2023-10-19-国际清算银行-累积风险溢价_73页_1mb

Cumulant Risk Premium (CRP)

• Key Definition: The CRP measures the difference in physical and risk-neutral cumulants (higher-order moments beyond variance) reflected in the returns of leveraged ETFs. It quantifies the compensation investors require for exposure to these risk factors.
• Methodology: Leveraged ETFs (constant-beta assets) are used due to their liquidity and ability to isolate higher-order risk. ETFs with opposite leverages generate a "short-both" strategy, capturing the even-order risk-neutral cumulant premium (CRPE).
• Key Findings:
  • CRP is negative (-7.4% annualized), indicating higher-order risk premiums explain asset pricing better than standard models like CAPM or Black-Scholes.
  • CRP is stress-dependent, spiking during market crises. The short-both strategy earns high Sharpe ratios (e.g., 1.56 for Financials).
  • Higher-order terms (beyond kurtosis) magnify with leverage, making leveraged strategies highly exposed to cumulant risks.
• Implications:
  • Fails the CAPM assumption of linear beta pricing, especially in non-lognormal markets (e.g., stochastic volatility or jumps).
  • Drives the flatness of the SML (Securities Market Line), penalizing high-beta assets.
• Economic Context: Assessed via VIX, providing a simple measure of market stress. The CRP complements VRP (Variance Risk Premium) analysis, with more liquidity-providing strategies dominating risk-based returns.

Relevant Work

• VRP and Jump Models: Contrasted with Heston (stochastic volatility) and jump-diffusions (e.g., Merton's 1976 model) to show similarities and differences in higher-order risk premiums.
• Factor Models: Stated that multi-factor models fit better by accounting for cumulative higher-order risks. Momentum factors correlate positively with even-order cumulants.