Can the intermediary capital risk predict foreign exchange rates?

Can the intermediary capital risk predict foreign exchange rates?

Journal Pre-proof Can the Intermediary Capital Risk Predict Foreign Exchange Rates? Libo Yin Associate Professor PII: DOI: Reference: S1544-6123(19)...

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Journal Pre-proof

Can the Intermediary Capital Risk Predict Foreign Exchange Rates? Libo Yin Associate Professor PII: DOI: Reference:

S1544-6123(19)30536-7 https://doi.org/10.1016/j.frl.2019.101349 FRL 101349

To appear in:

Finance Research Letters

Received date: Revised date: Accepted date:

1 June 2019 20 September 2019 2 November 2019

Please cite this article as: Libo Yin Associate Professor , Can the Intermediary Capital Risk Predict Foreign Exchange Rates?, Finance Research Letters (2019), doi: https://doi.org/10.1016/j.frl.2019.101349

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Highlights   

The intermediary capital risk is a useful predictor for exchange rates. The predictive pattern is robust when controlling for macroeconomic variables. The simple linear regression is sufficient to capture the predictive performance.

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Can the Intermediary Capital Risk Predict Foreign Exchange Rates? Author information: Libo Yin, Corresponding author. Associate Professor, School of Finance, Central University of Finance and Economics Address: 39South College Road, Haidian District, Beijing, 100081, China. Email: [email protected]

Acknowledgement This research is financially supported by the National Natural Science Foundation of China under projects No. 71671193, Program for Innovation Research in Central University of Finance and Economics, and the "Young talents" Support Program in Central University of Finance and Economics (QYP1901).

Abstract: The intermediary capital risk (ICR) is recently perceived as an important indicator of economic activities and risk premiums. In this paper, we provide individual time-series predictability of ICR for exchange rates of twelve major currencies against US dollar, in both in-sample and out-of-sample settings. This predictive pattern is robust when controlling for macroeconomic variables. Further analysis shows that a simple linear regression is sufficient to capture the predictive performance. Our results imply that the ICR factor is a useful predictor for exchange rates. Keywords: Intermediary capital risk; Exchange rates; Predictability

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1. Introduction The difficulty in predicting exchange rates has been a longstanding problem since the seminal work of Meese and Rogoff (1983). Voluminous variables have been proposed as potential predictor which contain useful information from economic fundamentals, such as traditional fundamentals (inflation, money balances, nominal GDP) (Lee and Kim, 2018; Sarno and Schmeling, 2014), macro news (Caporale et al., 2017), global equity volatility risk (Cenedese et al., 2016), economic uncertainty (Christou et al., 2018), external imbalance (Corte et al., 2016), the Baltic Dry Index (Han et al., 2019), commodity prices (Ferraro et al., 2015; Roubaud and Arouri, 2018), order flow (Rime et al., 2010) and etc. However, empirical results regarding the predictive performance are mixed due to the failure of models to reconcile the relation between exchange rates and economic fundamentals quantitatively (Rossi, 2013). In this paper, we shed new light on a novel indicator, the US intermediary capital risk (ICR). The intuition is straightforward. Financial intermediaries, which are broadly defined to include traditional commercial banks as well as investment banks and hedge funds, fit the assumptions of modern finance theory nicely. According to the intermediary CAPM theory, the marginal value of wealth of financial intermediaries is expected to price a broad class of assets and thus the intermediary capital risk exert a direct influence on risk premiums (He and Krishnamurthy, 2013; Brunnermeier and Sannikov, 2014; Frijns et al. (2018). While literature in this field is growing (Adrian et al., 2014), there is limited research about the time-series predictability of ICR in the context of currency markets. Therefore, we undertake an in-depth analysis at the daily level of the effect of intermediary capital risk on the dynamics for exchange rates. Our analysis of this predictive regression proceeds in the following steps. First, using daily

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data, we provide a pioneering study by exploring both in-sample and out-of-sample predictability for ICR over the 18-year period from 2000-2017. We find significant predictability from ICR to currency returns. Second, to explore whether ICR information has been covered by classical macro variables (Jurado et al., 2015; Neely, Rapach, Tu and Zhou, 2014), we include 5 fundamental variables that reflect financial and macroeconomic conditions in the benchmark autoregressive model and carry out a robustness analysis to determine whether ICR information still improves the predictive ability of these amended models. Our empirical results indicate that the revealed out-of-sample predictability is generally robust to alternative benchmarks. ICR information does not substantively overlap with traditional macro information. Third, our empirical analysis is further extended to nonlinear models including asymmetric effects and regime changes. However, we find little evidence supporting the superiority of nonlinear models over linear specifications in forecasting exchange rates. Our paper fills an important gap in the finance literature on exchange rate predictability. First, our paper is related to Fang (2019) and Pham (2018) who investigate the role of the capital ratio of financial intermediaries on the cross-sections of exchange rate returns. We provide a fresh time-series perspective that ICR can forecast currency returns. Secondly, because a model's in-sample predictive performance tends to correlate poorly with its ability to deliver good out-of-sample forecasts, our work provides systematic out-of-sample forecasting support for intermediary asset pricing theories, which are best viewed as a complementary and thorough attempt to He et al. (2017), suggesting that the in-sample forecasting relationship holds out-of-sample. The remainder of this paper is organized as follows. Section 2 briefly describes the empirical

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data. We report the in-sample and out-of-sample analyses in Sections 3 and 4, respectively. Finally, Section 5 concludes the paper.

2. Data We focus on 12 exchange rates of major currencies (US dollar per unit of foreign currency) which are the top traded currencies in OTC foreign exchange. Specifically, they include Euro (EUR), Japanese Yen (JPY), United Kingdom Pound (GBP), Canadian Dollar (CAD), Australian Dollar (AUD), New Zealand Dollar (NZD), Swedish Krona (SEK), Norwegian Krone (NOK), Mexican Peso (MXN), Singapore Dollar (SGD), South Korean Won (KRW) and Hong Kong Dollar (HKD). Daily spot exchange rate data is end-of-day and collected from Board of Governors of the Federal Reserve System. Currency returns are defined as the logarithmic difference of nominal exchange rate of the specific currency. In line with He et al. (2017), the intermediary capital risk factor is calculated as the AR(1) innovations to the market-based intermediary capital ratio of primary dealers, scaled by the lagged capital ratio. The (aggregate) primary dealer capital ratio at each trading day

t can be

constructed as

t 

 MarketEquity

i ,t

i

  MarketEquity

i ,t

i

 BookDebti ,t 

,

(1)

where i represents a primary dealer. The market value of equity for each intermediary i , which is arguably better at reflecting the financial stress, is share price times shares outstanding on the trading day

t . The book value of debt for each intermediary i is equal to total assets less

common equity, using the most recent data available for each intermediary i on the trading day

t . By estimating a shock

ut (an innovation in the auto-regression t    t 1  ut ) to the

5

capital ratio in levels, the risk factor can be proxied by the growth rate of the capital ratio as t  ut / t 1 .

(2)

See http://www.newyorkfed.org/markets/primarydealers.html for current and historical lists of primary dealers. Due to the possibility of data acquisition, our data cover the sample period from January 2000 through October 2017 (4605 trading days). The data of intermediary capital risk factor can be obtained from http://apps.olin.wustl.edu/faculty/manela/data.html.

3. In-sample analysis We start from a simple in-sample prediction models of currency returns, which could reveal the marginal predictive power of intermediary capital risk factor. The regressions are specified as follows: p 1

rt 1     i rt i   ICRt   t 1 ,

(3)

i 0

where ICRt is the intermediary capital risk factor in the t-th trading day, rt are the natural logarithm of daily currency returns, respectively. The maximum lag order p=1. [Insert Table 1 Here] Table 1 displays the estimated coefficients as well as the t-statistics based on the Newey-West covariance correction for serial correlation. We also report the increase in R2 for the regression with the intermediary capital risk factor relative to the benchmark AR(1) model, expressed as a percentage. The focus of our interest is the coefficient estimates of  . For all the twelve currencies, the coefficients are all sizable with values ranging from -0.0896 to -0.0012 and significantly at the 1% confidence level, clearly indicating the strong in-sample predictive power of the intermediary capital risk factor. Coefficients associated with the intermediary capital risk are all negative, indicating that foreign currency tends to appreciate when domestic intermediary 6

capital risk is relatively higher. The results for the R 2 statistic offer similar evidence. The increase in R 2 after adding the intermediary capital risk factor to the benchmark regression spans from 0.2152% to 5.6137%.

4. Out-of-sample analysis

4.1 Linear specifications Although the in-sample analysis provides efficient parameter estimates, out-of-sample tests seem more relevant for assessing genuine predictability in real time and avoid the in-sample over fitting issue. In this section, we conduct an out-of-sample forecasting exercise using a recursive window that suggests that the in-sample forecasting relationship holds out-of-sample.According to Meese and Rogoff (1983) and Rossi (2013), the random walk without drift serves as the toughest benchmark. None of economic models in the empirical analysis of Meese and Rogoff (1983), including the random walk with drift model, generally yield any forecasting improvement in root mean square error or mean absolute error over the random walk model. Therefore, we use the random walk with and without drift as the empirical benchmark for judging the predictive ability of the ICR factor. Specifically, we divide the total sample of T observations for the intermediary capital risk factor and each exchange rate series into an in-sample part containing the first M observations and an out-of-sample part containing the remaining T  M observations. The first out-of-sample forecast of currency returns based on intermediary capital risk is given by p 1

rˆM 1  ˆ M  ˆi , M rM i  ˆM ICRM ,

(4)

i 0

where ˆ M , ˆi , M and ˆM are the OLS estimates of  ,  i and  in Eq. (3), respectively.

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These estimates are obtained by regressing {rt }tM p 1 on a constant, {rt }tM j p  j 1 , for j  1, 2,..., p , and {ICRt }tM p1 . The second out-of-sample forecast is given by p 1

rˆM  2  ˆ M 1  ˆi , M 1rM i 1  ˆM 1 ICRM 1 .

(5)

i 0

In this manner, the parameter estimates ˆ M 1 , ˆi , M 1 and ˆM 1 are obtained by regressing {rt }tM p11 on a constant, {rt }tM j p  j , for j=1, 2, …, p, and {ICRt }tM p . Proceeding in this manner

through the end of the out-of-sample period, a series of T  M forecasts of currency returns is generated. The accuracy of the out-of-sample forecast is evaluated by the out-of-sample R-square (Campbell and Thompson, 2008) and MSFE-adjusted (Clark and West, 2007). [Insert Table 2 Here] Table 2 reports the evaluation results of the predictive regression. Nevertheless, Similar to their in-sample counterparts, the predictive power is sufficiently significant, as all twelve values of 2 are remarkably positive. The predictive content of the intermediary capital risk factor for Roos

KRW is the strongest, followed by AUD and NZD, while it is the weakest for EUR. In addition, 2 the Roos values are even larger during more recent sub periods (from Jan 2008 to Oct 2017),

indicating that the predictive ability of the ICR factor becomes stronger over time. This result is consistent with the increasingly important role of financial intermediaries. All twelve MSFE-adjusted statistics are also significantly positive, suggesting that the inclusion of the ICR factor on the right-hand side of the predictive regression can lead to a significant reduction in the MSFE over the entire out-of-sample evaluation period. The p-value of the CW test suggests that the improvement in the forecasting accuracy is significant.

4.2 Forecasting performance when controlling for macro variables In the spirit of Sarno and Valente (2009), Sarno and Schmeling (2014) and Husted et al. 8

(2018), that exchange rates has closely relationship with the real economy. It is possible that the forecast improvement obtained by adding the ICR factor is sensitive to omitted macro variables. To examine this question, we also perform a serious robustness check by including a vector of macro variables zt : p 1

rt 1     i rt i   zt   ICRt   t 1 .

(6)

i 0

We consider several popular macroeconomic variables: Treasury bill rate (TBL), long-term return (LTR), value-weighted stock index return (SR) and two uncertainty variables to rule out the influence of a large and near-exhaustive set of economic variables (Jurado et al., 2015). Further, as proxy for the real economy, we calculate the “observable fundamentals” (OF) as in Engel and West (2005), defined as the country differential in money supply minus the country differential in output. We use industrial production ( IPt ) as a measure of output. The growth rates of IPt are computed as the monthly log changes. We use monetary base growth rate as the growth rates of money supply ( M t ). Then we define the change in observable fundamentals as OFt   M t  M t*    IPt  IPt*  . Asterisks stands for the US money supply change and

industrial production change. [Insert Table 3 Here] Table 3 reports the forecasting results of the models based on a recursive window 1. We find that the incorporation of the ICR factor in all the benchmark models with these popular predictor variables significantly improves the predictive ability. When incorporating the information from 2 the 8 macro variables for the full out-of-sample period, the Roos values for all twelve currencies

1

For brevity, we only report the out-of-sample forecasting results during the 2004-2017 period.

The revealed predictability is very similar and even stronger over more recent sample periods. 9

are clearly positive, and the forecasting gains are statistically significant at least at the 5% level. These results suggest that the ICR factor cannot be substituted by any of these macro variables and indeed provides incremental predictive information. Remarkably, when incorporating all the variables, the improvement in the predictive performance of the ICR factor still holds, indicating that the salient information drawled out from a large set of macro conditions may not account for the specificities of financial intermediary information. To sum up, the ICR displays significant in-sample and out-of-sample predictive ability for exchange rates, and provides different information from traditional macro variables. Besides, the simple linear regression is sufficient to capture the predictive relationships between ICR and currency returns.

4.3 Non-linear specifications Considering the intermediary asset pricing literature emphasizes the state-dependent association between the risk premium and the degree of financial sector distress (He, Kelly and Manela, 2017), we investigate whether some nonlinear models are better candidates for currency forecasting by considering two specifications that account for the asymmetric effect and regime change. The first model takes an indicator of a positive intermediary capital risk factor as an additional variable: p 1

rt 1     i rt i   ICRt   ICRt I ( ICRt  0)   t 1 ,

(7)

i 0

where I(.) is an indicator function that is equal to 1 when the condition in parentheses is satisfied and zero otherwise. The second model that captures the asymmetric effect is based on a decomposition: a component that relates only to a positive intermediary capital risk factor and a 10

component that relates only to a negative intermediary capital risk factor: p 1

rt 1     i rt i    ICRt    ICRt   t 1 .

(8)

i 0

[Insert Table 4 Here] Table 4 reports the forecasting results of the two asymmetric models. We find that the benchmark model AR(1) cannot be significantly outperformed by regressions that capture the asymmetric effect of the intermediary capital risk factor for some cases, i.e., EUR and JPY. 2 Moreover, the gains in predictability from the asymmetric models measured by Roos are much

lower than those from simple symmetric models. Similar results can also be found by MSFE -adjusted statistics. Therefore, accounting for the asymmetry in the predictive regressions does not lead to more accurate forecasts and even worsens the forecasting performance. Thirdly, to address time-variation in the ICR effect, we consider a Marko regime switching model given by: p 1

rt 1     i rt i   st ICRt   st 1 ,  st i 0





i.i.d N 0,  s2t , st   0,1 .

(9)

For simplicity, our model just imposes regime switching on the coefficient of ICR and assumes that the intercept and autoregressive coefficient are regime-independent. However, their forecasting ability is still worse than that of the linear model for 11 out of 12 currencies, except for the HKD. Generally speaking, the regime switching model is also not a consistently better candidate.

5. Conclusions By using individual time-series regressions, we document the predictive power of the ICR is prominent for 12 major currency returns. Moreover, exchange rate returns are correlated negatively with changes in the ICR, namely, the currency depreciates as the ICR increase. 11

Consistent with in-sample results, the findings based on out-of-sample regressions reinforce the predictive ability of the ICR. In addition, the effect of the ICR is not diminished by macroeconomic variables. We further extend the forecasting exercise in nonlinear dimensions. However, we find little evidence to support the superiority of nonlinear models over simple linear models. Our results reveal that the ICR factor carry useful information about fundamentals which is useful for exchange rate predictability. From a trading perspective, investors might be able to trade profitably by entering into suitable positions due to the increase in currency returns that follows a negative capital ratio shock.

References Adrian T, Etula E, Muir T. Financial intermediaries and the cross-section of asset returns[J]. The Journal of Finance, 2014, 69(6): 2557-2596. Brunnermeier M K, Sannikov Y. A macroeconomic model with a financial sector[J]. American Economic Review, 2014, 104(2): 379-421. Campbell J Y, Thompson S B. Predicting excess stock returns out of sample: Can anything beat the historical average?[J]. The Review of Financial Studies, 2008, 21(4): 1509-1531. Caporale G M, Spagnolo F, Spagnolo N. Macro news and exchange rates in the BRICS[J]. Finance Research Letters, 2017, 21: 140-143. Cenedese G, Payne R, Sarno L, et al. What do stock markets tell us about exchange rates?[J]. Review of Finance, 2015, 20(3): 1045-1080. Christou C, Gupta R, Hassapis C, et al. The role of economic uncertainty in forecasting exchange rate returns and realized volatility: Evidence from quantile predictive regressions[J]. 12

Journal of Forecasting, 2018, 37(7): 705-719. Clark T E, West K D. Approximately normal tests for equal predictive accuracy in nested models[J]. Journal of Econometrics, 2007, 138(1): 291-311. Corte P D, Riddiough S J, Sarno L. Currency premia and global imbalances[J]. The Review of Financial Studies, 2016, 29(8): 2161-2193. Engel C, West K D. Exchange rates and fundamentals[J]. Journal of Political Economy, 2005, 113(3): 485-517. Fang, X. Intermediary leverage and currency risk premium[R]. Working paper. Available at SSRN: https://ssrn.com/abstract=3290317 or http://dx.doi.org/10.2139/ssrn.3290317. Ferraro D, Rogoff K, Rossi B. Can oil prices forecast exchange rates? An empirical analysis of the relationship between commodity prices and exchange rates[J]. Journal of International Money and Finance, 2015, 54: 116-141. Frijns B, Huynh T D, Tourani-Rad A, Westerholm P J. Institutional trading and asset pricing[J]. Journal of Banking & Finance, 2018, 89: 59-77. Han L, Wan L, Xu Y. Can the Baltic Dry Index predict foreign exchange rates?[J]. Finance Research Letters, 2019. Forthcoming. He Z, Kelly B, Manela A. Intermediary asset pricing: New evidence from many asset classes[J]. Journal of Financial Economics, 2017, 126(1): 1-35. He Z, Krishnamurthy A. Intermediary asset pricing[J]. American Economic Review, 2013, 103(2): 732-70. Husted L, Rogers J, Sun B. Uncertainty, currency excess returns, and risk reversals[J]. Journal of International Money and Finance, 2018, 88: 228-241.

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Jurado K, Ludvigson S C, Ng S. Measuring uncertainty[J]. American Economic Review, 2015, 105(3): 1177-1216. Lee S, Kim Y M. Inflation expectation, monetary policy credibility, and exchange rates[J]. Finance Research Letters, 2018. Forthcoming. Neely C J, Rapach D E, Tu J, Zhou G. Forecasting the equity risk premium: the role of technical indicators[J]. Management Science, 2014, 60(7): 1772-1791. Pham, A. Intermediary-based asset pricing and the cross-sections of exchange rate returns[R]. Working paper. Available at https://econ.columbia.edu/wp-content/uploads/sites/41/2018/09/pham_jmp-4.pdf Rime D, Sarno L, Sojli E. Exchange rate forecasting, order flow and macroeconomic information[J]. Journal of International Economics, 2010, 80(1): 72-88. Rossi B. Exchange rate predictability[J]. Journal of Economic Literature, 2013, 51(4): 1063-1119. Roubaud D, Arouri M. Oil prices, exchange rates and stock markets under uncertainty and regime-switching[J]. Finance Research Letters, 2018, 27: 28-33. Sarno L, Schmeling M. Which fundamentals drive exchange rates? A cross-sectional perspective[J]. Journal of Money, Credit and Banking, 2014, 46(2-3): 267-292. Sarno L, Valente G. Exchange rates and fundamentals: Footloose or evolving relationship?[J]. Journal of the European Economic Association, 2009, 7(4): 786-830.

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Tables Table 1 In-sample estimation results (The lag order of currency returns is equal to 1). EUR Coeff icient

GBP

CAD

AUD

NZD

Coeff icient

t-stat

Coeff icient

t-stat

Coeff icient

t-stat

Coeff icient

t-stat

Panel A: Parameter estimation results 0.000 -0.30 0.000 0.489  0 71 0 5 -0.00 -0.06 0.019 1.269 1 10 66 2 9 -0.01 -3.30 -0.02 -5.87  71*** 41 96*** 86

0.000 0 -0.03 44** -0.01 94***

0.248 0 -2.28 85 -3.57 01

0.000 0 -0.05 10*** -0.05 23***

-0.36 01 -3.32 76 -10.4 906

0.000 0 -0.07 65*** -0.08 64***

-0.35 89 -5.01 96 -12.4 410

-0.00 01 -0.02 95* -0.07 10***

-0.53 30 -1.94 09 -9.87 83

Panel B: Percent increase of R 2 0.215 0.723 R 2 2% 4%

0.254 7%

2.316 8%

3.235 2%

2.056 9%

MX N

SGD

KR W

HKD

t-stat

SEK Coeff icient

Coeff icient

JPY t-stat

NOK

Coeff icient

t-stat

Coeff icient

t-stat

Coeff icient

t-stat

Coeff icient

t-stat

Panel A: Parameter estimation results 0.000 -0.03 0.000 0.029  0 51 0 5 -0.04 -2.64 -0.02 -1.55 1 02*** 48 36 93 -0.04 -7.72 -0.03 -6.18  92*** 48 98*** 79

0.000 2 -0.01 41 -0.04 38***

1.528 9 -0.90 21 -7.43 09

0.000 0 -0.04 69*** -0.01 20***

-0.92 04 -3.08 90 -4.22 54

0.000 0 -0.03 66** -0.08 96***

-0.07 79 -2.50 99 -16.5 678

0.000 0 -0.00 96 -0.00 12***

0.118 9 -0.65 04 -4.84 34

Panel B: Percent increase of R 2 1.259 0.804 R 2 9% 5%

1.164 7%

t-stat

Coeff icient

t-stat

0.364 8%

5.613 7%

0.486 1%

Notes: This table reports the in-sample estimation results for the predictive regressions for daily currency returns with intermediary capital risk factor. The table presents the results from the regression of the specification p 1

rt 1    i rt i   ICRt   t 1 i 0

where ICRt is the intermediary capital risk factor in the t-th trading day, rt are the natural logarithm of daily currency returns, respectively. The maximum lag order p=1. For each predictive variable, we report the estimate of the slope coefficient ˆ or ˆ on it, as well as the related t-statistic. We also show the percent increase of R2 relative to the benchmark of AR(1) (the above model with   0 ). The asterisks *, **, *** denote rejections of null hypothesis at 10%, 5% and 1% significance levels, respectively.

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Table 2 Out-of-sample forecasting results based on recursive window under linear specifications (The lag order of currency returns is equal to 1). Random walk with drift

Random walk without drift

2004-2017

2004-2017

2008-2017 MSFE

R

2 oos

-adjuste d statistic

(%) EUR GBP JPY CAD AUD NZD SEK NOK MXN SGD KR W HKD

0.2118** 0.7701** * **

0.2432 2.3155** *

3.1487** *

2.1457** *

1.0610** *

0.8110** *

1.2338** *

0.3495** *

5.6972** *

0.5177** *

2.0028 3.3915 1.9165 5.7012 5.5952 5.4406 3.8380 3.4043 3.8664 2.5426 7.7202 3.0544

MSFE

R

2 oos

-adjuste d statistic

(%) 0.2728** 0.9661** * **

0.3080 2.8714** *

3.6255** *

2.5667** *

1.2664** *

1.0025** *

1.3299** *

0.3733** *

5.9659** *

0.6820** *

2.0127 3.3932 1.9121 5.5476 5.2802 5.1338 3.6391 3.4079 3.7727 2.3565 7.4385 2.9711

2008-2017 MSFE

R

2 oos

-adjuste d statistic

(%) 0.2115** 0.7712**

2.0002 3.3872

*

R

(%) 0.2724** 0.9664**

-adjuste d statistic 2.0106 3.3890

* **

0.2432 2.3279**

1.9124 5.7130

*

3.1542** 2.1453**

5.5829 5.4305 3.8399 3.4041 3.8583 2.5401

1.2667**

3.6377

1.0026**

3.4049

1.3261**

3.7613

0.3716**

2.3502

*

7.7122

*

0.5175**

5.1287

*

*

5.7037**

2.5658**

*

*

0.3490**

5.2669

*

*

1.2348**

3.6246**

*

*

0.8127**

1.9071 5.5484

*

*

1.0647**

0.3075** 2.8734** *

*

*

MSFE 2 oos

5.9662**

7.4273

*

3.0425

0.6817**

2.9602

*

Notes: The table reports the forecasting results for the predictive regressions with the intermediary capital risk factor under linear specifications. We present the results from the linear regression of the specification: p 1

rt 1    i rt i   ICRt   t 1 , i 0

where ICRt is the intermediary capital risk factor in the t-th trading day, rt are the natural logarithm of daily currency returns, respectively. The maximum lag order p=1. The forecasts are generated using a recursive window with the initial length of 1027 (2060) days for generating 2 forecasts January 2004 (January 2008) through October 2017. The table reports Roos , the

out-of-sample R2, defined by the percent reduction of mean squared predictive error (MSPE) of the predictive model with intermediary capital risk factor, relative to the benchmark of random

16

walk (with and without drift). The MSFE -adjusted statistics (Campbell and Thompson, 2008) and p-values of Clark and West (2007) (CW) tests for the equivalence of MSPEs between the predictive model with intermediary capital risk factor and the benchmark model are given in the parentheses. The asterisks *,

**

and

***

2 alongside Roos indicate rejections of null hypothesis at

10%, 5% and 1% significance levels, respectively.

Table 3 Out-of-sample forecasting results when controlling macro variables, recursive window (2004-2017). EUR

GBP MSFE

2 Roos

(%) T B L LT R S R G M G P O F F U M U A L L

-adju sted statis tic

JPY MSFE

2 Roos

(%)

-adju sted statis tic

CAD MSFE

2 Roos

(%)

-adju sted statis tic

AUD MSFE

2 Roos

(%)

-adju sted statis tic

NZD MSFE

2 Roos

(%)

-adju sted statis tic

MSFE 2 Roos

(%)

-adju sted statis tic

0.21 34**

2.01 25

0.77 08***

3.40 86

0.24 07***

1.93 21

2.32 63***

5.73 84

3.12 62***

5.61 15

2.12 67***

5.42 93

0.22 14** 0.23 67** 0.21 08** 0.21 47** 0.21 71** 0.21 40** 0.21 38**

2.03 99 2.05 26 1.99 09 2.00 63 2.02 26 2.00 91 2.00 48

0.78 26*** 0.77 44*** 0.76 69*** 0.76 78*** 0.77 25*** 0.76 58*** 0.78 78***

3.41 43 3.41 55 3.43 41 3.41 98 3.39 99 3.39 77 3.51 92

0.24 02*** 0.25 61** 0.24 11** 0.24 09** 0.24 37** 0.24 05** 0.25 41**

1.88 46 1.98 51 1.96 92 1.95 26 1.91 97 1.90 73 1.99 77

2.32 63*** 2.33 09*** 2.30 37*** 2.31 47*** 2.32 35*** 2.32 99*** 2.32 13***

5.69 92 5.80 49 5.77 37 5.73 71 5.70 47 5.72 23 5.82 30

3.15 19*** 3.25 97*** 3.14 44*** 3.16 52*** 3.14 79*** 3.18 38*** 3.17 70***

5.58 42 5.74 24 5.73 53 5.67 14 5.59 05 5.62 01 5.74 02

2.15 13*** 2.18 62*** 2.13 40*** 2.14 67*** 2.14 54*** 2.16 06*** 2.16 74***

5.44 29 5.52 48 5.50 23 5.47 01 5.43 44 5.45 96 5.58 14

0.12 93*

1.61 91

0.66 48***

3.19 25

0.20 95**

1.87 06

2.03 65***

5.47 96

2.93 07***

5.68 01

1.91 12***

5.23 12

SEK 2 Roos

(%)

NOK MSFE

-adju sted

2 Roos

(%)

MXN MSFE

-adju sted

2 Roos

(%)

SGD MSFE

-adju sted 17

2 Roos

(%)

KRW MSFE

-adju sted

2 Roos

(%)

HKD MSFE

-adju sted

2 Roos

(%)

MSFE

-adju sted

statis tic T B L LT R S R G M G P O F F U M U A L L

statis tic

statis tic

statis tic

statis tic

statis tic

1.06 15***

3.85 08

0.81 57***

3.42 71

1.23 76***

3.88 23

0.35 24***

2.55 79

5.69 79***

7.73 86

0.51 98***

3.08 00

1.06 04*** 1.111 3*** 1.04 48*** 1.06 60*** 1.05 65 1.07 19*** 1.07 10***

3.83 35 3.87 22 3.80 74 3.83 91 3.82 69 3.86 03 3.85 03

0.81 87*** 0.81 20*** 0.80 57*** 0.81 07*** 0.81 81 0.81 60*** 0.82 18***

3.41 15 3.41 17 3.43 01 3.42 27 3.41 57 3.42 54 3.48 73

1.24 16*** 1.22 05*** 1.22 92*** 1.22 85*** 1.23 38 1.23 35*** 1.26 11***

3.87 88 3.93 26 3.88 89 3.86 78 3.86 44 3.86 38 3.94 51

0.35 15*** 0.35 34*** 0.34 79*** 0.35 02*** 0.35 00 0.35 64*** 0.35 11***

2.55 02 2.60 20 2.53 79 2.54 44 2.53 98 2.56 96 2.56 15

5.69 86*** 5.71 88*** 5.68 27*** 5.68 41*** 5.68 19 5.70 16*** 5.72 21***

7.70 62 7.78 99 7.80 27 7.74 54 7.70 45 7.72 41 7.81 94

0.51 62*** 0.51 75*** 0.52 47*** 0.52 12*** 0.51 95 0.52 02*** 0.50 79***

3.00 67 3.10 13 3.10 95 3.07 92 3.03 92 3.06 11 3.05 13

0.84 54***

3.37 89

0.66 10***

3.07 99

1.04 53***

3.63 26

0.24 09**

2.06 28

5.17 52***

7.26 35

0.51 05***

3.19 85

Notes: The table reports the forecasting results for the predictive regressions with the intermediary capital risk factor. We present the results from the regression of the specification p 1

rt 1     i rt i   zt   ICRt   t 1 , i 0

where ICRt is the intermediary capital risk factor in the t-th trading day, rt are the natural logarithm of daily currency returns, respectively; zt denotes a vector with macro variables. These popular predictor variables are Treasury bill rate (TBL), long-term return (LTR), value-weighted stock index return (SR), the growth rates of money supply (GM), the growth rates of (GP), the change in observable fundamentals (OF), financial uncertainty (FU) and macroeconomic uncertainty (MU), the symbols of which are listed in the first column. The maximum lag order p=1. The forecasts are generated using a recursive window with the initial length of 1027 days. 2 The table reports Roos , the out-of-sample R2, defined by the percent reduction of mean squared

predictive error (MSPE) of the predictive model relative to the benchmark model, p 1

rt 1      i rt i   zt   t 1 . i 0

The MSFE -adjusted statistics (Campbell and Thompson, 2008) and p-values of Clark and West (2007) (CW) tests for the equivalence of MSPEs between the predictive model with intermediary capital risk factor and the benchmark model are given in the parentheses. The asterisks *, ** and *** 2 alongside Roos indicate rejections of null hypothesis at 10%, 5% and 1% significance levels,

respectively. 18

Table 4 Out-of-sample forecasting results based on recursive window under nonlinear specifications (2004-2017). Asymmetric model 1

Asymmetric model 2

MSFE

MSFE

MSFE

R (%)

-adjusted statistic

R (%)

-adjusted statistic

R (%)

-adjusted statistic

-0.0066 0.0994* -0.0110 0.6859*** 1.0760*** 0.5586*** 0.4193*** 0.2621** 0.3733*** 0.0734 2.5120*** 0.3258***

0.8268 1.3503 0.5750 3.5071 4.2471 3.1470 2.6076 2.3087 2.4233 1.1675 6.6648 3.1838

-0.0683 -0.0480 -0.0657 0.3088** 0.5821*** 0.2026** 0.2335** 0.0818* 0.1505** -0.0342 1.3659*** 0.1769**

0.0629 -0.0148 -0.3971 2.2936 3.1299 1.9757 2.0520 1.3304 1.5679 0.0765 5.2604 2.2523

-0.2217 -0.0886 0.1015*** 0.7672*** 0.7235*** 0.4458*** -0.0397* 0.2559** 0.3297** 0.1291 3.2245*** 0.5430***

-0.8412 0.3243 2.7299 3.0999 3.4793 2.6754 1.3653 2.2420 1.7473 1.1622 6.5231 3.7060

2 oos

EUR GBP JPY CAD AUD NZD SEK NOK MXN SGD KRW HKD

Regime switching model

2 oos

2 oos

Notes: The table reports the forecasting results for the predictive regressions with the intermediary capital risk factor under nonlinear specifications. We present the results from two nonlinear regressions of the specifications: p 1

Asymmetric model 1: rt 1    i rt i   ICRt   ICRt I ( ICRt  0)   t 1 , i 0

p 1

Asymmetric model 2: rt 1    i rt i    ICRt    ICRt   t 1 , i 0

p 1

Regime switching model: rt 1    i rt i   s ICRt   s ,  s t

i 0

t 1

t





i.i.d N 0,  s2t , st   0,1

where ICRt is the intermediary capital risk factor in the t-th trading day, rt are the natural logarithm of daily currency returns, respectively. The maximum lag order p=1. The forecasts are generated using a recursive window with the initial length of 1027 days for generating forecasts 2 January 2004 through October 2017. The table reports Roos , the out-of-sample R2, defined by the

19

percent reduction of mean squared predictive error (MSPE) of the predictive model with intermediary capital risk factor, relative to the benchmark of random walk (with drift). The MSFE -adjusted statistics (Campbell and Thompson, 2008) and p-values of Clark and West (2007)

(CW) tests for the equivalence of MSPEs between the predictive model with intermediary capital risk factor and the benchmark model are given in the parentheses. The asterisks *,

**

and

***

2 alongside Roos indicate rejections of null hypothesis at 10%, 5% and 1% significance levels,

respectively.

20