A new measure of cross-sectional risk and its empirical implications for portfolio risk management

Shape factors and cross-sectional risk

“…In summary, the data support the idea that shape factors more accurately model volatility than traditional PCA factors; and, more precisely, that a reduced number of shape factors accounts for the realized rate/price volatility more accurately than the same number of traditional PCA factors. This result confirms the empirical findings in Galluccio and Roncoroni (2006 Caplet price excess of fair value computed using shape volatility over fair value computed using constant Black volatility across varying times-tomaturity and strikes. Shape volatility is recovered using the first three most significant shape factors over the entire data set.…”

“…Empirical experiments not reported here suggest that t should be selected between 0.3 and 0.5. 14 The impact of the choice of basis functions is further studied in Galluccio and Roncoroni (2006).…”

“…Inspired by empirical evidence shown in and Engle and Ng (1993), Galluccio and Roncoroni (2006) provide a positive answer to the first issue above. They first introduce an empirical measure of risk accounting for an explicit link between yield curve shapes and volatility.…”

“…Section 4 provides a theoretical analysis of dynamic models driven by shape factors. Section 5 develops an empirical analysis of shape factors that complements the comprehensive study in Galluccio and Roncoroni (2006). Section 6 draws conclusions and sheds light on a few issues meriting future research.…”

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a b s t r a c t Galluccio and Roncoroni (2006) empirically demonstrate that cross-sectional data provide relevant information when assessing dynamic risk in fixed income markets. We put forward a theoretical framework supporting that finding based on the notion of ''shape factors''.

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