In order to effectively construct and evaluate portfolios, one must first establish future estimates of an asset classes performance through the lenses of both risk and return.
Exponential risk is calculated using the exponentially weighted moving average. Exponential risk has two main benefits over historical risk:
- Recent time series observations carry greater importance relative to observations in the past. This allows exponentially weighted risk estimates (covariance) to react faster to recent shocks in markets.
- 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.
Quiet and Turbulent Risk Periods
Quiet risk periods are statistically predictable asset movements within a certain date range.
Turbulent risk periods are statistically unusual asset movements within a specific date range, identified by calculating the multivariate vector distance. Turbulent periods are typically marked by large asset movements (volatility) and/or unusual correlation.
Correlation measures the degree and direction of the co-movement between two assets. A positive correlation indicates that the two assets tend to move in a similar direction, while a negative correlation indicates that they tend two move in opposite directions. A correlation of zero indicates that the returns of two assets are uncorrelated.
Capital Asset Pricing Model (CAPM)
The Capital Asset Pricing Model is a theory of market equilibrium which partitions risk into two sources: systematic risk and unsystematic risk. An asset’s systematic risk is equal to its beta squared multiplied by the market portfolio’s variance. The CAPM implies that investors should incur only systematic risk because they are not compensated for bearing unsystematic risk.
Beta is a measure of an asset or portfolio’s relative volatility with a reference portfolio. Within the context of the CAPM, when squared and multiplied by the market’s variance, beta represents and asset or portfolio’s systemic risk.
The Black-Litterman model is a mathematical model for portfolio allocation that combines the theories of modern portfolio theory, the CAPM, and mean-variance optimization. The Black-Litterman model is a method for calculating optimal portfolio weights based on the given inputs.