forecast.<sup>5</sup> For global term spread, the dispersion is computed from the monthly Consensus Economics survey for each country of the G20 and aggregated using real GDP weights.<sup>6</sup>

- The balance of risks for each factor is captured by the skewness of its forecast distribution. A negative skewness indicates a balance of risks that is tilted to the downside. The skewness of the risk-neutral probability distributions of option price on S&P 500 returns as well as on Brent and WTI prices are approximated from the slope of their respective implied volatility curves, following the methodology of Mixon (2011).<sup>7</sup> For the term spread, the skewness is computed from the monthly Consensus Economics survey for each country of the G20 and aggregated using real GDP weights.

Several episodes of heightened uncertainty stand out from the analysis of these risk factors (Figure 1). The first one is the global financial crisis of 2008-09. Its unexpected severity was associated with financial market disruptions and a broad-based increase in volatility and risk aversion (Stock and Watson 2012; Allen, Bali, and Tang 2012). This was also reflected in the rising degree of uncertainty of all three risk factors. The second and third, albeit milder, episodes were around intensifications in the Euro Area sovereign debt crisis in 2011 and 2012, when financial market indicators also pointed towards a greater level of uncertainty surrounding global growth forecasts. Recent episodes of market stress, such as those associated with the Taper Tantrum in 2013, sharply declining oil prices since mid-2014 and the ongoing emerging market slowdown have also raised forecast uncertainty. Around these episodes, downside risks to growth have been more prevalent.

# **3. Risk indicators and global growth**

To characterize the evolution of uncertainty around global growth forecasts, a similar approach to that proposed by Blix and Sellin (1998) and Kannan and Elekdag (2009) is used. More specifically, changes in the degree of uncertainty (dispersion) and balance of risks (skewness) of underlying risk factors are used to assess the potential size and direction of forecast errors at any point in time.

In order to calculate the degree of uncertainty and balance of risks of global growth forecasts from the selected risk factors, a number of assumptions are needed regarding the functional form of their respective distributions, as well as the weight given to individual risk factors. In line with other authors (Blix and Sellin 1998 and Kannan and Elekdag 2009), a two-piece normal distribution is

> 5 Ideally, the fan chart would extend into 2018. However, reliable market-based indicators derived from liquid option markets are not available at this horizon.

> 6 Only countries with available data on interest rates are used in the aggregations. These include: Australia, Canada, France, Germany, India, Indonesia, Italy, Japan, Netherlands, Republic of Korea, Sweden, Spain, Switzerland, the United Kingdom, and the United States.

> 7 The skewness is approximated based on the following measure of implied volatility skew: (25 percent Delta Call implied volatility-25 percent Delta Put implied volatility)/50 percent Delta implied volatility where Delta is the degree to which an option is exposed to shifts in the price of the underlying asset. The framework assumes that the option-implied distribution generates a volatility curve that is linear in delta. This model is considered as more empirically plausible than one assuming linearity in the percentage strike model (Mixon 2011). Among measures based on the slope of the implied volatility curve, this measure is the least correlated with the level of implied volatility. Robustness checks are undertaken with alternative skew measures such as the widely used (90 percent moneyness implied volatility – 110 percent moneyness implied volatility)/100 percent moneyness implied volatility measure, with largely similar results.

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