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

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.

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 '

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 %):

The DNB study concludes that in the period 1900-2008:

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

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...

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

**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**__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(!) of a shock (HLRP), with a confidence interval of [10 years -21 years]__half__

__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**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