MEAN REVERSION – AN INTANGIBLE CONCEPT?

It has been widely documented that Gilt yields are at their lowest level since records began in 1703. These historically low Gilt yields have resulted in pension schemes having to use record low discount rates when calculating the present value of their liabilities. With many pension schemes currently undergoing valuations, trustees had hoped that the Pensions Regulator would provide guidance. Specifically many had hoped that schemes would be allowed to adopt a ‘long running average yield’ approach when setting scheme specific discount rates; this turned out not to be the case. In April this year the Regulator released a statement in response to the concerns raised by pension scheme stakeholders. Whilst the Regulator acknowledged that current economic conditions were putting severe pressure on scheme funding they stated that they would not advocate schemes using a ‘mean reversion’ approach when discounting scheme liabilities.

Mean reversion – Any statistical basis?

The concept of ‘mean reversion’ has been widely debated in the defined benefit pension industry in the past 12-18 months, but what does it mean? Well, broadly speaking some believe that the current yields available on Gilts are so low that yields will certainly revert to a longer term average (also known as an arithmetic mean). If this is the case, what should one set as the arithmetic mean? Would it be a return to the high interest rates experienced in the 1980s? Perhaps we should be using the average yield since the inception of the series (which was 1703 for 10 year Gilts)? Or some may feel they could justify using the yields experienced in the boom years leading up to the financial crisis. Which approach would be the ‘appropriate’ measure of a long running average yield?

On 25 June 2012, the 10 year zero coupon Gilt rate, as calculated by the Bank of England, closed at 1.80%. The lowest yield published in this series to date was 1.63%, which was recorded just 3½ weeks earlier, on 1 June 2012. The data series, provided by Bank of England, dates back to 1982 and in contrast to the low yields highlighted earlier the highest yield recorded to date was 15.15% on 18 January 1982.

The extreme figures observed in the previous paragraph tell a story all by their selves but what about a long run “middle value”? We could use the median (another statistical measure) for this approach. The median of the series over the last 30 years has been 6.97%, considerably higher than the current level! If pension schemes were allowed to use a ‘long running median’ as a discount rate the funding situation among UK defined benefit pensions schemes would surely look very different to where we actually find ourselves today.

Going forward

So, strictly speaking, how likely is it that a situation like this will persist? We calculated the average yield for the 10 year zero coupon Gilt over the last 10 years and this figure came out at 4.19%. The corresponding standard deviation, a measure of how volatile the asset price is over each trading day, was calculated to be around 0.75% over the same period. Using this information was can observe that the 10 year zero coupon Gilt yield is currently providing a yield that is around 3.2 standard deviations away from the 10 year average. If we assume that investment returns are normally distributed, statistically speaking, the probability of a yield this low or lower being observed is 0.069%. Speaking in layman’s terms we would expect an event this extreme to occur once in every 1,455 days (4 years). However, if you determine that the appropriate mean reversion will be based on a 20 year average of the 10 year Gilt yield you arrive at an average yield over the period of 5.4%, and the current 1.8% yield or lower should be occur in 1.7% of your observations. In our final example we calculated the same statistic using the 30 year average of the 10 year zero coupon Gilt rate. Under these assumptions the probability of observing a 10 year gilt yield of 1.8% or lower about once in every 31 outcomes, i.e. a probability of 3.2%.

Some may find the results contained above startling. How can it be that the likelihood of observing a Gilt yield lower than the current level is less likely using data based on the last 10 years’ data (when Gilts yields have been lower in relative terms when compared against previous periods) than over the last 20 or 30 years when rates have historically been higher? The answer lies in volatility.

Unravelling the maths

The figure below shows the current Z-statistics based on sampling periods of 2002-2012, 1992-2012 and 1982-2012. Firstly we should start by asking “what is the Z-statistic?” The Z-statistic describes how many standard deviations from the arithmetic mean Gilts are currently yielding. By only looking at data over the past 10 years, it appears that the current 10 year Gilt yield is a less frequent occurrence in comparison to when we include the more volatile returns experienced during the 1980s and 1990s. No matter what period we examine, it appears that Gilts returning yields of around 1.8% is a very rare occurrence.

Having digested this information, does this mean that we are expecting yields to jump back up any time soon? No, not necessarily. Currently the Japanese 10 year government bond is yielding around 0.8%, this is around 1.8 standard deviations away from its corresponding 10 year average. This means that we would expect a yield of this level or lower to occur only once in around 28 observations. The Japanese stock markets peaked in 1989 and at this time represented roughly half of the world’s listed equity value. Needless to say, the bubble burst shortly after and the Japanese stock and real estate markets fell sharply during the early 1990s. Today, Japanese stocks are trading at around a quarter of the highs they reached 20 years ago.

The highest level the UK stock market has ever reached to date occurred in 1999. This level was almost topped during the credit fuelled boom of the late 2000’s but the index has now fallen back more than 20 per cent below this peak.

What next for developed countries?

The below chart depicts movements of Japanese Government Bonds (JGBs), German Bunds, UK Gilts and U.S treasuries since January 2007.

Whilst some may assume the purpose of this graph is to suggest developed economies are entering into a Japanese-style scenario, this is not the primary aim of this comparison, making a statement that bold would not be a decision we would take lightly.

Having said this, the UK has already experienced something resembling half a decade of lost growth. As at 30 June 2012 we are one of only two G20 countries to have entered into a double-dip recession, the first time our country has experienced such a difficult economic situation since the 1970s. At the same time our domestic economy is suffering from uncomfortably high national debt levels and this has left little space for fiscal policy changes.

In addition, the Bank of England (‘BoE’) has cornered the UK Gilt market, currently owning around £325 billion worth of UK Gilts, which the BoE has purchased through the secondary markets. 10 years ago many would have found it baffling that the BoE could own over a third of all Gilts in issuance!

What has the Bank of England done?

The Bank of England’s activity in the Gilt market, dubbed Quantitative Easing (‘QE’), has been aimed at encouraging growth. The theoretical concept behind quantitative easing is that banks, insurers, pension schemes, and other market participants will sell their Gilts to the Bank of England. The hope is that this money will then be used for lending and investment which should provide higher returns, thus encouraging domestic economic activity. Unfortunately this extreme approach to kick starting the UK economy appears to have been in vain so far.

One of the unfortunate side effects of QE is that demand for Gilts increases (due to the BoE entering the market) thereby causing yields to fall. This second order effect has been particularly unpalatable for pension schemes which have seen the present value of their pension liabilities skyrocket!

In the Bank of England’s June Monetary Policy Committee (‘MPC’) meeting, against the backdrop of falling inflation, four out of nine committee members voted for yet further easing measures. Continued economic uncertainty then resulted in the MPC in its July meeting voting in favour of restarting the QE programme. The BoE now intends to increase their total holdings in Gilts to £375bn over the coming months.

Concerns in Europe

Renewed concerns around the debt issues of peripheral countries in the Eurozone have resulted in many of us keeping a keen eye on developments in Brussels over the last few weeks. Despite continued efforts by all parties, our political brothers and sisters across the channel appear to be failing miserably to implement measures to control the debt crisis. Cyprus was the last country to formally request a bailout package and few expect this country will be the last to ask for help.

Short-term uncertainty has resulted in a ‘flight to safety’, with investors piling money into assets considered safe, such as Gilts, US treasuries and Japanese Government Bonds. This has been another contributing factor which has increased demand for UK Gilts, thereby causing yields to fall further. Counter-intuitively, over the last 12 months investors have accepted negative real yields at certain maturities in order to lend to the UK government. Prior to 2008 many believed this concept to be a purely academic exercise.

Summary

To summarise the findings of this paper, no one would deny that the current low yields available on UK Gilts are anything short of extraordinary. Having said this, we would advise restraint before investors assume that ‘mean reversion’ is a ‘dead cert’. 25 years ago few people believed that Japan would transition from an economic powerhouse to what many now view as the poster boy for negative returns on risky assets and setting record levels for debt to GDP ratios (many peripheral European countries look well positioned in comparison to Japan’s overall debt levels).

In Japan, what started out as a statistical anomaly quickly turned out to be an economic reality; this transition appears to have now firmly asserted itself as the modern day norm. As highlighted previously, the purpose of this paper is not to suggest that the UK is heading down a similar path. Having said this, we do believe there is a clear lesson to be learnt here: making assumptions with regards to the direction of future Gilt yield movements – based on either statistics, long running historic averages or similar quantitative approaches not only provides an incomplete picture of economic reality, it is also irresponsible.

 

[Please note that all opinions expressed in this blog are the author’s own and do not constitute investment advice.  Click here for full disclaimer]