Strategy #0000000149 · Hedging and risk management
Functionally generated and diversity-weighted portfolios
Enter three market caps, common return scenarios, diversity exponent and rebalance cost.
Stochastic portfolio theory constructs self-financing portfolios from generating functions of market weights. Diversity weighting applies a sublinear transform to cap weights, reducing the largest names. Theoretical relative arbitrage requires conditions such as market diversity, and practical results depend on costs and finite samples. This page compares a single set of weights and return scenarios only.
Omits continuous rebalancing, cumulative generation, financing constraints and theoretical conditions.
Three ways in
Understand the story. Then inspect the risk.
Start with a familiar situation, check the payoff, then test how the numbers change.
The idea · in two minutes
How does applying a sublinear power to cap weights perform on the same entered returns?
Stochastic portfolio theory constructs self-financing portfolios from generating functions of market weights. Diversity weighting applies a sublinear transform to cap weights, reducing the largest names. Theoretical relative arbitrage requires conditions such as market diversity, and practical results depend on costs and finite samples. This page compares a single set of weights and return scenarios only.
Enter three market caps, common return scenarios, diversity exponent and rebalance cost.
Omits continuous rebalancing, cumulative generation, financing constraints and theoretical conditions.
- Input assumptionsEnter three market caps, common return scenarios, diversity exponent and rebalance cost.
- Model outputOmits continuous rebalancing, cumulative generation, financing constraints and theoretical conditions.
Illustrative research examples only. They are not live signals or a recommendation.
The mechanics · payoff and exposure
w_i^{div}=m_i^\alpha/\sum_jm_j^\alpha,\quad 0<\alpha<1
m_i is market cap; a lower exponent makes weights more even. The output is not a proof of relative arbitrage.
Greeks: the directional intuition
- 模型
- Measures sensitivity to implied volatility.
- 合約
- Measures sensitivity to implied volatility.
- 執行
- Measures sensitivity to implied volatility.
w_i^{div}=m_i^\alpha/\sum_jm_j^\alpha,\quad 0<\alpha<1
Practical context · published observations
Functionally generated and diversity-weighted portfolios: read the record with its caveats.
The chart uses the published figures or explicitly labelled study inputs below. A historical index or model replay is not the same as an investor’s realised account return.
Omits continuous rebalancing, cumulative generation, financing constraints and theoretical conditions. Source ↗ · Methodology ↗
Change assumptions and inspect the scenario
Inputs illustrate the strategy mechanics; they are not live quotes, forecasts or investment advice.
Variants · same family, different risk levers
Models, contract terms and implementation can change results.
Compare relevant mechanisms and execution assumptions.
| Related strategy | Relationship | What changes | New cost or risk |
|---|---|---|---|
| Base scenario | Manual inputs | Stochastic portfolio theory constructs self-financing portfolios from generating functions of market weights. Diversity weighting applies a sublinear transform to cap weights, reducing the largest names. Theoretical relative arbitrage requires conditions such as market diversity, and practical results depend on costs and finite samples. This page compares a single set of weights and return scenarios only. | Omits continuous rebalancing, cumulative generation, financing constraints and theoretical conditions. |
| Conservative version | Higher cost/loss | Stress higher costs, larger losses or lower liquidity. | May lower scenario returns. |
| Validation version | Data review | Test model inputs with consistent contracts and timestamps. | Needs licensed, representative data. |
Omits continuous rebalancing, cumulative generation, financing constraints and theoretical conditions.
Read beyond the summary
References
Primary sources and research used to describe the strategy and its limits.