Spectral risk measure of holding stocks in the long run

We investigate how the spectral risk measure associated with holding stocks rather than a risk-free deposit, depends on the holding period. Previous papers have shown that within a limited class of spectral risk measures, and when the stock price follows specific processes, spectral risk becomes negative at long periods. We generalize this result for arbitrary exponential Lévy processes. We also prove the same behavior for all spectral risk measures (including the important special case of Expected Shortfall) when the stock price grows realistically fast and when it follows a geometric Brownian motion or a finite moment log stable process. This result would suggest that holding stocks for long periods has a vanishing downside risk. However, using realistic models, we find numerically that spectral risk initially increases for a significant amount of time and reaches zero level only after several decades. Therefore, we conclude that holding stocks has spectral risk for all practically relevant periods.

Optimization Problem of Insurance Investment Based on Spectral Risk Measure and RAROC Criterion

This paper introduces spectral risk measure (SRM) into optimization problem of insurance investment. Spectral risk measure could describe the degree of risk aversion, so the underlying strategy might take the investor's risk attitude into account. We establish an optimization model aiming at maximizing risk-adjusted return of capital (RAROC) involved with spectral risk measure. The theoretical result is derived and empirical study is displayed under different risk measures and different confidence levels comparatively. The result shows that risk attitude has a significant impact on investment strategy. With the increase of risk aversion factor, the investment ratio of risk asset correspondingly reduces. When the aversive level increases to a certain extent, the impact on investment strategies disappears because of the marginal effect of risk aversion. In the case of VaR and CVaR without regard for risk aversion, the investment ratio of risk asset is increasing significantly.

The theory and application of spectral risk measures in Vietnam

This paper aims to provide a new risk measure for portfolio management in Vietnam by incorporating investor’s risk aversion into current risk measures such as value at risk (VaR) and expected shortfall (ES). This measure shares several desirable characteristics with the coherent risk measures, as illustrated in Artzner et al. (1997). In Vietnam, our study makes the first attempt to utilize distortion theory, instead of utility theory, to facilitate the adoption of risk aversion level in the popular risk measures. We find that spectral risk measure is more flexible and effective to different groups of risk-adverse investors, compared to the more monotonic and conventional VaR and ES measures