Showing posts with label discount rate. Show all posts
Showing posts with label discount rate. Show all posts

Nov 1, 2011

Sustainable Discount Rates

Steering pension funds on a 'one point' Coverage Ratio is like trying to proof global warming on a hot summer day...... It's useless.


First of all the complete pension fund balance sheet is based on market value.

As there is no substantial market for pension liabilities, this implies that pension liabilities have to be valued on basis of some kind of arbitrary (artificial) method.

In the U.S. this has led to the (irresponsible) high discount rate of 8% for state pension funds based on the 'expected' long term return without a kind of correction (subtraction) for 'risk'.

In de Dutch market, pension funds have to rate their liabilities on basis of a maturity dependable risk free interest rate, the ‘Nominal interest Rate Term Structure’ (RTS), as ordered by DNB (the Dutch Regulator).

Here's the outcome of this risk free interest rate (RTS) over the past 10 years, including the 10-y average RTS...

Ever since DNB ordered this 'artificial discounting method', pension fund board members didn't get a good night sleep. As the RTS juggles on a daily basis, every morning pension members wake up with the latest 'RTS news surprise of the day'.

You can play the RTS juggle (worm) here:

As coverage ratios are based on the RTS, they shuttle hither and thither as well and executing a long term pension fund strategy becomes more or less like riding the famous (market) bull in a rodeo show.

On a Dutch IPE congress, Angelien Kemna - chief investment officer of the €270bn asset manager APG - warned that the current swap-curve discount criterion forces pension funds to take unwise "significant long-term measures".

Kemna favors an average yield curve or a more straightened version of the current one for discounting liabilities.

The new Dutch Pensions Agreement foresees that pension funds can choose their own discount rate, as pensions are no longer guaranteed!

Indeed, it's time to stop this complex discount circus. But it's also time to stop 'one point estimate' Coverage Ratio steering.

A new look
Let's take a look at a characteristic discount rate dependence of a traditional pension fund like ABP.

Valuing ABP at an (derived average) RTS of 2.69%  (September 2011), ABP's discounted assets fail to meet the discounted liabilities, leading to a coverage ratio of around 90%.

However this kind of risk free valuing is - for sure - too conservative, as ABP's aims at an underpinned strategic expected return of 6,1% on the long term and has a convincing track record of  5 and 10-year moving average returns:

Returns (%) Pension Fund ABP 2993-2010
Yearly Return16.5-1.016.411.811.912.910.03.2-0.7-

5Y MA Return

10Y MA Return

Or in Graphics:

As long as a pension fund (like ABP) continues to perform (on 5 or 10-years moving average) rates that outperform the (derived average) risk free discount rate, it's seems ridiculous to force such a pension fund to discount at a 'risk free rate', as this obliges the fund to change his strategic asset mix to a less risky mix and an suboptimal return.
In turn, these suboptimal returns will lead to an asset shortage. With a vicious cycle of decreasing risk as a fatal result in the end.

Sustainable Discount Rates
In an excellent discussion paper (2006) Jürg Tobler-Oswald proves that the optimal discount rate lies between the risk free rate (RFR) and the investment strategy’s expected return (ER) depending on how good the hedge against the fund’s cash  flow  provided by its investments  is:

Discount Rate1 = RFR + FCash Flow(RFR-ER)

Another - more simple and practible - discount rate could be defined as the average between the free discount rate and the X-year (e.g. X=5, or 10) Moving Average Return of the last X-Years (MAR(X)).

Discount Rate2 = [ RFR + MAR(X) ] /2

As long as MAR(10), MAR(5) and ER stay larger than the interest rate that matches a coverage ratio of 100%, discounting by means of one of the new sustainable discount methods seems sound and safe......

Whats left is that the average (geometric) risk premiums during the last 10 years have turned out negative:

Historical Equity Risk Premiums (ERP)
ERP: Stocks minus T.BillsERP: Stocks minus T.Bonds
PeriodArithmetic Geometric Arithmetic Geometric

This implies (moreover) that it is important that the discounting rate of a pension fund should be based on a sustainable sound weighted mix of:
(1) proven historical performance
(2) a 'save' risk free rate
(3) realistic future return assumptions

Related Links/ Sources
- Kemna IPE article (2011)
- An investment based valuation approach for pension fund cash flows (2006)
- Ignoring the risk in risk premium in State Pensions(2011)
- DB: What went wrong? (2011)
- Pension Fund Valuation and Market Values (2000)
- Aswath Damodaran: Equity-risk-premiums-2011-edition
- Dutch: ABP coverage ratio

Dec 26, 2010

Discounting the future

Actually, who are we actuaries to pretend that we can discount the future? Who's able to predict the future 50 years or more ahead in case of a pension fund?  No, we're not crystal ball discounters, we're risk managers 'pure sang'. And as discounting risk managers we're pretty sure about two things:
  1. The increasing uncertainty (fogginess) of future cash flows slowly kills its discounted predictability in time

  2. Risk free discount rates doubtlessly include the risk of changes in future discount rates, but nevertheless vary in time.

    Risk free discount rates are volatile and are unpredictable on the long run.
Historical development
Let's take a look at discounting developments from a helicopter's perspective...
A few decades ago, discounting was simple:

Discounting Around 1980
Whether you were in the insurance or pension business, way back in the last century actuarial business was simple. All you had to do as an actuary, was discounting the assets and liabilities at an explainable 'long term average' and 'realistic save' (whatever this means in today's perspective) discount rate and it was done. Subtracting discounted liabilities from the discounted assets, also resulted in a clear undiscussable equity size:(E= A - L) and - in case of a pension fund, the coverage ratio : (CR=A/L).  

Discounting Around 1990
As computer and calculation capacity increased around 1990, actuarial models became more complex. Instead of as single projected cash flow, more complex cash flows and scenarios entered the actuarial model scene. With more sophisticated computer calculation power we were able to calculate and underpin risk-return investment scenario's that led more to more risky 'risk controlled' investment policies.

'Risk' was translated into (replaced by?) 'volatility' and 'volatility' was translated into 'variance'. Thus future risks where estimated on basis of projected historical variance and (later) with help of VaR models.

However, 'Risk' was mainly defined on (and restricted to) the left side of the balance sheet: the assets. In line with this view, the insurer's  equity could be simply expressed as : E= A - kA.σA - L  (mp= minimum position) , or in case of a pension fund, the coverage ratio: CR=(A - kA.σA) / L   (mp).

Discounting Around 2000
More than a decade later, beginning 2001, fair value accounting and market value broke through. Not only stocks had to be valued at Market Value, but also bonds. As a consequence the volatility of the left side of the balance sheet increased more than ever.

As actuaries we thought we would be save on the right side of the balance sheet were things were steady and calm as always... However, a few years later the 'Actuarial Sleeping Beauties' were kissed to life as Market (consistent) Value was introduced with regard to discounting liabilities. This development fired the starting gun to a swapping right size of the balance sheet.

Now insurers (minimum) equity got squeezed up between two volatility monsters, assets and liabilities:  E= A - kA.σA - L -kL.σL (mp).
Pension funds had to become real acrobats to manage their new wobbly coverage ratio: CR= (A - kA.σA ) / (L + kL.σL)     (mp).

No wonder pension funds and insurers got into trouble when the credit crises caused the final blow.....

Rebuilding stability
In Europe insurers are trying to rebuild stability by means of "Solvency II". Pension funds are trying to find their way out by suggesting more conditional pension rights. Some have even suggested to steer (valuate?) pension funds on basis of a kind of "moving average method" (asset returns or coverage ratio).

Other  'actuarial pension experts' have told me that we should stick to market value and accept the consequences, e.g. just accept that coverage ratios can stay below minimal level for several months, without anyone panicking..... Simply explain to pension fund members that the pension fund is long term well funded and there's no reason for panic if the coverage ratio breaks down for a short period....

Don't Panic......
This reaction reminds me of a weird family experience, when we where on holidays many years ago in a village called Ballyheigue (west(ern) Ireland).

Don't panic!
That afternoon my wife, the kids an I arrived in Ballyheigue. We stayed in a lovely local hotel near the fantastic west coast of Ireland.

The local assistant manager welcomed us and pointed out that there was a small minor (2x!) problem that could occur: Last week, at irregular moments, the hotel alarm had gone off several times, this could probably happen again. Reassuringly, he explained  that in the unfortunate case the alarm would go off, we shouldn't panic and just stay calm, as it would probably be a false alarm.....

That night we confidently went to bed early......

Then, at 01.30 AM that night, suddenly the fire alarm goes off. An ear piercing sound cuts through our ear drums... Within 2 minutes we - all hotel guests including my family - are all outside, despite the reassuring words of the hotel assistant earlier that night.


From this simple experience we can conclude that 'reassuring words' don't help in panic circumstances. Ergo, it's impossible not to panic in case coverage ratios go down for several months....

Convincing people 'not to panic' in case of 'clear panic signs' is an almost impossible task.  Once one mentions the word 'panic', all human systems get in a kind of  non stoppable alarm mode. It's like the famous scene from Fawlty Towers :

Related Links:
- Pension Actuary's Guide to FINANCIAL ECONOMICS (2006)
- Pension contracts and developments in pensions in The Netherlands (2009)
- One of those superb hotels in Ballyheigue: White Sands Hotel

Mar 13, 2010

Magic Banking

Based on an idea as presented in a joshing blog by Henry Blodge, CEO of The Business Insider, here's the slightly changed formula for making thousands of investors happy, becoming a millionaire within months while having a successful career as well.

Become a banker!
All it takes, is to start a new bank. Don't worry, it's simple as will be shown.

This is how it works:
  1. Form a cooperative bank called: Cooperative Magic Bank (CMB).
    A cooperative bank is a financial entity which belongs to its members, who are at the same time the owners (shareholders) and the customers of their bank.
  2. Appoint yourself CFO together with two of your best friends as Board members. Set your yearly Board Bonus at a modest 10% of CMB's profits.
  3. Make a business plan (this blog IS the business plan)
  4. Raise $ 100 million of equity and $ 900 million of deposits, as follows
    • Offer your prospects/clients a guaranteed 4.57% guaranteed return on investment.
    • Offer a 70% yearly profit share. First year return on investment guaranteed 13,35% !
    • Everybody who wants to join the bank becomes a 'Lucky-Customer-Owner' (LCO)
    • Every LCO is obliged to invest 10% of his investment as shareholder capital.
    • The other 90% is invested in the CMB-Investment Fund (CMBIF).
    • CBMIF guarantees the return (and value) on the LCO's account based on a 30 year Treasury Bond
  5. Borrow $3 billion from the Fed at an annual cost (Federal Discount Rate) of x=0.75%.
  6. Buy $4 billion of 30-year Treasury Bonds paying y=4.57%
  7. Ready! Sit back and enjoy high client satisfaction and your Risk Free career and bonuses as a professional banker!

Magic Banking
Wrapped up in a 'Opening Balance Sheet and a first year ''Income Statement', this is how it looks like:

This is how the FED helps you to become a millionaire. but the party is not yet over.....

Pension Funds and Insurance Companies
If your the owner of a pension fund or an insurance company, starting a 'Magic Bank' could help you achieve a total 'risk free' return of 4,57% with an upward potential of 13,35% as well.

So why should you set up a complex investment model that you don't really see through, to achieve a risky 6% or 8% of return on investment, if you can have more than a 'high school comprehensible' 10% return without any substantial downside risk by starting a Magic Bank instead?

Together with the new Basel and Solvency regulation, this 'magic bank principle' will cause banks to sell their investments in more risky assets like insurance companies. On the other hand, insurance companies and pension funds will probably be interested in starting new banks to profit from the FED's 'free credit lunch'.

Criticasters and Risk
Some criticasters will rightfully point out that the magic bank is not completely risk free. Indeed there are some risks (e.g. the treasury bond volatility), but they can be adequately (low cost) managed by means of stripping or derivatives (e.g. swaptions).

Of course there's also the risk that the Fed will raise the short rates (Federal Discount Rate).In this case, instead of using derivatives upfront, one might simply swap or (temporarily) pay off the FED loan. Yes, your return will temporarily shrink to a somewhat lower level. But who cares?

Moreover, keep in mind that as long as we're in this crisis, the Fed's short money will be cheap. Don't ask why, just profit! By the time the crisis is over and Federal discount rates are more in line again with treasury notes, simply change your strategy again.

And if - regrettably - the federal discount rate and the treasury bond rate rise at the same time, simply book a life time trip to a save sunny island to enjoy your 'early pension' of $ 11.1 million (ore more).

For those of you who still doubt and for all of you who like a humorous crash course in investment banking, just click on the next video by Bird & Fortune....

Let's get serious
Although for us actuaries it's clear that because of the Asset Liability Mismatch, the magical bank is a running gag, the principles and consequences of the situation as described above are bad for the economy.

Financial Health Management
Banks and financial institutions in general are discouraged to act in their primary role as risk transfer institutes by performing on bases of professional calculated risk.

Why would they take any additional (credit) risk if they can generate their revenues almost 'risk free' with help of the Fed?

We all know that without risk, there's no economic added value either. Continuing this Fed policy will lead to Bob hopes:

A bank is a place that will lend you money, if you can prove that you don't need it.

Maintaining the current Fed policy keeps the banks alive, but ill.

What's needed is a new Federal Financial Health policy.

Over the last decades the relative equity (equity in % of assets) of Banks deteriorated from a 20% level to a 3-5% level in this last decade.

Banks need to be stimulated to take appropriate healthy risks again, while maintaining a sound individual calculated 'equity to assets ratio', increased with an all over (additional) 5% risk margin.

The Fed should therefore act decisively and:
  • stop the ridicule and seducing leverage risk levels
    Redefine the Capital Adequacy Ratio (CAR). The new Basel III leverage, calculated as 'total adjusted assets divided by Tier 1 capital', won't do. Strip the nuances, limit 'adjusting', add a surplus.
  • Limit and make all new financial products subject to (Fed) approval
  • Limit the proportion of participating in products that only spread risk (e.g. Citi's CLX) instead of neutralizing or matching risk
  • Raise the discount rate as fast as possible,

to prevent moral hazard and economical laziness that eventually undoubtedly ends in a global economic melt down.

However, there's one small problem..... The FED has to keep the discount rate low because otherwise financial institutions that run into trouble aren't able to finance their loss in a cheap way and will activate the nuclear systemic risk bomb (chain reaction).

It seems we're totally stuck in a governmental financial policy paradox. Nevertheless the FED should act now!

- Henry Blodge Video on Modern marketing...
- 30 year treasury bonds
- Historical Federal discount rates
- Can Basel III Work?
- The Economist: Base Camp Basel (2010)
- Citi's Financial Crisis Derivatives Should Be Banished From Earth
- Capital Adequacy Ratio (CAR)
- Treasury yields

Aug 30, 2009

DCF: Discounted Crash Flow

I remember in a 2007 client panel discussion I was chocked to hear that three large company CFOs of name and fame, without blinking an eye, stated that they were running their company on basis of a narrow quarterly time schedule, no longer. Long term investments? Out of the question. Pension obligations? Rather not, please... Project payback periods: 3-6 months, in exceptional cases a maximum of a year.

What was happening?
How come, CFOs have become that short term focused?

It's easy to come up with answers that pass the buck:
  • Extraordinary shareholder demands
  • Bonus Structure,
  • Greed, Grab Culture
However, despite and behind all this, there is a deeper cause.

Thinking concept
This short term focus, that is not limited to CFOs, is the logical consequence of the way our thinking and modeling has developed during the last decades:
  • we try to exclude risk at any price, instead of managing it.
  • we struggle and sometimes even fear to transform long term cash flows into discounted cash values or NPVs

According to a 2002 survey, more than 85% of the CFOs say they use NPV-analysis in at least three out of four decisions.
As actuaries we're also part of this family of Discounted Cash Flow (DCF) Experts. Some of us might even have thought there's nothing more to learn about DCF...

Of course we understand every technical detail of our DCF-model, but let's take a look at some classical aspects of the DCF technique from a different angle. I'll call this angle the I-View, with the I of Important.....

DCF properties
As we know the value of a future cash flow (cf ) , depends strongly on the choice of the discount rate (r) and the moment in time (t) of the cash flow. The further away (in time) the cash flow and the higher the discount rate, the lower the DCF value.

From an I-View perspective one might say that in the DCF of a constant cash flow, the contribution of the cash flow in year 10 is ruffly half as Important (UnImportant-effect) as a cash flow in year one, assuming a discount rate of 7%.

Another way of saying: This one off cash flow is only of 51% Importance to us.

Although this might not surprise you, a often heavy underestimated effect is that the UnImportant-effect rapidly increases in case a particular discounted cash flow in year (t) is part of and expressed as a percentage of a discounted fixed term (or perpetual) cash flow stream. This is illustrated in the next graph (base: r= 10% discount rate).

De relative contribution of a cash flow t, soon loses more and more Importance when it's part of a constant cash flow stream. As the term of this cash flow increases to infinity, the relative contribution of any 'one year cash flow' becomes rapidly UnImportant.

I-View 1: Discount Rate Adjustments
As we know, the choice of the discount rate depends on the type of cash flow. Cash flows with substantial risks are often discounted with an adjusted (higher) r, according to the (CAPM) formula:
r = rf + β×(rm - rf)
with: rf = risk free rate, rm = expected return on the market and β = (beta) a measure of the (opposed to the market) cash flow risk.

It's obvious this CAPM-method amplifies the mentioned 'UnImportant-effect' of long term cash flows.

In times of financial crisis, when we're inclined to become more risk averse, the 'UnImportant-effect' grows even more, as we are inclined to adjust r for fear:

r = rfear + rf + β×(rm - rf)

Moreover in general, the longer the cash flow term, the higher the (compound) expected risk, and therefore the higher the discount rate (r). Instead of a constant r, there's a need for a variable r, rt, that increases in time, intensifying the 'UnImportant-effect'.

I-View 2: Discount Rate of Liabilities
Another DCF example: A pension fund has extremely long term liabilities. A cash flow of - let's pick - 50 years ahead, is no exception, but only accounts for about 14% of its cash flow in the discounted liabilities of the pension fund (abstracting from mortality and assuming a discount rate of 4%), and is therefore implicit considered (rated) less Important compared to more recent cash flows. Because there's no real or substantial market for long term cash flow pension obligations, r is even harder to define. Increasing r for this risk is like putting the cart before the horse: The UnImportance effect will increase. For internal valuation r should be decreased instead of increased, but how.....?

I-View 3: Short term Ruin Probability Nonsense
A third effect is that a 0.5% yearly ruin probability sounds safe, but nevertheless compounds up to a risk of 14% over a period of 30 years and even more on the long term.
Years Cum.Ruin Risk
1 0.5%
10 4.9%
20 9.5%
30 14.0%
40 18.2%
50 22.2%
60 26.0%
70 29.6%
80 33.0%
90 36.3%
100 39.4%
FCLTOS, Financial Companies with Long Term Obligations, like banks, insurance companies or pension funds are by definition companies that have to stay ruin proof on the long term. Managing these kind of companies on short term ruin and certainty models is completely nonsense.

However, there's nothing much FCLTOS can do about it. A long-term certainty level of 99.5% (0.5% ruin risk) over a period of 40 years would imply a yearly certainty level of 99.9875% (0.0125% ruin risk). Even if it would be possible to minimize the technical risks to such a low level, it would be overshadowed by unquantifiable external outside risks (e.g. nature disasters). Anyhow, government regulators should define a target with regard to an appropriate choice of a long-term certainty level and should distinguish between short term and long term certainty in their models.

These examples illustrate that the management FCLTOS, giving these DCF-like methods, do not have another choice than to focus on the near future (5-10 years) and - by method - are not obliged and therefore also not will focus on the long term effects.

Managing FCLTOS, is like navigating an oil tanker from A to B between the ice floes. You have to avoid the short term (nearby)
risks (the ice floes) while at the same time keep sight and hold direction on your long term target (port B) in order to succeed.

Translated to a pension fund: manage your liquidity on the short term and your solvency and coverage-ratio on the long term. Any captain of an oil tanker would certainly be discharged immediately when he would make a dangerous change in course today to avoid an actual clear, but in the future certainly changing (moving targets) ice floe situation 50 km ahead. Yet, government regulators and supervisors are forcing pension fund 'captains' to undertake such ridiculous actions.

Steering on short term recovery plans , publishing and publicly discussing coverage-ratios and finally 'valuing pension funds' solely on market value (given that the market for extreme {> 30 years} long term assets and liabilities is extremely 'thin' and volatile), is therefore dangerous and apparently wrong (nonsense) and leads to discounted crash situations.

But there's more that contributes to discounted crash management......

One off negative cash flow in the future
Let's compare two (almost) equal cash flows, CFa and CFb:
- CFa: 30 year constant cash flow of yearly $1,
- CFb: like CFa, but in year 25 a one off negative cash flow : -$1

Although a negative cash flow of $1 in year 25 will probably ruin the activities an cash flows in later years, the NPV of the two cash flows only differ slightly and the calculated IRR of CFb (9.76%) is also just slightly lower than the IRR of CFa (10%).

One might argue that because CFb is obviously a more risky cash flow, the adjusted r has to be raised. This is true, but nevertheless intensifies the so called UnImportant-effect: the relative weight of the 'year 25 cash flow' in the NPV decreases.

Last but not least, what explains the short term attitude and those extreme short periods of several years or months, some CFOs practice as a time frame to run and control their company ?

Certainty Erosion
These extreme short periods are the consequence of the No. 1 concern for CFOs:

The fundamental and increasing lack of ability to forecast results

Let's do some rule of thumb exercise....

Assume the certainty level of calculating a sound financial forecast in the next period (year, quarter, month) is estimated by a CFO at C%.

Now take a look at the next table (on the right) that shows the average extrapolated certainty level (AC) over a number of periods P.

In formula:

Some examples from the table:
  • A CFO that estimates the 'next quarter result' with a certainty level of 70% (C=0.7), will probably not burn his fingers by presenting a full year forecast with an average expected certainty level of 44%.
  • A CFO of a company hit by the current financial crisis, estimates the certainty of his companies January results at 60%. The board announces it's not able to estimate the full year result. Right they are, with a 60% monthly certainty level, the full year result would have a certainty level of only 12%.....
  • Even a CFO with a superb forecast certainty level of 90%, will be cautious with a 5-year forecast (certainty level 74%).
  • A 'best of class actuary' that estimates the certainty level of his data at 90% on a yearly basis, will have a hard time in answering question about the certainty level of his projections over 14 years (50%?).

The I-View consequence of this 'compound certainty development' is that even at high levels of (yearly) certainty, the (average) certainty of cash flows after already a few years in the future, erodes.

The effects of Certainty Erosion are enormous. The wall of haziness that is created in a few years - at even high levels of certainty - is astonishing. Never 'believe' a long term one point forecast. Always request variance and certainty level(s) of presented forecasts.

We may conclude that DCF is a superb technique as such to analyze and value cash flows. To prevent ending up in a 'crash flow', DCF has to be implemented by professionals who realize that the essential point of DCF is not just the technique itself, but the way the parameters, used in the DCF-models, are defined.

In order to be able to really take responsibility in managing a company, the Board of a company should be involved in the selection and consequences of the deeper and underlaying DCF-parameters. Enough work for actuaries it seems....

Related Links:
- Some comments on QIS3, (Long term certainty levels)
- Quantifying Unquantifiable Risks

Dec 2, 2008

Client Lifetime Value (CLV)

In a Harvard Business Review called "Why satisfied customers defect", Jones & Sasser explain that even a 80% 'satisfied clients score', is no guarantee for sustainable success.

Common management misconceptions are:
  1. A client satisfaction level below complete or total satisfaction is adequate.
  2. It's not profitable to invest in changing customers from 'satisfied' to 'completely satisfied'.

Their conclusion is that, in most cases, 'complete customer satisfaction' is key in order to secure customer loyalty and generate sustainable financial performance.

Loyalty & Satisfaction
Despite of what sometimes intuitively is assumed, the relationship between loyalty and satisfaction is in most cases not linear, but depends on the competition level of a specific market segment.

In a Dutch presentation, called "CRM Myths", direct marketing professor Janny Hoekstra confirms this relationship and shows that even 'satisfied clients' are in the so called 'indifference zone'.

The 'art of client management' is obviously to create 'Apostles' and to avoid creating 'Terrorists'.

So stimulate, instead of discourage, your clients to give you feedback and to complain, because this is the only way to create new apostles.

A relatively new and, according to Harvard (The One Number You Need to Grow), probably better method to measure client loyalty is the 'Net Promoter Score' (NPS). Simply score your clients on a 0-10 points scale on the question: "Would you recommend company X ?'

Now simply calculate the NPS score (%) as:
NPS = Promoters% (rating 9&10) - Detractors% (rating 6 or less)

NPS scores of 75% or more prove world class loyalty.

Loyalty effect
Another, intuitively driven, perception is that the more customers are loyal, the more they generate profit.

In general this seems true, however as Hoekstra shows: not every 'more loyal' client is also per definition 'more profitable'.

Just like Reinartz (Insead) stated in his article : 'Not all custumors are equal'.

Reinartz defines different client groups called: Butterflies, Strangers, True Friends and Barnacles.

Each group urges a different approach in a Customer Client Strategy.

Investing in 'True friends' appears essential and eventually pays out.

Customer Lifetime Value
Actuaries that combine marketing an actuarial sciences could help by defining and calculating what is called: The Customer Lifetime Value (CLV)

The CLV of a specific client(group) could be defined as the discounted value of the yearly margin (m = profits - costs), with discounting rate (i) and the (client) retention rate (r).

CLV:Rule of thumb
In the strongly simplified case with constant margin, the CLV - as a rule of thumb - could be defined as the margin (m) multiplied with the so called margin multiple = r/(1+i-r).

Example: Discount rate = i =12%, Retention rate = r = 90%, results in a CLV of approximately 4 times the yearly margin.

As is clear from the formula and table above, the choice and impact of the discount rate is only significant in combination with a high (>90%) retention rate.

Modeling and creating Client Value is not only in the interest of the shareholder, but moreover a case of creating creating added value for clients, in particular 'best satisfied clients'.

More info at: Modeling CLV(insurance), Customer Metrics