Firm characteristics, consumption risk, and firm-level risk exposures

Robert F. Dittmar, Christian T. Lundblad. "Firm characteristics, consumption risk, and firm-level risk exposures." Journal of Financial Economics 125 (2017): 326-343.

Using a consumption-based asset pricing model, the authors measure the relation between exposures to consumption risk and portfolio-level characteristics. This model is then used to calculate risk exposures at the firm level.

Consumption Risk Premia in Average Returns

The authors choose the following model to represent an asset's price as determined by it's conditional covariance with respect to an inter-temporal marginal rate of substitution,

To estimate risk exposures and cross sectional risk premium, the authors regress returns on anomaly portfolios that are sorted on six firm characteristics: asset growth, book to market ratio, market capital, past 12 month returns, stock issues, and total accruals. This is done for different windows, K, where R is the portfolio return and Eta is the innovation (the difference in log consumption growth in quarter t minus j and its unconditional mean).

Consumption is measured as per capita real personal consumption expenditures on non-durable goods and services.

Risk exposures for a window of K=4 (this window produces risk exposures with the best cross sectional fit) show the following results,

The results suggest a positive relation between average returns and consumption risk exposures. Equities are positively exposed to consumption risk, and this suggests a positive premium for consumption risk.

The authors continue to investigate whether risk exposures are related to average returns. This is done in a two-step process:

1) Returns are regressed on sources of risk

2) Average returns are then regressed on the resulting risk exposure estimates

They use the following cross sectional regression with previous risk exposure estimates,

Following are results of the cross sectional regression,

The best results are found with K=4 windows. This can also be seen graphically with average returns over predicted returns,

Using Characteristics to Estimate Risk Exposures

The authors assume that the relation between an asset’s consumption risk exposure and a set of relevant characteristics can be captured by projecting the risk exposure onto a set of characteristics,

They hypothesize the reason portfolio characteristics are related to average returns is through the link between the characteristics and their exposure to risk in the stochastic discount factor. It is assumed that a linear relation exists between risk exposures and characteristics,

The following are results of the relation between portfolio betas and characteristics,

The authors hypothesize the relation that holds at the portfolio level also holds at the firm level. The relation between firm level exposures and portfolio level exposures and characteristics is given by,

They use firm level characteristics to form portfolios that are characterized by differences in ex-ante consumption risk exposure. For each month, t, they calculate a consumption growth innovation exposure for every firm using the panel regression coefficients (deltas) and firm characteristics at time t. They rank firms into quintiles by the exposure and form equal-weighted and value-weighted portfolios

The authors propose three questions:

1) Does sorting firms into portfolios by ex-ante predicted betas produce a positive risk premium?

2) Do resulting portfolios exhibit ex-post risk exposures that are consistent with the ex-ante ranking?

3) Can the time series variation in the ex-ante risk exposure of these portfolios be characterized in an economically meaningful way?

Following are results for mean returns, ex ante beta, ex post beta for 5 value weighted and equally weighted portfolios,

The model replicates increasing expected returns and ex post risk exposures in value weighted portfolios. These results indicate that with equally weighted portfolios, the ex-ante procedure produces consistent ex post beta rankings.

The authors were also interested in using their model for standard market betas, however, results are less than ideal. It is suggested that this is due to a weak relationship between market betas and firm characteristics.

Industry Costs of Capital

The authors investigate cost of capital for firms grouped by primary industry classification.

They create 24 Industry portfolios based on S&P GICS industry groups. Ex-ante risk exposure are found for each firm using the portfolio-level coefficients from the 55 portfolios sorted by characteristics. Equal-weighted portfolios are formed by industry groups and ex-ante betas are examined. Average industry betas are reported with the results of Fama-Macbeth regressions of industry portfolios at times t on portfolio betas.

The following are mean returns, betas, and standard deviations of betas for industry portfolios,

Firm Costs of Capital

To examine implied firm-level costs of capital, the authors run Fama-Macbeth firm-level regressions. They compute consumption beta exposures, then compute risk exposures for the five risk factors (Fama, French 2014) using rolling regressions of the past 60 months with respect to when return was measured. Month-by-month Fama-Macbeth regressions are then run.

Following are resulting average prices of risk and their respective t-statistics,

From the results, substantial variation in risk premia occur over time and differs significantly across different firms. The point estimates of the periodic regression coefficients are more stable for the consumption beta than the return factor betas. The authors suggest this is likely due to the difficulty in estimating risk exposures at the firm-level.