# What relevance might the Modigliani-Miller theorem have for weight of evidence?

Suppose in computing weight of evidence based on financial ratios of some bank, one finds that their debt ratio and equity ratio have largely (you pick how large I guess) differing weights of evidence. This does not violate the modigliani miller theorem because of its highly unrealistic assumptions, but how might MMT be relevant? Or is it completely irrelevant?

Oh and the point of computing weight of evidence is for building a logistic regression model to estimate probability of default for the banks' clients.

• It is not totally clear to me what you are asking for. Can you be clearer? – fni Jul 14 '17 at 20:11
• Nobody, and certainly not M&M, ever said that the probability of bankruptcy has nothing to do with $\frac{D}{E}$. – noob2 Jul 14 '17 at 21:30
• @noob2 that's the point of the model we were building. We computed financial ratios and tried to pick out the ratios that were the most important to bank where importance is measured on predictive power based on model validation. But based on MM assuming its assumptions, I think we would expect debt ratio and equity ratio to have around the same weight of evidence. Of course assumptions of MM don't hold so it's not like we expect the results of MM to hold but I'm wondering if MM might still have some relevance – BCLC Jul 15 '17 at 8:58

I understand your question to be, "Does the Modigliani-Miller theorem have any relevance for forecasting the probability of default based upon debt to equity ratios?"

Not really.

The Modigliani-Miller thoerem is about the total value of the firm, not probability of default. As @n00b2 said in the comments, "Nobody, and certainly not M&M, ever said that the probability of bankruptcy has nothing to do with $\frac{D}{E}$."

The M&M theorem doesn't say that $\frac{D}{E}$ doesn't affect the probability of default. Rather, the M&M assumptions imply that bankruptcy doesn't matter in the sense that it wouldn't affect total enterprise value.

# Quick review of Modigliani-Miller (M&M) theorem

The M&M theorem says that under the M&M assumptions, firm value is invariant to capital structure.

The basic idea is that if firm cashflows are taken as given and capital markets are rational, then the total value of a firm doesn't change based upon how those cash flows are split up between debt and equity (or in fact any type of security).

### Under M&M assumptions, bankruptcy doesn't matter!

In an M&M world, there is no cost of bankruptcy, there are no lawyer fees, there's no loss of consumer confidence in the firm, etc....

In an M&M world, bankruptcy doesn't mean anything besides that cash flows are going to creditors instead of equity holders.

### Example:

Let $D_f$ be the market value of the debt of Tesla if the debt has a face value of $f$. Let $E_f$ be the market value of the equity of Tesla if the debt has a face value of $f$.

Under the M&M assumptions $D_{\text{100 dollars}} + E_{\text{100 dollars}} = D_{\text{100 billion dollars}} + E_{\text{100 billion dollars}}$.

In the case of 100 of outstanding debt, virtually all the firm value of Tesla would be in the equity. In the case of 100 billion of outstanding debt, virtually all the firm value would be in the value of debt (and bankruptcy would be assured with probability near 100%).

• Wait I'm not asking about debt equity ratio. I'm talking about debt ratio and equity ratio. Before I read (I skimmed), is your answer essentially unchanged? – BCLC Jul 16 '17 at 15:15
• @BCLC Yeah, it wouldn't change. Under M&M assumptions, the level of debt (however you measure it) doesn't affect firm value not because more debt doesn't affect the probability of bankruptcy but because bankruptcy doesn't affect firm value. – Matthew Gunn Jul 16 '17 at 15:40