Variance of default and mitigants

It is not default itself but the variance of default that is the real risk to business

If the default is stable then one can argue that it can be priced it in but if the variance high then it cannot be priced.?

Factors that effect variance of default

1. Level of default- Ironically given the nature of default distribution the level of default and variance of default are correlated. Higher the default higher also is the variance of default. (Side note: levers to control default are same as levers for controlling the variance of default) From an intuition standpoint just think of marginal customers like a microfinance customer. One small event in their lives can lead to a default situation. So while their default is higher the variance of default is also higher for these customer. A customer who lives on the edge where 5000 Rs make the difference it is very easy to get wiped off in one month and then comeback again in the next month. Mathematically this is a bernoulli distribution. If p is chance of default in a year the variance of unit default is p*(1-p). The big insight really is that not everything can be priced in and all levels of default are not acceptable.?
2. Tenor - One of the easiest way of reducing default has been increasing the tenor. Increasing tenor reduces the EMI burden and hence the default level goes down. However, what is really happening is that while the level of default per period has gone down the variance of default across the tenor the loan might actually increase. if p is the default per period then Variance is n*p*(1-p). Not to mention overall default over the life is also higher which is n*p where n is the number of periods. One way to think about it is that if you hold a 6 inch scale with one end fixed vs. a 12 inch scale at one fixed, the 12 inch scale will have a higher amplitude of vibration for same impulse. (Side note: this is very similar to the role of Duration in bond pricing, higher duration means higher convexity and therefore higher volatility in prices due to spread or interest rate variation) Add to that smaller runoff of principal of and what results is even higher amount level default variation. How do we hedge against longer tenor in that case? FOIRs or LTVs have to be lower for higher Tenors not same
3. FOIR or EMI to Average Bank Balance(EMI/ABB)? - General thinking is that FOIR should be adjusted for only credit score of the customer.Now imagine a? customer A : 750+ cibil but with income 5000 vs. customer B: 750+ customer with income 500000. Who should get higher FOIR? Even if at 90% FOIR customer B is safe as disposable income left is still 50000 Rs while for customer A it is 500 Rs. so it is important to adjust the FOIR and EMI/ABB for credit quality as well as size. One important aspect which goes unnoticed is that for low income or ABB the estimate of income itself has a lot of variance. Imagine going 100 Rs off on 5000 Income vs going 100 Rs off on 50000 Rs. What does it imean? In the first case the variation is just 100/5000 vs 100/50000. So for that reason also we should reduce the FOIR or EMI/ABB for lower base
4. Loan to Value (LTV) ratios - The beautiful part about valuation in asset backed lending is that valuation itself is a myth and loan is the reality. Particularly true of LAP and usedcar loan. So if the car value is smaller then we need to reduce the LTV for simple reason that error in valuation is higher at a lower base. Also, for higher tenor the valuation might change a lot therefore one needs to hedge for that i.e for higher tenor loans we need to reduce the LTV. Other than that One direct reason is that for higher tenor the POS runoff is slower and hence equity build up is slower. So net net longer tenors should have lower LTV.