Casullo Financial Services

Casullo Financial ServicesCasullo Financial Services

Ya-Ling Chuang (Ambrosia) Ya-Ling Chuang (Ambrosia)

Udayan Shah Udayan Shah

Scott Holtorf Scott Holtorf

Supradipta DattaSupradipta Datta

Casullo Financial ServicesCasullo Financial Services

Exchange Rate Projections Exchange Rate Projections

ForFor

Nike Inc.Nike Inc.

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Four Models:Four Models:

1.1. The Purchase Power Parity Model (PPP)The Purchase Power Parity Model (PPP)

2.2. The Monetary (Asset) ApproachThe Monetary (Asset) Approach

3.3. Forward Exchange Rate ModelForward Exchange Rate Model

4.4. Ad-hoc ModelAd-hoc Model

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The PPP ModelThe PPP Model

SSFFt+1t+1 = S = SFF

tt * [ 1 + s * [ 1 + sFFt+1t+1]]

MAE 0fMAE 0f εε = S = SFFt+1t+1 – S – St+1t+1

In –sample:In –sample:

ssFFtt= I= Id,td,t – I – Iff,,tt

where Iwhere Id,t+1d,t+1 = CPI = CPId,t+1d,t+1/CPI/CPId,td,t

SSFFtt = S = Stt

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The PPP ModelThe PPP Model

SSFFt+1t+1 = S = SFF

tt * [ 1+ s * [ 1+ sFFt+1t+1]]

out-of-sample:out-of-sample:

Regress the equationRegress the equation

IIt+1t+1 = = αα00 + + αα11(I(Itt) + ) + εεtt

ssFFt+1t+1 = I = Id,t+1d,t+1 – I – If,t+1f,t+1

Casullo Financial ServicesCasullo Financial ServicesThe Monetary (Asset) ApproachThe Monetary (Asset) Approach

SSFFt+1t+1 = S = SFF

tt * [ 1+ s * [ 1+ sFFt+1t+1]]

MAE 0fMAE 0f εε = S = SFFt+1t+1 – S – St+1t+1

In –sample:In –sample:

sst,Tt,T = y = yf,Tf,T – y – yd,Td,T +m +mSd,TSd,T – m – mSf,TSf,T

SSFFtt = S = Stt

Casullo Financial ServicesCasullo Financial ServicesThe Monetary (Asset) ApproachThe Monetary (Asset) Approach

SSFFt+1t+1 = S = SFF

tt * [ 1+ s * [ 1+ sFFt+1t+1]]

MAE of MAE of εε = S = SFFt+1t+1 – S – St+1t+1

out-of-sample:out-of-sample:

After Regression AnalysisAfter Regression Analysis

ssFFt+1t+1 = = αα00 + + αα11(y(yf,tf,t – y – yd,td,t) + ) + αα22(m(md,td,t – m – mf,tf,t))

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Expectation HypothesisExpectation Hypothesis

SSFFt+1t+1 = S = SFF

tt * [1 + s * [1 + sFFtt]]

MAE of MAE of εε = S = SFFtt – S – Stt

in-sample:in-sample:

ssFFtt = (i = (id,td,t – i – if,tf,t) * T/360) * T/360

SSFFtt = S = Stt

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Expectation HypothesisExpectation Hypothesis

SSFFt+1t+1 = S = SFF

tt * [1 + s * [1 + sFFtt]]

MAE of MAE of εε = S = SFFtt – S – Stt

out-of-sample:out-of-sample:

ssFFtt = (i = (id,td,t – i – if,tf,t) * T/360) * T/360

Use of random walk in estimating (iUse of random walk in estimating (id,td,t – i – if,tf,t))

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Ad-hoc ModelAd-hoc Model

SSFFt+1t+1 = S = SFF

tt * [1 + s * [1 + sFFt+1t+1]]

MAE of MAE of εε = S = SFFtt – S – Stt

in-sample:in-sample:

ssFFtt = = αα + ß + ß11(I(Id,td,t – I – If,tf,t) + ß) + ß22 [(i [(id,td,t – i – if,tf,t) * T/360] ) * T/360]

+ ß+ ß3 3 (y(yd,td,t – y – yf,tf,t) + ) + εεtt

SSFFtt = S = Stt

Casullo Financial ServicesCasullo Financial ServicesAd-hoc ModelAd-hoc Model

SSFFt+1t+1 = S = SFF

tt * [1 + s * [1 + sFFt+1t+1]]

MAE of MAE of εε = S = SFFtt – S – Stt

out-of-sample:out-of-sample:

Random Walk used in estimating (IRandom Walk used in estimating (Id,td,t – I – If,tf,t), (i), (id,td,t – i – if,tf,t) and ) and (y(yd,td,t – y – yf,tf,t).).

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USD/GBPUSD/GBP In Sample MAEIn Sample MAE Out of Sample Out of Sample MAEMAE

PPPPPP 0.06660.0666 1.64591.6459

MAAMAA 0.09520.0952 0.03480.0348

FWD EXFWD EX 0.06650.0665 0.06660.0666

AD HOCAD HOC 0.06060.0606 0.14260.1426

Random WalkRandom Walk 0.06300.0630 0.02980.0298

RSQRSQ t-statst-stats

0.08510.0851 -0.39, -2.29, -0.79-0.39, -2.29, -0.79

Casullo Financial ServicesCasullo Financial ServicesUS-UK Exchange Rate Forecast Comparison

1

1.2

1.4

1.6

1.8

2

2.2

2.4

1980.0

1984.0

1988.0

1992.0

1996.0

2000.0

Time

US

D/G

BP

PPP (IS)

PPP (OS)

MAA (IS)

MAA (OS)

Ad Hoc (IS)

Ad Hoc (OS)

FWD EX (IS)

FWD EX (OS)

Actual

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USD/DEMUSD/DEM In Sample MAEIn Sample MAE Out of Sample Out of Sample MAEMAE

PPPPPP 0.12950.1295 0.20320.2032

MAAMAA 0.03300.0330 0.02760.0276

FWD EXFWD EX 0.02410.0241 0.11020.1102

AD HOCAD HOC 0.02280.0228 0.11580.1158

Random WalkRandom Walk 0.02340.0234 0.01810.0181

RSQRSQ t-statst-stats

0.04640.0464 1.31, -1.57, .0341.31, -1.57, .034

Casullo Financial ServicesCasullo Financial ServicesUS-GRM Exchange Rate Forecast Comparison

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1980.0

1984.0

1988.0

1992.0

1996.0

2000.0

Time

US

D/D

EM

PPP (IS)

PPP (OS)

MAA (IS)

MAA (OS)

Ad Hoc (IS)

Ad Hoc (OS)

FWD EX (IS)

FWD EX (OS)

Actual

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USD/JPYUSD/JPY In Sample MAEIn Sample MAE Out of Sample Out of Sample MAEMAE

PPPPPP 0.00190.0019 0.00160.0016

MAAMAA 0.00040.0004 0.00050.0005

FWD EXFWD EX 0.00030.0003 0.00040.0004

AD HOCAD HOC 0.00030.0003 0.00030.0003

Random WalkRandom Walk 0.00030.0003 0.00030.0003

RSQRSQ t-statst-stats

0.16450.1645 -.133, -3.28, 1.48-.133, -3.28, 1.48

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US-JAP Exchange Rate Forecast Comparison

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0.011

0.012

0.013

0.014

0.015

1980.0

1984.0

1988.0

1992.0

1996.0

2000.0

Time

US

D/J

PY

PPP (IS)

PPP (OS)

MAA (IS)

MAA (OS)

Ad Hoc (IS)

Ad Hoc (OS)

FWD EX (IS)

FWD EX (OS)

Actual

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USD/MXPUSD/MXP In Sample MAEIn Sample MAE Out of Sample Out of Sample MAEMAE

PPPPPP 2.87192.8719 0.04370.0437

MAAMAA 1.33341.3334 0.01140.0114

FWD EXFWD EX 0.40850.4085 0.03800.0380

AD HOCAD HOC 0.34310.3431 0.08160.0816

Random WalkRandom Walk 0.58280.5828 0.00190.0019

RSQRSQ t-statst-stats

0.48390.4839 2.97, .97, -.082.97, .97, -.08

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US-MEX Exchange Rate Forecast Comparison

0

5

10

15

20

25

30

35

40

45

50

55

1980.0

1981.0

1982.0

1983.0

1984.0

1985.0

1986.0

1987.0

Time

US

D/M

XP

PPP (IS)

MAA (IS)

Ad Hoc (IS)

FWD EX (IS)

Actual

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US-MEX Exchange Rate Forecast Comparison

0

0.2

0.4

0.6

0.8

1

1987.0

1991.0

1995.0

1999.0

2003.0

Time

US

D/M

XP

PPP (IS)

PPP (OS)

MAA (IS)

MAA (OS)

Ad Hoc (IS)

Ad Hoc (OS)

FWD EX (IS)

FWD EX (OS)

Actual

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USD/KRWUSD/KRW In Sample MAEIn Sample MAE Out of Sample Out of Sample MAEMAE

PPPPPP 1.69171E-41.69171E-4 2.0495E-42.0495E-4

MAAMAA 1.2164E-41.2164E-4 5.9246E-55.9246E-5

FWD EXFWD EX 7.700E-57.700E-5 1.1752E-41.1752E-4

AD HOCAD HOC 3.786E-53.786E-5 1.1752E-41.1752E-4

Random WalkRandom Walk 3.824E-53.824E-5 2.198E-52.198E-5

RSQRSQ t-statst-stats

0.41870.4187 3.48, 1.80, .843.48, 1.80, .84

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US-KOR Exchange Rate Forecast Comparison

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

0.0011

0.0012

0.0013

0.0014

0.0015

0.0016

0.0017

0.0018

0.0019

0.002

1990.0

1994.0

1998.0

2002.0

Time

US

D/K

RW

PPP (IS)

PPP (OS)

MAA (IS)

MAA (OS)

Ad Hoc (IS)

Ad Hoc (OS)

FWD EX (IS)

FWD EX (OS)

Actual

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GBPGBP DEMDEM JPYJPY MXPMXP KRWKRW

11 -0.252-0.252 1.5451.545 -0.138-0.138 0.6230.623 3.2733.273

22 -1.975-1.975 -1.611-1.611 -3.408-3.408 0.2540.254 2.2142.214

33 -0.196-0.196 0.0140.014 0.6740.674 -0.003-0.003 0.0740.074

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USD/DEMUSD/DEM In Sample MAEIn Sample MAE Out of Sample Out of Sample MAEMAE

PPPPPP 0.12950.1295 0.20320.2032

MAAMAA 0.03300.0330 0.02760.0276

FWD EXFWD EX 0.02410.0241 0.11020.1102

AD HOCAD HOC 0.02280.0228 0.11580.1158

Random WalkRandom Walk 0.02340.0234 0.01810.0181

RSQRSQ t-statst-stats

0.04640.0464 1.31, -1.57, .0341.31, -1.57, .034

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US-GRM Exchange Rate Forecast Comparison

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1980.0

1984.0

1988.0

1992.0

1996.0

2000.0

Time

US

D/D

EM MAA (IS)

MAA (OS)

Actual

FORECAST

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USD/JPYUSD/JPY In Sample MAEIn Sample MAE Out of Sample Out of Sample MAEMAE

PPPPPP 0.00190.0019 0.00160.0016

MAAMAA 0.00040.0004 0.00050.0005

FWD EXFWD EX 0.00030.0003 0.00040.0004

AD HOCAD HOC 0.00030.0003 0.00030.0003

Random WalkRandom Walk 0.00030.0003 0.00030.0003

RSQRSQ t-statst-stats

0.16450.1645 -.133, -3.28, 1.48-.133, -3.28, 1.48

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US-JAP Exchange Rate Forecast Comparison

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0.011

0.012

0.013

0.014

0.015

1980.0

1984.0

1988.0

1992.0

1996.0

2000.0

Time

US

D/J

PY Ad Hoc (IS)

Ad Hoc (OS)

Actual

FORECAST