Statistically, a “hot hand” in basketball doesn’t exist. In a detailed analysis of the 76ers and Celtics plus controlled experiments with Cornell’s varsity teams, researchers found that streaks were just positive random sequences with little evidence of correlation between outcomes and successive shots. However, what is influenced is the perception of that hot hand player so coaches and teammates often feed the ball to that player more. Statistically, this is a mistake as the reality is that when a player made their last shot, they are LESS likely to make their next shot, and conversely players that missed their previous shot are MORE like to make the next. Players tend to adjust and take more or less risk in shooting depending on their last shot and in general shooting percentages revert to their mean. In addition, a hot player may draw more defenders to him or her thereby increasing the odds of scoring for other teammates. Smart coaches understand this which underscores the paramount difference between team and individual sports. In team sports, like banking, the whole is more than the sum of the parts.
Lending goes on streaks as well, as sometimes owner-occupied does better than investment commercial real estate loans and sometimes the opposite. Overtime, however, the evidence is that there is very little probability of default distinction between commercial owner occupied and non-owner occupied CRE. However, the banking market continues to price owner occupied loans at thinner spreads (even after taking into account all non-loan related parameters such as deposits, fee business, and referral opportunities). The explanation is that the insightful banker appreciates and measures the benefit of diversification of the owner occupied business and the ability to increase profits and decrease risk through that diversification.
Default correlation or covariance measures whether risky credit assets are more likely to default together or separately. This correlation can be zero, positive or negative. If the correlation is zero, the analysis for bankers is very easy. For instance, the default probability of loan A is shown as P(A) and equals 10%. The default probability of loan B is shown as P(B) and also equals 10%. If the correlation between loan A and B is zero, then the probability of both loans defaulting at the same time is 10% X 10% or 1.0%. A banker can quickly build up diversification because every zero correlated loan improves the performance of the portfolio.
Unfortunately, default correlation for community bank loans is almost never zero – in fact loans at community banks tend to be highly correlated. Correlation is one of three important factors in determining the credit risk of a portfolio. The other two major factors are default rate (or probability of default and we will call it PD) and loss-given-default (LGD). Expected loss is the product of PD and LGD and we will call it EL. For community bank commercial loans, the causes of default correlation, in order of importance, are a) state of the economy, b) state of a particular industry, and c) relationship between the loan parties (cross ownership, industry integration etc.).
What yield should a banker accept for lower or negative correlated assets to be added to the loan portfolio? Let's work backwards to get our answer. Let’s assume the net interest margin (NIM) of an average loan to be 3.00% (a little low, but the industry is heading to that approximate level). Let’s assume an average PD of 2.0% per annum and an LGD of 50% (somewhat high, but it will make the math easier). Our average expected loss is 1.0% annually over the life of the loan. Since we are earning 3.0% NIM and expect a loss of 1.0%, the 2.0% excess is for overhead, profit, and, very importantly, the possibility that losses will be higher than the EL calculation (this is why banks are required to keep capital above the ALLL).
While on average we expect each loan in the portfolio to lose 1%, because of these correlations and because of our margin of calculation error, we may have much higher default rate and lower recoveries should there be a market shock. How much higher can our default rates go and how much lower can our recoveries trend? We use standard deviation to measure those possibilities.
Through 2008 to 2010 we witnessed relatively high standard deviations on PDs and LGDs. In fact we also saw that PDs and LGDs are positively correlated – for the sake of simplicity we will ignore that for now. In the above example with a 2% PD, the standard deviation of the PD is historically approximately 0.15%. With an LGD of 50%, the standard deviation of the LGD can vary greatly but in the most conservative case, it is at least 5%. Thus, our standard deviation of EL is approximately 3.5%. That is very striking – our expected loss is 1% but our standard deviation is 3.5%. Assuming a bell shape distribution (an incorrect assumption, and one that understates future unexpected losses), in 15% of the cases our EL jumps from 1.0% to 4.5%, and in 1.2% of the cases our EL jumps to 8.0%.
Choosing owner-occupied loans that have either a zero or negative correlation to the CRE portfolio allows a banker to decrease EL in the portfolio. In fact, assuming that the correlation of loans in an existing portfolio is +1, then any new loan with a -1 (negative) correlation decreases risk or adds extra value to the portfolio of 3.5%. This 3.5% value completely eliminates the risk premium for that loan (recall that our EL is only 1.0%). Stated another way, a loan with a -1 correlation to an existing portfolio (but still a 2% PD and 50% LGD) can be priced with no risk premium (just sufficient NIM cover overhead and profit).
This is one reason why larger and more sophisticated lenders price at more competitive loan rates. Their offsetting risks tend to partially cancel each other out resulting in a lower overall risk for the portfolio and a greater return. With owner-occupied real estate, smart banks can better target the diversification they need, thereby relieve return pressure on the whole portfolio. This helps explain why sophisticated banks can price selected owner-occupied loans at LIBOR + 2.00% (NIM of 2.00%) and still derive a positive ROE. Like basketball, a loan portfolio is more than the sum of the individual parts.
Submitted by Chris Nichols on October 20, 2014