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.

AftermathEmatics.......

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...

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

	Price Change	Dividend Distribution Rate	Total Return	Inflation	Real Price Change	Real 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

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