Tail risk hedging strategies are of vital interest to many market participants to protect
investment portfolios against extreme negative market moves. An obvious protection is the
purchase of a put option. However, such a strategy can be expensive, since the option premium
is payable each investment period, although the protection could prove unnecessary in the
majority of periods. A possible alternative are dynamic asset allocation strategies, which aim to
improve the downside risk profile of an investment strategy without jeopardizing its long‐term
return potential by dynamically shifting between a risky asset (or portfolio) and a risk‐free asset.
Risk targeting strategies
are one such possibility (Bollerslev, Hood, Huss, & Pedersen, 2018;
Hocquard, Ng, & Papageorgiou, 2013; Perchet, De Carvalho, Heckel, & Moulin, 2015). A risk
targeting strategy controls portfolio risk over time by taking advantage of the negative
relationship between risk and return. Specifically, the investment exposure of the portfolio is
adjusted according to updated risk forecasts in order to keep the ex ante risk at a constant target
level. A stricter way to limit downside risk is to apply portfolio insurance strategies, such as the
constant proportion portfolio insurance (CPPI) strategy (Black & Jones, 1987, 1988; Perold,
1986; Perold & Sharpe, 1988), where the investor defines a minimum capital level to be
preserved at the end of the investment period. The key element in determining the investment
exposure to the risky asset is the so‐called multiplier. This represents the inverse of the
maximum sudden loss of the risky asset, so that a given risk budget will not be fully consumed
and the portfolio value will not fall below the protection level. Initially, the multiplier was
assumed to be static and unconditional (e.g. Balder, Brandl, & Mahayni, 2009; Bertrand &
Prigent, 2002; Cont & Tankov, 2009). However, given the empirical characteristics of financial
assets, such as time‐varying volatility or volatility clustering (cf. Andersen, Bollerslev,
Christoffersen, & Diebold, 2006; Longin & Solnik, 1995), other studies (e.g. Hamidi, Maillet,
& Prigent, 2014) propose to model the multiplier as time‐varying and conditional. The
corresponding strategy is known as dynamic proportion portfolio insurance (DPPI).
The success of both dynamic tail risk protection strategies strongly depends on the success of
forecasting tail risk (Perchet et al., 2015). Given a plethora of available risk models, we
contribute to the existing literature on tail risk protection strategies by investigating suitable
risk models for timely management of the investment exposure in dynamic tail risk protection
strategies. At the same time, we contribute to the literature on risk model evaluation by
assessing not only its statistical performance but also its economical relevance when testing the
risk forecasts in a relevant portfolio application.
Risk targeting strategies have been extensively backtested using historical data, and are
known to show superior performance compared to a simple buy‐and‐hold strategy (Cooper,
2010; Giese, 2012; Ilmanen & Kizer, 2012; Kirby & Ostdiek, 2012). Hallerbach (2012, 2015)
demonstrates that the Sharpe ratio increases, even if the portfolio mean return is constant over
time. Constant volatility portfolios not only deliver higher Sharpe ratios than their passive
counterpart but also reduce drawdowns (Hocquard et al., 2013). Similar to the risk targeting
strategy that we apply, the dynamic value‐at‐risk (VaR) portfolio insurance strategy of Jiang,
Ma, and An (2009) aims to control the exposure of a risky asset such that a specified VaR is not
violated. However, their strategy can only be applied to parametric location‐scale models, while
Risk targeting strategies are also known as constant risk, target risk, or inverse risk weighting strategies.
For a comprehensive literature review on portfolio insurance and CPPI/DPPI multipliers, see Benninga (1990), Black and Perold (1992), Basak (2002), Dichtl
and Drobetz (2011), Hamidi et al. (2014), among others.
HAPPERSBERGER ET AL.