*2.3. Uncertainty Premium Hypotheses*

Equation (7) provides a dynamic regression framework pertinent to test uncertainties and stock returns, this section outlines each hypothesis as follows:

#### (i) *Local uncertainty premium hypothesis*

If a rise in *η<sup>t</sup>*−*i* signifies a potential deterioration of economic activities that endangers future cash flows (Bloom 2009; Leduc and Liu 2016), it is expected that *Et*−<sup>1</sup>[*Rmt*, *η<sup>t</sup>*−*i* ] = 0 would be rejected. Note a rejection of *Et*−<sup>1</sup>[*Rmt*, *ηt*] = 0 is consistent with the EMH (Li 2017; Chen et al. 2017; Lopez de Carvalho 2017). However, if *Et*−<sup>1</sup>[*Rmt*, *η<sup>t</sup>*−*<sup>i</sup>*] = 0 for *i* ≥ 1 is rejected and there is a positive relation,

<sup>3</sup> The popularity of this model is due to Bollerslev et al. (1992). Bollerslev (2010) provides different specifications of the conditional volatility models. In addition, some papers (Glosten et al. 1993; Chiang and Doong 2001) prefer to add an asymmetric term to the conditional variance equation to capture the bad news, which has a more profound impact on variance as compared to an equal amount of good news. Our specification indicates that this is redundant, since the inclusion of Δ*η<sup>t</sup>*−<sup>1</sup> and Δ*zt*−<sup>1</sup> already captures the effect arising from bad news.

then the market is inefficient and investors will be rewarded by an uncertainty premium from the local market.

#### (ii) *Global uncertainty premium hypothesis*

It is observed that an increase in uncertainty over the global market is soon learned by local investors via mass media, digital devices, trade connections or financial institution linkages, which will induce investors to reassess their portfolio positions (Chiang et al. 2007; Forbes 2012; Klößner and Sekkel 2014; Chen et al. 2018). This spillover hypothesis can be tested by examining *Et*−<sup>1</sup>[*Rmt*, *zt*−*<sup>i</sup>*] = 0. A rejection of *Et*−<sup>1</sup>[*Rmt*, *zt*] = 0 is consistent with the efficient-market hypothesis. However, if *Et*−<sup>1</sup>[*Rmt*, *zt*−*<sup>i</sup>*] = 0 is rejected, that is, *γi* = 0 for *i* ≥ 1 is rejected and *γi* > 0, evidence would go against the EMH, and investors will be rewarded by an uncertainty premium from a rise in lagged global EPU.
