Tag Archives: parity of interest

Euro dollar, parity of interest, cost of carry future trading notes

Euro dollar, parity of interest, cost of carry future trading notes
This came from my course 

Short-term interest rate on foreign US bank accounts based on LIBOR.

Attached images eurodollar

Euro dollar futures contract based on 90 day Eurodollar time deposits with prime London banks LIBOR
Reflect short-term commercial interest rates and is treated in Chicago London Singapore and Tokyo
Deliveries cash settlement contract size is $1,000,000.03 months deposit and quotes on index search that hundred minus the index equal euro dollar yield. There is no delivery on Eurodollar.
E.g. a quote of 93.18 for the June contract implies Eurodollar interest rate of 6.82 equals 100-93.18 and a contract price of 10,000 times [100-0.25×6.82] equaling $982,950

So it's 100 minus the interest rate minus I MM index this is the euro dollar index
100-6.82=93.18 is Price of the contract
As the Tbond on trades as a percentage of par 
There is a inverse relationship because of the hundred minus. If the interest rate rises, the index should fall. Just like T-bond there is an interest rate inverse relationship with price of bonds. 
The specifications is a deposit placed on a European bank for 90 day period. The interest rate of the index is the underlying assumption. The cash settlement takes place in the delivery month. If you don't reverse your position the clearinghouse will sell it for you at the LIBOR rate during that day. The LIBOR rate is the same as the interest rate. 
The interest rate that you see is usually an annualized rate. So in the above example 6.82% is an annualized interest rate. Remember that the Eurodollar is a 90 day contract so you need to divide that rate by four to calculate a quarter of the year. In the both example you multiply 100-.25×6.82 for the 90 day interest rate.

$1 million - interest rate divided by four times $1 million

For a eurodollar futures profit and loss example see attached photo
If you expect interest rates to the decline and go long. This is because it is the 100 minus the interest rate. 
If the interest rate is 5%, the index will be 95. If you think the interest rate will fall to 4%, The index will rise to 96 which means you'd want to go along.
By June euro dollar at $94.05 on October 25
Cell June Eurodollar at 94.56 on January 25
94.56-94.05 equals 51 basis points times $25 remember each basis point is worth $25 each
51 times $25 equals $1275 -$75 brokerage fee profit then becomes $1200

 If you think interest rates rise then you sell Eurodollar.

Yen
Contract  size is 12 1/2 million yen.  When you see a newspaper "you will need to move the decimal places by. The price of A Japanese yen is one penny what is .01. 

For yen futures contract example
If you expect US dollar to the client and go long
Remember the quotes are done US dollar per foreign-currency so see below
You buy  Japanese yen in June at .0104 on October 25
You sell the June Japanese yen at .010545 on January 25
.010545-.0104 equals .000145$/¥ * 12.5 million ¥
=$1812 -$75 brokerage fee
Profit equals $1737

$/¥ or $.0104 this is the cost of per yen in US dollars
If US dollar is to decline, You would buy the above contract since the price of dollars will rise as the yen will cost more. So if it moves from .0104 in US dollars to .0134 then you know yen has gone up. 
You also need to calculate $/¥ x 12.5 million ¥. The Yen is in the denominator so it will cancel each other out so the remainder will be just US dollar so see attached photo. Just always remember you want to contract to be in US dollars so this is how you calculate it. 

US exports minus US imports is called current account

Interest rate parity example see attached photo. 
Interest rates change all the time.
When you invest in a foreign country to get interest, you need to convert to that local currency but when you want it back you have to convert back to your local currency as well. As a result there is currency risk. When you look at the world financial markets, these markets are integrated to a Forward Currency prices ought too reflect interest rate differentials. There may be an arbitrage opportunity which will depend on forward rate of the currency. You could invest in Australia and hedge the currency risk when you come back out.there is a interest parity condition based around this. 

Interest rate parity example so see example photo attached
This examines nominal interest rate differentials between two countries and forward exchange rates.

This arbitrage opportunity condition still needs to hold.

I US equals I cdn + (e^f e^s)/e^s 
 Where I us is the US interest rate, i cdn is the interest rate in Canada, while there is a spread between the Forward spot rates of US and Canada. If you are getting a higher interest rate in Canada which is a good deal except when you lock in the Canadian dollar forward.  If there is a large discount on the price, when you bring back your money to the US the converted price with the differential in the interest rates, it is no longer there. This calculation in equilibrium if the markets arbitrage, the markets should be arbitraged. 
Financial institutions will move money around to take advantage of the interest rate spread but they will locking currency risk by hedging. That difference can be eaten away until the condition as held. The equation says that the differential on the interest rates should reflect on the foreword spread.

Suppose interest rate on a 90 day government T bill is 1.91% in Canada (i cdn) and 1.75% in the US (i us). Assume the spot exchange rate (US dollar per Canadian dollar) is 0.6242 and the spot exchange rate on a futures contract price for delivery in three months time is .62637

1.75 equals 1.91+ [.6237-.6242] /.6242
1.75 less than 1.909 so. Parity doesn't hold invest in Canada

Refer to cost of Carry model and attached photo

Interest rate futures prices theoretically adhere to the cost of a carry model

FrT=St(1+Clt) so sensually the future price is equal to the spot price plus the cost of storage
Where FtT is futures price for delivery at time T, Stis equal to spot price at time t and Clt is net cost of carry from time t to T 
For two different future months
FtT=Ft(1+Ct,t+1) if you have two different future months you have the features of delivery month one is equal to the futures price of the delivery plus the cost of Storage for a month one to the delivery month.
Supposed June treasury bond futures are trading at 97–30 and September futures of trading at 96–29

The cost of a bond will be the opportunity cost of that investment versus another investment
If you look at the intertemporal prices of bonds it ought to adhere to this cost of Carry model 
 
In the above example of June treasury bond future or trading at 97–30 in September futures are trading at 96–29 the question becomes does this adhere to the cost of carry 

Refer to attached photo
That cost of care in the barn from June to September [Ctt+1] has two components, the financing costs and interest paid by the bond which is the negative cost
 Supposed to 2.5% is a cost of financing and the 6% of $100,000 bond returns $1500 (this is annual but you want quarterly) to the holder for the June to September. That's the that cost of financing is [.02 5÷4] times $97,937 -$1500 equals -$888

Divided by four because you want quarterly. Dividend cost is $1500. The -$888 is your  storage cost but it is negative since the bond is paying you a dividend. This is why your September is lower than your June contract. The cost of Carry is $888. 

The arbitrage condition is $96,906 approximately equaling $97,937 -$880
$96,906 less than $97,04
 Price is very close to the September future.  If you adjust the June contract for the cost of storage, comes close to the price of September contract. If there is a large difference then there is a arbitrage opportunity if the difference is positive.  Arbitrage does not last very long in bondmarket.

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