Portfolio Rebalancing Error with Jumps and Mean Reversion in Asset Prices
Coauthor(s): Xingbo Xu.
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We analyze the error between a discretely rebalanced portfolio
and its continuously rebalanced counterpart in the presence of jumps
or mean-reversion in the underlying asset dynamics. With discrete
rebalancing, the portfolio's composition is restored to a set of fixed
target weights at discrete intervals; with continuous rebalancing, the
target weights are maintained at all times. We examine the difference between the two portfolios as the number of discrete rebalancing dates increases. With either mean reversion or jumps, we derive the limiting variance of the relative error between the two portfolios. With mean reversion and no jumps, we show that the scaled limiting
error is asymptotically normal and independent of the level of the
continuously rebalanced portfolio. With jumps, the scaled relative
error converges in distribution to the sum of a normal random variable and a compound Poisson random variable. For both the mean-
reverting and jump-diffusion cases, we derive "volatility adjustments"
to improve the approximation of the discretely rebalanced portfolio
by the continuously rebalanced portfolio, based on on the limiting
covariance between the relative rebalancing error and the level of the
continuously rebalanced portfolio. These results are based on strong
approximation results for jump-diffusion processes.
Source: Stochastic Systems
Glasserman, Paul, and Xingbo Xu. "Portfolio Rebalancing Error with Jumps and Mean Reversion in Asset Prices." Stochastic Systems 1 (2011): 1-37.