Due to the growing complexity of measuring financial risk, “risk has become a patchwork” of different models, said Phil Jacob, Senior Director at Axioma Risk Research. He was the sole presenter in a webinar about tailoring the right risk model to your investment strategy held on March 4, 2015, and sponsored by the Global Association of Risk Professionals (GARP).
Jacob identified four inherent challenges. “There are operational issues stemming from existing rigid approaches,” leading to “difficulty in aggregating risk.” There is a lack of consistency in modeling portfolios, which can run the gamut from very simple proxies all the way to highly elaborate non-linear models. There is “limited ability to communicate about risk cross-functions.” Lastly, due to different modelling across asset classes, there is limited ability to consider cross-asset risks, or correlations between different types of risk.
“At the top level, management has long horizons, and the models tend to be internally created,” often in an ad hoc fashion, Jacob said. At the asset class level, the models tend to be more short-term—a granular model, for tactical decisions, as opposed to a strategic model requiring fewer factors.
Multi-factor models depend on identifying the factors driving price changes across asset classes, from either a macroeconomic approach (using inflation, output, etc. as factors) or fundamental approach (inferring security sensitivities as factors).
Axioma proposes “risk resolution,” a “generally applicable idea that relates changes in the risk factors with changes in pricing,” Jacob explained. Risk resolution “allows an investment firm to tailor the factors in a risk model to the sources of risk in a portfolio strategy,” even for multi-asset class portfolios.
The traditional factor-based approach, such as the three-factor Fama -French model, has future prices modeled through returns over risk horizons, and returns modeled through linear decompositions. In such a model, future prices are modeled through present value functions that take into account both the chosen return function and the linear decomposition through exposures.
The general framework of risk resolution contains projected pricing factors modeled through projected risk factors over risk horizons and mapping functions. These are conditioned on current pricing factors and current risk factors. Future prices are modeled through projected pricing factors over risk horizons and present value functions. These are conditioned on current prices and current pricing factors.
For stress testing, he asked: “do you want to stress the risk factor or the pricing factors?” Jacob showed two forms of stress testing, Dodd-Frank (tweaking macroeconomic factors, at 3 levels of severity) vs credit-hedged convertible bonds.
Jacob described applying risk resolution methodology to an equity option example, and then to two trading strategies (passive vs pair trading).
He touched on Canadian equities. Axioma’s Canadian risk model, AX-CA, uses custom industry classifications to improve the predictive power. The Canadian market, as represented by the TSX, shown in Figure 1, is predominantly “energy, materials, and financial services,” he said, and this is reflected in the chosen GICS industry factors—more than 10, but not as granular as using the full 68.
“With growing complexity in market risk,” said Jacob, “risk resolution helps to control the complexity.”ª
The patchwork image for this posting is from oliviajanehandcrafted.com.
Figure 1, the composition of the Canadian market (TSX), is from an Axioma report.