  The aim of this paper is to examine the time scaling of the semivariance when
returns are modeled by various types of jump-diffusion processes, including
stochastic volatility models with jumps in returns and in volatility. In
particular, we derive an exact formula for the semivariance when the volatility
is kept constant, explaining how it should be scaled when considering a lower
frequency. We also provide and justify the use of a generalization of the
Ball-Torous approximation of a jump-diffusion process, this new model appearing
to deliver a more accurate estimation of the downside risk. We use Markov Chain
Monte Carlo (MCMC) methods to fit our stochastic volatility model. For the
tests, we apply our methodology to a highly skewed set of returns based on the
Barclays US High Yield Index, where we compare different time scalings for the
semivariance. Our work shows that the square root of the time horizon seems to
be a poor approximation in the context of semivariance and that our methodology
based on jump-diffusion processes gives much better results.
