黄色仓库

Declaration of interests

The author declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data Availability

The data that support the findings of this study are openly available at YahooFinance and from the author.

Introduction

While the need for foreign exchange (FX) transactions often arises merely as a by-product of buying or selling international securities, increasingly, there are also profit-seekers in currency markets, seeking to profit from selling and buying currencies (see Hafeez, 2007). With active currency management becoming more commonplace, the need for models to explain the comovements of currencies has increased. A parsimonious currency factor model may therefore help the implementation of international equity pricing models. It may also help characterize currency commovements for determining optimal currency hedge ratios (see Campbell, Serfaty-De Medeiros, and Viceira, 2010; De Roon, Eiling, Gerard, and Hillion 2012).

In this paper, I set out to examine the informativeness of various currency weighted averages to explain currency comovements. I note the Canadian dollar, Australian dollar, and New Zealand dollar are more capable in explaining other currencies where Euro and Sterling have the least explanatory powers. To ensure that all possible bilateral currency movements are studied, I use weighted average currencies based on the articulation of 28 forex pairs from eight major currencies for a period of 10 years from 2010 to 2020 (before the COVID-19 crisis). A weighted average currency is an equally weighted average of one currency relative to a basket of all the currencies. For example, the weighted average for Australian dollar is an equally weighted average of Australian dollar vs New Zealand dollar, Euro, Sterling, U.S dollar, Canadian dollar, Swiss franc, and Japanese yen. Since the weighted average currency derived from other currencies, it captures all possible bilateral currency movements.

I investigated two interrelated research questions that, taken together, aim to extend our understanding of forex market. The first question asks, when using currency weighted averages using SUR on joint models, which currency persist more. I rank the currencies based on their β coefficients of SUR in explaining other currencies and I find 1% change in CAD, AUD and NZD on average can lead to 0.86%, 0.73% and 0.69% change in other currencies where for EUR and GBP these ratios are just 0.19% and 0.14%, respectively. Practitioners recognise that there is a commodity factor in currencies, and the Australian, Canadian and New Zealand dollar are typically categorized as “commodity currencies,” see Chen and Rogoff (2003) and Ready, Roussanov, and Ward (2017). My finding also suggests that the differential persistence for CAD, AUD and NZD is down to the greater volume of information contained in these commodity currencies.

To my knowledge, no previous attempt has been made to rank currencies based on the β coefficient of SUR (the average amount by which each currency can change the other currencies). The second question asks whether using SUR estimation on joint models with an imposed currency constraint would change result as it produces lower prediction errors compared with each separate OLS. The SUR estimator produces more efficient estimates than simple OLS when equations are non-identical and non-nested (Zellner 1962a; Zellner and Huang 1962; Zellner 1963). My results remain the same after imposing currency constraint with commodity currencies are the most informative currencies and Euro and Sterling are the least informative currencies.

The paper is organised as follows. First it discusses the research design, models, and constraints, followed by a section on data and descriptive statistics. The last two sections report the empirical results and the conclusion.

Research Design

Although research into estimating forex from other currencies continues unabated (Lusting, Roussanov and Verdelhan (2011), Menkhoff, Sarno, Schmeling, and Schrimpf (2012a), Menkhoff, Sarno, Schmeling, and Schrimpf (2016)), the application of a currency weighted average to capture full currency identities is relatively new. Verdelhan (2018) introduced the weighted average USD—the average appreciation of USD relative to a basket of currencies—and showed that it has a very strong explanatory power for the contemporaneous bilateral exchange rate changes versus USD. Currency baskets may help characterise currency co-movements for determining optimal currency hedge ratios (see Campbell, Serfaty-De Medeiros, and Viceira, 2010; De Roon, Eiling, Gerard, and Hillion 2012).

A weighted average currency is an equally weighted average appreciation of one currency relative to a basket of all the currencies in my sample. To measure AUD, as shown in equation (1), I calculated weighted average AUD, which is an equally weighted average of the AUD versus the other seven currencies.[1]

Applied Models

As the current study investigate eight major currencies, I denoted each regression model by regressing each weighted average currency on the other remaining seven weighted average currencies.

Where W is the weighted average currency.

The currency constraint

The likely magnitude of the efficiency gain through SUR has been investigated by Zellner (1962a, Zellner (1962b), Revankar (1974), Binkley (1982),(Binkley, 1982) and Kmenta (1997). They noted that under conditions generally encountered in practice, the regression coefficients obtained using SUR are more efficient than those obtained through equation-by-equation application of least squares.

In line with Zellner (1962a), I have the following equation.

As demonstrated, can be contemporaneously codetermined through the resolution of multiple identities using the equations m = 1,2,…,M. The system may be written as follows.

The disturbance vector is assumed to have the following variance-covariance matrix:

where I is a unit matrix of order for t =l, 2,…,T, and μ and μ' = 1, 2,…, M.

In OLS, implies that the are the same for all variables and that there is no correlation between different independent variables’ disturbances. However, in the SUR approach, it is assumed that all explanatory variables for the regressions are comprised only of predetermined covariates, with the sole link between the equations being channelled through their error terms.

Equation (12) can be restated for all joint models in the current study as follows.

The following constraint can be imposed when simultaneously regressing the eight models (equations 2 to 9) using the constrained SUR.

Data and descriptive statistics

The initial sample, based on end-of-day rates, was drawn from Yahoo Finance. The data set covered 10 years from 24 February 2010 to 24 February 2020, one day before the COVID-19 crisis severely affected financial markets. In total, 2600 observations were used.

Table 1 reports summary statistics of weighted average currencies and currency pairs. Over the sample period, GBP had the highest mean of 1.57, which means that, on average, the value of sterling was 1.57 times greater than the other seven currencies, whereas NZD had the lowest mean of 0.72. Volatility ranged between 0.04 for NZD and 0.1 for GBP, USD and JPY.

Table 1: Descriptive statistics of weighted average currencies and currency pairs

Empirical results

Table 2 presents β coefficients of unconstrained SUR for Model 2 to 9. When using unconstrained SUR, joint regressions produce lower prediction errors compared with each separate OLS estimator. That is because regression errors for the eight models applied could be correlated and it is assumed that, the sole link among the regressions is channelled through their error terms.

The β coefficients of SUR in Tabel 2 shows the average amount by which each currency can change the other currencies. All coefficients are significant at 1% level. The average of coefficients absolute values presented in Table 2 shows on average how powerful each currency is in changing the currency stated as dependent variable.

For example, 1% change in CAD can lead to a 0.86% average change in other currencies. My results show CAD, AUD and NZD also known as commodity currencies are the most informative currencies as they are associated with greatest average β coefficients of SUR in contrast with EUR and GBP which are the least informative currencies.

Table 2: β coefficients for models 2 to 9 – Unconstrained 

Dependent Variables

All β coefficients are significant at 1% significance level.

To my knowledge, no previous attempt has been made to rank currencies based on their β coefficient of SUR using currency weighted averages which captures all possible bilateral currency movements.

Similar results derived in Table 3 when using constrained SUR with the summation of coefficients for each model constrained to be equal to the summation of coefficients for the other models. The constraint is checked in the last column with the summation of coefficients for each model being equal to 1.

Table 3: β coefficients for models 2 to 9 – Constrained

Dependent Variables

All β coefficients are significant at 1% significance level.

As before, EUR and GBP are still in the 7^th and 8^th position with AUD, NZD and CAD ranked as the 1^st, 2^nd and 3^rd. Although CAD is not the most informative currency under the constrained SUR but it is one of the top 3 currencies. Overall, once again, my results confirm the informativeness of commodity currencies.

Conclusion

In this study, I use weighted average currencies to investigate the informativeness of currencies based on β coefficients of SUR.

Under SUR, it is assumed that joint regressions of models produce lower prediction errors compared with each separate OLS estimator. That is because regression errors could be correlated. Consequently, estimates converged in their theoretically expected relationships according to the currency constraint. In fact, it is assumed that, using SUR, the sole link between the regressions is channelled through their error terms.

When using unconstrained SUR on joint models, I find commodity currencies, CAD, AUD and NZD are the most informative currencies as 1% change in on these currencies can lead to 0.86%, 0.73% and 0.69% average change in other currencies where EUR and GBP are the least informative currencies with average β coefficients of just 19% and 14%, respectively. I find fairly similar results when using constraint SUR.

References

Campbell, J.Y., Serfaty-De Medeiros, K., and L.M. Viceira. Global currency hedging. The Journal of Finance 65 (2010), 87--121.

Chen, Y., and Rogoff, K. Commodity currencies. Journal of International Economics 60, (2003), 133–160.

De Roon, F. Eiling, E., Gerard, B., and P. Hillion. Currency risk hedging: No free lunch. Working Paper (2012).

Hafeez, B. Deutsche Bank Guide to Currency Indices, Section Therein Titled “Currency Markets: Money Left on the Table?” Deutsche Bank, (2007).

Lustig, H., Roussanov, N. and Verdelhan, A., 2011. Common risk factors in currency markets. The Review of Financial Studies, 24(11), pp.3731-3777.

Ready, R., Roussanov, N., and Ward, C. Commodity Trade and the Carry Trade: a Tale of Two Countries. The Journal of Finance 72, 6 (2017), 2629–2684.

Menkhoff, L., Sarno, L., Schmeling, M. and Schrimpf, A., 2012. Carry trades and global foreign exchange volatility. The Journal of Finance, 67(2), pp.681-718.

Menkhoff, L., Sarno, L., Schmeling, M. and Schrimpf, A., 2016. Information flows in foreign exchange markets: Dissecting customer currency trades. The Journal of Finance, 71(2), pp.601-634.

Du, W., Tepper, A., & Verdelhan, A. (2018). Deviations from covered interest rate parity. The Journal of Finance, 73(3), 915-957.

[1] AUD/JPY was divided by a constant number of 100, as it is on average 100 times greater than other currency pairs.