Do firms with higher leverage deliver higher returns?
We review a classic question on the relation between financial risk and equity returns, and discover that the evidence defies the theory
Anyone who has taken a corporate finance course will have come across the propositions of Modigliani and Miller. And, my guess is, if they remember one formula from that course it is going to be that of Modigliani and Miller’s Proposition 2:
In this equation re represents the return on the firm’s equity, ra is the return on assets, and rd is the return on debt. E is the value of the firm’s equity and D is the value of its debt.
In words, the equation states that equity returns increase with the debt to equity ratio. As the debt to equity ratio is one way of measuring leverage, the equation can be read as to say that equity returns are increasing in leverage.
This proposition is the basic tenet of the relation between equity returns and firm leverage. The question is: does it hold in the data?
Let the data speak
Let’s take a look at the empirical evidence. The table below illustrates how equity returns vary across different quintiles of leverage.
The table shows that returns increase with market leverage, which would indicate that the basic intuition of Modigliani and Miller’s Proposition 2 may effectively hold in the data. However, the table also shows that returns are flat in book leverage, which would not be in line with Proposition 2. Of the two results, which one should we focus on, that of book or market leverage?
This is just the first problem that we are going to find in the data. As we show below, things are going to get messier.
Controlling for the risk of the assets
The results presented in Table 1 should be interpreted with caution. All they show is a correlation between leverage and returns. They simply illustrate how returns change when one moves across quintiles of the leverage distribution.
What must be observed is that as we move across quintiles of leverage, other things happen, beside a change in leverage. For example, the return of the assets may also change. The question we should ask ourselves is: are firms with high and low leverage investing in assets with a similar risk-return profile? Probably not…
If the return on the assets change when leverage changes, what is driving the change in equity returns? The change in the asset returns or the change in leverage? Hard to tell.
One way to go about this problem is to examine the relation between equity returns and leverage, controlling for asset returns.
The main issue here is that asset returns are not directly observable, because the assets are not traded in a market, as instead is the case for the equity shares.
The academic literature has proposed two measures: firm size and the ratio of book-to-market. Arguably, both measures may capture many other things beside asset risk. For example, size is likely to capture how stable profits are, but also financial frictions and the ability to provide collateral. Book-to-market may capture the ratio of assets in place versus real options, but it also captures how future profits compare to the historical cost of the assets. In any case, both size and book-to-market are likely proxies for the risk of the firm’s assets. Let’s use these two measures for now.
Firm Size
Let’s begin by looking at firm size. What we want to examine is how equity returns vary when leverage changes and firm size doesn’t. To do this, we construct a set of 25 portfolios, one for each quintile of size and leverage. The results are reported in Table 2. Size is computed as the market capitalisation of the firm. In each row, size is held constant while leverage changes. In each column, leverage is held constant while size changes.
Table 2 shows that equity returns are increasing within each quintile of market leverage. Instead, equity returns appear unrelated to book leverage within each quintile of size. Overall, Table 2 seems to confirm the robustness of the evidence provided by Table 1. The relation between equity returns and leverage is positive for market leverage and flat for book leverage, also after controlling for size.
Book-to-market
Let’s now examine what happens when we look at the relation between leverage and returns, controlling for the ratio of book-to-market. This variable is computed as the ratio between the value of equity as reported in the balance sheet of the firm and the market value of equity. The latter is computed as the numbers of shares outstanding times the price per share.
Table 3 shows that the relation between leverage and equity returns disappears when we control for book-to-market. This can be seen by looking at how equity returns change from column to column within each row. For both market and book leverage equity returns show no clear pattern as leverage increases. Should we conclude that returns are driven by something else other than leverage? Not quite yet…
Book-to-market and market leverage
The trouble with book-to-market is that it strongly covaries with market leverage. As can be seen in Figure 1, market leverage increases when book-to-market increases. This is likely due to the mechanical effect induced by variations in the market value of equity. While the book value of equity is fairly stable over time, the market value changes continuously with the stock price. Specifically, when the market value of equity drops, leverage goes up and so does the book-to-market ratio. This would suggest that book-to-market is not helping much in understanding the relation between leverage and returns.
To confirm this, examine the cumulative returns of a long-short strategy based on book-to-market reported in Figure 2. The returns correspond to buying the high book-to-market portfolio and selling the low book-to-market portfolio. The cumulative return represents the growth of a $1 initial investment made in June 1971. The strategy generates positive returns only when using raw (levered) equity returns. If instead of using raw returns, we delever them, the strategy yields a negative cumulative return. This indicates that a strategy based on book-to-market is really one based on market leverage.
What if we then build a long-short strategy directly based on market leverage. Would this strategy yield positive returns? Yes…to some extent. Figure 3 shows that the returns on this strategy are positive in the early years of the sample, and then they flatten out. So, returns may well increase in leverage, but trading profitably on leverage seems a tricky business.
Conclusions
All in all, it is fair to say that equity returns increase with market leverage, as originally predicted by Modigliani and Miller. This relation holds also after controlling for firm size, which is a possible proxy for the risk-return profile of the assets of the firm.
Controlling for book-to-market muddles the water, as it is highly correlated with market leverage. Thus, it is difficult to disentangle the effects of asset risk from leverage risk using book-to-market as a proxy for asset risk.
A whole different story is that of book leverage. It shows little relation to equity returns. It is unclear why this is the case, but a likely reason is that book leverage does not properly capture leverage risk. After all, book leverage is merely an accounting measure of equity, which is backward looking rather than forward looking. The book value of equity does not reflect the present value of the future cash flows to equity, but rather (indirectly) the assets at cost value. Perhaps it is best to just ignore book leverage and focus on market leverage.
Having said all this, one would expect a long-short strategy based on market leverage to yield positive returns…
Essential Bibliography
Doshi, H., Jacobs, K., Kumar, P. and Rabinovitch, R., 2019. Leverage and the Cross‐Section of Equity Returns. The Journal of Finance, 74(3), pp.1431-1471.
Fama, E.F. and French, K.R., 1992. The cross‐section of expected stock returns. the Journal of Finance, 47(2), pp.427-465.
George, T.J. and Hwang, C.Y., 2010. A resolution of the distress risk and leverage puzzles in the cross section of stock returns. Journal of Financial Economics, 96(1), pp.56-79.
Gomes, J.F. and Schmid, L., 2010. Levered returns. The Journal of Finance, 65(2), pp.467-494.
Ozdagli, A.K., 2012. Financial leverage, corporate investment, and stock returns. The Review of Financial Studies, 25(4), pp.1033-1069.
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