Description
international parity relationships, interest rate parity, purchasing power parity, fisher effects.
International Parity Relationships
Pratap Chandra Biswal MDI, Gurgaon
International Parity Relationships
Interest Rate Parity Purchasing Power Parity The Fisher Effects Forecasting Exchange Rates
1
Interest Rate Parity
Interest Rate Parity Defined Covered Interest Arbitrage Interest Rate Parity & Exchange Rate Determination Reasons for Deviations from Interest Rate Parity
Interest Rate Parity Defined
IRP is an arbitrage condition. If IRP did not hold, then it would be possible for a smart trader to make unlimited amounts of money exploiting the arbitrage opportunity. Since we don’t typically observe persistent arbitrage conditions, we can safely assume that IRP holds.
2
Interest Rate Parity Carefully Defined
Consider alternative one year investments for Rs.100,000: 1. Invest in India at irs. Future value = Rs.100,000 × (1 + irs)
2.
Trade your Rs. for $ at the spot rate, invest Rs.100,000/Srs/$ in the US at i$ while eliminating any exchange rate risk by selling the future value of the U.S. investment forward. Future value = Rs.100,000(1 + i$) ×
Since these investments have the same risk, they must have the same future value (otherwise an arbitrage would exist) (1 + i$) ×
Frs/$ Srs/$
Frs/$ = (1 + irs) Srs/$
Alternative 2: Send your Rs. on a round trip to the U.S. Rs.1,000
Rs.1,000 Srs./$
IRP
Step 2: Invest those dollars at i$ Future Value =
Alternative 1: invest Rs.1,000 at irs
Step 3: repatriate future value to India
Rs.1,000 × (1+ i$) Srs/$
Rs.1,000×(1 + irs) = IRP
Rs.1,000 × (1+ i$) × Frs./$ Srs/$
Since both of these investments have the same risk, they must have the same future value—otherwise an arbitrage would exist
3
Interest Rate Parity Defined
The scale of the project is unimportant Rs.1,000×(1 + irs) = Rs.1,000 × (1+ i$) × FRs./$ Srs/$ Frs/$ × (1+ i$) Srs/$
(1 + irs) =
Interest Rate Parity Defined
Formally, 1 + irs Frs/$ = 1 + i$ Srs/$
IRP is sometimes approximated as irs – i$ ? F – S S
4
Interest Rate Parity Carefully Defined
Depending upon how you quote the exchange rate ($ per ¥ or ¥ per $) we have: 1 + i¥ F = ¥/$ 1 + i$ S¥/$
or
1 + i$ F = $/¥ 1 + i¥ S$/¥
…so be a bit careful about that
IRP and Covered Interest Arbitrage
If IRP failed to hold, an arbitrage would exist. It’s easiest to see this in the form of an example. Consider the following set of foreign and domestic interest rates and spot and forward exchange rates.
Spot exchange rate 360-day forward rate Indian interest rate The U.S. interest rate S(rs/$) = Rs.45.00/$ F360(rs/$) = Rs.46.58/$ irs = 6.95% i$ = 3.50%
5
IRP and Covered Interest Arbitrage
A trader with $1,000 could invest in the U.S. at 3.50%, in one year his investment will be worth $1,035 = $1,000 × (1+ i$) = $1,000 × (1.035) Alternatively, this trader could 1. Exchange $1,000 for Rs.45000 at the prevailing spot rate, 2. Invest Rs.45000 for one year at irs = 6.95%; earn Rs.48127.5. 3. Translate Rs.48127.5 back into dollars at the forward rate F360(Rs./$) = Rs.46.5/$, the $1035.
Interest Rate Parity & Exchange Rate Determination
According to IRP only one 360-day forward rate, F360(Rs./$), can exist. It must be the case that F360(Rs./$) = Rs.46.58/$ Why? If F360(Rs./$) ? Rs.46.58/$, an arbitrage trader could make money.
6
IRP and Hedging Currency Risk
You are a U.S. importer of Indian woolens and have just ordered next year’s inventory. Payment of Rs.4500000 is due in one year.
Spot exchange rate 360-day forward rate Indian interest rate The U.S. interest rate
S(rs/$) = Rs.45.00/$ F360(rs/$) = Rs.46.58/$ irs = 6.95% i$ = 3.50%
IRP implies that there are two ways that you fix the cash outflow to a certain U.S. dollar amount: a) Put yourself in a position that delivers Rs.4500000 in one year—a long forward contract on rupees. You will pay (Rs.4500000)/(46.5/$) = $96774 in one year. b) Form a money/forward market hedge as shown below.
IRP and a Forward Market Hedge
To form a money market hedge:
Borrow $93286 in the U.S. (in one year you will owe $96608). Translate $93286 million into rupees at the spot rate Rs.45/$ to receive Rs.4197871. Invest Rs.4197871 in India at 6.95% for one year. In one year your investment will be worth Rs.4500000 exactly enough to pay your supplier.
7
Reasons for Deviations from IRP
Transactions Costs
The interest rate available to an arbitrageur for borrowing, ib,may exceed the rate he can lend at, il. There may be bid-ask spreads to overcome, Fb/Sa < F/S Thus
(Fb/Sa)(1 + i$l) ? (1 + i$ b) ? 0 Capital Controls
Governments sometimes restrict import and export of money through taxes or outright bans.
Transactions Costs Example
Will an arbitrageur facing the following prices be able to make money? 1 + i$ F Borrowing Lending = $/ € 1 + i€ S$/ € $ 5% 4.50%
€ 6% 5.50% Spot Forward Bid Ask $1.00=€1.00 $1.01=€1,00 $0.99=€1.00 $1.00=€1.00
8
Transactions Costs Example
Try borrowing $1000 at 5%: Trade for € at the ask spot rate $1.01 = €1.00 Invest €990.10 at 5.5% Hedge this with a forward contract on €1044.55 at $0.99 = €1.00 Receive $1034.11 Owe $1,050 on your dollar-based borrowing Suffer loss of $15.89
Purchasing Power Parity
Purchasing Power Parity and Exchange Rate Determination PPP Deviations and the Real Exchange Rate Evidence on PPP
Now try this backwards
9
Purchasing Power Parity and Exchange Rate Determination
The exchange rate between two currencies should equal the ratio of the countries’ price levels: PRs S(Rs/$) = P$ For example, if an ounce of gold costs Rs3000 in India and $60 in the U.S., then the price of one dollar in terms of rupees should be: PRs Rs3000 = Rs50/$ S(Rs/$) = = P$ $60
Purchasing Power Parity and Exchange Rate Determination
Suppose the spot exchange rate is $1.25 = €1.00 If the inflation rate in the U.S. is expected to be 3% in the next year and 5% in the euro zone, Then the expected exchange rate in one year should be $1.25×(1.03) = €1.00×(1.05) F($/€) = $1.25×(1.03) = $1.23 €1.00×(1.05) €1.00
10
Purchasing Power Parity and Exchange Rate Determination
The euro will trade at a 1.90% discount in the forward market:
F($/€) = S($/€)
$1.25×(1.03) €1.00×(1.05) $1.25 €1.00
=
1.03 1 + ?$ = 1.05 1 + ?€
Relative PPP states that the rate of change in the exchange rate is equal to differences in the rates of inflation—roughly 2%
Purchasing Power Parity and Interest Rate Parity
Notice that our two big equations today equal each other:
PPP
F($/€) 1 + ?$ = S($/€) 1 + ?€ =
IRP
1 + i$ F($/€) = 1 + i€ S($/€)
11
Expected Rate of Change in Exchange Rate as Inflation Differential
We could also reformulate our equations as inflation or interest rate differentials: F($/€) 1 + ?$ = S($/€) 1 + ?€
F($/€) – S($/€) 1 + ?$ 1 + ?$ 1 + ?€ = –1= – S($/€) 1 + ?€ 1 + ?€ 1 + ?€ E(e) = F($/€) – S($/€) ? – ?€ ? ?$ – ?€ = $ S($/€) 1 + ?€
Expected Rate of Change in Exchange Rate as Interest Rate Differential
E(e) = F($/€) – S($/€) = S($/€) i$ – i€ 1 + i€ ? i$ – i€
12
Quick and Dirty Short Cut
Given the difficulty in measuring expected inflation, managers often use ?$ – ?€ ? i$ – i€
Evidence on PPP
PPP probably doesn’t hold precisely in the real world for a variety of reasons.
Haircuts cost 10 times as much in the developed world as in the developing world. Film, on the other hand, is a highly standardized commodity that is actively traded across borders. Shipping costs, as well as tariffs and quotas can lead to deviations from PPP.
PPP-determined exchange rates still provide a valuable benchmark.
13
Forecasting Exchange Rates
Efficient Markets Approach Fundamental Approach Technical Approach Performance of the Forecasters
Efficient Markets Approach
Financial Markets are efficient if prices reflect all available and relevant information. If this is so, exchange rates will only change when new information arrives, thus: St = E[St+1] and Ft = E[St+1| It] Predicting exchange rates using the efficient markets approach is affordable and is hard to beat.
14
Fundamental Approach
Involves econometrics to develop models that use a variety of explanatory variables. This involves three steps:
step 1: Estimate the structural model. step 2: Estimate future parameter values. step 3: Use the model to develop forecasts.
The downside is that fundamental models do not work any better than the forward rate model or the random walk model.
Technical Approach
Technical analysis looks for patterns in the past behavior of exchange rates. Clearly it is based upon the premise that history repeats itself. Thus it is at odds with the EMH
15
Performance of the Forecasters
Forecasting is difficult, especially with regard to the future. As a whole, forecasters cannot do a better job of forecasting future exchange rates than the forward rate. The founder of Forbes Magazine once said: “You can make more money selling financial advice than following it.”
Thank You!!!
16
doc_115381594.pdf
international parity relationships, interest rate parity, purchasing power parity, fisher effects.
International Parity Relationships
Pratap Chandra Biswal MDI, Gurgaon
International Parity Relationships
Interest Rate Parity Purchasing Power Parity The Fisher Effects Forecasting Exchange Rates
1
Interest Rate Parity
Interest Rate Parity Defined Covered Interest Arbitrage Interest Rate Parity & Exchange Rate Determination Reasons for Deviations from Interest Rate Parity
Interest Rate Parity Defined
IRP is an arbitrage condition. If IRP did not hold, then it would be possible for a smart trader to make unlimited amounts of money exploiting the arbitrage opportunity. Since we don’t typically observe persistent arbitrage conditions, we can safely assume that IRP holds.
2
Interest Rate Parity Carefully Defined
Consider alternative one year investments for Rs.100,000: 1. Invest in India at irs. Future value = Rs.100,000 × (1 + irs)
2.
Trade your Rs. for $ at the spot rate, invest Rs.100,000/Srs/$ in the US at i$ while eliminating any exchange rate risk by selling the future value of the U.S. investment forward. Future value = Rs.100,000(1 + i$) ×
Since these investments have the same risk, they must have the same future value (otherwise an arbitrage would exist) (1 + i$) ×
Frs/$ Srs/$
Frs/$ = (1 + irs) Srs/$
Alternative 2: Send your Rs. on a round trip to the U.S. Rs.1,000
Rs.1,000 Srs./$
IRP
Step 2: Invest those dollars at i$ Future Value =
Alternative 1: invest Rs.1,000 at irs
Step 3: repatriate future value to India
Rs.1,000 × (1+ i$) Srs/$
Rs.1,000×(1 + irs) = IRP
Rs.1,000 × (1+ i$) × Frs./$ Srs/$
Since both of these investments have the same risk, they must have the same future value—otherwise an arbitrage would exist
3
Interest Rate Parity Defined
The scale of the project is unimportant Rs.1,000×(1 + irs) = Rs.1,000 × (1+ i$) × FRs./$ Srs/$ Frs/$ × (1+ i$) Srs/$
(1 + irs) =
Interest Rate Parity Defined
Formally, 1 + irs Frs/$ = 1 + i$ Srs/$
IRP is sometimes approximated as irs – i$ ? F – S S
4
Interest Rate Parity Carefully Defined
Depending upon how you quote the exchange rate ($ per ¥ or ¥ per $) we have: 1 + i¥ F = ¥/$ 1 + i$ S¥/$
or
1 + i$ F = $/¥ 1 + i¥ S$/¥
…so be a bit careful about that
IRP and Covered Interest Arbitrage
If IRP failed to hold, an arbitrage would exist. It’s easiest to see this in the form of an example. Consider the following set of foreign and domestic interest rates and spot and forward exchange rates.
Spot exchange rate 360-day forward rate Indian interest rate The U.S. interest rate S(rs/$) = Rs.45.00/$ F360(rs/$) = Rs.46.58/$ irs = 6.95% i$ = 3.50%
5
IRP and Covered Interest Arbitrage
A trader with $1,000 could invest in the U.S. at 3.50%, in one year his investment will be worth $1,035 = $1,000 × (1+ i$) = $1,000 × (1.035) Alternatively, this trader could 1. Exchange $1,000 for Rs.45000 at the prevailing spot rate, 2. Invest Rs.45000 for one year at irs = 6.95%; earn Rs.48127.5. 3. Translate Rs.48127.5 back into dollars at the forward rate F360(Rs./$) = Rs.46.5/$, the $1035.
Interest Rate Parity & Exchange Rate Determination
According to IRP only one 360-day forward rate, F360(Rs./$), can exist. It must be the case that F360(Rs./$) = Rs.46.58/$ Why? If F360(Rs./$) ? Rs.46.58/$, an arbitrage trader could make money.
6
IRP and Hedging Currency Risk
You are a U.S. importer of Indian woolens and have just ordered next year’s inventory. Payment of Rs.4500000 is due in one year.
Spot exchange rate 360-day forward rate Indian interest rate The U.S. interest rate
S(rs/$) = Rs.45.00/$ F360(rs/$) = Rs.46.58/$ irs = 6.95% i$ = 3.50%
IRP implies that there are two ways that you fix the cash outflow to a certain U.S. dollar amount: a) Put yourself in a position that delivers Rs.4500000 in one year—a long forward contract on rupees. You will pay (Rs.4500000)/(46.5/$) = $96774 in one year. b) Form a money/forward market hedge as shown below.
IRP and a Forward Market Hedge
To form a money market hedge:
Borrow $93286 in the U.S. (in one year you will owe $96608). Translate $93286 million into rupees at the spot rate Rs.45/$ to receive Rs.4197871. Invest Rs.4197871 in India at 6.95% for one year. In one year your investment will be worth Rs.4500000 exactly enough to pay your supplier.
7
Reasons for Deviations from IRP
Transactions Costs
The interest rate available to an arbitrageur for borrowing, ib,may exceed the rate he can lend at, il. There may be bid-ask spreads to overcome, Fb/Sa < F/S Thus
(Fb/Sa)(1 + i$l) ? (1 + i$ b) ? 0 Capital Controls
Governments sometimes restrict import and export of money through taxes or outright bans.
Transactions Costs Example
Will an arbitrageur facing the following prices be able to make money? 1 + i$ F Borrowing Lending = $/ € 1 + i€ S$/ € $ 5% 4.50%
€ 6% 5.50% Spot Forward Bid Ask $1.00=€1.00 $1.01=€1,00 $0.99=€1.00 $1.00=€1.00
8
Transactions Costs Example
Try borrowing $1000 at 5%: Trade for € at the ask spot rate $1.01 = €1.00 Invest €990.10 at 5.5% Hedge this with a forward contract on €1044.55 at $0.99 = €1.00 Receive $1034.11 Owe $1,050 on your dollar-based borrowing Suffer loss of $15.89
Purchasing Power Parity
Purchasing Power Parity and Exchange Rate Determination PPP Deviations and the Real Exchange Rate Evidence on PPP
Now try this backwards
9
Purchasing Power Parity and Exchange Rate Determination
The exchange rate between two currencies should equal the ratio of the countries’ price levels: PRs S(Rs/$) = P$ For example, if an ounce of gold costs Rs3000 in India and $60 in the U.S., then the price of one dollar in terms of rupees should be: PRs Rs3000 = Rs50/$ S(Rs/$) = = P$ $60
Purchasing Power Parity and Exchange Rate Determination
Suppose the spot exchange rate is $1.25 = €1.00 If the inflation rate in the U.S. is expected to be 3% in the next year and 5% in the euro zone, Then the expected exchange rate in one year should be $1.25×(1.03) = €1.00×(1.05) F($/€) = $1.25×(1.03) = $1.23 €1.00×(1.05) €1.00
10
Purchasing Power Parity and Exchange Rate Determination
The euro will trade at a 1.90% discount in the forward market:
F($/€) = S($/€)
$1.25×(1.03) €1.00×(1.05) $1.25 €1.00
=
1.03 1 + ?$ = 1.05 1 + ?€
Relative PPP states that the rate of change in the exchange rate is equal to differences in the rates of inflation—roughly 2%
Purchasing Power Parity and Interest Rate Parity
Notice that our two big equations today equal each other:
PPP
F($/€) 1 + ?$ = S($/€) 1 + ?€ =
IRP
1 + i$ F($/€) = 1 + i€ S($/€)
11
Expected Rate of Change in Exchange Rate as Inflation Differential
We could also reformulate our equations as inflation or interest rate differentials: F($/€) 1 + ?$ = S($/€) 1 + ?€
F($/€) – S($/€) 1 + ?$ 1 + ?$ 1 + ?€ = –1= – S($/€) 1 + ?€ 1 + ?€ 1 + ?€ E(e) = F($/€) – S($/€) ? – ?€ ? ?$ – ?€ = $ S($/€) 1 + ?€
Expected Rate of Change in Exchange Rate as Interest Rate Differential
E(e) = F($/€) – S($/€) = S($/€) i$ – i€ 1 + i€ ? i$ – i€
12
Quick and Dirty Short Cut
Given the difficulty in measuring expected inflation, managers often use ?$ – ?€ ? i$ – i€
Evidence on PPP
PPP probably doesn’t hold precisely in the real world for a variety of reasons.
Haircuts cost 10 times as much in the developed world as in the developing world. Film, on the other hand, is a highly standardized commodity that is actively traded across borders. Shipping costs, as well as tariffs and quotas can lead to deviations from PPP.
PPP-determined exchange rates still provide a valuable benchmark.
13
Forecasting Exchange Rates
Efficient Markets Approach Fundamental Approach Technical Approach Performance of the Forecasters
Efficient Markets Approach
Financial Markets are efficient if prices reflect all available and relevant information. If this is so, exchange rates will only change when new information arrives, thus: St = E[St+1] and Ft = E[St+1| It] Predicting exchange rates using the efficient markets approach is affordable and is hard to beat.
14
Fundamental Approach
Involves econometrics to develop models that use a variety of explanatory variables. This involves three steps:
step 1: Estimate the structural model. step 2: Estimate future parameter values. step 3: Use the model to develop forecasts.
The downside is that fundamental models do not work any better than the forward rate model or the random walk model.
Technical Approach
Technical analysis looks for patterns in the past behavior of exchange rates. Clearly it is based upon the premise that history repeats itself. Thus it is at odds with the EMH
15
Performance of the Forecasters
Forecasting is difficult, especially with regard to the future. As a whole, forecasters cannot do a better job of forecasting future exchange rates than the forward rate. The founder of Forbes Magazine once said: “You can make more money selling financial advice than following it.”
Thank You!!!
16
doc_115381594.pdf