# parity conditions

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PARITY CONDITIONS. IRP, PPP, IFE, EH & RW. Arbitrage in FX Markets. Arbitrage Definition It involves no risk and no capital of your own . It is an activity that takes advantages of pricing mistakes in financial instruments in one or more markets. There are 3 kinds of arbitrage - PowerPoint PPT Presentation

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• PARITY CONDITIONSIRP, PPP, IFE, EH & RW

• Arbitrage in FX MarketsArbitrage Definition It involves no risk and no capital of your own. It is an activity that takes advantages of pricing mistakes in financial instruments in one or more markets.

There are 3 kinds of arbitrage(1) Local (sets uniform rates across banks)(2) Triangular (sets cross rates)(3) Covered (sets forward rates)

Note: The definition presents the ideal view of (riskless) arbitrage. Arbitrage, in the real world, involves some risk. Well call this arbitrage pseudo arbitrage.

• Interest Rate Parity Theorem Q: How do banks price FX forward contracts?A: In such a way that arbitrageurs cannot take advantage of their quotes. To price a forward contract, banks consider covered arbitrage strategies.

Notation:id = domestic nominal T days interest rate (annualized).if = foreign nominal T days interest rate (annualized).St = time t spot rate (direct quote, for example USD/GBP).Ft,T = forward rate for delivery at date T, at time t.

Note: In developed markets (like the US), all interest rates are quoted on annualized basis.

• Consider the following (covered) strategy done simultaenously at t=0:1. At t=0, borrow from a foreign bank 1 unit of a FC for T days. 2. At t=0, exchange FC 1 = DC St. 3. At t=0, deposit DC St in a domestic bank for T days. 4. At t=0, buy a T-day forward contract to exchange DC for FC at a Ft,T.

Cash flows at time T:We get St(1+id x T/360)/Ft,T units of foreign currency.We pay the foreign bank (1+if x T/360) units of the FC.

This strategy will not be profitable if, at time T, what we receive in FC is less or equal to what we have to pay in FC. That is, arbitrage will force: :St (1 + id x T/360)/Ft,T = (1 + if x T/360).

Solving for Ft,T, we obtain the following expression:

• The Forward Premium and the IRPT Reconsider the linearized IRPT. That is,

Ft,T St [1 + (id - if) x T/360].

A little algebra gives us:

(Ft,T-St)/St x 360/T (id - if)

Let T=360. Then, p id - if.

Note: p measures the annualized % gain/loss of buying FC spot (at St, finance at id & deposit FC at if) and selling it forward (at Ft,T).

Equilibrium: p exactly compensates (id - if) No arbitrage opportunities No capital flows.

• IRP LineUnder the linear approximation, we have the IRP Lineid -if p (forward premium) B (Capital inflows)(Capital outflows)Look at point A: p > id if(or p + if > id), => Domestic capital fly to the foreign country (what an investor loses on the lower interest rate, if, is more thancompensated by the high forward premium, p). 45A

• The Behavior of FX Rates Fundamentals that affect FX Rates: Formal Theories

- Inflation rates differentials (IUSD - IFC)PPP- Interest rate differentials (iUSD - iFC)IFE- Forward rates EH- Efficient Markets:RW

• We want to explain St. Eventually, we would like to have a formula to forecast St+T.Like many macroeconomic series, exchange rates have a trend in statistics the trends in macroeconomic series are called stochastic trends. It is better to work with changes, not levels.

Chart1

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S(t)

MXN/USD

Sheet1

Start1/15/711/15/711/15/711/15/711/15/711/15/711/15/711/15/711/15/711/15/711/15/711/15/711/15/711/15/711/15/711/15/712/15/711/10/711/10/711/10/711/10/711/10/711/10/711/10/711/10/711/10/711/10/711/10/711/10/711/10/711/10/711/10/711/10/71

End9/15/119/15/119/15/119/15/119/15/119/15/119/15/119/15/119/15/119/15/119/15/119/15/119/15/119/15/119/15/119/15/118/15/119/10/119/10/119/10/119/10/119/10/119/10/119/10/119/10/119/10/119/10/119/10/119/10/119/10/119/10/119/10/119/10/11

FrequencyMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM

Code870002035870000700870001204870003423870006876870002678870002847595888771528889991730000128750000067744560248870000537870003171870004478870006343109996669S99721S99718S99696S99711S99703S99706S20363S99720S99713S99707S02397Y77133S99694S94316S99714S99710

1/15/7111.6436.216.6716.256.9733.866.8533.01119.070.0220.43.218.12.39724.31097.4857.1382357.82317.053.08451.01540.71781.115

2/15/7111.7136.3516.6716.256.9733.866.9932.4419.160.0220.43.218.42.41594.29727.48837.1412357.5319.153.06651.00860.71231.124

3/15/7111.836.5716.6816.346.9733.867.1232.29719.160.0220.53.318.82.41924.3047.47947.1352357.59320.753.06531.00360.71131.126

4/15/7112.0536.616.8516.346.9734.367.0931.89719.350.0220.53.319.22.41674.29517.48557.1278357.5322.853.06911.00680.7121.124

5/15/7112.133717.1116.436.9734.466.9632.2419.350.0220.63.319.42.41734.10767.50527.1103357.14325.353.06691.00840.71181.125

6/15/7112.2237.0317.1716.517.0834.666.9532.32519.440.0220.83.319.62.41934.08517.49637.1111357.4326.753.05621.02390.71121.126

7/15/7112.2937.1917.1916.67.234.567.0732.49719.630.0220.83.319.92.41834.10617.5017.1061357.4370.83.05531.0230.71151.125

8/15/7112.337.2517.2616.67.3434.567.1432.35419.820.0220.93.420.12.41874.05827.49637.0972357.39370.83.05341.01280.71141.125

9/15/7112.3237.

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