The profitability of carry trade related to the forecasting

The Profitability of Carry Trade relative to the Forecasting-Based Trading in the Foreign Exchange market

Taijas Kumar S3496493

Abstract – The objective of the project is to relate and compare the forecasting-based trading to that of profitability of the carry trade in the Foreign exchange market. This paper uses 3 models, which are, restricted PPP, restricted UIP and dynamic forecasting model. Based on the observations from the paper we could conclude that dynamic forecasting model could not beat random walk. 4 different strategies were applied toward the objective. All in all, forecasted-based strategy showcased the most profitability compared to the other strategies.

Disclaimer: The author is solely responsible for any omission and/or errors.

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Table of Contents 1.

Introduction ............................................................................................................................. 4

2.

Literature Review .................................................................................................................... 5

3.

Methodology.......................................................................................................................... 11 3.1

Unit root test ................................................................................................................... 12

3.2

Estimating the exchange rate models ............................................................................. 13

3.2.1

Restricted Purchasing Power Parity ........................................................................ 13

3.2.2

Restricted Uncovered Interest Rate Parity .............................................................. 13

3.3

Cointegration testing ...................................................................................................... 14

3.4

Estimating Full Forecasting Model ................................................................................ 14

3.5 Generation of In-Sample Forecast....................................................................................... 15 3.6 Trading strategy related towards estimated forecasts ......................................................... 18 3.7 Calculations for measuring Return and Risk....................................................................... 19 4.

Data and Empirical Results ................................................................................................... 21 4.1

Specification of Data and Variables ............................................................................... 21

4.2

Testing for Unit root and Cointegration ......................................................................... 26

4.3

Estimating and Testing the Exchange Rate Forecasting Model ..................................... 30

4.4

Measurement of Forecasting Accuracy .......................................................................... 33

4.5

Measures of Profitability of Trading Strategies ............................................................. 38

5.

Conclusions ........................................................................................................................... 39

6.

List of References .................................................................................................................. 41

7.

Appendices ............................................................................................................................ 45

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1. Introduction Comparing of the forecast-based trading in the FX market to that of the profitability of the carry trade involves vast amount of empirical literature. The comparison is based on risk, return and risk-adjusted return. Furthermore, the critical question here is whether the fluctuations in the exchange rate could be explained by the macroeconomic variables or not. Various research based on these critical questions would help in highlighting and comparing certain relevant arguments.

The random walk of the exchange rate is difficult to beat. According to Yongmiao et. al. (2007) and Rogoff (1996), their works indicated that any of the forecasted models that would be generated could not beat the random walk. Furthermore, Yongmiao et al. (2007) emphasized beating the random walk on a consistent basis would be a tougher task. Since the models used in this research paper are based on economic fundamentals, the question stands on whether variability of the variables used would be predictable or not. Secondly, if the research would hold for a long horizon with accuracy.

The objective of this research paper is to measure and compare the two strategies, i.e., the profitability of the carry trade to that of the forecasting-based trading in the FX market. All in all, three models are used, restricted PPP, restricted UIP and the dynamic forecasting model. These three models are derived from exchange rates, interest rates, consumer price index and the stock prices of Japan and Singapore. Apart from the estimating and testing of the exchange rate model, the comparison is also taken into consideration with regards to the profitability of each strategy.

By using such a unique data series, it is important to point out that the work is original as the exchange rate predictability has never been evaluated with such a data series.

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According to the findings from the empirical research work, the models could not beat the random walk. However, the model is structurally sound as it is stationary without unit roots and has no serial correlation which makes the forecasting a better predictor. In addition, the forecasting-based strategy was way more profitable than the carry trade strategy. 2 additional strategies i.e. stock market investment in Japan and Singapore was also compared and surprisingly the stock investment in Singapore proved to be a much profitable strategy as compared to the carry trade based on the measures of the forecasted accuracy.

The planning of the research paper is as follows. Section 1 is the introduction towards the research topic, which is followed on by Section 2, the literature review. Section 3 comprises of the methodology towards the empirical estimation and testing used within the research work. In Section 4, the results of the empirical work are showcased and lastly, summaries of conclusions are reported in Section 5.

2. Literature Review In this section, PPP, UIP, carry trade and currency trading would be discussed extensively based on the relative area of literature. This is done to critically evaluate and identify the major studies related to the objective of the research paper.

PPP is a simple empirical proposition which once converted to the common currency, equates that the national price levels should be equal (Taylor, 2002). Rogoff (1996) further highlights that the empirical failure of the law of one price is a significant building block in PPP which serves as a base argument on how similar goods should sell for the same prices across the countries. Talking about the long-run stance for PPP, Taylor M.P. (1995); Froot & Rogoff (1995) indicated that in the long run, PPP does hold true, as per observations from their research, as 5

certain mean reversion are exhibited by real exchange rates. However, O'Connell (1998), Engel (2000), Canzoneri, Cumby, and Diba (1999) and Papell (1997) cast their doubt on long-run stationarity of the international relative prices in spite of mostly relating the research on tradable goods.

Furthermore, according to Taylor (2002), a cursory inspection suggested that many countries real exchange rate is quite stable as far as the long run goes, which means that it supports the hypothesis of stationarity. However, certain long-run trends or random walk cases were distinctly observable in a few other countries. The most distinct case was of Japan. The random walk cases were argued on by Frankel (1986), that the reason for failure to reject the random walk model of the real exchange rate was because of the lack of power. By pointing out if deviations damp slowly for PPP, then it requires decades of sample to concretely reject the unit root (i.e. random walk component). The UIP on the other hand, takes a different approach to its modeling.

The uncovered interest rate parity (UIP) is the difference in the interest rates of two countries which is equal to the expected change in their exchange rates (Chang & Huei, 2009). The UIP was successfully tested with long-term interest rates by many researchers. Alexius (2001); Chinn and Meredith (2004), tested UIP with several OECD countries with maturity ranging from 5 to 10 years. They successfully tested it for the long-run however, Alexius & Sellin (2006) criticized the methodology as they mentioned about how long-run UIP suffer from the problem of the small samples. Nagayasu (2012) also showcased mixed conclusions as the paper analyzed for stationarity in the foreign exchange market and found out that the non-stationarity was mainly attributed towards the regime shifts and monetary policy changes.

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These mixed conclusions towards the UIP and PPP models have to be attributed towards the lack of empirical support because of lack of specification of the sampling distributions in the data (Katarina, 1995). The author further explains three properties that might invalidate the statistical analysis: (i) Neglecting towards time-series properties. (ii) Not accounting for interactions between the goods and capital markets which can only be done by jointly analyzing PPP and UIP parity. (iii) By not allowing different long and short-run effects in the models. This does not let the error correction term (ECM) of PPP and UIP be in a steady state. Hypothetically, an economy in steady state (with no shocks or changes), leads to the model being consistent with the two parities. The author moreover emphasizes on foreign and domestic economies by stating that the transmission of the foreign price inflation into the domestic economy is analyzed by assuming adjustment (goods market) to PPP or by assuming market clearing (capital market) based on UIP. These theoretical models of exchange rate determination prove to be not so accurate in predicting the movement of the exchange rates. However, according to Gerlow & Irwin (1991), a constrained dynamic exchange rate model has the right market timing ability for a 3 month time intervals for predicting the magnitude, direction and profitability. This has been supported by Katarina (2015) as well in her point no. (ii); as stated previously. Relatively, a more popular approach towards trading because of its more or less perceived profitability of its operation is the carry trade.

Carry trade is built on buying low interest rate currencies to fund the high interest rate currencies (Hottori & Shin, 2007). Since the Yen and Singapore dollar are the two currencies explored in detail for the basis of comparison of strategies, the „Yen carry tradeâ€&#x; will be discussed further to critique the nature of a low interest rate currency. Moreover, Hottori & Shin (2007) emphasis on how carry trade is often portrayed purely as a bet on the foreign exchange markets but, in some 7

instances such as in Japan, the domestic monetary policy has a global dimension to it. Shamim (2015) criticizes on this by saying that the foreign exchange market volatility is mainly related to the US macroeconomic fundamentals as far as the dynamics of the long-run component goes for the carry trade returns. In order to have a clearer understanding, we look at Moosa (2008), who talks about the consequence of the failure of the UIP. He further highlights how Gyntelberg and Remolona (2007) described carry trade as “essentially a bet against UIP”. This is because the target currency doesn‟t depreciate against the funding currency by the percentage which pretty much wipes out the interest rate differentials (Moosa, 2008). With a survey done on over 75 published estimates, Froot & Thaler (1990) showcased that in minor cases, the coefficient of the interest rate differentials was very consistent with the UIP. This does not imply that contravening the UIP would result in profits by the carry trade.

As far as the profitability of the carry trade goes, since there is significant failure of the UIP, the Sharpe ratios tend to be high. But, the overall money produced is low mainly because of price limits and transaction costs (Moosa, 2008). And to top it up, the bid-ask spreads are increasingly functions of the order size which means that carry trade return decreases as the transaction costs increases. According to the study by Gyntelberg and Remolona (2007), they found significant support in the view of the risk (downside), which tends to be a critical feature in the carry trade as using measures of downside risk reduces the Sharpe Ratio (Moosa, 2008). All in all, very large amounts of money are needed to get reasonable amount of profits which pretty much limits the carry trade‟s adequacy. Furthermore, the question of whether the carry trade could outperform the market index will be discussed below.

There lies a large amount of criticism on if the carry trade could outperform the stock market index or not. Gyntelberg and Remolona (2007) highlight that with/without the measures of the 8

stock price index and the risks, the carry trade will always have higher returns than the stock market investments. Burnside et al (2006) indicates otherwise stating that carry trade does not always outperform the stock market investment, which was backed by Moosa (2008) in his results from assessing risk and return in the carry trade using two low-interest rate currency (Swiss franc and Japanese Yen). To add to this, the use of mean square error isnâ€&#x;t exactly important in an economic standpoint as far as the forecasting factors go. Cheung argued that using the mean square error might miss out on predictability specifically on a long-term horizon (Cheung et al., 2005). Talking about forecasting factors, the interest-rate spreads are very important for buying currency pairs for the carry trade. In the past 10 years, investors have been interested in Japanâ€&#x;s low borrowing cost of Yen which has been a unique characteristic capitalized by the stock and equity holders. For example, shorting the yen and buying either the Chinese or U.S stocks have been quite common in these years (Hottori & Shin, 2007). In the process, it fueled a large speculative bubble in both the markets and that is why there has been a strong correlation between the stocks and the carry trades (Hottori & Shin, 2007). Keeping the facts in mind, it is important to understand the significant characteristics involved in speculative trading of the currencies.

As per Burnside et al., (2007), his indicative study compared the payoffs of the carry trade based on two portfolios. One with developed countries, the other one included emerging markets.

Significant empirical findings were closely related to currency trading. Firstly, bid-ask spreads are 2-4 times larger in the emerging markets as compared to the developed countries. Thus, the carry trade strategies that would ignore the bid-ask spreads would yield Sharpe ratios as negative. Secondly, over a long horizon, the payoff of carry trade was highly uncorrelated

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toward the US stock market1. Thirdly, Carry trade with an emerging markets currency has higher Sharpe ratio leading to higher average return earned.

In conclusion, the carry trade is highly useful, specifically if mixed with the Japanese‟s low borrowing „Yen‟ currency. However, many authors have found critical factors that affect the profitability in it, such as, interest rate-spreads, mean square error‟s predictability.

Outperforming the stock market investment is highly debatable as observed from studies by Gyntelberg and Remolona (2007), Burnside et al. (2007) and Moosa (2008), but apart from giving investors earnings from the interests, leverage could be used to an advantage as well.

Furthermore, forecast exchange rate model showcases strength in predictability of the magnitude, direction and ultimately profitability, but, the economies must be comparable and the assumption that the investors are neutral to risks is false (Rime et al., 2007). The PPP proves to hold true for the long run although it‟s not certain on how long and large, the deviation from the parity lasts. The UIP on the other hand, as per studies, proves that the deviations from the parity are not as large as they were previously (Lucio et al., 2006); therefore the forecasts results might prove to be more predictable in the future.

1

This is consistent with Burnside et al. (2006) who stated that it’s difficult to comparatively conclude payoffs of the carry trade towards the bearing risk’s agents.

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3. Methodology In this section, in order to identify the estimation and testing procedures with precision and accuracy, they are divided into subsections (3.1 till 3.7 respectively). E-views and Microsoft excel software are used to measure the profitability of the carry trade relative to the forecastingbased trading.

In order to fully understand the effectiveness of the estimation procedure, the original data consists of the stock price, interest rates (i) and consumer price index (CPI) for both countries.

Furthermore, the cross-exchange rate (S), price ratio (PR) and the interest rate differentials (ID) are calculated from the original data. Note that the sourced-statistical data is carefully manipulated from the original source „International Monetary Fund‟ and will be discussed further under Section 4.

The equation that we are using in excel are as per below to calculate S, PR and ID respectively, I.

Cross-exchange rate equation –

(

)

Where, and

II.

 Exchange rates

Price Ratio (PR) –

(

)

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III.

Measure of Interest rate differential (ID) –

It is important to note that the sourced-data for the interest rate is nominal. Therefore, the formula divides it by 400 to de-annualize it.

It is important to first estimate the model with the above 3 variables and to check with the linegraph to substantiate prior visualization. Observe if the residuals seem stationary or not. Tstatistics is then noted accordingly. Further details on the same are as per subsection 3.2, 3.3 and 3.4.

3.1 Unit root test The estimated model (S, PR and ID) is first tested at level (integration of order 0) and then at first difference (integration of order 1). These steps are taken, as the stationarity of the series strongly influences the properties and behavior of the variables (Brooks, 2002). As an example, the persistence in shocks would be infinite in a non-stationary series as compared to a stationary series.

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3.2 Estimating the exchange rate models To estimate the exchange rate determination models, ordinary least squares method was used.

3.2.1 Restricted Purchasing Power Parity Restricted purchasing power parity (RPPP) formula is showcased as per below,

( 

,

)

 The true values of the domestic and foreign prices respectively.



 Mean zero stationary error.



 The nominal spot exchange rate (domestic currency, ¥ YEN, per unit of foreign base currency, $ SGD).

RPPP helps in interpreting by implying that the foreign and domestic prices measured in a common currency are equal (Boyd & Smith, 1998).

3.2.2 Restricted Uncovered Interest Rate Parity The Restricted Uncovered Interest Rate Parity (RUIP) formula is as showcased below,

[

]

Where,   

 Interest rates.  Mean zero stationary error.  The lagged spot exchange rate (domestic currency, ¥ YEN, per unit of foreign base currency, $ SGD).

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The RUIP is a parity condition which concludes that the expected change in the exchange rates between 2 countries is equal to the difference in interest rate between them. Fact is, if this parity does not exist, then, there is an opportunity to make profit (James et. al., 2011).

3.3 Cointegration testing In order to test for cointegration, ADF unit root testing is done to the residual series developed from the two models at level with intercept (if needed, trend). Also, note the lag lengths were automatically randomized as per Schwarz Information Criterion which selected the max-lag of 9 on the tests. T-statistic is now noted from the tests and is compared with the „Critical value tableâ€&#x; sheet to check if they matched with the t-statistics. They didnâ€&#x;t approximately match, therefore, Augmented ADF is used after which the t-statistic and the critical value from the table sheet matched. The behavior of the stationarity of residuals is also checked by using line-graph.

3.4 Estimating Full Forecasting Model The dynamic model is a combination of the PPP and UIP. Its combined specification is as follow,

(

)

(

)

[

]

[

]

The forecasted model is used in Eviews in order to estimate the forecasted stock prices. These values are now noted and will be used in calculating the In-sample forecasts as per subsection 3.5.

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3.5 Generation of In-Sample Forecast The in-sample forecasts are generated on the basis of the 2 estimated models (PPP & UIP). The following 7 forecasts help in understanding the accuracy of the predictability for the exchange rate.

1. Mean Absolute Error (MAE): The difference calculated between the actual and the estimated forecasted values at the same time is the absolute errors. The average of these absolute errors is termed as MAE. The reasons its values are calculated at the same time is so that the negative values do not cancel out the positive values. In other terms, MAE is a quantity which highlights how close the eventual outcomes are towards the forecasts.

∑|

̂

|

According to Robert & Monnie (2000), the MAE is based on the mean error. There is always a probability of understating the big and infrequent errors. In order to adjust for the rare-large errors, we use the root mean square error as per below.

2. Mean Square Error (MSE): The MSE helps to relay the concept of precision, accuracy and biasness in the statistical estimation between the forecasted and actual values of the exchange rate. It‟s calculated by taking the square of the errors i.e. the difference in the forecasted and actual values. Moreover, the MSE is the variance in the estimator, as the method to its measurement is the same as compared to the square of a quantity being calculated (Robert & Monnie, 2000).

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∑(

̂

)

3. Root mean square error (RMSE): By taking the square root of the MSE, we get RMSE. By calculating RMSE, we arrive at the measure of the size of the error which gives more importance to the large and infrequent errors in the mean. Formula is as per below, √ 4. Theil’s inequality coefficient (U): It is the measure of the accuracy of the set of forecasts towards the actual values. The advantage of the Theil‟s inequality coefficient is that its statistical results are bounded to an interval comparison of 0 and 1 (Raymond, 1975).

√ ∑

(

̂

)

√ ∑

Where,  

Model produces a perfect forecast. ; Model outperforms the random walk model but produces less than perfect forecasts.



Model is as good as the random walk



Model is worse than the random walk therefore should not be used for the purpose of forecasting.

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5. Directional accuracy (DA): The values are showcased as the percentage of samples in which the direction was predicted correctly.

∑

Where, 

̂



̂



If DA =1 ; Perfect forecast

In other words, if the DA is 100%, this would mean that the predicted change for every sample was correct. If DA is 50%, it implies the direction was correct half the time which is equivalent to tossing a coin whilst choosing a random direction.

6. Confusion Rate (CR): Indicates the incorrect forecast direction.

Where, 

If CR = 0 ; Perfect model

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7. Adjusted Root Mean Square Error (ARMSE):

̂ ∑(

√

)

3.6 Trading strategy related towards estimated forecasts A carry trade is built by borrowing on the low interest rate currency which is used to purchase the high interest rate currency. This could also mean selling currencies forward that are at a significant forward premium (Hottori & Hyun, 2007).

The trades correlate towards the expected return which is estimated from the forecasts. Keeping that in mind, we undertake the below strategy, A short position is taken on low-interest currency, YEN and a long position on highinterest currency, SGD. I.

If ̇

.

Therefore, the rate of return

II.

(

=

̇

Else, if ̇

The rate of return

(

=

̇

18

Where,  Rate of return (realized at time„t‟) ̇  Percentage change in the exchange rate between„t-1‟ and „t‟.

After collection the estimated trading calculations, the results from the calculations are further used to measure risk and return (subsection 3.7).

3.7 Calculations for measuring Return and Risk The calculations involved are divided into 3 categories, I.

Measures of Return a. Percentage of positive returns

b. Mean return ̅

∑

c. Cumulative return (CR) [∏ II.

]

Measures of Risk a. Standard Deviation (SD)

√

∑

̅

19

b. Down-side semi standard Deviation (DSSSD)

√

∑

̅

Where, and c. Value at Risk (VAR) It is the 95% of the cumulative return average. This is done to highlight the negative return percentage. The task of VAR is to calculate the quantile of loss.

III.

Measures of risk-adjusted Return a. Sharpe Ratio (using SD) ̅

b. Sharpe Ratio (using DSSSD) ̅

c. Sharpe Ratio (using VAR) ̅

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4. Data and Empirical Results This section is covered in 5 subsections which are as follows. Subsection 4.1 defines and specifies the variables used. Subsection 4.2 tests the model and itâ€&#x;s variables for unit root and cointegration. Subsection 4.3 estimates and tests the forecasted exchange rate model for serial correlation and heteroskedasticity and subsection 4.4 and 4.5 estimates the measure of forecast accuracy and uses them to predict the profitability of the 4 strategies used.

4.1 Specification of Data and Variables The data used for the research is sourced from the International Monetary Fund database. All the elements for the data are within the time period of 2001:Q1-2010:Q3 (quarterly data) consisting of two countries, Japan and Singapore. This raw data set (appendix 4.1) consists of: two interest rates, two consumer price index, two stock price indices and two underlying currencies.

Wherein, one of the underlying currency (currency YEN) is the funding currency and the other currency (currency SGD) is the target currency. The funding currency denominates the short position while the target currency is for the long position.

Furthermore, a new set of variables were derived from the raw data (as seen in appendix 4.2): cross exchange rate between $SGD and ÂĽYEN, price ratio, interest rate differentials and the forecasted exchange rate. Table 1 as per below showcases the specifications of the variables used in the research paper.

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Table 1 – Variable specifications S.No.

Variables

1

S

Specifications Cross-exchange rate between $ SGD/¥ YEN.

2 Measure of interest rate differential between Singapore and Japan.

(

3

) Price ratio level between Singapore and Japan.

Where, (

)

The relative graphs for the variables would be covered within Figures 1 to 6.

Exchange Rate ($ SGD/¥ YEN)

Exchange Rate 85 80 75 70 65 60 55 50 2001Q1

2002Q3

2004Q1

2005Q3

2007Q1

2008Q3

2010Q1

Time (per Quarter)

(Figure 1 – Cross exchange rate historical graph) The cross exchange rate between the two currencies shows a steady rise till when the global recession hit in 2008Q2 (figure 1). Pairing of the Japanese YEN as the target currency is contributing to the immense strength of the exchange rate even now.

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Consumer Price Index 120.00

CPI ($ SGD, ¥ YEN)

115.00 110.00 105.00 Japan

100.00

Singapore

95.00 90.00 85.00 2001Q1

2003Q2

2005Q3

2007Q4

2010Q1

Time (per Quarter)

(Figure 2 – CPI of Japanese and Singaporean currency) A distinctive increase is visible starting from 2009Q2, wherein the SGD Singapore currency jumps 4.2% by the end of 2010Q3 whereas the Japanese currency declines further by 2.3% till 2010Q3 (figure 2). The jump in the Singapore dollar is attributed mainly towards the monetary policy easing against a trade-weighted basket of currencies of Singapore‟s major competitors and partners (Monetary Authority of Singapore, 2016).

Stock Prices Stock prices ($ SGD, ¥ YEN)

250.00 200.00 150.00 Japan 100.00

Singapore

50.00 0.00 2001Q1

2003Q2

2005Q3

2007Q4

2010Q1

Time (per Quarter)

(Figure 3 – Stock prices of the Japan and Singapore) 23

Heavy impact of the global recession is clearly observable in both stock price indices starting from 2007Q3 onwards (figure 3). While the Japan stock prices dipped gradually, the Singapore stock price took a strong dive till 2008Q4.

Interest Rates Interest Rate ($ SGD, ÂĽ YEN)

3.45 2.95 2.45 1.95 Japan

1.45

Singapore

0.95 0.45 -0.05 2001Q1

2003Q2

2005Q3

2007Q4

2010Q1

Time (per Quarter)

(Figure 4 – Interest rate of the two countries) For a decade, Singapore enjoyed continuous economic growth, regardless of the state of the rest of the world. Despite two oil crises and a major recession, the economy grew robustly as observable (pre-2000 technology boom). But the interest rates (figure 4) took a heavy dive which according to Ministry of Trade and Industry of Singapore (2016), blames the global demand conditions, U.S trades and U.S regional economic problems for it. The graph showcases that they have not shown signs of improvement till 2010 while Japan maintains its low borrowing currency record.

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Price Ratio 1.05

Price ratio level

1 0.95 0.9 0.85 0.8 2001Q1

2003Q2

2005Q3 2007Q4 Time (per Quarter)

2010Q1

(Figure 5 – The price ratio level relative to Japan and Singapore) Steady decline till 2009Q2 after which the price ratio levels take a steep dive. We will research further on the same in the below steps.

Level of inerest rate differential

Interest rate differential 1.01 1.005 1 0.995 0.99 2001Q1

2003Q2

2005Q3 2007Q4 Time (per Quarter)

2010Q1

(Figure 6 – Interest rate differential between Japanese YEN and Singapore SGD currencies.)

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The carry trade earns interest on the interest rate differential. Also, investors in the foreign exchange market usually use interest rate differentials when pricing the forward exchange rates.

The interest rate differential seems to be positive in the 10 years with a minor 1% level in the end of 2010Q3.

4.2 Testing for Unit root and Cointegration Below are the results from unit root testing using ADF which is showcased below in Table 2 & 3, Table 2 – Results of the Unit Root Testing of variables (ADF- with intercept) (Appendix 1.2 & 2.2) Variable

Level

First difference

Second difference

S

-1.70

-6.97

n/a

ID

-2.61

-2.86

-9.72

PR

2.11

-5.04

n/a

Table 3 – Order of integration of the unit root test Variable

First difference

Order of integration

S

-6.97

I(1)

ID

-2.86*

I(2)

PR

-5.04

I(1)

*Variable ID has no unit root at second difference.

 

Null Hypothesis – The variable has a unit root Alternative Hypothesis – The variable does not have a unit root 26

Looking at table 2 & 3, it is observable that 2 of the variables are stationary at the first difference. The t-statistics for the variables is highly negative as compared to the critical value (table 2). Therefore, by rejecting the null hypothesis and concurring with the alternative hypothesis, it is stated that the variables are stationary since they do not have a unit root at first difference. This means that the data series of the variables of the order of integration 1 (table 3).

This persists with the financial data pattern wherein as stated by Andries et al. (2015) tests resulted

in

the

financial

variables

to

be

of

the

order

of

integration

of

1.

However, the measure of interest rate differential (ID) seems to have a unit root even at I(1). In order to further investigate this, we re-test the variable, ID but with a trend and a intercept this time (table 4).

Table 4 – Unit root result with trend and intercept for ID variable.

Variable ID

First difference -9.69

Order of integration I(1)

With the addition of a trend, the variable resulted in no unit root at order of integration 1. To further highlight the significance of the test, the p-value is 0.000 which is lower than 0.05. All in all, the three variables confirmed stationarity at first difference.

To confirm towards a long-run relationship and cointegration between the variables, the cointegration testing is done on the model. As per Javier & Hualde (2015), residual-based ADF test statistic allows for detection of the cointegration since the difference in the residual is stationary; hence, they donâ€&#x;t go too far away from the mean.

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Table 5 – Results of cointegration tests Model Restricted PPP Restricted UIP

ADF result -1.77 -7.62

For our models, the cointegration test was done by comparing the ADF for restricted PPP first, which was compared with the critical value sheet (appendix 2.3) for accuracy purposes. Since 1.77 is less than the 5% critical value of 3.67 therefore, the PPP was not cointegrated (Appendix 1.2). Furthermore, figure 7 shows how the residuals are not stationary. Therefore, PPP does not hold as a long-run model. As previously stated in our relevant literature as per O'Connell (1998), Engel (2000), Canzoneri, Cumby, and Diba (1999) and Papell (1997), the PPP does not hold true for the long-run relationship between the variables, which supports our research on the same.

Frankel (1986) stated on how if deviations damp slowly for the residuals it would mean that decade of sample size might be the only way of concretely removing the unit root. Figure 7 showcases how the deviations are dampening slowly which proves Frankelâ€&#x;s statement.

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(Figure 7 – Residual line graph on the basis of the PPP model) However, after adding the interest rate differential to make it a UIP model, the ADF was 7.62 which is much higher than the critical value 5% of 3.67, meaning that the UIP model is highly cointegrated and there is clear long term relationship between the variables (Appendix 2.2). Our research lies in line with that of Alexius (2001); Chinn and Meredith (2004) as mentioned in the literature review. To double check the behavior of the stationary residuals, figure 8 expresses the stationarity to prove the same. It also means that the model is not consistently over predicting or under predicting, therefore, the graph of errors is systematic, as it does not showcase any pattern.

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(Figure 8 – Residual line graph on the basis of the UIP model)

4.3 Estimating and Testing the Exchange Rate Forecasting Model To estimate the exchange rate forecasting model, the regression of the model was done by combining the price ratio, interest rate differentials and their respective one lags. R-square, White test for heteroskedasticity and Breusch-Godfrey LM test for serial correlation is used to test for the forecasted exchange rate model.

In order to summarize the discrepancies between the predicted values and the observed values under the model it is critical to take into consideration the goodness of fit (Sueiro & Abad, 2011). We look at the result of the adjusted R-square value (table 6 - based on appendix 3) since we have two or more independent variables within the forecasting model. The adjusted R-square

30

is 39.0% which showcases that it‟s a fairly reasonable model. More will be discussed later during the prediction-realization diagram of the forecasting model.

Table 6 – Result of the exchange rate forecasting model (adjusted R-square purposes) (Appendix 3.1) R-square Adjusted R-square

0.4555 0.3900

Now to check for the variability of the variable across the long-term horizon, the focus would be on heteroskedasticity test, specifically the White test (appendix 3.2). Table 7 shows the results of the test.

Table 7 – Results of Heteroskedasticity test (White test – taken from appendix 3.2)

 

Null Hypothesis – There is no heteroskedasticity in the errors.

Alternative Hypothesis – There is heteroskedasticity in the errors.

The obs*R-squared shows the value of the testing statistic which is 7.94. The p-value of 0.53 leads to accepting the null hypothesis and reject the alternative hypothesis to conclude that there is no heteroskedasticity in the errors. Gilles (2011) specifies that heteroskedasticity arises from several factors such as insufficient data transformation, major outliers or model misspecification.

The result (table 7) implies that the financial data series used, does not have linear dependency towards volatility.

31

Now to check if the errors are related to each other, the serial correlation test is used. This is highly important for forecasting as predicted values are directly affected by the measurement errors. Since the forecasted model has two lags, the LM test is used to check for serial correlation.

The results from the test taken (Appendix 3.3) indicate that the null hypothesis has to be accepted and to reject the alternative (as the prob. Chi-Square value, 0.054 is more than 0.05 or 5%), meaning that there is no serial correlation present within the errors (table 8).

Table 8 – Breusch-Godfrey LM test result for serial correlation using 2 lags.

 

Null Hypothesis – There is no serial correlation in the errors.

Alternative Hypothesis – There is serial correlation in the errors.

In conclusion, looking at table 7 & 8, the forecasting model fulfills the requirement of a good regression model as there is no heteroskedasticity and serial correlation present.

32

4.4 Measurement of Forecasting Accuracy To accurately predict using the forecasting model, certain key measures showcased as per table 9 are used as forecasting predictors. The graph highlights mean absolute error (MAE), root mean square error (RMSE), Theilâ€&#x;s inequality coefficient (U), directional accuracy (DA), mean square error (MSE) and confusion rate (CR).

Table 9 – Result of the measures of forecasting accuracy (taken from Appendix 4.3.0 & 4.3.1)

Measure MSE

Dynamic forecasting model 28.80

MSE(RW)

20.69

U

1.18

RMSE

5.36

RMSE (RW)

4.54

ARMSE

3.48

MAE

4.47

DA

60.5%

CR

39.5%

Upon the analysis of table 9, looking at the RMSE and MAE values, it was confirmed that RMSE > MAE which is a sign that the calculations are right. MAE of 4.47 percentage point highlights how significantly close the eventual outcomes are towards the forecasts. With 28.80 and 5.36 percentage points for MSE and RMSE respectively, the dynamic forecasted measurements would be compared with the Random walk measurements of MSE (RW) and RMSE (RW) which are 20.69 and 4.54 respectively. Small RMSE means that the model produced sturdy forecasts (Wooldridge 2013).

An 8.8 percentage point difference in the MSE and its random walk highlight a significant variation from the predicted to the actual changes. However, as mentioned under methodology

33

wherein Robert & Monnie (2000) stated that there is always a probability of understating the big and infrequent errors; therefore, RMSE should be taken into consideration to adjust for rare-large errors. A 0.82 percentage point difference between RMSE and its random walk value highlight how close the variation is towards each other. Also, Theilâ€&#x;s coefficient with a value of 1.18 means that the model is worse than the random walk (as stated under methodology) holds true.

As per research done by Frankel (1986) and Yongmiao et al. (2007), the random walk outperforms most structural and economic time-series models.

Actual change

Actual vs Predicted changes

Predicted change

Exchange rate change

15.00 10.00 5.00 0.00 2001Q2 -5.00

2002Q4

2004Q2

2005Q4

2007Q2

2008Q4

2010Q2

-10.00 -15.00

Time (Quarterly)

(Figure 9.1 – Actual versus predicted changes in the exchange rate)

34

(Figure 9.2 – Variations in the predicted exchange rate) The Theil‟s coefficient is showcasing 0.027 which means that the model is better than the random walk (figure 9.2). This result is flawed the observations as per table 9 suggest otherwise.

Observational results as per Figure 9.1 indicate -0.16%, meaning that it actually goes down by 0.16% as compared to the predicted +6.10%. However, looking at the figure 10 it is seen that the forecasted exchange rate (SF) is swerving around the actual exchange rate (S).

Analysis (figure 10) 1. When SF < S  S goes down with time.

2. When SF > S  S goes up with time.

However, direction of accuracy is zero and it‟s significantly biased (according to figure 10).

35

85.00

Actual(S) vs Forecasted exchange rate (SF)

S SF

Exchange rate

80.00

75.00

70.00

65.00

60.00 2001Q2

2003Q2

2005Q2

2007Q2

2009Q2

(Figure 10 â&#x20AC;&#x201C; Comparison of the predicted and actual exchange rate) For further analysis we look at the Prediction-Realization diagram (figure 12) and the control chart (figure 11) to get a visual representation of the magnitude and direction or errors.

Control chart of cummulative errors Cummulative errors

40.00 30.00 20.00 10.00 0.00 2001Q1 -10.00

2003Q1

2005Q1

2007Q1

2009Q1

-20.00 -30.00 -40.00

(Figure 11 â&#x20AC;&#x201C; Control chart for cumulative errors)

36

The upper and the lower control limit is -40 and +40 respectively which is determined from the historical data. As observable, the cumulative errors of the forecast model which are well within the control limit, which make the forecast model robust in nature.

Prediction - Realization diagram 15

Predicted change

10

-15

5 0 -10

-5

0

5

10

15

-5 -10 -15 Actual change

(Figure 12 – Prediction Realization diagram) According to figure 12, the sample plots are spread along the „Line of perfect forecast‟ which is heavily inclined towards the 1st and the 3rd quadrant. The direction accuracy is 60.5% (table 9) which means that 60.5% of the data of the scatter plot lies in line with the 1st and the 3rd quadrant. The confusion rate is 39.5% which showcases the percentage of scatter plot towards the 2nd and the 4th quadrant. Major plots are above the line of perfect forecast, which means that the scatter plot is slightly over predicted.

37

4.5 Measures of Profitability of Trading Strategies Table 10 â&#x20AC;&#x201C; Strategies based profitability (taken from Appendix 4.3.2 to 4.3.4) Strategy 1

Strategy 2

Strategy 3

Strategy 4

Carry Trade

Forecastbased trading

Stock market investment in Japan

Stock market investment in Singapore

2.07%

80.95%

-4.31%

20.23%

0.59

6.59

-0.59

2.37

0.607 17.57

0.605 16.26

0.447 9.64

0.605 12.27

0.03 13.84

0.41 7.95

-0.06 7.75

0.19 8.07

-27.65

-18.70

-13.98

-20.51

Risk/Return

Cumulative Return Mean Return Positive percentage (+ %) S.D Sharpe Ratio DSSSD Value at Risk (VAR)

Looking at table 10, the results of the measure of return and risk are highlighted. The cumulative returns are 2.07%, 80.95%, -4.31% and 20.23% towards carry trade, forecast-based trading, stock market investment in Japan and Singapore respectively. The forecast-based trading strategy outperforms all the other three by a large margin with an 80.95% return.

The mean return for forecast-based trading is also the highest with 6.59 as compared to -0.59, 2.37 and 0.59 for the other three. However, for the percentage of positive returns, carry trade strategy outperforms the other three by just 0.002 %. Furthermore, the standard deviation is the highest for the carry trade with 17.57 followed closely by forecast-based trading with 16.26 which means that the forecast-based strategy carries less risk than the carry trade strategy. This is 38

supported by the downside semi-standard deviation (DSSSD) measure, wherein stock market investment (Japan) strategy has the lowest risk, however, as far as comparing the forecast and carry trade strategy goes, the forecast-based strategy yet again has comparatively much lower risk of 7.95 as compared to the carry trade which is 13.84.

Last but not least, the value at risk showcases yet again that the forecast-based strategy (18.70%) is the better one as compared to carry trade (27.65%). Theoretically, you can be 95% sure that the negative returns would not grow more than 18.70% for the forecast-based strategy.

All in all, the forecasting-based strategy has the best profitability out of the 4 strategies with substantially low standard deviation and DSSSD, and the highest Sharpe Ratio of 0.41.

5. Conclusions The objective of the study is to compare the profitability of the forecasting-based trading towards the carry trade in the Foreign exchange market. The model estimated and tested was the forecasting-based exchange rate model (dynamic model comprised of PPP and UIP). All the variables to estimate the model were of order of integration 1. In the process, Restricted PPP model had a unit root and was non-stationary whereas the Restricted UIP model showcased no unit root and was stationary.

During the testing for the forecasted exchange rate model, neither heteroskedasticity nor serial correlation was present in the model with a substantially reasonable goodness of fit. This made the model fit for forecasting. Empirical studies showcased that random walk could not be beaten.

The measure used was called Theilâ&#x20AC;&#x;s coefficient. Furthermore, after assessing the measures used for forecasting accuracy such as MAE, MSE, RMSE, DA, CR etc., it was easy to analyze the

39

predictive power of the two main strategies, which were the carry trade-based trading and the forecasting-based trading strategies.

As far as the profitability goes, the forecasting-based strategy has a very high profitability as compared to the carry trade. Stock investments for Japan (strategy 3) have a negative return while for Singapore (strategy 4) it is comparatively better than the carry trade. Forecasting-based strategy is dominant for cumulative returns, Sharpe Ratio and DSSSD. The stock investment in Singapore turned out to be a surprise package with a second best return, substantial Sharpe Ratio and mean returns.

Strength of the study is that the research work compiled is free from heteroskedasticity and serial correlation which acts as a very important component for forecasting. As stated by Wooldridge (2013), the prediction interval for a particular model depends on the distribution of the residuals and the variability of the variables. Therefore, the model was robust for forecasting which led to sturdy result based on research and interlinks with other authors.

Weakness of the study however was that the data was not properly shielded from outliers and data mining since restricted or in-sample forecasts were used.

It would be recommended that further research be done. Using out-of-sample forecasting, the model would be less sensitive towards outliers and data mining resulting in a more refined forecast for the objective. Also, the stock market investment in Japan showcased strong profitability and it would be encouraged to further research on the strategy even more.

40

6. List of References Alexius, A. (2001), Uncovered interest rate parity revisited. Review of International Economics, 9, 17-505.

Alexius, A. and Sellin, P. (2006), Exchange rates and long-term bonds Working Paper, Uppsala University, 2-12.

Andries, A., Corovei E. and Mutu S. (2015), Liquid Reserves Accumulation during the Financial Crisis: Empirical Evidence from the European Banking System, Transformations in Business and Economics, 14(2), 443-463.

Boyd D. and Smith R. (1998), Testing for purchasing power parity: econometric issues and an application to developing countries, The Manchester School, 287-303.

Brooks C. (2002), Introductory econometrics for Finance, Cambridge University Press, 367-369.

Burnside, C., M. Eichenbaum, I. Kleshcelski, and S. Rebelo. (2006), “The returns to currency speculation,” NBER Working Papers, No 12489.

Burnside, C., Eichenbaum, M. and Rebelo Sergio (2007), “The returns to currency speculation in Emerging markets”, American Economic Review, 97(2), 333-338.

Canzoneri, M. B., R. E. Cumby and B. Diba (1999), Relative Labor Productivity and the Real Exchange Rate in the Long Run: Evidence for a Panel of OECD Countries, Journal of International Economics, 47, 245-266.

Chang-Chiang C. and Huei-Mei L. (2009), The long-run uncovered interest rate parity in view of trady strategy, Applied Economics, 41(21), 2727-2739.

41

Cheung, Y-W., M.D Chinn and A.G. Pascual (2005), “Empirical exchange rate models of the nineties- Are any fit to survive?”, Journal of International Money and Finance, 24(7), 1150-1175.

Chinn, M and Meredith, G. (2004), Monetary policy and long-horizon uncovered interest rate parity. IMF Staff Papers, 51, 30-409.

Engel, C. (2000), Long-Run PPP May Not Hold After All, Journal of International Economics, 57, 243-273.

Frankel, Jeffrey A (1986), “International Capital Mobility and Crowding-out in the U.S. Economy: Imperfect Integration of Financial Markets or Goods Markets?”, Lexington Books, 33-67.

Froot, K. A., and K. Rogoff (1995), Perspectives on PPP and Long-Run Real Exchange Rates, Handbook of International Economics, 3, 1647-1648.

Gilles Zumbach (2011), Characterizing Heteroskedasticity, Quantitative Finance, 11(9), 13571369.

Gurlow Mary & Irwin Scott (1991), The performance of the exchange rate forecasting models – an economic evaluation, Applied Economics, 23(1), 133-142.

Gyntelberg, J. & Remolona, E.M. (2007), Risk in Carry trades- A look at Target Currencies in Asia and the Pacific, BIS Quarterly Review, December, 73-82.

Hottori, M. & Shin, H.S. (2007), “The Broad Yen Carry Trade”, Bank of Japan, Institute for Monetary and Economic Studies, Discussion Paper No. 2007-E-19.

42

James R. Lothian, Liuren Wu (2011), Uncovered interest-rate parity over the past two centuries, Journal of International Money and Finance, 30(3), 448-473.

Javier Gomez-Biscarri and Javier Hualde (2015), A residual-based ADF test for stationary cointegration in settings, Journal of Econometrics, 184(2), 280-294.

Katarina Juselius (1995), “Do purchasing power parity and uncovered interest rate parity hold in the long run? An example of likelihood inference in a multivariate time-series model”, Journal of Econometrics, 69(1), 211-240.

Lucio S., Giorgio V. and Hyginus L. (2006), “Nonlinearity in deviations from uncovered interest parity- An explanation of the forward bias puzzle”, International Monetary Fund, IMF Working paper 06/136, 10-44.

Ministry of Trade and Industry of Singapore (2016), accessed on 20th May‟2016 <https://www.mti.gov.sg/ResearchRoom/Documents/app.mti.gov.sg/data/pages/885/doc/econ.pd f> Monetary

Authority

of

Singapore

(2016),

accessed

on

23rd

May‟2016

<http://www.sgs.gov.sg/The-SGS-Market/Monetary-Policy.aspx > Moosa, I.A. (2008), Risk and Return in Carry Trade, Journal of Financial Transformation, 22, 813.

Nagayasu, J. (2012), Long-run implications of the covered interest rate parity condition: Evidence during the recent crisis and non-crisis periods, Business & Economics, Federal Reserve Bank of St Louis, 2-20.

O'Connell, P. G. J. (1998), Market Frictions and Relative Traded Goods Prices, Journal of International Money and Finance, 17, 71-95.

43

Papell D. H. (1997), Searching for Stationarity: Purchasing Power Parity Under the Current Float, Journal of International Economics, 43, 313-332.

Raymond, (1975), On the use of Theil‟s inequality coefficient, American Journal of Agriculture economics, Vol 57(2), 344-346.

Rime, D., et al. (2007), Exchange Rate Forecasting, Order Flow and Macroeconomic Information, Journal of International Economics, 80(1), 3-39.

Robert A. Yaffee and Monnie Mc Gee, (2000), Introduction to time series analysis and forecasting, Academic Press, 1st Edition, 16-22.

Rogoff, K. (1996), The Purchasing Power Parity Puzzle. Journal of Economic Literature, 34(2), 647-668.

Shamim A. and Giorgio Valente (2015), Understanding the price of volatility risk in carry trades, Journal of Banking & Finance, 57, August, 118-129.

Sueiro, M. and Abad, Francisco (2011), Assessing goodness of fit in item response theory with nonparametric models, Educational and Psychological Measurement, 71(5), 834-848.

Taylor, M. P. (1995), The Economics of Exchange Rates, Journal of Economic Literature, 33(1), 13-47.

Taylor, A. (2002), A Century of Purchasing-Power Parity. The Review of Economics and Statistics, 84(1), 139-150.

Wooldridge Jeffrey M. (2013), Introductory econometrics- A modern approach, International Edition (Fifth), 23-175.

Yongmiao Hong, Haitao Li and Feng Zhao (2007), “Can the random walk model be beaten in out-of-sample density forecasts? Evidence from intraday foreign exchange rates”, Journal of Econometrics, Volume 141, Issue 2, 736-776.

44

7. Appendices Appendix 1.1 â&#x20AC;&#x201C; Purchasing Power Parity (PPP) model estimation

45

Appendix 1.2– Purchasing Power Parity (PPP) model; Unit root test – ADF

46

Appendix 2.1 â&#x20AC;&#x201C; Uncovered Interest Rate Parity (UIP) model estimation

47

Appendix 2.2– Uncovered Interest Rate Parity (UIP) model; Unit root test – ADF

48

Appendix 2.3â&#x20AC;&#x201C; Critical value sheet for cointegration comparison

49

Appendix 3.1â&#x20AC;&#x201C; Exchange rate forecasting dynamic model (PPP & UIP)

50

Appendix 3.2 â&#x20AC;&#x201C; Heteroskedasticity check (White test)

51

Appendix 3.3 â&#x20AC;&#x201C; Serial Correlation check (Breusch-Godfrey LM test)

52

Appendix 4.1â&#x20AC;&#x201C; Original data sourced from the International Monetary fund (IMF)

2001Q1 2001Q2 2001Q3 2001Q4 2002Q1 2002Q2 2002Q3 2002Q4 2003Q1 2003Q2 2003Q3 2003Q4 2004Q1 2004Q2 2004Q3 2004Q4 2005Q1 2005Q2 2005Q3 2005Q4 2006Q1 2006Q2 2006Q3 2006Q4 2007Q1 2007Q2 2007Q3 2007Q4 2008Q1 2008Q2 2008Q3 2008Q4

Exchange Interest Rate Rates YEN SGD YEN(i) SGD(i) 124.60 1.8000 0.06 1.91 124.05 1.8200 0.02 2.05 119.30 1.7700 0.01 1.92 131.80 1.8500 0.03 0.77 133.20 1.8400 0.00 0.84 119.45 1.7600 0.01 0.76 121.55 1.7800 0.00 0.89 119.90 1.7400 0.01 0.76 120.15 1.7700 0.02 0.64 119.85 1.7600 0.01 0.54 111.20 1.7300 0.03 0.71 107.10 1.7000 0.00 0.70 104.30 1.6800 0.01 0.70 108.38 1.7200 0.02 0.72 111.00 1.6900 0.01 1.17 104.12 1.6300 0.00 1.26 107.35 1.6500 0.01 1.74 110.40 1.6800 0.00 1.96 113.15 1.6900 0.00 1.99 117.97 1.6600 0.00 2.55 117.40 1.6200 0.07 2.75 114.95 1.5900 0.34 2.82 117.80 1.5900 0.34 3.11 118.95 1.5300 0.42 3.15 117.65 1.5200 0.59 2.89 123.23 1.5300 0.63 2.11 115.05 1.4900 0.55 2.25 114.00 1.4400 0.55 2.17 100.10 1.3800 0.62 1.20 106.40 1.3600 0.60 0.79 104.30 1.4300 0.64 0.98 90.75 1.4400 0.36 0.67

Consumer Price Index YEN(cpi) SGD(cpi) 100.00 100.00 99.93 99.90 99.67 99.90 99.31 99.38 98.62 99.15 99.05 99.48 98.88 99.48 98.78 99.51 98.39 99.84 98.82 99.67 98.65 99.96 98.49 100.16 98.26 101.08 98.53 101.53 98.55 101.87 98.98 101.80 98.29 101.33 98.43 101.57 98.26 102.34 98.26 102.95 98.16 102.71 98.58 102.82 98.85 103.12 98.58 103.52 98.06 103.25 98.53 103.79 98.72 105.96 99.12 107.79 99.02 110.13 99.86 111.55 100.85 112.87 100.13 113.59

Stock Price YEN(sp) 100.00 105.13 90.80 83.03 80.70 85.79 76.01 68.06 65.86 65.84 78.07 81.42 85.77 91.82 89.44 87.77 92.40 91.24 99.50 119.40 131.44 130.45 125.57 128.49 137.07 137.61 130.34 122.53 102.96 107.01 97.89 68.68

SGD(sp) 100.00 103.13 78.82 96.99 107.71 92.77 80.77 80.11 75.73 86.49 97.41 105.40 111.04 109.79 118.55 123.42 127.92 132.17 137.69 140.21 151.33 145.47 153.44 178.36 193.01 211.94 221.39 208.01 179.63 176.06 140.90 105.23 53

2009Q1 2009Q2 2009Q3 2009Q4 2010Q1 2010Q2

98.10 95.95 89.77 92.06 93.25 88.60

1.5200 1.4500 1.4100 1.4000 1.4000 1.4000

0.27 0.16 0.15 0.12 0.12 0.12

0.34 0.22 0.31 0.48 0.39 0.32

98.88 98.88 98.58 98.09 97.74 97.97

112.96 111.83 112.84 113.19 113.97 115.33

61.81 69.69 74.06 69.87 73.21 73.19

101.55 139.37 159.64 173.08 172.48 169.38

Appendix 4.2 â&#x20AC;&#x201C; Variables created from raw data S 69.22222

P.R

SF

1

I.D 0.995397

68.15934

1.000332

0.994951

67.40113

0.997675

0.995248

71.24324

0.999336

0.998154

72.3913

0.994657

0.997904

67.86932

0.995643

0.998129

68.28652

0.993963

0.99778

68.90805

0.99267

0.998129

67.88136

0.985486

0.998452

68.09659

0.991439

0.998677

64.27746

0.986934

0.998303

63

0.983256

0.998253

62.08333

0.972089

0.998278

63.01163

0.970407

0.998253

65.68047

0.96749

0.997108

63.8773

0.972321

0.99686

65.06061

0.970032

0.995694

65.71429

0.969049

0.995124

66.95266

0.960172

0.99505

71.06627

0.954464

0.993665

72.46914

0.955687

0.993346

72.2956

0.95885

0.993843

74.08805

0.958579

0.993128

77.7451

0.952331

0.993228

77.40132

0.949731

0.994291

80.54248

0.949236

0.996319

77.21477

0.93172

0.995774

79.16667

0.919498

0.995972

72.53623

0.899103

0.998554

78.23529

0.895255

0.999526

72.93706

0.893447

0.999152

69.86749 71.60137 74.11422 65.83088 66.66003 65.7 67.11956 66.79036 65.73911 64.97452 66.02441 66.57621 66.29987 65.08307 67.75776 67.26498 69.86981 71.73723 70.33039 73.68502 75.08071 72.89841 75.29167 76.2521 75.63894 69.96485 71.86463 74.97126 68.54422 65.33979

2001Q1 2001Q2 2001Q3 2001Q4 2002Q1 2002Q2 2002Q3 2002Q4 2003Q1 2003Q2 2003Q3 2003Q4 2004Q1 2004Q2 2004Q3 2004Q4 2005Q1 2005Q2 2005Q3 2005Q4 2006Q1 2006Q2 2006Q3 2006Q4 2007Q1 2007Q2 2007Q3 2007Q4 2008Q1 2008Q2 2008Q3

54

63.02083

0.881513

0.999226

64.53947

0.875316

0.999825

66.17241

0.884178

0.99985

63.66667

0.873652

0.9996

65.75714

0.866632

0.999101

66.60714

0.857555

0.999326

63.28571

0.849429

0.9995

63.18182

0.838707

0.99955

66.93919 67.44017 65.27439 65.5348 65.70183 67.603 67.31363 67.14386

2008Q4 2009Q1 2009Q2 2009Q3 2009Q4 2010Q1 2010Q2 2010Q3

55

Appendix 4.3.0 â&#x20AC;&#x201C; Sample of forecast spreadsheet.

2001Q1 2001Q2 2001Q3 2001Q4 2002Q1 2002Q2 2002Q3 2002Q4 2003Q1 2003Q2 2003Q3 2003Q4 2004Q1 2004Q2 2004Q3 2004Q4 2005Q1 2005Q2 2005Q3 2005Q4 2006Q1 2006Q2 2006Q3 2006Q4 2007Q1 2007Q2 2007Q3 2007Q4 2008Q1 2008Q2 2008Q3 2008Q4 2009Q1 2009Q2 2009Q3 2009Q4 2010Q1 2010Q2 2010Q3

S 69.22 68.16 67.40 71.24 72.39 67.87 68.29 68.91 67.88 68.10 64.28 63.00 62.08 63.01 65.68 63.88 65.06 65.71 66.95 71.07 72.47 72.30 74.09 77.75 77.40 80.54 77.21 79.17 72.54 78.24 72.94 63.02 64.54 66.17 63.67 65.76 66.61 63.29 63.18

SF

E

69.87 2.51 71.60 6.23 74.11 4.03 65.83 -9.06 66.66 -1.78 65.70 -3.79 67.12 -2.60 66.79 -1.61 65.74 -3.46 64.97 1.08 66.02 4.80 66.58 7.24 66.30 5.22 65.08 -0.91 67.76 6.07 67.26 3.39 69.87 6.32 71.74 7.15 70.33 -1.04 73.69 1.68 75.08 3.85 72.90 -1.61 75.29 -3.16 76.25 -1.48 75.64 -6.09 69.96 -9.39 71.86 -9.22 74.97 3.36 68.54 -12.39 65.34 -10.42 66.94 6.22 67.44 4.49 65.27 -1.36 65.53 2.93 65.70 -0.08 67.60 1.50 67.31 6.36 67.14 6.27 MAE MSE RSME

abs( E )

E2

2.51 6.28 6.23 38.83 4.03 16.24 9.06 82.13 1.78 3.17 3.79 14.35 2.60 6.74 1.61 2.58 3.46 11.99 1.08 1.18 4.80 23.05 7.24 52.37 5.22 27.23 0.91 0.83 6.07 36.90 3.39 11.48 6.32 39.99 7.15 51.07 1.04 1.07 1.68 2.81 3.85 14.84 1.61 2.58 3.16 9.96 1.48 2.20 6.09 37.07 9.39 88.16 9.22 85.08 3.36 11.27 12.39 153.44 10.42 108.50 6.22 38.66 4.49 20.20 1.36 1.84 2.93 8.61 0.08 0.01 1.50 2.24 6.36 40.51 6.27 39.32 4.4773 28.8096 5.3675

F(RW)

68.16 67.40 71.24 72.39 67.87 68.29 68.91 67.88 68.10 64.28 63.00 62.08 63.01 65.68 63.88 65.06 65.71 66.95 71.07 72.47 72.30 74.09 77.75 77.40 80.54 77.21 79.17 72.54 78.24 72.94 63.02 64.54 66.17 63.67 65.76 66.61 63.29

E(RW) E2(RW) AC

1.12 -5.39 -1.59 6.66 -0.61 -0.90 1.51 -0.32 5.94 2.03 1.48 -1.47 -4.06 2.82 -1.82 -0.99 -1.85 -5.79 -1.94 0.24 -2.42 -4.70 0.44 -3.90 4.31 -2.47 9.14 -7.28 7.26 15.73 -2.35 -2.47 3.94 -3.18 -1.28 5.25 0.16

MSE(RW) RMSE(RW) U

-1.54 1.27 -1.11 29.08 5.70 2.52 1.61 44.39 -6.25 0.37 0.61 0.81 0.91 2.29 -1.49 0.10 0.32 35.30 -5.61 4.11 -1.99 2.18 -1.46 2.17 1.50 16.51 4.24 7.97 -2.75 3.31 1.85 0.99 1.00 3.42 1.88 33.51 6.14 3.75 1.97 0.06 -0.24 5.85 2.48 22.13 4.94 0.20 -0.44 15.21 4.06 18.57 -4.13 6.08 2.53 83.56 -8.38 53.06 7.86 52.77 -6.77 247.59 -13.60 5.54 2.41 6.09 2.53 15.49 -3.79 10.11 3.28 1.63 1.29 27.54 -4.99 0.03 -0.16

20.6903 4.5487 1.1800

FC 0.93 5.05 9.96 -7.60 -7.92 -3.20 -1.71 -3.07 -3.16 -4.58 2.72 5.68 6.79 3.29 3.16 5.30 7.39 9.17 5.04 3.68 3.60 0.83 1.62 -1.92 -2.28 -13.13 -6.93 -5.30 -5.50 -16.48 -8.22 7.01 1.14 -0.96 3.20 2.81 1.06 6.10

DA CR ARMSE

D.A

Cum E

0.00 2.51 0.00 8.74 1.00 12.77 0.00 3.71 1.00 1.92 0.00 -1.86 0.00 -4.46 1.00 -6.07 0.00 -9.53 1.00 -8.44 0.00 -3.64 0.00 3.59 1.00 8.81 1.00 7.90 0.00 13.98 1.00 17.36 1.00 23.69 1.00 30.83 1.00 29.80 1.00 31.48 0.00 35.33 1.00 33.72 1.00 30.57 1.00 29.08 0.00 23.00 1.00 13.61 0.00 4.38 1.00 7.74 0.00 -4.65 1.00 -15.06 1.00 -8.85 1.00 -4.35 1.00 -5.71 1.00 -2.77 1.00 -2.86 1.00 -1.36 0.00 5.00 0.00 11.27

0.6053 0.3947 3.3723

56

Appendix 4.3.1 â&#x20AC;&#x201C; Sample of the trading spreadsheet R(exp)

SPx

SPy

R(CT)

R(FB)

R(SPx)

R(SPy)

100.00

100.00

5.578674

105.13

103.13

-4.29185

-4.29185

5.132334

3.131219

22.2299

90.80

78.82

-2.41964

-2.41964

-13.6307

-23.5688

41.74963 -29.6481

83.03

96.99

24.71148

24.71148

-8.55591

23.04326

80.70

107.71

7.185867

-7.18587

-2.81178

11.05335

-30.8283

85.79

92.77

-24.1463

24.14635

6.310014

-13.8704

-12.0353

76.01

80.77

3.208835

-3.20884

-11.4018

-12.9291

-5.94565

68.06

80.11

4.530714

-4.53071

-10.4594

-0.82129

-11.5428

65.86

75.73

-5.20977

5.209769

-3.22342

-5.46539

-12.0035

65.84

86.49

1.888301

-1.8883

-0.03056

14.20813

-17.8091

78.07

97.41

-21.9036

21.90363

18.56946

12.62464

11.55133

81.42

105.40

-7.26964

-7.26964

4.292343

8.199401

23.4061

85.77

111.04

-5.12011

-5.12011

5.339266

5.34995

27.85695

91.82

109.79

6.670958

6.670958

7.051508

-1.12319

13.84959

89.44

118.55

17.64192

17.64192

-2.58658

7.975831

13.81086

87.77

123.42

-9.82148

-9.82148

-1.86769

4.107443

22.47367

92.40

127.92

8.669865

8.669865

5.27402

3.644378

31.29753

91.24

132.17

5.748897

5.748897

-1.25245

3.32953

38.6214

99.50

137.69

9.497947

9.497947

9.043785

4.175868

22.16979

119.40

140.21

26.56618

26.56618

20.00607

1.830796

17.28979

131.44

151.33

10.44613

10.44613

10.08007

7.929599

17.09482

130.45

145.47

1.722139

1.722139

-0.75033

-3.87515

5.815265

125.57

153.44

12.39736

12.39736

-3.74142

5.481576

9.26832

128.49

178.36

22.51433

22.51433

2.32409

16.23865

-4.9515

137.07

193.01

0.961234

-0.96123

6.680764

8.212453

-6.80773

137.61

211.94

18.53315

-18.5331

0.389105

9.809583

-51.0519

130.34

221.39

-15.0465

15.04653

-5.28009

4.457243

-26.0156

122.53

208.01

11.81155

-11.8115

-5.99135

-6.04099

-19.5778

102.96

179.63

-31.8811

31.88114

-15.974

-13.6433

-21.4339

107.01

176.06

32.0074

-32.0074

3.939009

-1.98685

-65.7419

97.89

140.90

-26.8987

26.8987

-8.52925

-19.9699

-32.5534

68.68

105.23

-54.0424

54.04239

-29.8345

-25.3202

28.36

61.81

101.55

9.948973

9.948973

-10.0073

-3.49262

4.624833

69.69

139.37

10.19057

10.19057

12.74829

37.23543

-3.79426

74.06

159.64

-15.0868

15.08678

6.267148

14.54684

12.94637

69.87

173.08

13.29388

13.29388

-5.65294

8.419215

11.58833

73.21

172.48

5.530541

5.530541

4.781795

-0.34496

4.512711

73.19

169.38

-19.6764

-19.6764

-0.02749

-1.8

24.58557

66.56

185.03

-0.45668

-0.45668

-9.06091

9.243303

57

Mean S.D Sharp R

0.589662 17.57322

6.594306 16.26392

-0.59055 9.635524

2.368307 12.27066

0.033555

0.405456

-0.06129

0.193006

Appendix 4.3.2 â&#x20AC;&#x201C; Sample of the trading spreadsheet (continued in 4.3.3) %+

%+FB

%+RSPx

%+RSPy

DSSSD

DSSSD^2

carry trade 0

0

1

1

-4.88

23.83

0

0

0

0

-3.01

9.06

1

1

0

1

0.00

0.00

1

0

0

1

0.00

0.00

0

1

1

0

-24.74

611.87

1

0

0

0

0.00

0.00

1

0

0

0

0.00

0.00

0

1

0

0

-5.80

33.63

1

0

0

1

0.00

0.00

0

1

1

1

-22.49

505.95

0

0

1

1

-7.86

61.77

0

0

1

1

-5.71

32.60

1

1

1

0

0.00

0.00

1

1

0

1

0.00

0.00

0

0

0

1

-10.41

108.39

1

1

1

1

0.00

0.00

1

1

0

1

0.00

0.00

1

1

1

1

0.00

0.00

1

1

1

1

0.00

0.00

1

1

1

1

0.00

0.00

1

1

0

0

0.00

0.00

1

1

0

1

0.00

0.00

1

1

1

1

0.00

0.00

1

0

1

1

0.00

0.00

1

0

1

1

0.00

0.00

0

1

0

1

-15.64

244.49

1

0

0

0

0.00

0.00

0

1

0

0

-32.47

1054.35

1

0

1

0

0.00

0.00

0

1

0

0

-27.49

755.61

0

1

0

0

-54.63

2984.66

1

1

0

0

0.00

0.00

58

1

1

1

1

0.00

0.00

0

1

1

1

-15.68

245.75

1

1

0

1

0.00

0.00

1

1

1

0

0.00

0.00

0

0

0

0

-20.27

410.71

0

0

0

1

-1.05

1.09

0.605263

0.605263

0.447368

0.605263 DSSSD VAR

CT

13.836665 27.646067

Appendix 4.3.3 â&#x20AC;&#x201C; Sample of the trading spreadsheet (continued from 4.3.2) DSSSD

DSSSD^2

DSSD

forecasting

DSSSD^2

DSSD

spx

DSSSD^2 spy

-4.88

23.83

0.00

-3.01

9.06

-14.22

202.22

0.00

0.00

0.00

0.00

-9.15

83.64

-24.16

583.63

-7.78

60.46

-3.40

11.57

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

-3.80

14.43

-11.99

143.79

-14.46

209.09

-5.12

26.22

-11.05

122.08

-13.52

182.76

0.00

0.00

-3.81

14.54

-1.41

1.99

-2.48

6.14

-0.62

0.38

-6.06

36.66

0.00

0.00

0.00

0.00

0.00

0.00

-7.86

61.77

0.00

0.00

0.00

0.00

-5.71

32.60

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

-3.18

10.09

-1.71

2.93

-10.41

108.39

-2.46

6.04

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

-1.84

3.39

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

-1.34

1.80

0.00

0.00

0.00

0.00

-4.33

18.76

-4.46

19.93

0.00

0.00

0.00

0.00

0.00

0.00

-1.55

2.41

0.00

0.00

0.00

0.00

-19.12

365.68

-0.20

0.04

0.00

0.00

0.00

0.00

-5.87

34.45

0.00

0.00

59

-12.40

153.79

-6.58

43.31

0.00

0.00

0.00

0.00

-16.56

274.36

-6.63

43.97

-32.60

1062.57

0.00

0.00

-14.23

202.58

0.00

0.00

-9.12

83.15

-2.58

6.64

0.00

0.00

-30.42

925.63

-20.56

422.69

0.00

0.00

-10.60

112.30

-25.91

671.32

0.00

0.00

0.00

0.00

-4.08

16.67

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

-6.24

38.97

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

-20.27

410.71

-0.62

0.38

-0.93

0.87

-1.05

1.09

-9.65

93.13

-2.39

5.71

FB

7.9511103 18.704634

SPx

7.752993 -13.98221

Spy

8.066355 -20.50969

60

Appendix 4.3.4 â&#x20AC;&#x201C; Sample of the trading spreadsheet (cumulative return of 4 strategies) 1+r(ct)/400 C.T

FB

spx

0.989

0.989

1.013

0.994

0.994

1.062 1.018

product spy

C.T

FB

spx

spy

1.008

0.989

0.989

1.013

1.008

0.966

0.941

0.983

0.983

0.978

0.948

1.062

0.979

1.058

1.044

1.044

0.957

1.003

0.982

0.993

1.028

1.063

1.025

0.951

1.031

0.940

1.060

1.016

0.965

0.999

1.087

0.966

0.995

1.008

0.992

0.971

0.968

1.007

1.078

0.938

0.963

1.011

0.989

0.974

0.998

1.018

1.066

0.914

0.961

0.987

1.013

0.992

0.986

1.005

1.080

0.906

0.948

1.005

0.995

1.000

1.036

1.010

1.075

0.906

0.981

0.945

1.055

1.046

1.032

0.954

1.134

0.948

1.012

0.982

0.982

1.011

1.020

0.937

1.113

0.958

1.033

0.987

0.987

1.013

1.013

0.925

1.099

0.971

1.047

1.017

1.017

1.018

0.997

0.940

1.117

0.988

1.044

1.044

1.044

0.994

1.020

0.982

1.167

0.982

1.065

0.975

0.975

0.995

1.010

0.958

1.138

0.977

1.076

1.022

1.022

1.013

1.009

0.978

1.163

0.990

1.086

1.014

1.014

0.997

1.008

0.993

1.179

0.987

1.095

1.024

1.024

1.023

1.010

1.016

1.207

1.009

1.106

1.066

1.066

1.050

1.005

1.084

1.288

1.060

1.111

1.026

1.026

1.025

1.020

1.112

1.321

1.087

1.133

1.004

1.004

0.998

0.990

1.117

1.327

1.085

1.122

1.031

1.031

0.991

1.014

1.151

1.368

1.074

1.138

1.056

1.056

1.006

1.041

1.216

1.445

1.081

1.184

1.002

0.998

1.017

1.021

1.219

1.442

1.099

1.208

1.046

0.954

1.001

1.025

1.275

1.375

1.100

1.238

0.962

1.038

0.987

1.011

1.227

1.426

1.085

1.251

1.030

0.970

0.985

0.985

1.264

1.384

1.069

1.233

0.920

1.080

0.960

0.966

1.163

1.495

1.026

1.191

1.080

0.920

1.010

0.995

1.256

1.375

1.036

1.185

0.933

1.067

0.979

0.950

1.172

1.468

1.014

1.125

0.865

1.135

0.925

0.937

1.013

1.666

0.939

1.054

1.025

1.025

0.975

0.991

1.039

1.707

0.915

1.045

1.025

1.025

1.032

1.093

1.065

1.751

0.944

1.142

0.962

1.038

1.016

1.036

1.025

1.817

0.959

1.184

1.033

1.033

0.986

1.021

1.059

1.877

0.946

1.209

1.014

1.014

1.012

0.999

1.074

1.903

0.957

1.208

0.951

0.951

1.000

0.996

1.021

1.809

0.957

1.202

61

CUM R

2.07%

80.95%

4.31%

20.23%

62