How to Price Whole Loans: The Definitive Guide

What Is Whole Loan Pricing?

Whole loan pricing is the process of determining the fair value of individual loans or loan pools traded outside the agency securitization market. Unlike agency MBS, where TBA pricing provides a liquid benchmark, whole loans trade over-the-counter, and each pool has unique characteristics that affect value.

The core question is simple: given a stream of future cashflows (principal and interest), what price should a buyer pay today to achieve their target return? The answer depends on prepayment assumptions, default expectations, loss severity, and the discount rate applied to those cashflows.

Whole loan pricing matters because it drives every transaction in the non-agency loan market. Credit unions buying solar loan participations, banks selling SBA 7(a) guaranteed portions, insurance companies acquiring CRE debt: all rely on the same fundamental framework.

Step 1: Build the Cashflow Projection

Every whole loan price starts with a cashflow projection. You need to model the monthly stream of principal and interest payments the loan (or pool) will generate over its remaining life.

For a fixed-rate amortizing loan, the scheduled cashflow is deterministic: you know exactly what the borrower owes each month. But actual cashflows differ from scheduled cashflows because of prepayments (borrowers paying early) and defaults (borrowers stopping payment).

The key inputs for cashflow projection are:

Current Balance (UPB): The outstanding principal balance as of the pricing date. This is your starting point.

Note Rate: The gross coupon rate on the loan. For a pool, use the weighted average coupon (WAC).

Remaining Term: Months until maturity. For a pool, use the weighted average remaining maturity (WARM).

Servicing Fee: The annual servicing strip retained by the servicer, typically 25-50 basis points. Net rate = Note Rate - Servicing Fee.

CPR (Conditional Prepayment Rate): The annualized rate at which borrowers prepay. A 10% CPR means roughly 10% of the remaining balance prepays each year. The monthly equivalent is SMM (Single Monthly Mortality): SMM = 1 - (1 - CPR)^(1/12).

CDR (Conditional Default Rate): The annualized rate at which loans default. Like CPR, it converts to a monthly rate (MDR).

Loss Severity: The percentage of defaulted balance that is actually lost after liquidation and recovery. A 40% severity means 60% of the defaulted balance is recovered.

Each month, the cashflow model calculates:

Scheduled Principal + Interest → minus Defaults → plus Prepayments → minus Losses = Net Cashflow

The result is a month-by-month vector of net cashflows that the investor expects to receive.

Step 2: Calculate Bond-Equivalent Yield (BEY)

Once you have a cashflow projection, the next step is to calculate the yield: specifically, the Bond-Equivalent Yield (BEY). BEY is the standard yield convention in the whole loan market because it allows direct comparison with Treasury securities and corporate bonds.

BEY is the annualized internal rate of return (IRR) that equates the present value of projected cashflows to the purchase price. It uses semi-annual compounding to match Treasury convention:

BEY = 2 × [(1 + monthly_IRR)^6 - 1]

To calculate BEY: (1) Take the monthly cashflow vector from Step 1, (2) Given a purchase price (e.g., 99.50 = 99.5% of par), solve for the monthly discount rate that makes the present value of cashflows equal to the price, (3) Convert the monthly rate to BEY using the formula above.

BEY is price-dependent. A lower price produces a higher BEY. Market participants typically quote yields at specific CPR assumptions: for example, "6.25% BEY at 10 CPR" means the yield is 6.25% if prepayments run at 10% CPR.

For government-guaranteed loans (SBA 7(a)), defaults are economically equivalent to prepayments because the government pays the investor at par. So the CPR input represents Total CPR = Voluntary CPR + Involuntary CPR, and CDR and loss severity are zero.

Step 3: Compute Weighted Average Life (WAL)

Weighted Average Life measures how quickly you get your principal back. It is the weighted average time (in years) to receive each dollar of principal:

WAL = Σ(t × Principal_t) / Total Principal

Where t is the time in years to each principal payment and Principal_t includes both scheduled principal and prepayments (net of losses).

WAL matters because it determines the appropriate Treasury benchmark for spread calculations. A loan pool with a 3.2-year WAL should be compared to the 3-year Treasury, not the 10-year.

WAL is highly sensitive to CPR assumptions. Higher prepayment speeds shorten WAL dramatically. For example, a 30-year mortgage pool might have a WAL of 12 years at 0% CPR but only 4.5 years at 15% CPR.

For pricing purposes, you calculate WAL alongside BEY using the same cashflow projection. The WAL then determines which Treasury yield to subtract when computing spread.

Step 4: Measure Spread Over Treasuries

Spread is the yield premium over the risk-free Treasury rate. It compensates investors for credit risk, prepayment risk, liquidity risk, and structural complexity.

Nominal Spread: The simplest measure: BEY minus the interpolated Treasury yield at the WAL point. If BEY is 6.25% and the 3.2-year Treasury yields 4.50%, the nominal spread is 175 basis points.

Z-Spread (Zero-Volatility Spread): A more precise measure that adds a constant spread to the entire Treasury zero-coupon curve and discounts each cashflow individually. Z-Spread accounts for the shape of the yield curve, not just a single point.

OAS (Option-Adjusted Spread): The most sophisticated measure. OAS uses a stochastic interest rate model (typically Hull-White) to simulate thousands of rate paths, adjusting prepayment speeds on each path based on the rate environment. The OAS is the constant spread that, when added to all simulated rate paths, makes the average present value equal to the market price.

OAS strips out the value of the borrower's prepayment option, giving you a "pure" credit and liquidity spread. A loan with a high nominal spread but low OAS has significant prepayment risk embedded in its price. The difference between Z-Spread and OAS is the Option Cost: the value of the borrower's prepayment option.

Step 5: Run Scenario Analysis

No single set of assumptions captures the full risk profile of a loan pool. Scenario analysis tests how price and yield respond to changes in key variables.

Rate Scenarios: Shift the Treasury curve by -300, -200, -100, 0, +100, +200, +300 basis points. This reveals convexity: how much the price changes for a given rate move. Negative convexity (common in mortgage loans) means the price drops more when rates fall (due to faster prepayments) than it rises when rates increase.

Prepayment Scenarios: Test BEY and WAL at multiple CPR assumptions (e.g., 5%, 10%, 15%, 20%, 25%). This shows prepayment sensitivity: how much yield compression occurs at faster speeds.

Default Scenarios: Vary CDR and loss severity to stress-test credit performance. Base case, adverse, and severely adverse scenarios mirror CECL methodology and help quantify expected vs. unexpected losses.

Combined Scenarios: The most realistic analysis combines rate shocks with prepayment and default response. When rates drop, CPR rises (more refinancing) but CDR may also change. Monte Carlo simulation handles this interaction naturally by modeling rate-dependent prepayment and default behavior.

Step 6: Duration and Convexity

Duration measures interest rate sensitivity: how much the price changes for a 1% move in rates. Modified Duration approximates the percentage price change:

Modified Duration ≈ -(ΔP / P) / Δy

Where ΔP is the price change and Δy is the yield change. A duration of 3.5 means the price drops approximately 3.5% for a 100bp rate increase.

Effective Duration accounts for the fact that cashflows change when rates change (because prepayments are rate-sensitive). It uses the scenario analysis from Step 5:

Effective Duration = (P_down - P_up) / (2 × P_base × Δy)

Convexity measures how duration itself changes with rates. Positive convexity (like Treasury bonds) means the price rises faster when rates fall than it drops when rates rise. Whole loans typically exhibit negative convexity because faster prepayments cap the upside when rates decline.

Key Convexity = (P_down + P_up - 2 × P_base) / (P_base × Δy²)

These risk metrics are essential for portfolio management and hedging. A portfolio manager needs to know not just the yield, but how much mark-to-market risk they are taking.

Practical Example: Pricing a Consumer Solar Pool

Consider a $10M pool of consumer solar loan participations with these characteristics: WAC 6.50%, WARM 168 months (14 years), WALA 24 months, weighted average FICO 745, weighted average LTV 0% (unsecured), servicing 25bp.

Step 1: Cashflows: Each loan amortizes at its gross note rate (6.50% WAC); the 25bp servicing strip is charged as a separate monthly cost against interest, so the investor receives interest at a 6.25% pass-through rate. Using 8% CPR and 1.5% CDR with 50% severity (recovered principal returns as cash), project monthly cashflows over 168 months.

Step 2: BEY: At a price of 101.50 (premium), the BEY solves to approximately 5.85%.

Step 3: WAL: At 8% CPR, the WAL is approximately 5.8 years.

Step 4: Spread: With the 5.8-year Treasury at 4.25%, the nominal spread is 160bp. Z-Spread might be 155bp. OAS (after Monte Carlo adjustment for prepayment optionality) might be 120bp, implying 35bp of option cost.

Step 5: Scenarios: At 15% CPR, WAL shortens to 3.8 years and BEY drops to 5.55%. At 5% CPR, WAL extends to 7.5 years and BEY rises to 6.00%.

This analysis tells the buyer: at 101.50, you earn about 120bp of OAS with 5.8 years of duration and moderate negative convexity. Whether that is attractive depends on the buyer's required return, alternative investments, and risk appetite.

Common Pitfalls in Whole Loan Pricing

Using MBS Conventions for Whole Loans: Agency MBS trades on a TBA basis with standardized pool factors. Whole loans have unique characteristics: applying MBS prepayment models to consumer or CRE loans produces misleading results. Use sector-appropriate models.

Ignoring Servicing Economics: The servicing fee is not just a cost: it determines who bears the operational risk. A 25bp servicing strip on a $100M pool generates $250K annually. That is real revenue and must be accounted for in the net yield calculation.

Static CPR Assumptions: A single CPR assumption ignores the reality that prepayments are rate-dependent and time-varying. Newly originated loans prepay slowly (seasoning ramp), then accelerate, then slow again for seasoned loans (burnout). Use at minimum a CPR vector, and ideally a prepayment model that responds to rate changes.

Conflating Nominal Spread with OAS: A pool trading at +200bp nominal spread might have only +80bp of OAS if it has significant prepayment option cost. Comparing nominal spreads across pools with different coupons and WALs is misleading.

Neglecting Liquidity Premium: Whole loans are inherently less liquid than agency MBS. A buyer should demand additional spread for the inability to exit quickly. This premium varies by sector: SBA guaranteed portions are relatively liquid, while esoteric consumer loan types may require 50-100bp of additional spread.

How LoanBook Handles Pricing

LoanBook automates the entire pricing workflow described in this guide. Upload a loan tape, and the platform automatically:

Builds per-loan cashflow projections through one canonical cashflow engine, using sector-appropriate prepayment, default and severity models (the LoanBook Prepay, Default and Severity Models).

Calculates BEY and WAL at user-specified or model-derived CPR/CDR/severity assumptions.

Computes OAS, Z-Spread and Option Cost from one Hull-White Monte Carlo run (200 simulated rate paths in production pricing).

Runs 7-point scenario analysis (-300bp to +300bp) with rate-dependent prepayment adjustment.

Calculates effective duration and convexity for risk management.

All calculations use the same central engines regardless of loan sector: residential, consumer, commercial, government-guaranteed or lease. The models are calibrated with empirical data: Fannie Mae loan performance data for the shape of residential prepayment and default, NCUA and FDIC call report loss history for the through-the-cycle level of residential default, and SBA FOIA records for SBA and commercial real estate payoffs.