Multi-Asset Simulation

This article presents the nuances of multi-asset simulation, including a Python case study using the Investment Simulation module.

Multi-asset market simulation using the Fully Flexible Resampling method from the Investment Analysis module.

My recent article presented how to define the core broad risk factors in a multi-asset macro model.

These core risk factor can be used for sophisticated views and stress-testing analysis, especially at the Chief Investment Officer (CIO) level.

While the main risk factors, real rate, inflation, and growth, are useful for views and stress testing, they are not necessarily the best ones to capture the market state, which is essential for simulation.

For example, the growth risk factor is typically not very persistent in its first moment, at least according to the definition in the multi-asset macro model.

Hence, some adjustments must be made to properly capture the more persistent state of the growth factor. This article presents a suggestion for how you can do that, including a Python case study that uses the Investment Simulation module.

The simulation framework

We use the investment simulation framework that is thoroughly described in Chapter 3 of the Portfolio Construction and Risk Management book.

In summary, we have raw historical data

\(D\in\mathbb{R}^{T\times N}.\)

We transform the raw data into something that is (approximately and locally) stationary

\(ST\in\mathbb{R}^{\tilde{T}\times\tilde{N}}.\)

We then project the stationary transformations H steps into to future, generating S joint paths

\(\tilde{ST}\in\mathbb{R}^{S\times\tilde{N}\times H}.\)

Finally, we transform the simulated stationary transformations back to the risk factors that we need for pricing and compute the P&L for our instruments and strategies

\(\tilde{R}\in\mathbb{R}^{S\times\tilde{I}\times H}.\)

This gives us joint paths for both risk factors and instrument P&L that we can use for sophisticated analysis using the next generation investment framework.

The details of this market simulation framework are more carefully described in the Portfolio Construction and Risk Management book, including several market simulation Python case studies.

Python case study using Fully Flexible Resampling

In this case study, we use four publicly available ETF time series, so you can replicate the analysis yourself.

Specifically, we use the tickers IVV (S&P 500), HYG (US high-yield), LQD (US investment-grade), and IEF (7-10y US government bonds).

These are the same ETFs as for the tactical asset allocation performance lower bound analysis.

We use the Fully Flexible Resampling method to simulate the joint paths that you can see in the cover image to this article.

Market simulation factors definition