Standard Deviation, a Poor Measure of Risk

As actuaries and/or risk managers we've been professionally brought up with some deep-rooted assumptions about what 'risk' is....

Difference between Science and Religion
One of my favorite statements is that there is no fundamental difference between a religion (believe) or science. Both depend on a number of axioms, the basic assumptions. Assumptions, we 'believe' or 'take for granted' on basis of our intuition and/or personal experience. Only by means of those axioms we're able to 'prove' other theorems in our system or model.

So what we have to conclude is that what we prove in our our statistical models, is as strong as the foundation (assumptions) on which our models are based.

Main problem is that the assumptions in our models are so trivial and often so frequently implicitly used, that we don't realize their impact. We've developed a blind spot.......


Risk Axioms
With regard to 'risk' I'll just discuss two of the most dangerous (risky ;-) ) assumptions on which most of our investment risk models are build:

1. Risk = Standard Deviation (SD)
2. Mean Reversion
   The theory that a given value will continue to return to an average value over time, despite fluctuations above and below the average value.

Explication

Risk is a much wider concept than just 'standard deviation'.
First of all there's an 'impact difference' between a downside risk and an upside risk. In general, what we perceive as risk is more in terms of downside risk. But yet..., we keep measuring and concluding  about risk on basis of 'standard deviation'.

Why SD Fails as a measure of risk
To illustrate the failure of Standard deviation (SD) as a measure of risk, take a look at the next example in which we compare the performance of two different asset classes, AC-I and AC-II, with the next characteristics:

• AC-I and AC-II have the same average (compound) return of 2.5% per year
• AC-I has a Standard Deviation of  13,9% and AC-II a SD of 27%
• AC-I has a maximum deviation of minus 40.0% and AC-II of 76.3%

By definition AC-II is more risky than AC-I.....

However.., a two year old child will point out AC-I as far more risky than AC-II. First, downside deviations are  more risky than upside deviations and secondly, the 'incremental downside risk' of AC-II can be 'managed' much more effective than the 'crash downside risk' of AC-I.

Conclusion
The times of modeling risk on basis of Standard Deviation are over. We need more sophisticated models that describe and measure risk multidimensional and with respect to downside risk and not upward potential.

Let's conclude with a final question to test your 'stock crash insight'.

What was the worst performance of the S&P 500 and in which year?

Click on 'answer' to find out!

ANSWER

Read more about the S&P 500 performance on: S&P 500 Five Worst One Year Performances (in %)


Related Links
- Actuary-Info: Equity Returns and Mean Reversion (2010)
- Risk is more than standard deviation (2005)
- Our Monetary Blind Spot
- Black Ducks Comic Strips

Why Life Cycle Funds are Second Best

Life Cycle Funds (LCFs) are seen as the ideal solution for pension planning. Unfortunately they aren't..... They're Second Best....

Pension Funds solutions (PFs), are far more superior to LCFs, as will be shown in this blog with regard to the performance of a pension plan.

Life Cycle

A Life Cycle approach presumes that, while your young and still have a long time before retirement, you can risk to invest more than an average pension fund in risky assets like stocks, with an assumed higher long term return than bonds,

As you come closer to the retirement age, you'll have to be more careful and decrease your stock portfolio incrementally to zero in favor of (assumed) more solid fixed income asset classes like government bonds.

A well known classic life cycle investment scheme is "100-Age", where the investment in stocks depends on your age. Percentage stocks = 100 -  actual age.
E.g.: If you're 30 years old, your portfolio consists of 70% stocks and 30% bonds.

Here's what the average return of a life cycle '100-Age' investment looks like when you start your pension plan at the age of 30 and assume a long term 7% average yearly return on stocks and 4% on bonds.
The return of this life cycle fund is compared to a pension fund with continuously 50% in stocks.

Key question is however, is the younger generation also risk minded and the older generation risk averse?

As often in life and also in this case, what would be logical to expect, turns out just to be a little bit more complicated in practice....

Misunderstanding:Younger people have a high risk attitude
Research by Bonsang (et al.; 2011) of the University of Maastricht and Netspar shows that on average 25% of the 50+ generation is willing to take risk.

 The research report shows evidence  that  the  change  in  risk  attitude  at  older age  is driven by 'cognitive decline'.  About 40 to 50% of the change in risk attitude can be attributed to cognitive aging.

Unfortunately other recent research also shows that only 30% of people under age 35 say they're willing to take substantial or above-average risks in their portfolios (source:Investment Company Institute).

This implies that -  although they would theoretically be better of on the long run - younger people will certainly not put all their eggs in one basket, by investing all or most of their money in stocks.

Pension Fund Investment Horizon
In contrast to individual pension member investors, a pension fund has a long term perspective of more than 20-50 years as new members (employees) keep joining the pension fund in the future. Therefore a pension fund can keep its strategic allocation in stocks relatively constant over time instead of decreasing it.

This implies that a pension fund on the long term has an advantage (longer horizon) above a life cycle fund. Let's try to find the order of magnitude of this difference.


Comparing a Life Cycle fund with a Pension Fund
First of all, we have to take into account that younger people will not over invest in stocks.

Let's assume:

• A 30 year old 'pension plan starter', retiring at age 65
• Contribution level   (€, $, £, ¥,): 1000 a year
• A long term 7% average yearly return on stocks and 4% on bonds
• Life Cycle Investment scheme
  A modest 50% stocks, with a yearly 2% decrease as  from age 50
• Pension Fund Investment Scheme
  A constant 50% investment in stocks (and 50% in bonds)
• Inflation 3%, Pension and Contribution indexation: 3%

 This leads to the next yearly return of these portfolios, as follows:

To find out the overall difference in return between LCF en PFS, we calculate the Return on Investments (ROI) of both investment schemes with help of the:

Pension Calculator

The outcome looks like this:

As you can see the ROI outcomes (left axis) on the investments (yearly contribution) from 'dying age' 65 to age 69 are negative as the cumulative payed pensions (compared to your contribution) didn't (yet) result in a positive balance. Or to put it in another way, if you die between age 65 and 69, you died too early to have a positive return on your paid contribution.

Overperformance
The right axis shows the difference between the LC ROIs and the PF ROIs.
As you may notice,  the pension fund has a structural yearly overperformance of more than 0.3%  and an average overperformance between 0.4% and 0.5% per year.

Overperformance expressed in pension benefits
Expressed in terms of yearly pensions the differences are as follows:

Investment Scheme	Pension at 65	Relative
LC 55year -2% p/y	11673	83%
LC '100-Age'	12304	93%
PF 50% stocks	13172	100%

For a 40 year old pension plan starter, the differences are:

Investment Scheme	Pension at 65	Relative
LC 55year -2% p/y	5359	82%
LC '100-Age'	5578	92%
PF 50% stocks	6040	100%

Conclusion

Investing in life cycle funds ends up in a 7% to 18% lower pension than investing in a pension fund with 50% investment in stocks.


So..., Be wise and choose a pension fund for your investment if you can!


Aftermath
Of course, every pension vehicle has its pros and cons ... So do Life Cycle AND Pension Funds.....

Related Links/Sources
- CNNMoney:The young and the riskless shun the market (2011)
- Cognitive Aging and Risk Attitude (2011)
- America’s Comm. to Ret.Security: Investor Attitudes and Action (2012) 
-  “Saving/investing over the life cycle and the role of pension funds” (2007)
- Excel Pension Calculator Blog
- Benny AND Boone Comic Strips
- Study: Public employee pensions a bargain (2011)

Investment Herding Risk

What was suspected, has now been proved:

Investment Herding Exists!

Dutch Pension Funds are active Traders
In a 2011 research document called "Herd behavior and trading of Dutch pension funds", researchers Rubbaniy, Lelyveld and Verschoor of the Dutch Erasmus University in Rotterdam, provided evidence that repudiates the popular belief that - in specific - Dutch pension funds are long-term passive institutional traders.

De facto Dutch pension funds are active traders and trade about 8.5%  of their portfolio on a monthly basis!

Conclusions

Main conclusions of Rubbaniy (et al.) are:

• Significant feedback trading strategies, both momentum and contrarian
• Robust herding behavior in investments of Dutch pension funds
  Overall (LSV) herding level of 8.14% (significant at 1% level !!)
  On average if 100 PFs are active in the same security in the same month, there are 8.14 more PFs trading on the same side of the market than what would be expected under null hypothesis of random selection of securities.
• Herding asymmetry in buying and selling of securities
  Across asset classes there is a higher degree of herding in less-risky assets.
• Recent financial crises have a positive impact on both turnover and herding while it negatively affects feedback trading.

Explanations
Possible explanations of these herding effects are:

• Possibly outsourcing of portfolio management and small PFs imitation of large PFs’ lead to the same kind of asset allocation strategy.
• Many small Dutch PFs often hire the same large and reputed asset management firms for their portfolio management and are likely to have same asset allocation of their portfolios. 
• Even if they do their own portfolio management, small Dutch PFs may mimic the investment behavior of large PFs - a widespread belief about the small investors - and thus, add to (LSV) herding measure.

Remarks

Let's conclude with some remarks....

• Dangerous Big Brother Hedge
  Although large PFs (investors) have some 'economics of scale' and budget for experimenting on a small scale with (alternative) non-conventional investments, their investment strategy probably strongly differs from a small PF, as liabilities, sponsor obligations and pension benefits conditions are often are fund specific. 
  
  Therefore, following a large PF asset strategy as a small PF, is extremely dangerous and will eventually not turn out to be the 'big brother hedge' the fund was aiming at.
   
• Unfounded First Mover Risk
  Key question remains if all this herding, hedging and active trading results in an outperformance above a long term sustainable asset-location strategy.
  
  Probably not. But although investors pretend tot act on a rational basis, in reality irrational and conformist behavior take the upper-hand. Small investors often don't dare to formulate a unique fund specific asset allocation strategy because of 'first mover risk'.

Keep care and formulate yur own specif pension fund strategic asset mix!

Related Links & Sources
 - "Herd behaviour and trading of Dutch pension funds" (2011, PDF)
 - Momentum or Contrarian Investment Strategies:
    Evidence from Dutch Institutional Investors (2011)
- Momentum and Contrarian Stock-Market Indices