# Mapping the Quant Mechanics of a Commercial Bank: The Live Oak ESFIB Model (Q2 2025)

## Overview

This section applies the **ESFIB 1.2** (Equation System of Financial Institution Business) framework to **Live Oak Bank** (NASDAQ: LOB) using its **Q2 2025** results.
Data come from:

* **Live Oak Bancshares Q2 2025 Press Release** ([investor.liveoak.bank](https://investor.liveoak.bank/news/news-details/2025/Live-Oak-Bancshares-Inc--Reports-Second-Quarter-2025-Results/))
* **2024 Annual Report / 10-K**
* **FFIEC Call Report (031)**
* **Investor presentation (Q2 2025 overview)**

All numbers below are in $ thousands unless noted.

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## 1. Input Data (Period-End Balances and Quarterly Rates)

| Variable | Description | Source / Computation | Value (Q2 2025) |
| ----------------- | ------------------------------------------ | ----------------------------- | --------------: |
| **B** | Loans & leases held for investment (gross) | Balance sheet (press release) | 11 014 055 |
| **S** | Investment securities (AFS) | Balance sheet | 1 325 206 |
| **Z** | Cash & balances with banks + CDs | Balance sheet (press release) | 663 005 |
| **W** | Deposits (total) | Balance sheet | 12 594 790 |
| **D** | Borrowings | Balance sheet | 107 659 |
| **E** | Shareholders’ equity | Balance sheet | 1 067 265 |
| **A = B + S + Z** | Simplified total assets | – | 13 002 266 |

### Quarterly Rates (from income statement & average balances)

| Parameter | Meaning | Estimation | Value (Q2 2025) |
| --------- | -------------------------- | --------------------------------------------------------- | --------------: |
| (rB − φB) | Loan yield – expected loss | Interest income on loans – provision / avg loans | 1.598 % / qtr |
| rS | Yield on securities | Interest income / avg securities | 0.827 % / qtr |
| rZ | Yield on cash balances | Interest income / avg cash balances | 1.116 % / qtr |
| rW | Deposit cost | Interest expense on deposits / avg deposits | 0.909 % / qtr |
| rD | Borrowing cost | Interest expense / avg borrowings | 1.538 % / qtr |
| cA | Operating cost ratio | (Non-interest expense − non-interest income) / avg assets | 0.399 % / qtr |
| τ | Tax rate | Income tax / pre-tax income | 25 % |
| ζ | Dividend payout | Dividends / net income (≈ $1.37M ÷ $23.4M) | 5.8 % |

Citations → company press release & 10-Q (interest and balance data), FFIEC 031 (call report loan balances).

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## 2. Income Equation (INC)

**Equation:**


Meaning: Net profit (Π_t) equals after-tax income from loans, securities, and cash minus interest expense on debt and deposits, minus operating costs.

**Computation (Q2 2025):**

Π_t = (1 − 0.25)[ 0.01598B + 0.01116Z + 0.00827S − (0.01538D + 0.00909W + 0.00399A) ]

Result ≈ **$19.8 million (model)** vs. **$23.4 million reported** — a close fit for a parsimonious model.

---

## 3. Balance Sheet Equation (BS)

**Equation:**


Interpretation: Assets = liabilities + prior equity + retained earnings (this period’s profit kept after dividends).

Retained earnings ≈ 94.2 % of profit (1 − ζ_t).
Retained ≈ $18.7M added to equity (E_t ≈ $1.086B).
Minor gap from GAAP assets (~$13.83B) is due to excluded “other assets.”

---

## 4. Liquidity Equation (LQ)

**Equation:**


Where H_t = high-quality liquid assets (cash + securities = $1.99B).

Using class ratios λ_D = 5 %, λ_X = 20 %:

Required = 0.05×107.7M + 0.20×12.595B ≈ $2.52B

So strictly, H_t < required ⇒ apparent shortfall.

However, LOB’s loan book is ~70 % government-guaranteed SBA loans, which can be sold quickly. Including them as liquid assets (as their presentation notes “41 % of assets are cash or guaranteed”) removes the shortfall.

---

## 5. Capital Equation (CAP)

**Equation:**


### (a) Regulatory-Aware Spec

Loans split: unguaranteed $3.71B, guaranteed $7.70B (from presentation).
CET1 ratio ≈ 10.67 %.

Required ≈ 10.67 % × (3.71B + 0.2 × 1.33B) ≈ $424M

Equity ≈ $1.07B ⇒ strong capital surplus.

### (b) Simplified Classroom Spec

Using κ_B = 10 %, κ_S = 5 %, κ_Z = 0 %:

Required ≈ 0.10B + 0.05S = 1.10B + 0.066B = 1.17B

That appears tight vs. equity (1.07B), explaining why risk-adjusted treatment is preferred.

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## 6. Interpretation & Takeaways

| Area | Outcome | Intuition |
| ------------- | ------------------------------------------------ | ----------------------------------------------------------------------------- |
| Income | Model profit ≈ $19.8M (close to reported $23.4M) | Net interest margin dominates; high loan yield offset by deposit cost & opex. |
| Balance Sheet | Assets ≈ 13B vs. GAAP 13.8B | Minor difference from excluded “other assets.” |
| Liquidity | HQLA 1.99B vs. requirement 2.5B (but 41% liquid) | SBA-guaranteed loans boost effective liquidity. |
| Capital | CET1 10.7 % ⇒ ample surplus | Strong equity relative to risk-weighted assets. |

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## 7. Citations

1. Live Oak Bancshares Inc. “Reports Second Quarter 2025 Results.” Press Release (July 2025).
2. Live Oak Bancshares 2024 Annual Report / Form 10-K.
3. FFIEC 031 Call Report (2025 Q2).
4. Investor Presentation Q2 2025 (“41 % of assets are cash or guaranteed”).
5. Author’s calculations based on public filings.

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### Summary

| Perspective | What It Means for Live Oak |
| ------------------------ | ---------------------------------------------------------------------------------------------------- |
| **Profitability** | Core lending business yields strong net income (~$20–23 M per quarter) despite higher funding costs. |
| **Balance Sheet Health** | Assets ≈ $13 B are well-matched by deposits + equity; retained profits steadily grow capital. |
| **Liquidity** | Roughly $2 B of high-quality liquidity; when including SBA-guaranteed loans, liquidity is robust. |
| **Capital Strength** | CET1 ≈ 10.7 % vs. ~4–5 % required → ample cushion. |

The ESFIB system connects **income**, **balance**, **liquidity**, and **capital** channels:

1. **INC** → how profits arise from interest margins and costs.
2. **BS** → how profits feed back into equity.
3. **LQ** → how liquid assets buffer withdrawals.
4. **CAP** → how capital covers risk-weighted assets.

For Live Oak, this shows how its **SBA-backed loan model** yields strong income and capital cushions even with a modest cash position.