Effectiveness Verification of Multi-Manager and Multi-Strategy Investment

This is the verification of the fundamental basic model. In the framework of asset return models based on multivariate normal distribution, we statistically verify the risk reduction and Sharpe ratio improvement effects brought by multi-strategy (equal allocation of multiple assets). We quantitatively evaluate the statistical significance of these effects using two methods: the bootstrap method and Monte Carlo simulation.

Key Research Areas

Construction of Theoretical Foundation: Mathematical formulation of multi-strategy based on multivariate normal distribution models.
Statistical Verification Methods: Double verification using bootstrap methods and Monte Carlo simulations.
Evaluation of Effect Size: Quantification of practical significance using Cohen's d.

Theoretical Model

Basic Model

Asset return vector $\bm{R}_t$ follows a multivariate normal distribution:

$\bm{R}_t \sim \mathcal{N}(\bm{\mu}, \bm{\Sigma})$

Definition of Multi-Strategy

$R_{multi,t} = \frac{1}{n} \sum_{i=1}^{n} R_{i,t}$

Effect Indicators

Indicator	Definition	Meaning
Risk Reduction Effect	$\Delta\sigma = \bar{\sigma}_{single} - \sigma_{multi}$	Volatility reduction through diversification
Sharpe Ratio Improvement	$\Delta SR = SR_{multi} - \overline{SR}_{single}$	Improvement of risk-adjusted return

Empirical Analysis Results

Risk Reduction Effect

Method	Mean	t-value	p-value	Cohen's d	Probability of Positive Effect
Bootstrap	0.0106	1,175.3	< 0.000001	16.62	100%
Monte Carlo	0.0106	994.7	< 0.000001	14.07	100%

Sharpe Ratio Improvement Effect

Method	Mean	t-value	p-value	Cohen's d	Probability of Positive Effect
Bootstrap	0.296	101.2	< 0.000001	1.43	92.6%
Monte Carlo	0.295	100.2	< 0.000001	1.42	92.3%

Economic Implications

Economic Value of Risk Reduction

Monthly Volatility Reduction: 1.06%
Annualized Volatility Reduction: 3.66% ( $\times\sqrt{12}$ )
Certainty: Positive effect with 100% probability.

Meaning of Sharpe Ratio Improvement

Average Improvement: 0.29 – 0.30
Probability of Improvement: Over 92%
Effect Size: Cohen's d ≈ 1.4 (Very large effect)

Conclusion

Through this research, the statistical superiority of the multi-strategy investment approach has been confirmed mathematically and empirically. It is shown that the diversification inequality $\sigma_{portfolio} < \frac{1}{n}\sum_{i=1}^{n}\sigma_i$ holds with an extremely high probability, strengthening the empirical foundation of Modern Portfolio Theory.