Work out the hurdle rate and use it to reach business decisions through RAROC.

FRM® Part II · Operational Risk and Resilience · Risk Capital Attribution and Risk-Adjusted Performance Measurement · FRM2.ORR.18.e

The idea

The hurdle rate is the minimum RAROC a project must earn to leave shareholders better off. In the standard treatment it is the after-tax cost of equity, the return investors demand for the risk of the bank's equity. Write Rf for the risk-free rate, β for the bank's equity beta and Rm for the market return. The CAPM then gives the hurdle as the risk-free rate plus beta times the market risk premium: Hurdle = Rf + β × (Rm − Rf). The decision rule is simple: accept if RAROC is above the hurdle and reject if it is below, and the excess over the hurdle times economic capital is the value added. Two mistakes recur. The first is mixing bases, because a pre-tax RAROC must not be compared with an after-tax hurdle. The second is stale inputs: when the risk-free rate rises, the hurdle rises, and projects accepted yesterday may fail today. The hurdle is not the cost of debt and not the risk-free rate. It is the required return on equity, and the comparison must use the same tax basis on both sides.

Formulas

Hurdle rate from the CAPM

Hurdle = Rf + β × (E(Rm) − Rf)

Rf: the risk-free rate
β: the bank's (or project's) equity beta
E(Rm): the expected market return

The hurdle is the after-tax cost of equity. Beta multiplies only the premium, so a rise in Rf lifts the hurdle one for one.

After-tax RAROC

RAROC(after tax) = RAROC(pre-tax) × (1 − t)

RAROC(pre-tax): the RAROC before tax
t: the tax rate

Needed before comparing with an after-tax hurdle. Dividing by (1 − t) instead of multiplying inflates the return.

A practice question

From the question bank, with the reason each wrong option is wrong.

What is the hurdle rate in a RAROC framework?

The minimum RAROC that satisfies shareholders, normally the after-tax cost of equity. - correct
The bank's pre-tax cost of borrowing in the wholesale market, as set by its lenders and funding desk.Why not: Uses the cost of debt, whereas RAROC is a return on equity capital.
The risk-free rate on government securities of the same maturity as the project's life.Why not: The risk-free rate omits the premium shareholders require for bearing risk.
The average RAROC of all of the bank's business units over the past several financial years.Why not: An internal average is not the shareholders' required return.

Because RAROC is a return on equity-like capital, it is compared with the return shareholders require, the after-tax cost of equity, which is the hurdle rate.

A harder one

The hurdle rate is 11.0%. The RAROCs of four proposed loans are: A 8.0%, B 12.5%, C 10.4% and D 15.0%. Which loans create shareholder value?

D onlyWhy not: Accepts only the highest RAROC, but B also exceeds the hurdle and adds value.
B, C and DWhy not: Includes C, whose 10.4% is below the 11.0% hurdle, perhaps by using a lower benchmark such as a cost of debt.
A and CWhy not: Selects exactly the proposals that are below the hurdle.
B and D - correct

A project creates value when RAROC exceeds the hurdle rate: B (12.5%) and D (15.0%) pass; A (8.0%) and C (10.4%) do not.

The hardest tier

A project has a pre-tax RAROC of 15.2% on its economic capital. The tax rate is 30% and the after-tax cost of equity (the hurdle) is 11.0%. What is the after-tax RAROC and the correct decision?

10.6%, reject - correct
15.2%, acceptWhy not: Compares a pre-tax return with an after-tax hurdle.
21.7%, acceptWhy not: Divides by (1 - tax rate) instead of multiplying, which inflates the return.
7.4%, rejectWhy not: Applies the 30% tax twice, so the number is wrong even though the decision matches.

After-tax RAROC = 15.2% x (1 - 0.30) = 10.64%, below the 11.0% hurdle, so the project is rejected. The two sides of the comparison must be on the same tax basis.

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