Quant Approach to Optimal Leverage Ratio for a Lender

[Weekend musings of a bored quant enthusiast]

The evolution of standard deviation as measure of risk=>efficient frontier=>changing efficient frontier with risk free asset=>market portfolio=>CAPM model?culminating in Sharpe Ratio has always fascinated me and I keep coming back to it from time to time.?Sharpe Ratio is the risk adjusted return or excess return per unit of additional risk. Mathematically it is (Expected Return- Risk free rate)/(stdev of return). This is taught in every MBA/Financial mathematics class but with equity/stock investment/portfolio management perspective. This concept keeps appearing in multiple places in quant finance(market price of risk, risk neutral pricing) but never makes it way to corporate finance or at least I have not come across its references in Corporate finance other than using it for WACC calculations and discount factors.??

Off late I have been wondering about how to determine the right leverage ratio for lending institutions. In my mind Leverage Ratio is one of the most important metric that proves(market validation) that a lender is able to generate consistent asset returns i.e. its operations have stabilized. Initially all lending is on equity and then slowly starts converging towards the optimal leverage depending on the loan product type and book size. One way to know the right leverage ratio is just to look up money control or ICRA reports and close the case. However, why did the market choose to operate at a particular leverage ratio? Is there a way to define this quantitatively? I think the answer lies in Sharpe Ratio.??

So connecting the dots, Return on Equity is nothing but return to equity investor (similar to stock returns). ROE = Leverage * ROA(Return on asset).?So one can operate at a very high leverage in expectation of high ROE but then the variance on ROE also increases, i.e. with slight movement on ROA?return to equity investor changes significantly. Similarly when one looks at lower leverage expected return to equity investor comes down but then variability of return is also low. Can one then formulate a method to determine optimal level of debt by maximizing Sharpe ratio for ROE.

Framework roughly?

Maximize - (Expected ROE - Risk Free Rate)/Std dev of ROE

Steps

1. Simulate Scenarios or Paths of Loan book Returns using montecarlo simulation and Vintage curves

2. Yield, Cost of funds, Cost of operations and Default are pretty much decided by Size of Book and Loan Product type combine so this is known with good certainty. (More on this in some later post but just to define Product type = ticket size, Tenor and secured vs unsecured)

3. For a given leverage then compute?ROA and ROE for each path

4. Since one has ROE distribution one can come up with Sharpe Ratio

5. Repeat 3 to 4 by changing Leverage Ratio?

6. Plot ROE vs. Leverage Ratio graph and pick the leverage ratio that maximizes Sharpe Ratio

(Risk free rate should be read off from Tsy curve where maturity = Weighted Average Life of the Asset Book)?

My expectation is that given a book, one should be able to backout the market leverage ratio at least for mature NBFCs(book Size >7K+ crores with X+ years of operations). If that is the case then one could determine the right leverage ratio for transient NBFCs.?

I have been thinking about Risk Based Pricing along similar lines. Traditional thinking is that a person borrowing at high interest rate, there by a risky customer, has no intention to return the money. Fintech thinking typically is based on cost plus approach to pricing but it is flawed because it is based on point estimates of cost of default(i.e. ignores stability of default of customer segments completely). The answer is somewhere in between and probably one could marry the two worlds by looking at risk adjusted return.(will write detailed post later on Risk Based Pricing)??