Risk & Relationship based Pricing Part 3.2

So what was your recommendation to the bank for the quiz in my last blog?

  • Client A (20 year mortgage at 4.803%)?
  • Client B? (4 year consumer loan at 4.734%)?
  • 80% A, 20% B a mixed portfolio?
  • 20% A, 80% B, a mixed portfolio?

And the answer is… Well it is not an easy straight forward one. First let’s check if:

  • We have all the information needed to make an informed decision?
  • We are sure that we know and understand, the performance criterias used by the bank?
  • We know and understand the financial models used to calculate all the decision variables, the risk and relationship value drivers?

To make a good decision, we must:

  1. Focus on the value drivers of the different opportunities. But how to define and measure value?
  2. Analyse the risk adjusted financial performance of each opportunities. But which risk and how to measure them?
  3. Analyse the value of the relationships we will gain and the value of the one we will lose! But what is customer value and how should we measure it?
  4. Plus, plus, plus…

A very simple question, but a complex problem to model and a tougher management decision than it looks! The data used in the calculations of this simple example are simple indication of the real world conditions. The models use standard, simplified formulas. I will not go into the detail of the calculations (if you need to understand the methodologies proposed you will need to contact me on cw@bankstrat.com).
The financial performance analysis.
To start the analysis let’s decompose the total interest rate revenue for the four portfolios. The results of this decomposition is summarised in the following table.


Interest Rate Revenues

Gross Interest Margin

Interest Margin less   Liquidity premium

Risk adjusted Margin

Net Operating Margin

Client A






Client B






C = 80% A +   20% B






D = 20% A +   80% B






Notice the huge differences in the results depending on the level of the analysis and the total reversal of conclusions: Portfolio B starts as the best option with 1.43% gross interest margin, but drops to the worst position if the margin is credit and liquidity risk adjusted (the interest rate risk is hedged in the Gross Interest rate Margin) and adjusted for operating expenses!

Based on the models used, the cost of hedging risks and the allocation of fixed and variable direct operational expenses, the asset portfolio with the highest return is Portfolio A which is a surprise, as it is higher than diversified portfolios C and D. This of course is due to the fact that the diversification benefits are not integrated in the price, in other words they are not handed over to the clients but reserved to the shareholders.

The shareholders need to invest in the bank enough capital to cover the expected risks and unexpected risks (as defined in principles by the Basel Accord). That amount of equity should include the diversifications benefits or deficits. The Economic Equity calculations indicate that the minimum requirements (Basel II without the additional cushions of BIII) as expressed as a % of the total asset (loan portfolio), are of:

Portfolio A:         0.78%

Portfolio B:         1.35%

Portfolio C:         0.80%

Portfolio D:         1.17%

Surprisingly portfolio C requires more capital than portfolio A, it is this more risky than A, although it is a diversified portfolio. This is due to the relative levels of the expected losses (a function of the Probability of Default, Exposure at Default and Loss Given Default), the variance of Probability of Default and the covariance of the portfolio PD’s.

The RORAC (risk adjusted Return on Risk Adjusted Capital) is calculated of the Economic Equity based on expected and unexpected risks, i.e. using the loan loss provision estimations and the diversified value at risk of the portfolios. On that basis the bank should decide on investing in portfolio A as the risk adjusted return is the highest, although Portfolio C is also attractive thanks to the benefits of diversification:

Portfolio A:         25.65%

Portfolio B:         11.12%

Portfolio C:         23.66%

Portfolio D:         13.70%

In theory, and in practice, the bank needs to generate value for its shareholders, hence the risk adjusted return (RAROC) must be greater than the Cost of Equity as this and only this will produce economic added value for the shareholders.

I used some hypothesis to calculate the minimum return to cover the cost of equity or “hurdle rate”. These cover the solvency strategy of the bank (single A), the beta of the shares, the market premium… i.e. all the variables of a classic economic value model as per the Capital Asset Pricing Model (CAPM). The hurdle rate calculated is 18.63% and consequently the Economic Value Added contributions (EVA) of the 4 portfolios are:

Portfolio A:         + 7.02 %

Portfolio B:         –  7.51 %

Portfolio C:         + 5.04 %

Portfolio D:         –  4.93 %

Only two portfolios create shareholder value the other 2 destruct value potentially because loans B is mispriced! Can I improve those conclusions by looking at a Return on Risk as defined in the Sharp Ratio (excess return on the standard deviation of returns)? This show that the diversification benefits of portfolio C would favour that investment rather than portfolio A.

Portfolio A:         1.27

Portfolio B:         0,63

Portfolio C:         1,41

Portfolio D:         0,83

Anything above 1 indicates that expected excess returns exceed the risk associated with that return, and C with a ratio of 1.41 is a clear winner.

The diversification benefits will be influenced by multiple factors and dependant of the valuation models used.

Diversified Portfolio STD   Undiversified Portfolio STD    Diversification benefit

A:  0.15789%                                0.15789%                                      0.00000%

B:  0.23844%                               0.23844%                                     0.00000%

C:  0.13501%                               0.17400%                                      0.03898%

D:  0.19335%                              0.22233%                                     0.02898%

We have not optimised the portfolios on a variance, covariance basis (correlation of 0.60), nor have we optimised pricing en operational efficiency. These management strategies would be defined in a pricing strategy and model.

Is the financial analysis complete? There is a last aspect that should be analysed.

If we calculate the Present value of the future Net Operating Profit contribution of each portfolio, we will also integrate another important aspect of annual profitability, which is the fact that each contract will produce annual returns over its whole life. In other words RORAC is an annual profitability measure not a measure of value of the whole stream of revenues! The equity values of contract with a return of 1% per year maturing in one year, is different to one producing 1% every year for the next 10 years.

We can estimate the value of the contract profits flows as the Present Value of those cash flows discounted at the appropriate risk adjusted discount factor. Again note I’m not calculating the total value of the contracts but only of the value of the excess returns after cost of risks and operational costs allocations.

Taking some calculation shortcuts, the values are as indicated in the table below. We can now calculate the “Fair Value” of the excess net returns generated. Without surprise Portfolio C remains the best choice if you look at the relative excess value to per value of risk unit, between ( ).

Portfolio A:         € 2,549 (462%)

Portfolio B:         € 529      (  63%)

Portfolio C:         € 2,117  (449%)

Portfolio D:         € 899      (133%)

This indicated that the sustainable long term excess value of portfolio A outweighs the reduced risk of portfolio C.

Relationship Adjusted Value decomposition

The last missing factors to be integrated are the relationship variables: the value of the expected behavioural attitudes of clients with the existing product holdings (attritions, prepayments, drawdown…) but also probability/ propensity that these clients will “buy” other products because of the relationship built on the back of the initial contract A and/ or B (cross sale, up-sale…).

There are many approaches to estimate the value of this potential activity growth (positive or negative growth). The most logic being to estimate the “fair Value” of the expected contracts sold, adjusted for their sales propensities, attrition risks and financial risks.

Combining both values will give us the true Life Time Value of the client or Client Fair Value.

From a financial perspective we are calculating the financial value of the bank’s goodwill created by the growth generated by using its business capacity (distribution network, operational back offices…). Hence we can try to reconcile the market capitalisation value of the bank by adding the fair value of the goodwill with the accounting fair net asset value.

Is this important? I believe that if you don’t measure something you will not manage it. By making the effort of measuring the drivers of value contribution you will define client relationship variables to be managed and priced. Examples of value drivers and business risks that can be quantified and managed include: cost of attrition risk, return on marketing campaigns, and contribution of next best product… plus of course “price the relationship value”!

It is not uncommon to see (even large and advanced banks) budget marketing strategies based on incomplete and sometimes misleading information. One was planning campaigns to reduce attrition of the least profitable clients will doing nothing to retain the more profitable ones, only because they were using average profitability data to segment their client base. Using Life Time Value over 85 % of the client would have been assigned a different profitability segment!


The consequence of mispricing and of approximate profit and value contribution are not trivial.

The mathematics does not need to be rocket science, but a robust analytical model adapted to the business model of the bank and its sales and marketing strategy should be implemented.

In the following blogs I will review the core principles of good pricing strategies.


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April 6, 2013 · 4:56 pm

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