Assessing the Impact of Macroeconomic Surprises

The Scientific Portfolio risk model uses fundamental factors as the basis for analyzing asset returns; however, they do not tell the whole story as portfolios may also be impacted by macroeconomic events. Macroeconomic models make use of macroeconomic risk factors to gain a better understanding of how economic changes may impact returns. Unexpected, unforeseen changes in macroeconomic states are known as surprises. There is an abundance of academic literature that has analyzed the relationship between macroeconomic surprises and asset returns. The results of these studies indicate that unexpected changes to macroeconomic states can have a significant impact on asset returns. Additionally, Flannery et al. ^[1] and Amenc et al. ^[2] demonstrate that different stocks can have substantially different reactions to shifts in macroeconomic conditions. For instance, the utility sector typically outperforms in low-rate environments while the materials sector is traditionally perceived as an inflation hedge.

Surprises provide information about a portfolio's behavior in moments where the impact of macroeconomic risk is at its highest. Using our methodology to identify unexpected surprises, investors can assess a portfolio's average return, average risk and other standard statistics over different market regimes.

Below, we discuss the methodology behind identifying surprises in different macroeconomic states and analyzing the effects of macroeconomic shifts on a portfolio. By viewing risk through a macroeconomic lens, we can identify potential sources of macroeconomic risk and optimize portfolios to best withstand these macroeconomic surprises.

Methodology

In macroeconomic models, risk factors represent surprises in macroeconomic variables that can help to explain asset returns. By surprises, we mean unexpected changes in macroeconomic variables measured as the difference between the actual value of the factor and its predicted value. For instance, if inflation were expected to be 4% but the realized value is 3%, then the result is a surprise of 1%. Surprises can be defined as upward or downward.

• An upward surprise represents an event where the macro series increases. For example, an upward surprise for long-term interest rates corresponds to a date when the recorded change in the long-term rate is higher than predicted by the model.

• A downward surprise represents an event where the macro series decreases. For example, a downward surprise in volatility corresponds to an unexpected decrease in the broader market volatility as measured by VIX.

To identify these unexpected surprises, we use a methodology that is inspired by Petkova ^[3]. An autoregressive model is used to determine the current nominal level of a macroeconomic indicator based on its history. In this way, we can extract the unexpected component which represents the amount over or under the value expected from the model. Mathematically, the model is expressed as

where ​represents a state variable (short-term rate, long-term rate, default risk, term spread, inflation or volatility) and the residuals. The only variable that we are interested in is the residuals since they represent the unexpected shocks to a given macroeconomic regime. Within these shocks, the extreme values at the top and bottom ends of the range of residual values are extracted as surprises - that is, percent (where on the Scientific Portfolio platform) of the largest and smallest values of the model residuals are labeled as upward and downward surprises. To be considered an upward surprise, the residuals must be greater than the quantile of the full set of residuals. For downward surprises, the residuals ​ are less than the quantile of the full set of residuals. Accordingly, we extract the dates when positive and negative surprise arise as

In contrast to our approach, Petkova ^[3] specifies a vector autoregressive model over the demeaned state variables. Our analysis suggests a negligible difference between our and Petkova's methodology. As noted by Amenc et al. ^[2], identifying surprises on first-order differenced state variables produces identical results to those identified on the residuals of the regression.

Regime statistics

For a portfolio return series ​ and a list of identified surprise dates for each state variable, we assess the effects of macroeconomic shifts on the portfolio with a few key metrics. Conceptually, these metrics summarize the surprise conditional distribution of the portfolio returns. In the context of macroeconomic analysis, the time period, , is defined as the day when an analyzed macroeconomic state, , exhibits a surprise. In the following metrics, ​ represents the portfolio returns and​ is either a reference return or a risk-free rate. Each metric is computed for all macroeconomic states and for both upward and downward surprises.

Note that the conditional regime analyses are computed on a market-adjusted basis; that is, outputs are computed on residual returns unrelated to the market factor (i.e., conditional returns are zero for the CW benchmark).

A summary of each metric is provided below:

Conditional Return: The conditional return is the conditional average return of a portfolio over upward or downward surprise dates, defined as

Conditional Risk: The conditional risk is the conditional average volatility of a portfolio over upward or downward surprise dates, defined as

Conditional Sharpe Ratio: The conditional Sharpe Ratio is the Sharpe Ratio of a portfolio computed over upward or downward surprise dates, defined as

Conditional probability of outperformance: Conditional probability of outperformance (CPO) assesses the likelihood of positive performance over a reference or risk-free rate in a given macroeconomic state. CPO is therefore defined as

References

1 Mark J. Flannery and Aris A. Protopapadakis. (2002). Macroeconomic Factors Do Influence Aggregate Stock Returns. Review of Financial Studies. 15(3): 751-782. 10.1093/rfs/15.3.751.

2 Noël Amenc et al. (2019). Macroeconomic risks in equity factor investing. Journal of Portfolio Management. 45(6): 39-60. 10.3905/jpm.2019.1.092.

3 Ralitsa Petkova. (2006). Do the Fama-French factors proxy for innovations in predictive variables?. Journal of Finance. 61(2): 581-612. 10.1111/j.1540-6261.2006.00849.x.

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