Portfolio Rules

introduction currently, mantarisk offers the following portfolio construction models (rules) equal weight / constant weights maximum average true range (atr) maximum volatility risk parity maximum sharpe diversified minimum risk minimum conditional value at risk maximum diversification tracking error minimization a quantitative comparison between these rules can be found in https //docs mantarisk com/comparison between optimization strategies the optimizer supports not only the linear instruments but also the derivatives especially the cvar optimizer can cope with any nonlinear pay off, resulting in senseful results let us look in more details at the above rules and their corresponding dispersion relations and optimization strategies shared parameters all portfolio rules share a common set of parameters designed to control the portfolio rebalancing algorithm parameters include stop/limit if true, the tactical risk management engine will also manage the stops and limits of each proposed orders, provided that the risk management rules contain stop or limit rules permissible values are true or false default is false size rebalance trigger rebalancing a portfolio every day is inefficient due to transaction costs thus the rebalancing algorithm aim to keep the proportion of each of the portfolio's components within a specific tolerance of its ideal value the rebalancing is triggered when the open size of a component is x% different to its target size a value of 10 equates to 10% default is 5% rules overview equal weight the equal weight portfolio rule gives equal weights to each instrument, no matter its market capitalization or asset class the details can be found in docid\ dbz5yqmcwfkkxdd7kulrc atr the constituent weights are proportional to their average true range (atr), meaning that an instrument with a higher atr will also have a higher weight in the portfolio the main difference between atr and volatility is that atr considers the true prive range (daily highs / lows) whereas volatility operates based on closing prices see docid\ xk j 8xrkpttquqibniod for further details volatility the constituent weights are proportional to their volatility, meaning that an instrument with a higher volatility will also have a higher weight in the portfolio the main difference between atr and volatility is that atr considers the true prive range (daily highs / lows) whereas volatility operates based on closing prices see docid\ xk j 8xrkpttquqibniod for further details risk parity risk parity optimization is an investment strategy that aims to achieve a higher sharpe ratio by allocating assets based on their risk contributions rather than their expected returns this means that assets with higher volatilities will receive larger allocations than assets with lower volatilities this can help to reduce the overall risk of the portfolio while still maintaining the potential for high returns see docid\ xk j 8xrkpttquqibniod for further details sharpe maximization the portfolio which maximizes the sharpe ratio is the portfolio with the highest expected excess rate of return (above the risk free rate) per unit of risk, making it the solution preferred by many investors the implementation in mantarisk is explained in docid\ h8awfv50cqxrlks6qirdy where the dispersion relation corresponds to the mixture cvar and the optimization strategy to the maximization of sharpe ratio diversified minimum risk this strategy combines the minimization of risk while maximizing the diversification ratio and is thus a compromise between a diversified portfolio (aka assets which a decoupled from each other from a volatility perspective) and a portfolio which minimizes risk minimum conditional value at risk conditional value at risk (cvar) optimization is a risk management technique used to minimize the potential for large losses in a portfolio of investments the optimized portfolio will be the minimum risk portfolio on the efficient frontier (the left most portfolio) the exact implementation in mantarisk is based on mixture cvar with the optimization strategy "minimization of risk" (see docid\ h8awfv50cqxrlks6qirdy for further details) maximum diversification portfolio the maximum diversification portfolio (mdp) is an investment strategy that aims to maximize the diversification of a portfolio by selecting assets with low correlations this approach is based on the idea that a portfolio with uncorrelated assets will have lower overall risk than a portfolio with correlated assets the implementation in mantarisk is explained in docid\ h8awfv50cqxrlks6qirdy where the dispersion relation corresponds to the mixture cvar and the optimization strategy to the maximum diversification portfolio tracking error minimization tracking error minimization is a strategy aimed at reducing the deviation of a portfolio's returns from the returns of a benchmark index it is particularly relevant for investors and portfolio managers who want to replicate the performance of a benchmark while exercising limited active management see docid\ oszs4oibv6yme5deqtil0 for more details