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ADMS 4503 (13)
Lecture

Lecture5.docx

5 Pages
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Department
Administrative Studies
Course Code
ADMS 4503
Professor
Nabil Tahani

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Arbitrage dividend PDF :
= $50
R = 6%
(t= 6months) = $51.30 .
Assume that the market prices are fair prices
a. T = 6 months,
= 51.30 = 
51.30 =  
51.30/ 50 = 
Ln (51.30/50) =   
Q = 6% - ln( 51.3/50)
= 0.8665%
b. T = 1 year ,  = 54
= 50  = 52.6338 < 54
herefore this is over priced
So how do we arbitrage , we :
- Short one contract
- Buy  units of asset =  = 0.9914
- Borrow ( tbuy 0.9914 units @ $50 x 0.9914 = $ 49.5687
Today
At T
Short one contract = 0
Upon delivery + 54
Buy -49.5687
Borrow 49.5687
You return = -52.6338 =
Your gain is $ 1.36
Arbitrage currency pdf
1 year from now, you’ll need 0.8665 US to buy one cad $
a. One year forward CAD/ EUR = 1.2355 / 0.8665 = 1.4259
= 
=  = 1.4259 4
 046
b.  = 1.44 ( over priced)
- t the contract
- Borrow 1000CAD @ 4% for 1 year
- Convert to EUR 1000/1.4046 = 711.94 EUR
- Invest EUR @ 2.5% for 1 year
Today
At T
0
+1000 CAD
-1000 = -1040.81 CAD
-1000 CAD
CAD 1051.14 = 729.96 x 1.44
+ 711.94 EUR
-711.94 EUR
+711.94  = 729.96EUR
HEDGING
Static hedge : do something today and forget about it till maturity.
Dynamic hedging requires continuous adjustment
Perfect hedging means that you know exactly how the outcomes would affect you in the future.
Short hedge : you take a short position to offset a risk on a position already taken. ( short position with
short futures, long position with long futures)
Eg. Short futures position when you have a long on an asset whose price might be falling in the future.
Note: in the world of hedging, the spot market is different and separate from those of the futures where
cash settlements are made. And the spot market is for buying and delivery of commodity.
Slide 4
Assume the oil price in Aug 15
17.5
19.5
Spot sale
+17.50
Sale price : 19.5
Short
futures
- = 18.75 17.5 = 1.25
Short future = ( 18.75 19.5) = 0.75
Effective price = 17.5 + 1.25 = 18.75
or
Effective price = 19.5 0.75 = 18.75
Slide 7
= 1.2 … this is known ………………… Copper spot price on may 15 = T
Spot buy
-1.25
1.05
Long future
- = 1.25 1.20 = 0.05
= 1.05 1.20 = -0.15
Effective price
-1.25 + 0.05 = -1.2
-1.2

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Description
Arbitrage dividend PDF : S0= $50 R = 6% F0(t= 6months) = $51.30 . Assume that the market prices are fair prices a. T = 6 months, F 0 51.30 = S e0 (r−q t 6%−q 1/2 51.30 = 50 e 51.30/ 50 = S e (6%−q 0.5 0 Ln (51.30/50) = 6% − q 0.5) Q = 6% - ln( 51.3/50) = 0.8665% b. T = 1 year , F mkt = 54 (6%−0.8665% ) F 0 50 e = 52.6338 < 54 Therefore this is over priced So how do we arbitrage , we : - Short one contract - Buy e−qt units of asset = e−0.8665% x 1 = 0.9914 - Borrow ( tbuy 0.9914 units @ $50 x 0.9914 = $ 49.5687 Today At T Short one contract = 0 Upon delivery + 54 Buy -49.5687 Borrow 49.5687 You return = -52.6338 = F 0 Your gain is $ 1.36 Arbitrage currency pdf 1 year from now, you’ll need 0.8665 US to buy one cad $ a. One year forward CAD/ EUR = 1.2355 / 0.8665 = 1.4259 F 0 S e0 (rCAD− rEUR)T − r CAD− rEUR)T − 4%− 2.5% 1 S 0 F e0 = 1.4259 e 4 = 1.4046 b. F mkt = 1.44 ( over priced) - short the contract - Borrow 1000CAD @ 4% for 1 year - Convert to EUR 1000/1.4046 = 711.94 EUR - Invest EUR @ 2.5% for 1 year Today At T 0 +1000 CAD 4% -1000e = -1040.81 CAD -1000 CAD CAD 1051.14 = 729.96 x 1.44 + 711.94 EUR -711.94 EUR +711.94 e 2.5% = 729.96EUR HEDGING Static hedge : do something today and forget about it till maturity. Dynamic hedging requires continuous adjustment Perfect hedging means that you know exactly how the outcomes would affect you in the future. Short hedge : you take a short position to offset a risk on a position already taken. ( short position with short futures, long position with long futures) Eg. Short futures position when you have a long on an asset whose price might be falling in the future. Note: in the world of hedging, the spot market is different and separate from those of the futures where cash settlements are made. And the spot market is for buying and delivery of commodity. Slide 4 Assume the oil price in Aug 15 17.5 19.5 Spot sale +17.50 Sale price : 19.5 Short F0- F T 18.75 – 17.5 = 1.25 Short future = ( 18.75 – 19.5) = 0.75 futures Effective price = 17.5 + 1.25 = 18.75 Effective price = 19.5 – 0.75 = 18.75 or F0 Slide 7 F = 1.2 … this is known ………………… Copper spot price on may 15 = T 0 Spot buy -1.25 1.05 Long future F T F 0 1.25 – 1.20 = 0.05 = 1.05 – 1.20 = -0.15 Effective price -1.25 + 0.05 = -1.2 -1.2 Today: 1 2(spot deal date ) maturity date of the contract ------------------------------------------------------------------------------------------------------------ F1 F2 S S 1 2 For short hedge: At Time 2 - Spotsale + S2 - Close at short futures (
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