Alternative volatility proxies

An interesting question is whether using changes in a proxy for global (exchange rate) volatility would generate a similar boost in trading rule performance. To test this possibility, we test the performance of our proposed multi-fuzzy strategy using proxies for the change in global risk aversion and uncertainty as the second input. As outlined below, increases in

global risk aversion and uncertainty should increase the volatility of the individual currency pairs; we therefore use this analysis as a further test for the robustness of our proposed approach.

We focus on changes in the Chicago Board Options Exchange volatility index (VIX) and economic policy uncertainty (EPU). The VIX measures the implied volatility of index options of the S&P 500 index, which is shown to be a close proxy for the volatility of the constituents of the S&P 500 (Fleming, Ostdiek, and Whaley, 1995), their price jumps (Becker, Clements, and McClelland, 2009) and their expected returns (Whaley, 2000). The VIX is, in itself, a forward-looking measure, as it is based on the options’ implied volatility, which is the expected market volatility over the next 30 days and is commonly termed “fear index” (Whaley, 2000) as it reflects option implied volatility which rises given there is a higher demand for put options.

The EPU index consists of three underlying components: media coverage of policy- related economic uncertainty, reports by the Congressional Budget Office on tax code provisions and uncertainty about policy-related macroeconomic variables. Its applications in the literature have not only evaluated EPU-based volatility predictions, as outlined in Liu and Zhang (2015), but have also indicated the existence of a link between policy uncertainty and macroeconomic fundamentals (Baker, Bloom, and Davis, 2015).

The intuition is that all exchange rates display a larger volatility when global risk aversion or uncertainty increases, which is reflected by strong increases in the VIX and EPU. Based on the reasoning outlined before, increases (decreases) in the VIX (EPU) should result in an appreciation (depreciation) of the USD relative to all other foreign currencies. A behavioural explanation for this argument is that increases in uncertainty (EPU) or risk aversion (VIX) could cause a flight to quality or flight to liquidity, thereby causing an

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increased demand for USD holdings, as the USD is the major reserve currency. Note that although the EPU and the VIX have a strong correlation to each other, conceptually, they measure something different. The VIX measures changes in risk aversion, whereas the EPU is a measure for (policy related) economic uncertainty.

The testing procedure is same as before: evaluating the risk-adjusted returns from each trading strategy, we test for differences in the Sharpe ratios generated by both proxies used as inputs in the multi-fuzzy strategy against the benchmark of the neuro-fuzzy approach, replicated from Gradojevic (2007). To avoid confusion, we will label the baseline multi-fuzzy strategy as MF–GARCH and the multi-fuzzy strategies using changes in the VIX and EPU as MF–VIX and MF–EPU.

Table 4.8 shows the results of this analysis. The MF–GARCH results are replicated from Table 4.6. At first glance, regardless of the volatility proxy used, the multi-fuzzy approaches (MF–GARCH, MF–VIX and MF–EPU) typically yield higher risk-adjusted returns than the neuro-fuzzy approach (NF). A second general observation is in order. The MF–VIX typically yields higher risk-adjusted returns than the MF–EPU and closely matches the MF–GARCH.

Looking at the differences in detail, we find that the MF–GARCH (MF–VIX) is always preferred over the MF–EPU strategy during the first out-of-sample period, regardless of the exchange rate pair evaluated. The differences between the MF–GARCH and MF–VIX are small by comparison, and no clear pattern emerges. For the USD–EUR and USD–NZD the MF–GARCH approach results in the highest Sharpe ratios generated (4.75and 2.32), whereas the MF–VIX approach results in the highest Sharpe Ratios for the USD–GBP, USD–AUD and USD–CAD pairs. As before, no multi-fuzzy strategy outperforms the neuro-fuzzy strategy for the USD–JPY pair.

For the second out-of-sample period, the same pattern remains, as the MF-GARCH and MF- VIX typically dominate the MF-EPU strategy. Taking the USD–NZD as an example, the Sharpe ratio generated by the MF–VIX (MF–GARCH) is equal to 4.69 (4.64) compared with 4.00 for the MF-EPU, a difference of 17.2 (16) %. A similar conclusion applies to USD–EUR and USD–AUD. Note that during this period, the MF–VIX provides a significantly larger Sharpe Ratio than the neuro-fuzzy strategy for an USD–JPY trader, whereas both MF- GARCH and MF-EPU result in a smaller Sharpe ratio than the NF trading strategy. Summarising the findings for this period, the MF–VIX is the preferred strategy for five out of the six exchange rate pairs, and the MF–GARCH for the other currency pair.

For the out-of-sample period of the third subsample, the MF-EPU strategy generates the highest Sharpe Ratio for trading USD–AUD (0.55), the MF-VIX generates the largest Sharpe ratio for trading USD–CAD (2.07) and the MF-GARCH is preferred for the other four exchange rates.

Although the fuzzy logic setting incorporating the EPU generates lower Sharpe ratios than using other volatility proxies on average, this does not mean that the EPU is less informative proxy for the change in the underlying volatility. The lower Sharpe ratios generated are a result of the distribution of the EPU index: the index shows massive spikes followed by calm periods, which makes the normalisation of EPU changes to any interval problematic95. By contrast, changes in the VIX and GARCH based volatility estimates are easier to model for an interval, as they are less volatile. Overall, it seems that the MF– GARCH is the most consistent approach; however the MF-VIX also provides substantially higher risk adjusted returns than the NF strategy. We take this finding as a confirmation for the robustness of our approach.

95_{See Section 4.4.2. The proxy for the global volatility change and the network based return prediction both fall} within the range [-1,1].

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Table 4.8Out-of-sample performance comparisons of different volatility proxies

USD–EUR USD–GBP USD–JPY USD–CAD USD–AUD USD–NZD

Panel A. January 2002 – December 2005

NF* 4.23 4.27 3.38 1.55 3.12 1.65

MF–GARCH* 4.75** 4.45 3.04 1.81* 3.93*** 2.32***

MF–VIX* 4.54 4.32 3.08 2.02** 3.98*** 1.87**

MF–EPU* 4.25 3.84 3.11 1.30 2.54 1.82

Panel B. January 2006 – December 2009

NF* 3.22 2.27 3.40 2.47 2.97 4.25

MF–GARCH* 3.60** 2.66*** 3.14 2.49 3.25 4.64**

MF–VIX* 3.77*** 2.32 3.82** 3.25*** 3.57** 4.69**

MF–EPU* 3.54** 2.53 3.24 2.72 2.73 4.00

Panel C. January 2010 – December 2013

NF* 1.88 3.40 2.36 0.81 0.24 4.45

MF–GARCH* 2.01 4.25*** 2.17 1.34** 0.50* 5.20***

MF–VIX* 2.00 3.48 2.50 1.02 0.48* 4.70

MF–EPU* 2.09 3.53 2.53 1.00 0.55* 4.49

This table presents annualised Sharpe ratios generated by the neuro- and the multi-fuzzy trading strategy. NF refers to a trading strategy using the ANN-based exchange rate prediction as a fuzzy logic input directly; The MF–GARCH uses the change in the underlying (conditional) volatility as an additional input. The MF–VIX and MF–EPU use changes in a proxy for global exchange rate volatility, measured by changes in the VIX and EPU, as an additional input. The performance of each strategy is net of transaction costs. The MF setting is displayed in Figure 1. Panel A. reports the results for the out-of-sample period of the first subsample, and Panels B and C do the same for the out-of-sample periods of the other subsamples. The out-of-sample period used in the analysis is equal to the last 200 observations of each subsample. We use the test outlined in Jobson and Korkie (1981) and Memmel (2003) to evaluate whether the differences in Sharpe ratios are statistically different from zero. The asterisks next to the Sharpe ratios indicate that the Sharpe ratios generated by the MF strategy are statistically different from the NF strategy *** denotes significance at the 1% level, ** at the 5% level and * at the 10% level.