We have written a number of blogs on the relationship between commercial loan pricing, loan-to-value (“LTV”), amortization terms and riskiness of leverage. Our major theme is that the common secondary source of repayment (liquidation of collateral) is much less consequential than the common first source of repayment (cash flow). There are a few reasons why this is the case. The primary three reasons are as follows: 1) cash flow, not collateral, is a causal relationship to payment defaults, 2) variability around loss-given-default as measured by LTV is very large, and 3) credit loss is magnified more by cash flow variability than by LTV.

**Cash Flow and LTV**

Let’s consider the above in greater detail. Borrowers will trigger payment default much more frequently because of a shortage of cash flow, versus an increase in LTV. Especially in circumstances where personal guarantees are involved, borrowers will continue to service credit as long as cash flow is present - regardless of the LTV. This is the reason why investment grade facilities are typically unsecured, as the probability of default approaches zero, the collateral becomes unnecessary. We are not advocates of unsecured lending, we are simply quantifying the variables of default triggers and those are cash and not collateral.

Now let us examine the variability of collateral value. When a bank advances 75% of the collateral value, what are the risks in an event of default? If we expect the collateral to maintain value, then the expected loss is zero. We assume that 25% excess collateral is sufficient to pay off the cost of liquidation (foreclosure, legal, servicer and receiver costs). Of course, this is not reality. While we may have advanced 75% of today’s appraised value, there is a chance that that value may increase or decrease.

**The Asymmetry of Collateral Value**

Unfortunately for us lenders, two things are stacked against us, first the decrease potential is a fat-tail event (it happens more often than appreciation in value), and, two, as senior lenders, we do not participate in the upside plus do not gain higher return if the property appreciates. What is that variability around that terminal collateral value? That is very difficult to answer generically. However, we can approximate the variability of collateral value by examining the following. Empirical evidence shows that severity of loss for senior secured loans has historically averaged 30%. Furthermore, the industry standard equation for the variability of loss given default (“LGD”) is this: (LGD´(1- LGD) / 4)^0.5. So while we expect a loss of 30% on average after liquidating collateral, the one standard deviation around the mean of 30% is 54% and 6% (that is just how the math works). That means that in only 17% of cases our LGD will exceed 54%. This variability is so large compared to other variables in lending, that it makes LTV less reliable than other credit variables for predicting losses. While it would appear that an LTV of 60% has 15% less leverage than 75% LTV, because of the variability around the two numbers, the expected loss given a default, over a large sample size, is very similar between 60% and 75% initial LTV loans.

**Expected Loss Variability **

Finally, let’s consider the expected loss equation: expected loss = probability of default X loss given default X exposure at default (the exposure at default is 1.00 for most term loans). We discussed that the industry average loss given default for senior secured loans is 30%. We do expect that higher initial LTVs lead to higher loss given default numbers (but not by much as shown above because of fat tails and variability around the LGD). What are the differences in expected loss between 60% and 75% initial LTV loans? Because of the equation above, the LGD is multiplied by the probability of default, the impact of LGD is tempered by the PD number (and vice versa of course). The average PD number in the community bank industry is 1.5% per annum. That means that any changes in LGD (driven by LTV at default) is being tempered by an average multiple of 0.015. Therefore, an LGD of 30% and 35% is really only a difference in 0.075% of expected loss (7.5 basis points). Also, recall that to go from 30% to 35% LGD, LTV must be substantially higher than 5% (in the order of 10% to 15%). The end result is that the expected loss difference between a 60% and 75% initial LTV loan is approximately 7.5 basis points.

The math may be esoteric, but the adage is well founded: “We must underwrite to three things – cash flow, cash flow and cash flow.”

Submitted by Chris Nichols on April 08, 2015