
0,5 mln
Profit (loss)
4 PLN:E 1
4,5 PLN:E 1
3,5 PLN:E 1
4 mln PLN
4,5 mln PLN
3,5 mln PLN
zero
(0,5 mln PLN)
0,5 mln PLN
CASE STUDY 1
Company value
(Euro)
1 mln
Profit (loss)
1,5 mln
Profit (loss)
0,5 mln
Profit (loss)
4 PLN:E 1
4,5 PLN:E 1
3,5 PLN:E 1
4 mln PLN
4,5 mln PLN
3,5 mln PLN
zero
(0,5 mln PLN)
0,5 mln PLN
6 mln PLN
6,75 mln PLN
5,25 mln PLN
(2 mln PLN)
(2,75 mln PLN)
(1,25 mln PLN)
CASE STUDY 1
Company value
(Euro)
1 mln
Profit (loss)
1,5 mln
Profit (loss)
0,5 mln
Profit (loss)
4 PLN:E 1
4,5 PLN:E 1
3,5 PLN:E 1
4 mln PLN
4,5 mln PLN
3,5 mln PLN
zero
(0,5 mln PLN)
0,5 mln PLN
6 mln PLN
6,75 mln PLN
5,25 mln PLN
(2 mln PLN)
(2,75 mln PLN)
(1,25 mln PLN)
2 mln PLN
2,25 mln PLN
1,75 mln PLN
2 mln PLN
1,75 mln PLN
2,25 mln PLN
CASE STUDY 2
On the 7th of March 2006 the company received
40.000 euro from the French parntner as the payment of
previously recorded receivables. Exchange rate at that
day accounted for 3,7884 zł/euro. This day the company
has set the forward transaction in which it has agreed to
sell 40.000 euro on the 13 march using exchange of
3,8410 zł/euro.
On the 9th March 2006 r. has sold the currency with
3,8926 zł/euro. Receivables and the contract are
registered separately.
In the General Journal of the comapny the entity shuold
account for:
1. The constitution of the contract forward for the amount
- 153.640 zł (40.000 euro x 3,8410 zł/euro):
Dr Accounts receivable from the contract,
Cr Accounts payable from the contract.
The contract has been closed on 13th of March 2006 on
the basis of the exchange rate 3,9480 zł/euro. So the
difference on the contract is:
In the accounting record it has to be reflected by the
following postings:
1. The collection of the amount due to the forward
contract - 4.280 zł [(3,8410 zł/euro
- 3,9480 zł/euro) x 40.000 euro]:
Dr Financial cost,
Cr Cash;
2. Closing of the contract - 153.640 zł:
Dr Accounts payable from the contract,
Cr Accounts receivable from the contract..
CASE STUDY 3
Polish company sells the goods at 1st December 2002 for
the amount $10000 to the investor from the USA. The
current exchange rate: 3,50 PLN:$1.
Date
1/12/08
Amount
35000 PLN
Debit
Accounts receivable ($)
Credit
Sales
To avoid the risk connected with the receivables made on
the transaction, the company signs the sales of $10000 in
90 days period. If the financial futures price (90 days)
accounts for 3,40 PLN:$1, then the company agrees to
transfer to the bank for 34000 PLN The difference
constitutes the future income, so it is to be recorded as
the discount.
Date
1/12/08
Amount
Debit
Credit
34000 PLN Accounts receivable from
the future contract
1000 PLN Discount (future cost)
35000 PLN
Accounts payable from
the contract (to pay in $)
If the current exchange rate at the end of the year 2008
(spot rate) achieves 3,45 PLN:$1, then the accounts
receivable and payable will account for 34500 (10000*3,45)
what results in the following posting:
Date
31/12/08
Amount
Debit
500 PLN Currency loss
500 PLN Accounts receivable from
the contract
Credit
Accounts payable from
the contract
Currency income
It is clearly visible that currency incomes and losses are
leveling themselves.
After one month period the part of the discount
constitutes the cost. Thus: 31  90 1000  344
Date
31/12/08
Amount
Debit
344 PLN Financial cost of the
collateral
Credit
Discount
At 1st March 2009 the payment becomes due for the
accounts receivable and the contract. If the rate of
exchange accounts for 3,30PLN:$1, the value of $10000
was equal to 33000 PLN. Thus the postings require to be
written as follows:
Date
1/03/09
Amount
Debit
500 PLN Accounts receivable from
the contract
500 PLN Currency loss
1000 PLN Currency loss
1000 PLN Accounts payable from the
contract
Credit
Currency income
Accounts payable from the
contract
Accounts receivable from
the contract
Currency income
Cash collection from the investor from the USA:
Date
1/03/09
Amount
Debit
33000 PLN Cash
Credit
Accounts receivable
The payment of 10000$ to the bank as an implication of
the contract:
Date
1/03/09
Amount
Debit
33000 PLN Accounts payable from the
contract
Credit
Cash
Inflows connected with the contract:
Date
1/03/09
Amount
Debit
34000 PLN Cash
Credit
Accounts receivable from
the contract
Closing of the contract (zero out the contract):
Date
01/03/09
Amount
Debit
Credit
2000 PLN Accounts payable from the Accounts Receivable
contract
Whats more the discount must be recorded as the cost of
the interest:
Date
01/03/09
Amount
Debit
656 PLN Financial cost of the
collateral
Credit
Discount
Despite quite remarkable changes in the exchange rate in
90 days period the company held only 1000 PLN cost of
the collateral. All profits and losses balance themselves.
The company have received 24000 PLN as signed in the
contract.
EXCHANGE RATE THEORY
To understand the exchange rate we have to understand
the essence of money unit.
„This is the wage productivity that has the basic influence
on the exchange rate recorded between two countries”
(Dobija 2003)
EXCHANGE RATE IN YEARS
1993-2003 PLN:$
4,5000
4,0000
3,5000
3,0000
2,5000
2,0000
1,5000
1,0000
lut-03
lut-02
lut-01
lut-00
lut-99
lut-98
lut-97
lut-96
lut-95
lut-94
0,0000
lut-93
0,5000
LABOUR AND MONEY
• A basic formula describes labour (L) as
product of acting force (F) and the
distance, or path, (s) along which a body
was shifted. Thus:
• L = F  s = F  v  t = P  t, where:
v –velocity, t – time , P - power
• Therefore labour is seen as an product of
power and time
• kWh = kW [kilowatts]  t [hours]
• 5 kWh
=
500 Watt  10 hours
LABOUR AND MONEY
• Cost of labour = Coefficient of power * Time of labour
• Cost of labour [labour units] =
Productivity of labourer * Time [hours]
• 6 [ labour unit]
=
3/5 [ ] *
10 hours
WP RATIO
wage paid for the particular work
wp 
the highest wage (in the company)
H (T )
wp 
H max (Tmax )
EXCHANGE RATE THEORY
Using the presented theory of money and money unit to
the explanation of the changes of the exchange rate, the
labour productivity issue observed in two countries must
be considered and implemented to the exchage rate
cathegory.
The exemplification may focus on the economic systems
of Poland and the USA. If we assume that the systems are
almost equally productive, we can formulate the equation:
QUSA (Q  N )USA
APUSA
 $ 


 ER

QP
(Q  N ) P
APP
 PLN 
Q – value of manufactured product,
N – average amount of money paid for the labour unit,
AP – average wage, ER – exchange rate
EXCHANGE RATE THEORY
In practice the equal economic systems happen very
rarely so we have to add the coefficient U to equalise both
economic systems:
QUSA 1
(Q  N )USA APUSA
 $ 1
 

 ER

QP U
(Q  N ) P
APP
 PLN  U
Where U is treated as the quotient of Polish and American
GNP quoted in USD per one worker. Using GNP per
worker we can formulate the comparison of the labour
cost in both countries:
APUSA
 $  PKBRCUSA [$]
 ER

APP
 PLN  PKBRC P [$]
EXCHANGE RATE THEORY
Thus:
 $  PKBRCUSA [$]
APP  APUSA  ER

 PLN  PKBRC P [$]
The comparative analisys considering two countries
without using coefficient U is useless. The relationships
between the inflation rate and productivity determine the
price of one currency to the another. So:
PDPP /USA
 PLN 
ER

 $  WPPP /USA  ER0 [$ / PLN ]
PDPP/USA – the inflation parity measured with the GNP deflator,
WPPP/USA – the work productivity parity.
EXCHANGE RATE THEORY
So we can formulate the conclusion that the right form of
PPP can be written as follows:
*
RWP
ER  ER0 
RWP
RWP* – the real work productivity abroad,
RWP – the real domestic work productivity,
ER0 – the latest recorded exchange rate.
So this is not the labour cost relationships in two
countries that decide about the exchange rate but the
relationships between work productivity of this countries.
EXCHANGE RATE THEORY
WP
RWP 
(1  i )
EXCHANGE RATE THEORY
Taking into regard an infite time horizon we can write:
RWPn* RWP1*
ERn  ER0 

RWPn
RWP1
Assuming the equal annual changes in the productivity:
ERn  ER0 (1  e)  e  n
n
ERn
1
ER0
EXCHANGE RATE THEORY
THIS IS THE WORK PRODUCTIVITY
WHICH MAINLY DETERMINES THE
CHANGES IN THE EXCHANGE
RATE BETWEEN TWO COUNTRIES
ESTIMATION OF THE EXCHANGE RATE
To the approximation the method of the direct estimation
was choosen:
yn 1 
n 1
n
i 1
i 1
Rn (tn )   hi (tn )   yi hi (tn )
hn 1 (tn )
Rn(tn) – the estimator used to find the yn+1 value (in this case it is
conditioned suspected value),
hi(tn) – cumulated value of the density function for the parameters of the
time trend,
hn+1(tn) – cumulated value of the density function for the considered
parameter.
Period
t – tśr
t
(t – tśr)2
hi(tn)
yi
yi hi(tn)
I 2000
1
6,5
42,25
0,0000
4,1181
0,0000
II 2000
2
5,5
30,25
0,0000
4,3860
0,0000
III 2000
3
4,5
20,25
0,0000
4,3957
0,0000
IV 2000
4
3,5
12,25
0,0000
4,5137
0,0000
I 2001
5
2,5
6,25
0,0000
4,0830
0,0000
II 2001
6
1,5
2,25
0,0000
3,9985
0,0000
III 2001
7
0,5
0,25
0,0000
4,2345
0,0000
IV 2001
8
0,5
0,25
0,0000
4,0785
0,0001
I 2002
9
1,5
2,25
0,0007
4,1270
0,0027
II 2002
10
2,5
6,25
0,0109
4,0583
0,0442
III 2002
11
3,5
12,25
0,0805
4,1499
0,3343
IV 2002
12
4,5
20,25
0,2674
3,9944
1,0682
I 2003
13
5,5
30,25
0,3989
3,8314
1,5285
II 2003
14
6,5
42,25
0,2674
y14
SUM
105
227,5
1,0259
AVERAGE
2
7,5
16,25


1,25
1,1180
2,9780
ESTIMATION OF THE EXCHANGE RATE
3,878 1,026  2,98
y14 
 3,74 PLN/$
0,2674