Defining Risk

What is risk? Total Risk and Factor, Specific Risk Decomposition Explained

Written by Edgar Nuñez
Updated over a week ago

# What is Risk?

There are many definitions of risk, but in Omega Point we implicitly refer to risk as 'predicted market risk' - i.e. the predicted volatility of equity assets traded in public markets. At a high level, predicted risk is simply the predicted standard deviation of forward looking returns.

Risk can be decomposed into two high level categories: Systematic/Factor and Idiosyncratic/Alpha. The Systematic/Factor risk can be further broken down into Categories (Style, Industry, Country), and both Systematic/Factor and Idiosyncratic/Alpha can be decomposed down to the asset level.

Risk is quantified using a factor model and relies on:

• Asset level exposures - what is the characteristic of my asset?

• Factor covariance matrix - how risky are the factors I'm exposed to and how do they correlate with other factors?

• Idiosyncratic covariance matrix - how much risk is coming from a name that is not explained by factors?

# Security Risk

A security's risk comes in different flavors: total risk (standard deviation), and risk decomposition (factor & specific variance). The total risk is the predicted standard deviation of returns, and the risk decomposition is in terms of % of total risk. All risk decompositions use a 'covariance distributed' approach to calculating risk: all factors "share" the component of risk derived from factor correlations.

These values are retrievable from the security risk node from the Omega Point API (which drives all the data displayed within the web application):

`# The security's risk values as Std Dev & Variance Decompositiontype SecurityRisk {  # The security's predicted risk (std dev)  standardDeviation: {    # The security's total predicted risk    total: Float  }  # The risk decomposition of the security, as a % of total risk  varianceDecomposition:{    # The aggregate decompositions of the security's risk    summary:{      # The % of the security's risk attributed to specific risk (as       a variance decomposition to total risk)      specific: Float            # The % of the security's risk attributed to factor risk (as a       variance decomposition to total risk)      factors: Float    }  }}`

The total risk value itself comes directly from the underlying risk model, though the definition of total risk across models remains consistent, and can be thought of in the following terms:

`factor variance = X * F * X.Twhere X are the exposures, X.T is the transposeF is the factor covariance matrixspecific variance = W * S * W.TwhereW = security weightsS = security covarianceW.T  = weight transposetotal variance = factor variance + specific variancetotal risk = sqrt(total variance)`

# Portfolio Risk

Portfolio risk is calculated using the portfolio weights, the factor exposures, the factor covariance matrix, and the specific risk matrix. This number is displayed as a portfolio's total risk in terms of predicted portfolio volatility of returns.

All risk decompositions use a 'covariance distributed' approach to calculating risk: all factors "share" the component of risk derived from factor correlations. We can back out the factor and specific decomposition in terms of standard deviation of (total) risk, as follows:

`variance = (standard std risk)^2variance(total)= variance(factor) + variance(specific)variance(total)= (%variance factor) * variance(total) + (%variance specific) * variance(total)(std risk total)^2 = (std factor risk)^2 + (std idio risk)^2= (%variance factor) * variance(total) + (%variance specific) * variance(total)(std factor risk)^2= (% variance factor) * variance(total)`
`Note that % variance should always be positive for all factors and the idiosyncratic component and will sum to 100%. % variance for an individual factor can be negative due to the 'covariance distributed' approach - in this case the factor in question would be diversifying to risk.`