Our senior analysts are often asked how we construct the discount rate we use to calculate loan (and deposit) fair values. The Fair Value Disclosure section of our A/L BENCHMARKS Executive Report sums it up pretty nicely.

For a given balance sheet category, the model will employ one of two techniques to construct the discount rate. They are the Build-up approach or the Risk Premium approach.

Build-up Approach

The Build-up approach views the discount rate as consisting of four possible components:First the

Risk-Free Rateforms the foundation of the discount rate and is derived from the Treasury yield curve. It is the point on the Treasury yield curve which corresponds to the maturity structure for future principal and interest cash flows. A geometric interpolation is used between the discrete points of the yield curve to approximate the curvilinear shape of the yield curve. Thus the values of this component vary across time to reflect the term structure of interest, while the remaining components are constant across all time periods. This component also includes an adjustment to reflect the value of imbedded prepayment options.Next the

Credit Riskcomponent is the annualized yield needed to cover the loss of value expected over the entire life of a portfolio. For loans, the derivation of this component is based on an analysis of underperforming loans and the gross charge-off experience of the past four quarters. For funding sources, the derivation of this component is based on financial ratios that reveal the “credit-worthiness” of the financial institution for which present values are being computed. In both cases, the higher the credit quality component, the higher the credit risk.Next the

Operating Expensecomponent represents an annualized cost rate derived from operating expense allocations. This component is used to adjust the risk-free rate in order to compensate for operating expenses. When dealing with core deposits, the operating expense component is reduced by a service charge component (see below).Finally the

Service Chargecomponent represents an annualized income yield derived from operating income allocations. It is used to reduce the operating expense component.

Risk Premium ApproachThe risk premium approach views the discount rate as the sum of two components: the risk-free rate, and a risk premium. The risk-free rate is the same as defined above. The Risk Premium is the annualized yield needed to cover the risk reflected in the portfolio. It incorporates all forms of risk in a single spread to the treasury yield curve. Consistent with an entry rate concept of selecting a discount rate, the marginal pricing rate for each account serves as the basis for determining an appropriate risk premium to the Treasury yield curve. This risk premium is calculated by subtracting the value on the curve which corresponds to the average maturity of the account from the account’s marginal pricing rate.

I notice that we published this nearly ten years ago in our old “Communicator” newsletter. The approach is still the same, although we have updated the weightings and allocations in the Credit Quality and Operating Expense components with newer statistical data.

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