Robust Asset Allocation for Long-Term Target-Based Investing

Abstract

This paper explores dynamic mean-variance (MV) asset allocation over long horizons. This is equivalent to target-based investing with a quadratic loss penalty for deviations from the target level of terminal wealth. We provide a number of illustrative examples in a setting with a risky stock index and a risk-free asset. Our underlying model is very simple: the value of the risky index is assumed to follow a geometric Brownian motion diffusion process and the risk-free interest rate is specified to be constant. We impose realistic constraints on the leverage ratio and trading frequency. In many of our examples, the MV optimal strategy has a standard deviation of terminal wealth less than half that of a constant proportion strategy which has the same expected value of terminal wealth, while the probability of shortfall is reduced by a factor of two to three. We investigate the robustness of the model through resampling experiments using historical data dating back to 1926. These experiments also show much lower standard deviation and shortfall probability for the MV optimal strategy relative to a constant proportion strategy with approximately the same expected terminal wealth.

Mean-variance dynamic optimality for DC pension schemes

“…It must be noted that a similar result was observed by Forsyth and Vetzal (2017), in a comparison between precommitment strategy and constant proportions strategy: they, too, found that smallest values for the precommitment strategy were notably lower than the smallest values for the constant proportion strategy. They also found that the difference between the two strategies in the bad market scenarios was wider in the presence of leverage (unconstrained strategy) than with a no-leverage constraint.…”

“…On the other hand, whether the naive strategy always yields a more effective reaction in a period of bad market returns can be debatable. This is true when the bad returns keep on also in the future, because the precommitment strategy keeps on investing in the risky asset when returns are poor because of the unchanged high target (in that sense the precommitment approach is said to be contrarian, seeForsyth and Vetzal;. But if a (short) period of bad returns is then followed by a period of good returns, the precommitment strategy might turn out to be better off than the naive one.…”

Optimal Asset Allocation for Dc Pension Decumulation With a Variable Spending Rule

“…To avoid known problems with other approaches, we use the method described in Dang and Forsyth (2016) and Forsyth and Vetzal (2017) based on the thresholding technique of Mancini (2009) and Cont and Mancini (2011). A tuning parameter α is required which, in intuitive terms, identifies a jump if the absolute value of the detrended log return is more than ασ √ t, where σ is the annualized diffusive volatility and t is the time interval (measured in years) between observations of the data series.…”

Defined Contribution Pension Plans: Who Has Seen the Risk?

“…The glide path and constant proportion asset allocation strategies can be considered to be typical of many DC plan holders. The optimal QS strategy is effectively a best case scenario, in terms of reducing the probability of shortfall (over a wide range of the terminal wealth distribution) compared to glide path or constant proportion strategies (Forsyth and Vetzal, 2017b); Forsyth and Vetzal (2019).…”