Windham Portfolio Advisor
  • Windham Portfolio Advisor Support
  • Installation
    • Installing the Windham Portfolio Advisor
    • Installation Prerequisites
    • Installation FAQ
      • License Key Management
  • Time Series
  • Managing Custom Time Series
  • Custom Time Series Excel Add-in
  • Custom Time Series Utility
  • Updating the Windham Time Series Database
  • Mixing Data Periodicities within a Case File
  • Hedged and Unhedged Time Series
  • Overlays
  • Expected Risk
    • Annualizing Volatility and Return
    • Correlation
    • Covariance
    • Exponential Risk
    • Quiet and Turbulent Risk
    • Series Filter
    • Views (Risk and Correlation)
  • Expected Returns
    • Historical Returns
    • Equilibrium Returns
    • Implied Returns
    • Black-Litterman
    • Blend
    • Estimating Future Value: Arithmetic or Geometric
  • Optimization
    • Multi-goal Optimization
    • Transaction Costs and Turnover Controls
    • Risk Aversion
    • Full-Scale Optimization
  • Simulation
    • Simulation Methods
  • Exposure to Loss
    • Value at Risk
    • Probability of Loss
  • Risk Budgets
    • Risk Budgets
    • Value at Risk Sensitivities
  • Factor Analysis
    • Windham Factors
    • Factor Analysis
  • Cash Flow Analysis
    • Cash Flow Rules
    • Distribution of Wealth
    • Target Wealth Probability
  • Miscellaneous
    • Effective Tax Rates
    • Shadow Assets, Shadow Liabilities, and Illiquidity
    • Asset-liability Optimization
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  • Decay Factor
  • Half-life
  1. Expected Risk

Exponential Risk

Exponentially Weighted Moving Average (EWMA)

Exponential risk is calculated using the exponentially weighted moving average (EWMA). Exponential risk has two main benefits over the equally weighted risk model (Historical Risk)

  1. Recent time series observations carry a higher weight (importance) relative to observations in the past. This allows exponentially weighted risk estimates (covariance) to react faster to recent shocks in markets.

  2. Risk estimates in this model have a shorter memory following a shock. The risk estimates decline smoothly and rapidly as the significance of shock observations decreases through time. In contrast, shocks observed by the equally weighted historical risk model will increase risk estimates for the full observation period and will cause an abrupt shift when they fall out of the observation window.

Decay Factor

The decay-factor, λ\lambdaλ , is a parameter that controls how quickly the significance of older observations is reduced. The nthn^{th}nth observation is weighted by λn\lambda^nλn. The decay factor ranges from 0 to 1, where 1 will equivalent to the same weighting as the equally weighted model (historical risk).

Half-life

The half-life describes the time it takes for the weight on time series observations to fall to one-half of the weight assigned to the most recent observation. Half-life is a function of the decay-factor and can be solved by

half-life=log(12)log(λ)\text{half-life}=\frac{log(\frac{1}{2})}{log(\lambda)}half-life=log(λ)log(21​)​

For example, to calculate the half-life of the standard deviation of monthly returns with a decay-factor of 0.97, we calculate the log of 1/2 divided by the log of 0.97. The half-life for this example is 22.76 months.

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Last updated 4 years ago