Taxonomy of Risk

Investment decisions are intertemporal choices that trade off present and future consumption. Because the future can only be anticipated, then these choices must rest upon some expectation of uncertain future payoffs. If we admit the possibility that future payoffs are state-dependent (for example, the asset pays a dollar on a rainy day and zero otherwise), then we allow, in principle, the possibility that an uncertain future can be modeled as a set of contingent claims whose payoffs (receiving a dollar) depend on whether certain future conditions are met (a rainy day) with respect to a set of related factors (humidity, barometric pressure). This suggests that there is a distinction, a la Frank Knight, between uncertainty and risk with risk as a refined state of uncertainty in the sense that although future outcomes may not be known, their probabilities are.

Knight didn't mean that the difference between risk and uncertainty was an arbitrary set of probabilities. Markets, after all, are not card decks whose outcomes, though uncertain, can be modeled with a well-defined probability distribution and whose risks are perfectly known. Instead, market models will necessarily contain model risk in varying degrees, depending on our inability to model the problem's structure precisely. Attempts to model risk in market environments must therefore incorporate an awareness of this additional source of risk. Value at Risk (VaR), for example, is a flawed model, and to the extent that return distributions are non-normal with time dependent correlations, the advice from static risk models will often prove inadequate. Models that incorporate alternative distributional assumptions and more dynamic correlation structures can help minimize predictive errors but, ideally, model risk is best mitigated by using a broad array of risk models, which, while not necessarily independent of each other, bring different perspectives of risk to the end user.

Risk managers use a broad range of models. Several models are often tasked to the same problem (for example, competing volatility models) while simultaneously, other models address the cross-section of risks (for example, credit, counterparty) in an attempt to create a network of mutually supportive diagnostic tools that provide management a more complete picture of plan-level risks.

For pension funds, there are four readily agreed-upon sources of liability risk—solvency, longevity, inflation, and interest rate risk. The last two are applicable to the asset side of the balance sheet as well. Pension plan asset liability modeling (ALM) analyzes, for example, funded status under stress environments with variable discount rates, inflation scenarios, and mortality assumptions, as well as volatility regimes.

On the asset side of the balance sheet, we need to address three broad risk classes: market risk, counterparty risk, and model risk. We must also recognize the challenges posed by operational risk, and endogenous risk. Market risk is extensive, incorporating macro risks, including inflation and interest rates, exogenous shocks such as spiking oil prices, return volatilities at various frequencies, correlations, and various dynamics. In an efficient market, risks would be reflected in the time series of returns. Hence, the volatility of returns would be a primary risk signal. Virtually all portfolio managers examine returns volatility, usually in discrete historical examples. Attempts to uncover evolving volatility usually entail using some type of simple moving average of returns. RiskMetrics, for example, uses an exponentially weighted moving average of returns to estimate volatilities and applies this basic methodology to various returns frequencies. More efficient models of returns volatility include GARCH methods, which are optimally weighted exponential weightings that describe volatility regimes (high and low periods of volatility). Generalized autoregressive conditional heteroscedasticity (GARCH) and ARCH models are developed in most time series texts. Extensions to multivariate GARCH models help uncover dynamic correlations in returns across assets. GARCH methods provide a window onto volatility regimes at the asset level as well as correlation spikes across assets, strategies, managers, and programs. These are powerful tools that support the risk manager's objective in capturing changes in absolute and relative risks as the market incorporates new information into observed returns.