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?

Answers
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.



I-View
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.

Navigating
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.

Conclusion
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
- NPV

Aug 15, 2009

Success

We all want to be successful. But what is success?

Success could perhaps be defined as achieving the Result you want by using your core Qualities at the right Time given the right Circumstances (place,people,weather, atmosphere).

In formula: R = Q x T x C

Another way of looking at success has been defined by Hevizi:


It’s not WHAT you know.
It is not WHO you know.
It is not HOW you deliver.
It is ALL of it.


In the new world of tough competition for positions, careers and recognition it is important to remind ourselves that it takes 3 to be successful and compete.

We can look at this as the following formula:

SUCCESS = IQ * EQ * XQ

Success explained
A more sophisticated, humorous yet interesting approach of success has been defined by Alain de Botton in the next TED video. Alain examines our ideas of success and failure:
Is what you define as success really your personal defined success or perhaps the unconscious copied succes definition of somebody else?

He points out that believing in winners and loosers is a narrow and wrong way of defining the world. On top of this, he gives randomness a place in the definition of success and stresses that there can be no success without loss....




Wrapped up, success could be defined as being satisfied and happy with your choices, actions, gains and losses.....

So never give up, discover the secrets of success and enjoy it!

Youtube Success Links:
Quest for success
Success by Deepak Chopra


Jul 27, 2009

Actuarial Fallacies

Just some light stuff, to chew the cud during holidays...

A good friend tells you that a certain 'John Nevermet' is an introverted professional and is either an actuary or a salesman.

Which one do you think John most probably is?


If your first thought was: an actuary, congratulations(!), you just got caught in what is called a classical

Thinking Trap

Most people - not actuaries of course ;-) - are tempted to think John is almost certainly an actuary.On the other hand, they think of a salesman as 'outgoing', 'extrovert' or maybe 'pushy', but certainly not as 'introvert'. Wrapped up : John is an actuary....

Sorry, but - as you know - this logic conclusion is definitely wrong. It neglects the fact that salesmen outnumber actuaries at most 100 to 1. Before you would even start to consider John's character, you should have concluded that even when all the actuaries were introvert, there would only be a small 1% probability that John is actually an actuary (only in the unlikely case that less than 1% of the salesmen would be introvert, this option would be logically to consider).

Top 10 Thinking Traps
This foregoing simple example is just one of the fabulous Top 10 Thinking Traps Exposed by Luciano Passuello.

On his blog Litemind, Luciano explains in a 5 minute 'must read' called 'How to Foolproof Your Mind' the next interesting and most harmful Thinking Traps, including suggestions on how to avoid each one of them. :

  1. Anchoring Trap: Over-Relying on First Thoughts
    Your starting point can heavily bias your thinking
  2. Status Quo Trap: Keeping on Keeping On
    We tend to repeat established behaviors
  3. Sunk Cost Trap: Protecting Earlier Choices
    Sunk cost shouldn’t influence a decision, but it does
  4. Confirmation Trap: Seeing What You Want to See
    Being less critical of arguments that support our initial ideas
  5. Incomplete Information Trap: Review Your Assumptions
    Overlooking a simple data element can mislead our intuition
  6. Conformity Trap: Everybody Else Is Doing It
    Other people’s actions do heavily influence ours
  7. Illusion of Control Trap: Shooting in the Dark
    The tendency to overestimate our personal control
  8. Coincidence Trap: We Suck at Probabilities
    A “miracle” is - given enough attempts - possible!
  9. Recall Trap: Not All Memories Are Created Equal
    “Special events” have the potential to distort our thinking
  10. Superiority Trap: The Average is Above Average
    People have much inflated views of themselves

Thinking traps are a special form of fallacies.

Example
A nice and triggering example of a composition fallacy is:
I fit into my shirt... My shirt fits into my luggage...
Therefore I fit in my luggage...

Can you tell what's going wrong here?
Yes? Then get ready for the next fallacy phase.

Although there a complete list of fallacies, another new interesting subset could be defined as 'Actuarial Fallacies'....

Actuarial Fallacies
Except for a 1988 homonymous, humorous intended, nevertheless still actual and relevant document by Charles L. McClenahan, nothing much has been published on actuarial fallacies.

Apparently fallacies are not an issue on the Actuarial Globe.

Therefore, I'll confine my remarks to a few actuarial events, of which each one could easily be nominated for the fictional 'Grand Actuarial Fallacy Prize':

  1. Longevity risk can be easily managed
    Longevity slowly but steadily increases. It's not a yearly smashing or impressing risk, but over the years it has the characteristics of a killing sniper: when you finally discover the accumulated longevity loss after a few years, it's almost too late to handle and take appropriate measures.

    Actuaries could have foreseen a few decades ago that the average life span would keep rising and adequate measures had to be taken at once. Instead, actuaries failed to catch the implications of the rise in longevity and were caught by the proverbial 'boiling frog effect'. In short: actuaries failed to act in time....

  2. Stocks are a hedge against fixed-income liabilities
    Already in 1994 in a document called 'On The Risk of Stocks in the Long Run', nobody else than Zvi Bodie already proved that stocks are not a hedge against fixed-income liabilities even in the long run.

  3. Credit Crisis
    Actuaries have failed in foreseeing the credit crisis. We have greatly underestimated the developments and put our head in the sand. We have trusted business plans promising ROEs of 15% and more.Read more in Actuary-Info's : "Wir haben es nicht gewußt!"

  4. VAR Model
    As an article in The Actuary shows, we got intimidated and overruled by the 'magic' quants with their Value at Risk (VaR) models. We did and do know better as actuaries, but missed the boat. Actuaries should be more than professionally trained in giving 'push back'.

  5. The relationship between risk and return
    As we know this risk-return relationship is central to strategy research and practice.

    In measuring risk as the variance of a series of accounting-based returns, Bowman obtained the puzzling result of a negative association between risk and mean return.The expected positive association between risk and return turns out to be elusive.

    Henkel explains in two must-read articles 'Risk-Return Fallacy' (2000) and The Risk-Return Paradox for Strategic Management: Disentangling True and Spurious Effects the problems and solutions in this field.

    Instead of only following what's happening on the other side of the balance sheet, actuaries should mobilize themselves and add some new insights!

    Asset Actuaries, please rise!


    Es ist nicht genug zu wissen, man muss auch anwenden
    - Johann Wolfgang von Goethe -

Now that we've unmasked several fallacies, in special the 'introvert actuary fallacy', let's conclude our fallacy course with a 'lessons learned?' actuarial anecdote:

Why it's better to work with an imperfect actuary
We all know: A perfect actuary draws perfect conclusions form perfect datasets.

Then of course : A perfect actuary certainly draws "wrong conclusions" from imperfect data.

It's a fact that the data are always imperfect.

So that we can conclude that there is at least a small chance that an imperfect actuary may draw the right conclusion.


That's why it's better to work with an imperfect actuary.

Client Quote
As we know, clients are always right. Remarkably, the next client quote seems to stress the mentioned successful outcome of the imperfect actuary:
I once had an actuary tell me that, because the future is uncertain, his numbers were almost certainly wrong, but he believed they were less wrong than guessing outcomes with no analysis.

You think - by now - you know everything about fallacies?
Well, test it by taking the next fallacy Quiz:


Success!

Original source :
The November 1983 Random Sampler article Actuarial Fallacies