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Table 3 Performance results of CTP solutions (RN and RA) versus S1, when \(\left( {\pi_{u} , \pi_{d} } \right) = \left( {1.25\% , 3.75\% } \right)\)

From: Foreign exchange trading and management with the stochastic dual dynamic programming method

Currency

Policy

Mean

Median

\(VaR_{1\% }\)

\(CVaR_{1\% }\)

USDCLP \(S_{0} = 800.0\)

RN1

7.1 (0.9)

6.2

3.6

4.8 (0.6)

RA0.5

6.2 (0.8)

4.7

0.7

1.2 (0.1)

S1

9.6 (1.2)

7.8

− 3.3

− 3.0 (− 0.4)

USDBRL \(S_{0} = 5.5\)

RN1

0.0816 (1.5)

0.0677

0.0489

0.0604 (1.1)

RA0.5

0.0723 (1.3)

0.0497

0.0128

0.0204 (0.4)

S1

0.1115 (2.0)

0.0883

− 0.0361

− 0.0331 (− 0.6)

USDTRY \(S_{0} = 10.0\)

RN1

0.1730 (1.7)

0.045

0.2612

0.3581 (3.6)

RA0.5

0.0148 (0.1)

0.0004

0.1259

0.2657 (2.7)

S1

0.2877 (2.9)

0.2398

− 0.0253

− 0.0231 (− 0.2)

AUDUSD \(S_{0} = 0.7\)

RN1

0.0076 (1.1)

0.0055

0.0046

0.0057 (0.8)

RA0.5

0.0068 (1.0)

0.0039

0.0022

0.0036 (0.5)

S1

0.0109 (1.6)

0.0082

− 0.0032

− 0.0029 (− 0.4)

GBPUSD \(S_{0} = 1.0\)

RN1

0.0077 (0.8)

0.0062

0.0044

0.0054 (0.5)

RA0.5

0.0069 (0.7)

0.0045

0.0015

0.0024 (0.2)

S1

0.0108 (1.1)

0.0085

− 0.0035

− 0.0032 (− 0.3)

EURUSD \(S_{0} = 1.5\)

RN1

0.0098 (0.7)

0.0083

0.0036

0.0045 (0.3)

RA0.5

0.0092 (0.6)

0.0076

0.0015

0.0023 (0.2)

S1

0.0124 (0.8)

0.0101

− 0.0032

− 0.0029 (− 0.2)

USDJPY \(S_{0} = 105.0\)

RN1

0.8 (0.8)

0.6

0.2

0.2 (0.2)

RA0.5

0.8 (0.8)

0.6

0.1

0.1 (0.1)

S1

1.0 (0.9)

0.8

− 0.2

− 0.1 (− 0.1)

  1. The performance is measured based on speculative total profits (in domestic currency) divided by the bound L = 1. The numbers in parenthesis are the P&L divided by \(S_{0}\), that is, the P&L in terms of the foreign currency (US dollar cents for USDCLP, USDBRL, USDTRY, USDJPY, pennies for GBPUSD, euro cents for EURUSD, Australian dollar cents for AUDUSD). The bid/ask equals 5 pips for every currency