On the maximum drawdown during speculative bubbles

A taxonomy of large financial crashes proposed in the literature locates the burst of speculative bubbles due to endogenous causes in the framework of extreme stock market crashes, defined as falls of market prices that are outlier with respect to the bulk of drawdown price movement distribution. This paper goes on deeper in the analysis providing a further characterization of the rising part of such selected bubbles through the examination of drawdown and maximum drawdown movement of indices prices. The analysis of drawdown duration is also performed and it is the core of the risk measure estimated here.Comment: 15 pages, 7 figure

Choices and constraints over retirement income streams: comparing rules and regulations

The new Simplified Superannuation regulations for Australian superannuation provide tax concessions to retirement income streams which comply with legislated minimum drawdown rules. We evaluate these new drawdown rules against four alternatives, including three formula-based ‘rules of thumb’ and the previous legislated minimum drawdown limits for allocated pensions. We find that the new regulations are a substantial improvement on the previous rules for allocated pensions and, when compared with the four formula-based rules, are a good compromise in terms of simplicity, a dequacy and risk. We also find that welfare is lower for most individuals who follow the Simplified Superannuation compared with welfare under an optimal path or a simple fixed percentage drawdown rule, but that outcomes could be improved through a further simplification of the rules.

Choices and Constraints over Retirement Income Streams: Comparing Rules and Regulations

The new Simplified Superannuation regulations for Australian superannuation provide tax concessions to retirement income streams which comply with legislated minimum drawdown rules. We evaluate these new drawdown rules against four alternatives, including three formula-based ‘rules of thumb’ and the previous legislated minimum drawdown limits for allocated pensions. We find that the new regulations are a substantial improvement on the previous rules for allocated pensions and, when compared with the four formula-based rules, are a good compromise in terms of simplicity, adequacy and risk. We also find that welfare is lower for most individuals who follow the Simplified Superannuation compared with welfare under an optimal path or a simple fixed percentage drawdown rule, but that outcomes could be improved through a further simplification of the rules.

On Inefficiency of Markowitz-Style Investment Strategies When Drawdown is Important

The focal point of this paper is the issue of "drawdown" which arises in recursive betting scenarios and related applications in the stock market. Roughly speaking, drawdown is understood to mean drops in wealth over time from peaks to subsequent lows. Motivated by the fact that this issue is of paramount concern to conservative investors, we dispense with the classical variance as the risk metric and work with drawdown and mean return as the risk-reward pair. In this setting, the main results in this paper address the so-called "efficiency" of linear time-invariant (LTI) investment feedback strategies which correspond to Markowitz-style schemes in the finance literature. Our analysis begins with the following principle which is widely used in finance: Given two investment opportunities, if one of them has higher risk and lower return, it will be deemed to be inefficient or strictly dominated and generally rejected in the marketplace. In this framework, with risk-reward pair as described above, our main result is that classical Markowitz-style strategies are inefficient. To establish this, we use a new investment strategy which involves a time-varying linear feedback block K(k), called the drawdown modulator. Using this instead of the original LTI feedback block K in the Markowitz scheme, the desired domination is obtained. As a bonus, it is also seen that the modulator assures a worst-case level of drawdown protection with probability one.Comment: This paper has been published in Proceedings of 56th IEEE Conference on Decision and Control (CDC) 201

Probability distribution of drawdowns in risky investments

We study the risk criterion for investments based on the drawdown from the maximal value of the capital in the past. Depending on investor's risk attitude, thus his risk exposure, we find that the distribution of these drawdowns follows a general power law. In particular, if the risk exposure is Kelly-optimal, the exponent of this power law has the borderline value of 2, i.e. the average drawdown is just about to divergeComment: 5 pages, 4 figures (included

Maximum drawdown, recovery and momentum

We test predictability on asset price using stock selection rules based on maximum drawdown and consecutive recovery. Monthly momentum- and weekly contrarian-style portfolios ranked by the alternative selection criteria are implemented in various asset classes. Regardless of market, the alternative ranking rules are superior in forecasting asset prices and capturing cross-sectional return differentials. In a monthly period, alternative portfolios constructed by maximum drawdown measures dominate other momentum portfolios including the cumulative return-based momentum portfolios. Recovery-related stock selection criteria are the best ranking measures for predicting mean-reversion in a weekly scale. Prediction on future directions becomes more consistent, because the alternative portfolios are less riskier in various reward-risk measures such as Sharpe ratio, VaR, CVaR and maximum drawdown. In the Carhart four-factor analysis, higher factor-neutral intercepts for the alternative strategies are another evidence for the robust prediction by the alternative stock selection rules.Comment: 28 pages, 6 subfigures; minor revisio

Leptokurtic Portfolio Theory

The question of optimal portfolio is addressed. The conventional Markowitz portfolio optimisation is discussed and the shortcomings due to non-Gaussian security returns are outlined. A method is proposed to minimise the likelihood of extreme non-Gaussian drawdowns of the portfolio value. The theory is called Leptokurtic, because it minimises the effects from "fat tails" of returns. The leptokurtic portfolio theory provides an optimal portfolio for investors, who define their risk-aversion as unwillingness to experience sharp drawdowns in asset prices. Two types of risks in asset returns are defined: a fluctuation risk, that has Gaussian distribution, and a drawdown risk, that deals with distribution tails. These risks are quantitatively measured by defining the "noise kernel" -- an ellipsoidal cloud of points in the space of asset returns. The size of the ellipse is controlled with the threshold parameter: the larger the threshold parameter, the larger return are accepted for investors as normal fluctuations. The return vectors falling into the kernel are used for calculation of fluctuation risk. Analogously, the data points falling outside the kernel are used for the calculation of drawdown risks. As a result the portfolio optimisation problem becomes three-dimensional: in addition to the return, there are two types of risks involved. Optimal portfolio for drawdown-averse investors is the portfolio minimising variance outside the noise kernel. The theory has been tested with MSCI North America, Europe and Pacific total return stock indices.Comment: 10 pages, 2 figures, To be presented in NEXT-SigmaPh