Showing posts with label return. Show all posts
Showing posts with label return. Show all posts

May 1, 2011

The Ten Actuarial Commandments

We all (think to) know The Ten Commandments from the holy scripts by heart, do we?

Now close your eyes to see how far you can get in quoting those simple ten guidelines in life.............

The Ten Commandments for Investors
Just like the Ten Commandments for Man, God - more specific - created The Ten Commandments for Investors. Let's compare the two, while - at the same time - you can check out your Commandment-Memory on Man as well:

Risk-Return-Supervision Development
As you may have noticed, The Ten Commandments are a mix of rules-based and principles-based principles.

Just as in our own life, it's interesting to see how we apply and implement these two different kind of rules during the evolution of a financial institution (insurance company, pension fund, bank, etc.):

In time, the ideal supervision model consists of three phases:

  • Phase I: No rules
    In this phase we cannot value or the company. Chances are substantial the company is 'at risk'.

  • Phase II: Rules-Based Supervision
    In phase Ia 'Rules' are mostly perceived as 'Have to's" . As a result Risk will be reduced, but Return as well. Once the board, actuaries and financial specialists are becoming aware and will see the advantages and new possibilities of managing risk. 'Have to's" will develop into 'Want to's" . The Risk-Return Ratio will increase  and even a better Return will result.

  • Phase III: Principles-Based Supervision
    Just like with the implementation of Rules-based Supervision, in case of Principles-Based Supervision, the Financial Institution needs time to adept to the new situation. At first there might be a unbalance between Risk and Return. It takes time to calibrate Risk and Return again.

    After a while actuaries, investors and management will translate Rules-Based principles into own rules that fits the company's specific risk in an optimal way. The company will be able to take more risk and to optimize its own Risk-Return Ratio.

Take a look at your own company's development and see for yourself where you fit in on the Risk-Return-Supervision lines....

It might be possible that you have to conclude that you aren't able to increase your Risk-Return ratio in the end. In this case it's likely you've become (so called) 'Supervisory Compliant': Your risk appetite probably corresponds more or less with the supervisor's minimal risk view. Instead of redefining your own risk appetite and restructuring your products from a risk-management perspective you merely implied new regulations and supervisor guidelines. As a result your Return and Risk-Return Ratio implode....

Ten Actuarial Commandments
Having learned the possible effects of supervisory rules in practice, we may now conclude with The Ten Commandments for Actuaries.

The Ten Commandments for Actuaries
  1. There's only one God, as he's omnipotent he's also an actuary.
    As you're only an actuary: be humble.....    Remember: As God wants something in Return, you'll have to take Risk!!
  2. Reality can't be comprised in a model.
    Use your brains. A model is a help, not a decision machine. Don't mix up God with Risk or Chaos. Chaos for us humans (actuaries) can be defined as "Unrecognized Order" (quote). 
  3. Never blame anything or anyone than yourself for an unexpected or negative outcome.
  4. Be consistent, act sustainable. But change your opinion just in time, if circumstances or facts urge you to do so.
  5. Alway show respect to others, even if you think different. Appreciate where you come from. Nobody is perfect, not even you.
  6. As there is no 'right' model, never criticize other models, actuaries or other people. Try to give your opinion without slaughtering the other.
  7. Never advice or state anything you do not really mean or cannot defend.If you're not sure or don't know, tell it or get help.
  8. Always cite your sources or give credits to others that helped you.
  9. Don't 'steal' the advice.
    Never include the final decision to be taken in your advice. Wrap up arguments, consequences and present scenario's so the board has to make a choice and not you.
  10. Don't get carried away by results, reports or performances of others.
    Stick to your own consistent approach.

Apply supervisory rules and actuarial commandments in a conscious way...

Feb 27, 2011

Gold: Risk or Rescue?

For those of you who are still doubting...we live in a crazy world....

The Dutch Central Bank (DNB) has ordered (by court !) the glass-workers pension fund (SPVG) to decrease its 13% Gold allocation to less than 3% within two months.

DNB and Court arguments in short:
  1. An investment of 13% is not in line with the Prudent Person Rule, which includes the principle that: assets must be invested in such a manner as to ensure the security, quality, liquidity and profitability of the portfolio as a whole.

  2. Gold is a commodity and holding 13%  is classified as 'overweight' in comparison to the 2.7% average that Dutch pension funds have invested in commodities.

  3. 15% allocation in Gold is a 'concentration risk' that could lead to a coverage shortage if the gold price imploded (volatility of Gold is relatively large).

At first, it seems unbelievable that important decisions, with substantial financial impact  - even in Court - are not based on financial facts, but on 'general principles' and the way the market 'used to do it'.

A decision based on an argument that refers to 'the average pension fund,' would more or less imply that pension funds would not be allowed to base their investment strategy on their own specific situation or a changing market outlook. Pension Fund Boards appear to be  'captured' by the market and a Supervisor who obviously has a hard time to develop 'own standards'....

Secondly, DNB actually takes over the investment responsibility of the pension Board. One could wander if DNB is (sufficiently) aware of the possibility that it can be hold financially responsible for the effect of a negative outcome if it turns out in the near future that SPVG has suffered a substantial financial loss, caused by this DNB-designation.

Is Gold really a risk?....  or a rescue?

Checking the facts.... 
Let's just check if DNB's and Court's arguments are valid.....

Yearly Return
We start by comparing the yearly returns of Gold, the S&P-500 Index and '10-Y Treasury Bonds' over the period 1971-2010.

To make Bonds risk-comparable with Gold and the S&P-500 Index, the yearly average Bond interest rate is translated into a yearly Market Value performance. This is done by assuming that each year, all '10-Y Bonds' bought in a specific year are valued, and sold at the average interest rate one year later (approximation).

Here is the result:

To bring some sense and order into this chart, we calculate the 'Moving Compound Annual Growth Rate' (MCAGR).
We start in 2010 and calculate the  compound average yearly return backwards moving up (year by year) to 1971. This is the result:

Now, this looks better... and a bit surprising as well!!! On the long term Gold (μ=9.2%) and the S&P-500 (μ=10.2%) are tending to a rough 9-10% yearly return......  A little bit Surprising is that Bonds (μ=7.6%) get along very well with their big risky brothers...
Take your time to 'absorb' the impact of this chart.....

Next, we take a look at Risk. We define Risk at first as the Standard Deviation (SD). We directly cut trough to the 'Moving Risk' (Moving SD).
We might conclude here that during recent years there was an increase of risk with regard to the S&P-500 (the 'red' crisis 'Mount K2' is clearly visible). Note that also for a longer period, i.c. the last 30 years, the S&P-500 Risk is substantial higher than the Risk of Gold and much higher than the Risk of Bonds. Only looking at a period of 40 years, Gold shows 'optical' up as more risky (SD=σ=25.8%) than the two other asset categories, Bonds (SD=σ=6.9%) and S&P-500 (SD=σ=18.1%).

However this way of presenting Risk is strongly discussable. Another view of Risk that comes closer to what we naturally 'perceive' as Risk, is to define Risk as only as the Downside Standard Deviation (look up : Sortino ratio ), where all positive yearly returns are eliminated (DSD) or set to zero (DSDZ).....
Let's have a look:
Now, these charts give us a quite a different sight on Risk-reality....
It shows that -on the long term -  not Gold (DSD=Dσ=7.5%) is the riskiest asset, but the S&P-500 (DSD=Dσ=10.6%). Bonds (DSD=Dσ=0.5%), as aspected, have the least volatility and are therefore less risky.

Perhaps the Risk of Bonds is a bit underestimated (very few observations) by the DSD-method (excluding positive yearly returns). In this case the downside deviation of yearly Bond-returns, replacing positive returns by zero, which generates a standard deviation of 3.2%, gives a better indication of a more likely standard deviation on the long run.

Why Gold? 
Although these simple calculations already put the DNB conclusions in a different light, let's get to the main point that should be addressed in defending why Gold should be a substantial part of any Pension Fund portfolio:
 Gold Reduces VaR

In a 2010 (october) publication the World Gold Council published a document called Gold: Hedging Against Tail Risk. This interesting report concludes:
  1. Gold is first and foremost a consistent portfolio diversifier
  2. Gold effectively helps to manage risk in a portfolio, not only by means of increasing risk-adjusted returns, but also by reducing expected losses incurred in extreme circumstances such tail-risk events (VaR).
Following this excellent WGC report, let's test the balancing and risk-reducing  power of Gold by analyzing (classical) Risk (SD) in combining Gold with different allocations (0% up to 100%)  in an asset mix with Bonds, respectively investments in S&P-500 stocks.

This chart clearly shows that Gold has the power to reduce the S&P-500 Risk (SD) from18.1% to 13,3% with an optimal asset location mix of  approximately 60% S&P-500 and 40% Gold. 

In case of Bonds the Risk (SD) is reduced from 6.9%  to 4.8% with an optimal mix of 80% Bonds and 20% Gold.

Asset Liability Model (ALM)
In practice it is necessary to optimize, by means of an adequate ALM study, the  allocation mix of stocks, Bonds and Gold. Just as a 'quick & dirty' excercise, let's take a look at the next asset-combination scenarios, based on data over the period 1971-2010:
Just some head line observations:
  • From scenario M1 it becomes clear that even a 100% Bond scenario is't free from Risk. So diversification with other assets is a must.
  • Looking at M2-M5 we find that the optimal mix, defined as the mix that best maximizes Return (Compound Annual Growth Rate)  and Sharpe Ratio (at a Risk free rate of 3% or 4%) and minimizes Risk (Standard deviation), is something something in the order of: 70% Bonds, 15% stock and 15% Gold.
  • Scenarios M6-M8 and M9-M11 take todays most common (but strongly discussable!) practice as a starting point. Most pension funds have allocated around 50% or 40% to Bonds and 50% or 60% in more risky asset categories (stocks, etc.). It's clear that even in this situation Risk can be reduced and Return can be optimized, if Stocks are exchanged to Gold with a maximum allocation of 20% or 30%.

Although this 'rule of thumb exercise' on this website provides some basic insights, please keep in mind that finding the optimal mix is work for professionals (actuaries).

A serious ALM Study is always necessary and should not only take into account a broad range of diversified asset categories, but should also focus and optimize on:
  • The impact of the liabilities (duration) and coverage ratio volatility
  • The Timing: Mean values and Standard Deviations are great, but the expected return highly depends on the actual moment of  investment or divestment in the market.
  • Future expectations. In the current market situation (2011) the risk of interest rates going up and therefore Bond market value going strongly down, isn't hypothetical. Secondly, the stock market has been pumped up by trillions of 'investments' (?) in the US economy. Once this crisis-aid definitely stops, the question is if these 'cement investments' will be strong enough to keep stocks up. Personally I fear the worst...
    Not to mention a scenario with declining stock rates in combination with increasing interest rates and inflation......
    Who said the life of an actuary was easy???

We may conclude that:
  • Investing in Gold up to a 10% to 15% allocation, reduces the Risk of a portfolio consisting of Bonds and S&P-500 Stocks substantially. 
  • Gold is less Risky than investing in S&P-500 Stocks

Therefore the 'not with facts' underpinned intervention of DNB looks - to put it euphemistically -  at least strongly discussable....

A wise and modest underpinned allocation of Gold is no Risk, it's a Rescue!

Related Links:
- Spreadsheet with Data used in this Blog
- Prudent person Rule
- IPE: Dutch regulator orders pension scheme to dump gold
- Downside Risk:Sortino ratio
- Dutch Central Bank Orders Pension Fund To Sell Its Gold
- Pension Fund Benchmarking 
- Strategic Risk Managment and Risk Monitoring for Pension Funds

Bonus: Gold, Hedging against Tail Risk Video

Oct 3, 2010

Investment Strategy: The Price of Doubt

Most actuaries have seen it happen: A perfect designed investment strategy......., turning into a real nightmare. How could it come that far? What happened?

Life of an actuary...
Let's dive into a real life simplified actuarial case....:

As the actuary of your company, you've developed a perfect ALM study. Together with the head of the investment department, you've been able to convince your Board of the new developed 'Investment Strategy'. A consequent mix of 50% Bonds and 50% stocks, resulting in an average expected 6% return on the long term, turned out to be the best (optimal) investment mix given the risk appetite of your Board and the regulatory demands. All things are set for execution.

Now let's see how your strategic plan would develop (scenario I) and how it would probably be executed by the Board (scenario II) over the next ten years.

Although your investment strategy plan was designed on a rational basis and the execution of this plan was also intended to be a rational process, in practice they are not.....

Let's follow the discussion in the Board from year to year...

Year 1
The company's average portfolio return performs according plan (6%). Stocks: 8%, Bonds 4%, on average 6%. The Board concludes they have the right strategy. You, as an actuary, agree.

Year 2
Compliments from the Board. Stocks perform even higher (10%), leading to a 7% average return.
You sleep well that night.

Year 3
Another fabulous Stock performance year. A stock return of 20%, leading to an average return of 12%! Some Board members start to doubt and question your ALM-model. They are arguing that if stock prices are that high three years in a row, they would like to profit more from this development. They suggest to adjust the asset mix in favor of stocks. Your ALM model should me more flexible.

You are defending your Asset Liability Model to the grave, but after extensive discussions all board members agree that a slight 'temporary' adjustment to 70% stocks and 30% bonds would be 'worth the risk' to profit from this high stock return. With great reluctance, you agree....

Year 4
Although the performance of stocks is not as high as the year before, it's still relatively high (15%) and leads to an average return of 11.7%, which is 2.2% (!) higher than the 9.5% return that would have been achieved with a 50/50% mix.  The Board concludes that it took the right decision last year, to adjust the asset mix to 70/30%.

You - as the responsible actuary - warn again, but the facts are against you. Disappointed and misunderstood you return to your office as the President of the Board tries to cheer you up by thanking you for your 'constructive response' in the board meeting. You abstain from joining the festive Board Party that evening.

Year 5
Stocks are dramatically down to 0%, leading to an average mixed return of 1.2% this year.
The board meeting this year is chaotic. Some members support you as the 'responsible actuary' to readjust the asset mix to the original mix of 50/50%. Others argue that this stock dip is only temporary and that this year's average return is only 0.8% lower than would have been achieved with a 50/50% mix. On top of, most members strain that this year's 0.8% negative return is still lower than the 2.2% positive difference of last year. After two stressful board meetings, the Board decides to stick to their 70/30% investment mix.
The board president's eye fails to meet you, as you leave the board room that night.

Year 6
What was most feared, has become true.. A negative stock return of 10%, leading to an average return of -5.8% ....   When you walk into the board room that night, all eyes are on you as the 'responsible actuary'. You hold your breath, just like all other board members. After a short moment of silence the board president states that he proposes to bring back the asset mix to the original 50/50% mix. Without further discussion this proposal is accepted. There's no board party this year.

Year 7
Negative stock returns have increased to 15%, leading to an average return of -5.5% this year.
Some Board members fear that if stock prices will be down for another few years, the average 'needed' return of 6% will not be met. They doubt the current strategy.

Also the Regulator and some Rating Agencies insist on higher confidence and solvency levels with corresponding measures to be taken. Both are not positive and doubt the outlook on stock returns on the long term...

After a long meeting that night, the Board chooses for reasons of 'savety' (!) to adjust the asset mix to 30/70% in favor of the still 4% stable performing Bonds (Better something than nothing (!) ).

Again... you explain that night, that changing the asset mix following actual market performance, is the worst thing a company can do....  But again, you lose the debate.

The power of emotion is greater than the power of rationality. Now not only the Board seems against you, but the Regulator as well. Who wants to fight that! After all, 'ethical' rule number one is 'complying with the Regulator'. That evening you brainwash yourself and reprogram your attitude to 'actuarial follower' instead of 'actuarial leader'.

After two Johnnie Walkers you see the future bright again and seem ready for the new year.

Year 8
To everybody's surprise stocks performed extremely well at 25% this year. As a result the average return reaches a satisfying performance of 10.3%. With 'mixed feelings' board members take notice of the results. What nobody dears to say and everybody seems to think is: 'Had we stuck to our 70/30% asset mix, the performance would have been: 18.7% (!)......'

The Board President cautiously concludes that the Board took the right decision last year, leading to a proud 10.3% return this year. Compliments to everyone, including the actuary! Supported by your 'converted' mind, the 30/70% asset mix is continued. That evening you accept the invitation to the board party. Lots of Johnnie Walkers help you that night to cope with the decisions taken.

Year 9
Stocks perform at 20%, leading to an 8.8% average mixed return. No Board member dears to raise questions about the possibility of readjusting the asset mix to a 'more risky' (what's that?) one. After all, the overall performance is still higher than the needed 6%. So who may complain or doubt the new 'On the Fly Strategy'? Who cares or who dears? You go to bed early that night.

Year 10
Stocks returns have come down to a more 'realistic' level of 7%. As a consequence the average return is down to 4.9%, way down beneath the critical level of 6%. Board members have to strike a balance. Some of them doubt again. Continuing the 30/70% asset mix will not bring them the needed long term 6% objective return. Adjusting to a 50/50% mix probably will, but is more risky. What to do?

All eyes are on you as the 'final advising actuary'. With restrained pride you state: "Dear colleagues, what about our good friend, the original '50/50% asset mix'. Can we confirm on that?" Without anyone answering, the President takes a look around.... His gavel hits the table and the decision seems to have been taken.

That night you decide to change Johnnie Walker for a well deserved glass of 'actuarial wine': a simple  'Mouton Rothschild 1945' (at the expense of the Board of course). You enjoy the moment and the pleasure of being an actuary. Even after the Rothschild you realize that the decade price of doubt was high: 0.9% p.a. ...

When you go to bed for a good night sleep, you smile...., as some little voice in your head tells you that next year this madness decade-cycle will probably start again...

Sep 26, 2010

Equity Returns and Mean Reversion

One of the most triggering questions - given the current crisis - is:

Will equity returns recover?

Mean Reversion
In 2009 the S&P-500 index - as most stock market indices - reached the lowest level since the turn of the century. In less than two years time world stock indices had dropped around fifty percent of their value. Since then, stock indices increased about forty percent.

It's tempting to think that this recovery could have been predicted in advance. This suspected predictable effect of recovering stock prices returning to their long-term average, is called: 'Mean Reversion'.

More explicitly: 'Mean Reversion of stock prices' is the effect that abnormal stock prices gradually return to their long-term historical average or equilibrium price.

Reversion Speed
In a 2010 working paper, the Dutch regulator DNB provides an answer to this question of recoverability.  In this paper, authors Spierdijk, Bikker and Van den Hoek analyze 'mean reversion in international stock markets' in seventeen developed countries during the period 1900-2008.

One of the outcomes of this study is not only an interesting country spread between 'mean returns' and volatility (risk, standard deviation), but also a mind boggling country difference in 'reversion speed' (rs).  Reversion speed can be defined as the 'yearly interest speed to return to the long-term average. RS differs strongly per country, as the next slide shows:

Ranked by average return (all %):

Reversion conclusions
The DNB study concludes that in the period 1900-2008:
  • Average Return
    The average World Stock Return is estimated at 8.0% with a volatility of 16.7% (S.D.).

  • Half-Life Reversion Period (HLRP)
    It takes 'World Stock Prices' on average about 14 years  to absorb half (!) of a shock (HLRP), with a confidence interval of [10 years -21 years]

  • High Half-Life Uncertainty
    The uncertainty of the half-lives estimates is very high. This is due to the fact that the lower bounds for the corresponding median unbiased estimators are close to zero. The upper bounds of the confidence intervals for the half-lives are therefore very high.

  • Mean Reversion, a Trading Strategy?
    The relative low value of the mean reversion rate, as well as its huge uncertainty, severely limits the possibilities to exploit mean reversion in a trading strategy

Concluding Remarks
We should keep in mind that - no matter how well investigated - historical data - as always - only have a limited predictive power.

Looking with a 'actuarial eye' at the volatile annual development of the S&P-500 returns and their moving averages, it's hard to deny some kind of visual proof of an increasing volatile yearly return and a structural declining 10- or 15-years average return.....

This 'visual proof', combined with the results of the 'DNB Mean Reversion paper',  is perhaps the best indicator that the future average long term World Stock return of 8% is probably way too optimistic and still includes too much the optimist mood and hope of the last decades of the 20th century...

S&P-500, averages annual returns and inflation 1950-2010

Distribution Rate
Inflation Real
Price Change
Total Return
1950's 13.2% 5.4% 19.3% 2.2% 10.7% 16.7%
1960's 4.4% 3.3% 7.8% 2.5% 1.8% 5.2%
1970's 1.6% 4.3% 5.8% 7.4% -5.4% -1.4%
1980's 12.6% 4.6% 17.3% 5.1% 7.1% 11.6%
1990's 15.3% 2.7% 18.1% 2.9% 12.0% 14.7%
2000's -2.7% 1.8% -1.0% 2.5% -5.1% -3.4%
1950-2009 7.2% 3.6% 11.0% 3.8% 3.3% 7.0%

Key question is : What would be a save 'long-term total return of stocks' as a base for an investment strategy, without the 'Hope Bubbles' of the last two decades of the last century?

Probably a long term stock return of about 6% would turn out to be a save basis for a kind of investment reversion strategy......
However, now we know where we are going, it's absolutely necessary to know where we are now? Unfortunately.... we don't know.... ;-) 

Sources, related links:
- DNB 2010: Mean Reversion in International Stock Markets
- (Dutch) DNB-2010: Herstel aandelenmarkten is niet vanzelfsprekend
- Wikipedia: S&P-500 Annual Returns 
Simple Stock Investing: S&P-500 historical data

Mar 10, 2009

How Defined Benefit Plans work(ed)

Pension plans suffer, from a rare disease....

According to IPE more than 90% of UK Defined Benefit (DB) schemes are underfunded. The aggregate funding position of almost 7,800 schemes reported a deficit of £218.7bn at the end of February 2009.

The situation in the Netherlands is hardly better.Figures from the Dutch regulator,DNB, show around half of the country’s 650+ pension schemes are under-funded. The Dutch government has extended the recovery period for pension funds from three to five years. The main question is: "Is that long enough?"

How Defined Benefit Plans work(ed)

Pension funds, especially DB schemes, have to face that their worst dreams, a complete doom scenario, is becoming true :
  • First the subprime market collapsed
  • Then, as trust broke down, the stock market went down as well
  • On top of that Interest rates dropped dramatically

Titanic lessons
Just like the 'unsinkable' Titanic was protected by compartments, we had protected our pension schemes with diversification. And just like the Titanic, we actuaries, asset managers, and quants made a fundamental mistake. We underestimated the correlation between the different compartments (bonds, subprimes, stocks). One hit in the vital front compartment was enough to draw our pension dreams to the bottom of the ocean.

Optimistic view
But let's not stay pessimistic.

Do you know how long it took the market to recover after 1929? .....


Global Investment Returns Yearbook 2009
And there are more reasons to stay positive about the equity results on the long term, as is shown in the very interesting downloadable Credit Suisse Global Investment Returns Yearbook 2009, that analysis returns from 1900 until the end of 2008.

As this yearbook shows us in more detail, it is only a matter of statistical faith, that equity performance on the long term will recover.

So the only thing we can do is, just like a sick patient: stay cool, rest (don't move), don't panic and wait until trust and the markets recover.

God bless you....