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The conventional quadratic optimization methods are applicable only for convex single extreme objective functions typically incorporating the mean-variance framework (the standard deviation) to measure risks. Since the mean-variance methodology is hardly appropriate for hedge funds due to their non-normality, other, more advanced measures of risks should be used. However, using the more advanced risk metrics (a classic VaR or Omega, for example) may result in non-convex objective functions, which, in turn, leads to multi-extreme optimization.

Employing alternative metrics like CVaR, LPM or MVaR does not require multi-extreme optimization, however, inherits all the pitfalls and drawbacks of these metrics (see the Quant knowledge base for more information). Nevertheless, these metrics can provide a better approximation yet offering faster optimization routines.

Portfolio optimization itself, even if a right methodology applied, could be difficult or impossible to implement in practice due to liquidity restrictions or imposed strategy concentration limits. Therefore, a more sensible approach implies finding an acceptable risk/return extreme within the given range, while taking into account a broad set of constraints.

Despite the Quant Optimum framework incorporates one of the most powerful genetic optimization routines capable of optimizing multi-extreme objective functions with virtually unlimited constraints, we strongly recommend analyzing the generated portfolio allocations thoroughly by applying additional techniques, ex. factor analysis or style analysis. Often, the best results are obtained by combining purely machine-generated baskets with a heuristic approach.

Instead of chasing tails and trying to construct a truly optimal portfolio, we recommend constructing *quasi-optimal *portfolios with risk-return profiles in close proximity to Efficient Frontiers. This way we may also include instruments based on other considerations rather than an optimization output only.

- VaR derivatives: VaR, CVaR, MVaR
- Lower Partial Moments
- Omega
- Semi-deviation
- Standard deviation
- Maximum drawdown
- Correlation to a factor
- Trend variance

- Min and max allocations
- Liquidity
- Strategy allocation
- Factor correlation

- Optimizing portfolio risk/return profile
- Constructing market-neutral portfolios
- Applying custom constraints and risk metrics for portfolio construction
- Enhancing returns (minimizing risks) for a given portfolio
- Eliminating excessive risk assets
- Analyzing a real efficient frontier with VaR-based metrics

- Genetic optimizatrion routine for VaR-based risk metrics
- Quadratic optimization for non-convex functions (MVaR and CVaR)
- Various types of optimization: VaR, CVaR, Omega, LPM, Semi-deviation, MVaR, volatility, local correlation, max drawdown
- Interactive efficient frontier charts
- Background optimization option
- Seamlessly integrates stochastic simulation providing a distribution of return function as an output

- Linear and Quadratic programming
- Non-linear GRG
- Genetic Global optimization
- OptQuest (optional)
- KNITRO(optional)
- Variables: 32,000
- Constraints: 32,000

- Minimization of VaR with the mean return within the given range
- Maximizzation of the mean return with VaR within the given range
- Minimization of local correlation with the VaR and the mean return within the given range
- Maximization of the mean return with the VaR and local correlation within the given range
- Minimization of the CVaR with the mean return within the given range
- Maximization of the correlation to a benchmark (trend following portfolio) with VaR within the given range

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The optimal number of funds in a multi-manager portfolio should be in the range of 11-20. Increasing the number of funds over the above limit brings no significant risk enhancement or performance improving.

Increasing a number of funds leads to excessive negative skewness and kurtosis for the Event Driven and Fixed Income Arbitrage funds. Thus, diversification across these categories may create problems rather than mitigating risks. Increasing a number of funds over 10 results in an excessive intercorrelation across the portfolio.

Portfolios of over 20 funds exhibit a high correlation with hedge fund indices (over 0.9). In that respect, it makes sense to invest into indices rather than choosing 20+ fund portfolios.

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- Fund managers may use multiple strategies, which makes it difficult to categorize
- The whole TAA framework relies on the style-weighted allocation (read index-weighted allocation) that predetermines allocation across individual funds. Since the majority of hedge funds are not correlated with their corresponding indices, the applicability of the TAA becomes questionable.

The TAA framework should not be applied for constructing portfolios of hedge funds (hedge fund of funds) .

**Tactical Asset Allocation**: why it is inapplicable to hedge funds. Major problems and drawbacks of TAA for hedge funds. Analysis of correlations between individual funds and their indices. Outlining Quant Suite alternative solutions. Duration 10:15 min.

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