Risk Factor Exposures
Systematic and Non-Systematic Risk
Modern investment analysis categorizes the traditional sources of risk causing variability in returns into two general types: market risk, which is pervasive in nature and risks that are specific to a particular security.
Total risk = General risk + Specific risk
= Market risk + Issuer risk
= Systematic risk + Nonsystematic risk
= Diversifyable risk + Undiversifyable risk
By structuring the portfolio in a certain way (buzzword 'Markowitz'), an investor can eliminate the diversifiable part of total risk. What is left is the nondiversifiable portion or the market risk.
Different securities develop differently in terms of price movements and often also in terms of direction. The non-complete co-movement of securities causes the risk of a portfolio to differ from the sum of the individual risks: Security related specific risks will cancel one another out partially. Therefore, the risk of a portfolio is always smaller than the sum of the risks of its constituents. For risk measurement, this has the consequence that risk cannot be simply summed up.
Risk in the Single-Index or Factor Models
The single-index model...
r(p) - rf = a + b * {r(b) - rf} + e
r(p)... security returns, for securities
rf... riskfree rate
a... alpha
b... beta
r(b)... benchmark returns
e... noise
Taking variance of the single-index model...
var[r(p) - rf] = var[a + b * {r(b) - rf} + e]var[r(p)] = var[a] + var[b * {r(b) - rf}] + var[e]
var[r(p)] = {b^2}*var[r(b)] + var[e]
{b^2}*var[r(b)]... systematic risk
var[e]... un-systematic risk
The single-index case is generalized to more than one 'index in so-called 'factor models'. Disaggregating risk with the help of a factor model is called 'risk attribution'.
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