What is the relation between asset risk and leverage?
We discuss how financial risk and asset risk are co-determined, and how this is reflected in the beta of assets and in the beta of equity
Asset risk refers to the volatility of operating profits. It is a measure of the riskiness of the underlying assets of a business. This risk stems from the uncertain nature of revenues and costs.
Asset risk is largely influenced by the nature of the investments that a firm makes, and it varies across industries and technologies. It can be separated into two components, a systematic and an idiosyncratic component. The systematic component of asset risk is correlated with the state of the economy (or more precisely with that mysterious object known as the stochastic discount factor), it is priced in the cost of capital, and it cannot be diversified. The idiosyncratic component of asset risk is specific to each given firm, and can be diversified by investors by holding a large enough portfolio of stocks.
Asset risk can be separated into a systematic and an idiosyncratic component.
In this article, we ask the following question: what is the relation between leverage and asset risk? This question is of great interest because it goes straight to the heart of the sources of equity risk. Is equity risk driven by asset risk or by leverage? Put it another way: are equity returns driven by asset returns or by leverage? Well, the short answer is… by both.
The problem at hand is a complex one, because investing and financing are jointly determined. We should resist the temptation of taking a unilateral view on the issue, asking questions like: are firms with high leverage investing in low risk assets? The question can be equivalently put as: are firms with low risk assets using more leverage. There is no chicken and egg. Investing and leverage are codetermined.
The problem at hand is complex, because investing and financing are jointly determined.
Before we get going, let's first address an issue, which, perhaps, many readers have already thought about: that of asset betas. It is tempting to think about asset risk in terms of asset betas in the context of the capital asset pricing model (CAPM). Indeed, that is traditionally how finance has approached the subject. One would start from a leveraged equity beta, delever it, possibly accounting for taxes, and obtain an unlevered beta, which would be interpreted as the beta of assets. That is not wrong, if one believes in the CAPM as the reference asset pricing framework. But who does nowadays...? The concept of asset betas can survive the death of the CAPM, but it requires thinking about it in the context of a multifactor model.
Why firms with riskier assets should rely less on leverage financing
Conceptually, the volatility of operating profits and leverage are two substitute sources of risk, firms with high volatility should rely less on debt financing, while firms with low volatility should use more debt.
Let’s give some more structure to this idea. The trade-off theory of capital structure states that there are benefits and costs associated with the use of debt finance. More precisely, debt finance has the advantage that interest expenses are tax deductible and give rise to a tax shield. However, debt finance has the disadvantage that it can lead to bankruptcy. The risk of facing a value destructing bankruptcy lowers the value of the firm. In a formula, the value of a leveraged firm can be written as:
The question that we focus on is, what does the probability of bankruptcy depend on? In essence, it depends on two components: asset risk and leverage. For any given level of debt, the higher the volatility of the operating cash flows, the higher the probability of bankruptcy. For any given level of asset risk, the higher the interest expenses, the higher the probability of bankruptcy. We can think of the two sources of risk as substitutes.
The probability of bankruptcy depends on asset risk and leverage
It then follows that a firm with highly volatile operating profits should leverage up less. This is if you take the perspective that asset risk is given and leverage is chosen. Alternatively, you could say that a firm with high leverage should invest in less volatile assets. This is if you take the perspective that leverage is given and asset risk is chosen.
Is this what we observe in the data?
Taking the above prediction to the data, the first problem that we encounter is that asset risk is not directly observable, in general… Of course, in the special case of unlevered firms, asset risk is observable. But that does not help us address our question.
How do we measure asset risk? We need to rely on proxies. Here are some proxies that are commonly used in empirical work:
Firm Size: larger firms have lower asset risk because of a more consolidated business, lower financial constraints, better governance, etc...
Market-to-book: firms with high market-to-book ratios have more growth options than assets in place. Because growth options are generally regarded as riskier than assets in place, market-to-book proxies for asset risk
Delevered Equity Volatility: By deleveraging the volatility of equity returns observed in the market, we obtain a measure of the volatility of the assets.
Tangibility: In case of bankruptcy, tangible assets tend to be worth more than intangibles. This means that, all else equal, firms with tangible assets are charged a lower interest rate on debt. Thus, higher tangibility of assets implies lower risk.
Profitability: Greater ability to pay interests on debt, so lower risk.
R&D expenses: Higher risk because more growth options
It is unclear whether it is correct to include tangibility and profitability in the list of measures of asset risk. Neither of them is a measure of the absolute riskiness of the assets. Both variables capture the ability of the firm to pay interests. In this sense, they may proxy more for financing risk than for asset risk.
Let us now move to the evidence in the data. Table 1 reports a series of regressions of market leverage on a number of firm characteristics, which include the proxies of asset risk that I have listed above. The table shows that size and tangibility are positively related to leverage, while profitability, market-to-book, R&D expenses and profitability are negatively related to leverage.
Table 2 reports a similar set of regressions as those of Table 1, with the addition of a market-based measure of the volatility of asset returns. This volatility is computed by deleveraging the volatility of equity returns. The table shows that the volatility of asset returns is negatively related to leverage.
The evidence so far shows that all but one of the proxies of asset risk relate to leverage as predicted by the trade-off theory of capital structure. The only variable that goes against the prediction is profitability.
How do we explain the negative sign of profitability? Surely, if a firm is more profitable it should carry more debt. The sign of profitability has been at the center of a long debate among academics. For a long time, the negative sign of profitability has been used as the central argument against the validity of the trade-off theory of capital structure. Opponents of this theory suggested that the negative sign of profitability should be seen as a key finding in support of the pecking order theory of capital structure.
More recently, these conclusions have been revised. Strebulaev (2007) offers a compelling argument (and evidence) for why we may observe a negative sign of profitability in the data. The argument goes as follows: more profitable firms can raise more debt, because they can pay more interests. Additionally, they benefit more from the tax shield. This suggests a positive relation between profitability and leverage for firms that refinance. However, mechanically, an increase in profitability lowers leverage by increasing future profitability and thus the value of the firm. Similarly, a decrease in profitability increases leverage. This results in a negative relation between profitability and leverage for firms that do not refinance.
Because there are costs of adjusting the capital structure, firms adjust their capital structure infrequently. Thus, at any one moment, most firms are not refinancing. Because the subset of firms that do not refinance dominates in terms of number of observations, in the data the cross-sectional relation between profitability and leverage is negative. However, if one restricts the analysis only to the firms that refinance, the relation between profitability and leverage is positive. Mystery solved! The trade-off theory lives to see another day.
Conclusions
All in all, we conclude that the evidence offered in the data indicates that leverage and asset risk are negatively related. Let’s be clear. There is no smoking gun in support of this conclusion! Because asset risk is not directly observable, we need to rely on proxies, and our results are robust only insofar as these proxies are reliable.
the data show that leverage and asset risk are negatively related
Let’s take our results a bit further. What are the implications for equity returns? The formula below shows that the return on equity depends on leverage, on the return on assets and on the return on debt.
In their famous Proposition 2, Modigliani and Miller argue that equity returns are linearly related to the debt to equity ratio. This is true if the return on assets and the return on debt stay constant when the debt to equity ratio changes.
However, the discussion and the evidence provided in this article indicate that this assumption clearly does not hold in the data. The risk (and therefore the return) of the assets decreases with leverage.
This implies that when leverage increases, the return on equity is pulled up by the debt to equity ratio, and it is pulled down by the return on assets. These two opposing forces could potentially lead to a negative relation between equity returns and leverage.
In practice, we know that at least for market leverage the relation between returns and leverage is positive. This indicates that (disregarding other possible forces at work) the “leverage effect” dominates over the “asset effect”.
Essential Bibliography
Fama, E.F. and French, K.R., 2002. Testing trade-off and pecking order predictions about dividends and debt. The Review of Financial Studies, 15(1), pp.1-33.
Faulkender, M., Flannery, M.J., Hankins, K.W. and Smith, J.M., 2012. Cash flows and leverage adjustments. Journal of Financial Economics, 103(3), pp.632-646.
Faulkender, M. and Petersen, M.A., 2005. Does the source of capital affect capital structure?. The Review of Financial Studies, 19(1), pp.45-79.
Flannery, M.J. and Hankins, K.W., 2013. Estimating dynamic panel models in corporate finance. Journal of Corporate Finance, 19, pp.1-19.
Strebulaev, I.A., 2007. Do tests of capital structure theory mean what they say?. The Journal of Finance, 62(4), pp.1747-1787.
Comments