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

Sep 11, 2010

Coverage Ratio Solution Space

Dutch pension funds are in deep trouble. The average coverage ratio of many pension funds has fallen to a level well below 100% (underfunded). Some major Dutch pension funds with coverage levels around 90%, called Government to dissuade the planned pension rights cuts.

A delay in pension rights cuts seems justifiable. Key question is the reason for this requested delay. For reasons of reformulating new pension policies and ambitions, delay seems reasonable. With the intention to just 'buy time' in order to continue 'desperate hope' that the markets and low returns will recover, further delay could prove catastrophic.

Facing Reality
Pension funds have to cope with several hurricanes at the same time:
  1. Relatively low interest rates
  2. Underperforming stock market
  3. Underestimated longevity risks
  4. Need for higher confidence levels

Although low interest rates and underperforming stock markets could continue for several years, on the long term interest rates and stock markets will most likely recover, simply because economic growth imply higher returns on the long term.

Underestimating The Longevity Monster
One of the 'big' (?) surprises seems the recent development in longevity. For decades now, actuaries and researchers are structurally underestimating the effect of longevity.

Maggid's Longevity Forecast
Although longevity has been studied a lot, a decrease of the steady growth of the human lifespan in the coming decades will most likely turn out to be idle hope....

Lessons learned, we actuaries will seriously have to take into account that the linear increase of lifespan probably will continue until at least the age of 90 (Maggid forecast). This implies that we'll have to 'spice up' our mainly retrospective life expectancy models and corresponding forecasts with a healthy portion of common sense.

What about the 'risk free' discount rate?
More actu(ari)al trouble is caused by the fact of the low interest rates and sticky stock markets.
Pension funds face the substantial volatility and the low level of the so called "risk free discount rate" that drives the coverage ratio. Paradoxically we could state:

There's nothing more risky than a  'risk free' discount rate

The - artificial - low level risk free interest rate pulls down the coverage ratio of a pension fund.

At the same time it's necessary to level up the existing 97.5% confidence level of pension funds. A 97.5% confidence level implies that a pension fund will turn into default (underfunding) twice in an average person's lifespan.

Despite the fact that a 'twice in a life meltdown' is probably hard to explain to anyone, new upcoming Solvency demands for pension funds will be inevitable in order to create a level playing field on the financial market. Good governance, common sense and upcoming new regulatory initiatives will therefore certainly urge a higher pension fund confidence level like the 99,5% level in the insurance industry (Solvency II) or the 99,9% level in the banking industry (Basel II) .

Sitting Ducks
As is clear from the above image, successfully financing a pension-fund (portfolio) on the long term at the current ambition level, calls - in general - for high (unrealistic) interest rates. The 'solution space' for achieving the necessary  high coverage ratios that match the (new) capital requirements appears to be very narrow.

Therefore (there is no other way), most pension funds have to take time and redefine their (future) ambition instead of playing 'sitting ducks' and hoping for the best.

Used Sources, Links:

- Dutch life expectation 2010-2060
- Japanese life expectation: 86.5 years
- Dutch life expectation 2010-2060
- Japanese life expectation: 86.5 years
- Dutch - De risico's van het leven (risks of life) ...
- Will Life Expectancy Continue To Increase Or Level Off