Strategy #0000000044 · Asset allocation and portfolio risk
Cross-asset diversification
Calculate portfolio risk from weights, volatilities and correlation; low correlation is not a guaranteed hedge.
A two-asset portfolio return is weighted; variance also includes a correlation term. With correlation below one, portfolio volatility may be below the weighted standalone volatility. Risk depends on weights and estimated volatility/correlation. A low-correlation asset is not automatically a crisis hedge.
Diversification comes from co-movement; correlations shift in stress and do not prevent all losses.
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 do portfolio variance and scenario return change when an asset with different volatility and correlation is added?
Jack holds asset A with 18% volatility and considers adding asset B at 12%. Rose looks beyond B’s standalone risk and uses correlation to calculate portfolio volatility.
Even if B has a lower assumed return, low correlation may reduce portfolio volatility; it does not guarantee higher expected return. Costs, rebalancing and correlation instability matter.
Assets can fall together and correlations may rise in a crisis. Historical average correlation is not fixed; stress scenarios, rolling windows and out-of-sample data matter.
- Weighted standalone volatilityEnter two-asset weights, volatility, correlation and assumed return; normalise weights and compare portfolio with weighted standalone volatility.
- Portfolio vol at 0.20 assumed correlationStatic two-asset variance and one-period return only; excludes estimation error, rebalancing, tail dependence and observed data.
- Weighted assumed return less costsIllustrative expiry outcome.
Illustrative research examples only. They are not live signals or a recommendation.
The mechanics · payoff and exposure
\sigma_p^2=w_A^2\sigma_A^2+w_B^2\sigma_B^2+2w_Aw_B\rho_{AB}\sigma_A\sigma_B,\quad w_A+w_B=1
w are normalised weights; σ are asset volatilities and ρAB is return correlation over a matching horizon. Scenario return is calculated separately as a weighted return.
Greeks: the directional intuition
- 相關性漂移
- Measures sensitivity to implied volatility.
- 權重
- Measures sensitivity to implied volatility.
- 估計
- Measures sensitivity to implied volatility.
\sigma_p^2=w_A^2\sigma_A^2+w_B^2\sigma_B^2+2w_Aw_B\rho_{AB}\sigma_A\sigma_B,\quad w_A+w_B=1
Practical context · published observations
Cross-asset diversification: 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.
只算兩資產靜態方差和單期報酬；不含估計誤差、再平衡、尾部依賴或真實資料。 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
Related methods change their signal or exposure.
Each entry states the mechanism and trade-off.
| Related strategy | Relationship | What changes | New cost or risk |
|---|---|---|---|
| Strategic diversification | Long-horizon allocation | Sets cross-asset weights from long-term risk and return. | Historical relationships can fail in new regimes. |
| Risk parity | Risk contribution | Balances risk contribution across assets. | Leverage in low-vol assets and estimation risk. |
| Tail-hedge overlay | Crisis protection | Uses options or trends to hedge tail states. | Premium, carry and hedge-timing costs. |
Static two-asset variance and one-period return only; excludes estimation error, rebalancing, tail dependence and observed data.
Read beyond the summary
References
Primary sources and research used to describe the strategy and its limits.