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From pollen particles suspended in
water to complex financial products:
Brownian Motion
Alejandro Vidal Crespo
Service Director, Investment Strategy
MONTHLY STRATEGY REPORT
February 2015
Monthly Strategy Report. February 2015
From pollen particles suspended in water to complex
financial products: Brownian Motion
As you know, when we choose assets our contention is that the value of what we are buying
is what interests us and sooner or later that value will become apparent. As a result, often
we don’t become nervous over inexplicable movements in the market or, we take advantage
of them to buy or sell depending on our valuations. In this article, we demonstrate how
applied mathematics support our way of thinking...
In 1827 the Scottish botanist, Robert Brown, was in his laboratory studying and classifying vegetable
species. Upon observing a closed jar with pollen particles suspended in water, he noticed that the
particles moved for no apparent reason in a dance which seemed endless and random. Initially, he
deduced that the pollen particles, having come from an animate
object, might contain a type of propulsion mechanism which caused
them to move in this way, but his scientific curiosity led him to repeat
the experiment with dust particles and he obtained the same result.
This lead him to rule out the pollen’s self-propulsion, but he was
unable to come up with a theory which would explain the origin and
nature of the movement, although he described it empirically with
incontrovertible detail.
This observation was not entirely new. Lucretius had described a
similar process in ancient Rome (60 BC), in dust particles suspended
in air reflected by sunlight. Lucretius had already tried to link this
movement to the nature of matter.
In 1880 the scientist Thorvald Thiele came close mathematically to a description of the movement
but it was not until 1905 when the great Albert Einstein fully defined it as a way to demonstrate that
matter is made up of atoms and molecules which move in a chaotic manner.
What happens to pollen particles in water that makes them move in this apparently senseless manner?
What happens is that they are hit randomly and irregularly about their surface by the water molecules
causing them to move in every direction and no direction at the same time in an apparently chaotic
manner. However, it is only apparently chaotic because this imbalance of forces is only momentary. In
an instant an imbalance can move the particle towards the right but it will quickly be offset by another
imbalance which moves it in another direction so that if we take a large number of observations we
will conclude that the sum of the imbalances approaches zero and the particle must return to its
original place. Although the particle moves, it will do so without a defined trend and, moreover, the
movements over short periods of time will tend to be identical in intensity. Beneath this chaos lies a
mathematical pattern subject to a normal (or Gaussian) probability distribution and with an average
of zero.
This is the definition of the process known as Brownian Motion or the capacity to describe the
movement or behaviour of things we do not know how will act in the very near future, where they will
move completely randomly, but we will be able to predict how they will act over longer periods, since
the sum of these small moments of chaos must approach zero. This idea is very useful for many things,
among others, to describe physical processes such as diffusion or osmosis and, also, movements in
financial markets.
In the 1960s, two economists and mathematicians, Fischer Black and Myrton Scholes, worked on a
Monthly Strategy Report. February 2015
mathematical model which would allow them to calculate the price of financial options. Until then,
this type of instrument was priced through a very tedious process, essentially based on attempting
to simulate all of the possible scenarios a very large number of times and taking the average of the
results to determine the instrument’s fair value (applying what is known as the Law of Large Numbers).
Black and Scholes used a model based on Brownian Motion to price options, since it simplified the
calculation work enormously (they obtained a value so close that it could only be obtained through
the repetitive methods if tens of thousands of observations were used, not the simplest thing to do
with the calculation methods of the pre personal computer age). Furthermore, it allowed the options
to be priced in continuous time and significantly reduced the possibilities of arbitrage in the market
using a risk-neutral probability.
Myrton Scholes, together with Robert Merton, (who applied the theory model to the real world)
received the Nobel Prize for this work. Fischer Black was not as lucky; when they were awarded the
prize in 1997, he had already passed away, although the model was named Black-Scholes in honour
of both researcher and represents one of the greatest advances in the history of finance. Basically, it
defines a long-term trend which will be altered in the short term by a Brownian process, unpredictable
in short periods of time but which approaches zero at long term: market noise.
However, aside from the precision and the simplicity of the application, the Black-Scholes Model
presents various interesting possibilities regarding the behaviour of things in the markets. The first of
these is that what a financial asset will do in a short period of time is random, the more unpredictable
the asset, the more volatile (or of greater risk), but at long term, these movements approach a sum of
zero, leaving the tendency at long term unaltered, which is influenced by fundamentals. The market
sentiment, volatile scenarios, will tend to become diluted over time and their effect will be neutral to
the extent that the investment fundamentals have not changed. Even without transaction costs, it will
be very difficult for us to derive value from continually entering and exiting the market.
The second is that a mathematical principle, known as the Markov chain is fulfilled. When something
moves in a Brownian manner, the path it has followed to get to that point is irrelevant when predicting
its next movement because it will once again be random and independent from the previous movement.
Assuming that something will rise or fall because yesterday it did the opposite does not, in general,
produce very good results over time if the valuations of the fundamentals remain unchanged.
The markets celebrate the ECB’s
stimulus measures
Banca March Market Strategy Team:
Miguel Ángel García, Unit Director, Market Strategy
Rose Marie Boudeguer, Service Director, Research Service
Pedro Sastre, Service Director, Market Strategy
Alejandro Vidal, Service Director, Market Strategy
Paulo Gonçalves, Technical Specialist, Research Service
MONTHLY STRATEGY REPORT
February 2015
Monthly Strategy Report. February 2015
The markets celebrate the ECB’s stimulus measures
An auspicious start to the year in the markets...
The elections in Greece and the ECB meeting were the protagonists in the markets. The European
markets closed with gains, even disregarding the positive effect of the new stimulus measures.
...although political uncertainty continues to reign. Greece’s new government must negotiate new
aid with the Troika...
Political uncertainty remained with the early general elections in Greece. The elections ended
with a comfortable win for Syriza (149 seats, very close to the majority). The new Greek
government will be comprised of a coalition between Independent Greeks (ANEL), a party
which only shares with Syriza the intention to renegotiate its debt and mitigate the adjustment
measures imposed by the Troika. The first decisions adopted by this government (to raise the
minimum wage, increase public contracting and stop privatizations) clash directly with the
Troika’s criteria, resulting in significant uncertainty regarding the future of international aid.
...while armed conflict returns to Ukraine.
Fighting has renewed in Ukraine. It continues to accuse Russia of supporting the Ukrainian
separatists and the European Union imposed another round of sanctions. These sanctions
and the decline in oil prices are punishing the Russian economy and Mr. Putin’s government
adopted, on the one hand, a significant budgetary adjustment plan, cuts of up to 10% and, on
the other, recapitalisation measures for banks facing difficulties (amounting to EUR 31 billion).
In this context, the economy would shrink more than 3%.
The ECB takes an important step with new monetary stimulus.
The ECB did not disappoint expectations and announced a new plan to purchase EUR 60 billion
in public and private debt monthly starting in March and lasting until at least September 2016.
As a whole, these purchases exceed 10% of the eurozone’s GDP and confirm that the monetary
authority will use all of the tools in its arsenal to avoid the risk of deflation and stimulate
economic recovery in the region. Moreover, it reduced the costs to banks in the upcoming
liquidity auctions (TLTRO).
Other European central banks, whose currency was tied to the euro exchange rate also
readjusted their monetary policies.
The most crucial decision was made by the Swiss Bank which removed the floor on the Swiss
franc (EUR 1.20/CHF), causing its value to soar with massive repercussions in the currency
markets.
The Fed did not provide significant clues.
In the US, the Fed maintained its monetary policy but showed more optimism with regard
to economic performance, indicating that growth is progressing at a steady pace. Likewise, it
confirmed that it will remain patient with respect to raising official interest rates in the future.
The IMF revised its forecast for growth downwards.
At the macroeconomic level, the IMF lowered its global economic growth forecast to 3.5% for
this year (three tenths less than its October estimate). The factors leading to this reduction are
lower levels of investment and a weakening of the emerging economies which, as a whole, will
Monthly Strategy Report. February 2015
grow 4.3% in 2015 (vs. 4.9% in 2014).
By country, the upward revision of US economic growth stood out. Its GDP is expected to
increase by 3.6%. It revised eurozone growth downwards to 1.2%, with Spain being the only
large economy in the region with an improved outlook (up to +2%). In Asia, China could grow
by 6.8% (vs. 7.1% in 2014) and Japan by 0.6% (vs. 0.8% in 2014).
The US economy maintained a good rate of growth.
US economic data continued to confirm its steady rate of growth with GDP growing in the
fourth quarter at an annualized quarterly rate of 2.6%. Likewise, the unemployment rate at
2014 year end was 5.6% and 2.95 million jobs were created during the year, the best figure since
1999. With regard to prices, inflation eased by five tenths in December to +0.8% year-on-year,
with a core rate of 1.6%.
Confidence is improving in the eurozone but the fall in prices is worrisome.
In the eurozone, the composite PMI rose in January to 52.2 (vs. 51.4 in 2014) improving business
confidence. Consumer confidence also grew, likely a reflection of lower energy costs. The
unemployment rate dropped by one tenth in December to 11.4%. The CPI dropped more sharply
in January (-0.6% year-on-year), with core inflation moderating to +0.6% year-on-year, a historic
minimum.
Spain’s economic recovery is becoming a reality.
Spain’s economy continued to recover with GDP growing at a year-on-year rate of 2% in the
fourth quarter of 2014. Activity was bolstered by improved internal demand; retail sales
increased in December by +6.5% year-on-year. The unemployment rate at 2014 year end fell by
2 percentage points to 23.7%, the first time, in annual terms since 2006. Prices fell faster with
a -1.4% year on year CPI in January.
The economic data from the UK was also positive. GDP grew by 2.6% year-on-year in the fourth
quarter and unemployment dropped further. However, the low inflation rate (the CPI slowed
to 0.5% year-on-year in December) provides the Bank of England more room for manoeuvre, a
bank which decided unanimously to keep interest rates low (0.5%).
The big emerging economies diverge: China achieves its objectives...
The data for big emerging economies were mixed. In 2014 China grew by 7.4%, and although
this is the slowest pace since 1990, it was in line with the Government’s objectives (7.5%).
Retail sales and industrial production managed to pick up in December, data which confirms a
marginal slowdown.
...while Brazil and Russia show greater imbalances.
The data was less favourable for other economies, such as Brazil, where inflation continues
to be high and its central bank once again raised interest rates to 12.25%, curbing growth. In
2014 Brazil’s government budget became imbalanced and it recorded a primary deficit (without
expenditure on debt interest) of 0.34% of its GDP for the first in 18 years. In Russia, in addition
to the deterioration of its activity, the rouble’s depreciation increased inflationary pressure (the
CPI for December was +11.4% year-on-year).
Uneven growth in the stock markets: European markets stood out positively.
The year began differently on opposite sides of the Atlantic. The European stock markets were
invigorated by the ECB’s new stimulus measures, with Euro Stoxx 50 up 6.5%. By country, the
German stock market’s performance improved –up 9%– due to the increased weight of export
Monthly Strategy Report. February 2015
companies which benefit from a weak euro. The Ibex 35, on the other hand, lagged a bit (+1.2%
in the month). In the US, the stock markets were tempered by business results where forecasts
for certain large US multinationals were weaker due to the negative impact the exchange rate
was expected to have on their profit. In this context, the S&P 500 closed the year with a 3%
slide. The MSCI Emerging Markets index rose 0.5%, but with uneven results according to region.
There were sharp increases in Asia (MSCI Asia ex - Japan; +2%), while Latin America and Eastern
Europe experienced declines.
Bonds benefits from low inflation.
The moderation of inflation at a global level –with lower energy costs– and an expansive
monetary policy, continued to bolster bonds. 10-year German bond yields dropped by 24 b.p.
to 0.3% and in the US to 1.64% (-53 b.p.). Spanish sovereign debt benefited from the ECB
announcement and the index rose 1.4%, The credit market also recorded gains, especially that
of the level of investment, which rose by 2.4% globally during the month.
The euro depreciates as a result of the ECB’s measures, falling 7% against the dollar.
The euro depreciated significantly when the ECB confirmed that it would adopt important
stimulus measures entailing an increase in its balance sheet (more euros on offer). The dollar
appreciated 6.5% against the euro which closed the period below EUR 1.13/USD. Likewise, the
pound sterling appreciated 2.6% against the euro to stand at EUR 0.75/GBP The yen rose since
the Bank of Japan did not announce new monetary stimulus, disappointing a portion of the
market. It appreciated 8.4% against the euro, closing under EUR 133/YEN.
The price of commodities continue to fall.
Commodity prices fell even further. The increase in inventories and OPEC’s preservation of
production rates applied pressure to oil prices. The price of a barrel of Brent crude oil fell 9%
to $53. Diminished demand in China took its toll on basic metal prices. The exception to these
drops in commodity prices was gold which closed with a revaluation of 7.7% to $1,276/ounce.
Monthly Strategy Report. February 2015
Strategy for February 2015
ASSET ALLOCATION
Positive
Neutral
Shares
Negative
Bonds
Cash
ASSET ALLOCATION
Equities
Positive
Neutral
Europe
Japan
Negative
USA
Emerging countries
Bonds
Peripheral Bonds
Government Bonds
(AAA, AA+)
Corporate Debt
“High Yield”
Corporate Debt
“Inv. Grade”
Convertible Bonds
Emerging debt
The world’s central banks relax their monetary policies.
In January it became clear that the majority of the world’s central banks are implementing more
relaxed monetary policies. Together with cuts in interest rates in Switzerland and Denmark,
and the ECB’s announcement that it will purchase bonds, another 15 banks –including those
of Singapore, Peru, India, Canada, Australia and Turkey– have lowered interest rates this year.
Thanks to inflationary pressures easing up, they have been able to use monetary policy to
stimulate their economies and, at the same time, prevent their currencies from appreciating.
The geopolitical risks will come mainly from Greece.
Politics and geopolitics will continue to be crucial for market performance in the coming weeks,
with the negotiations between Greece and the Troika taking front stage. Before the end of
February, when the current aid programme will come to an end, they must reach an agreement
which will provide financing to Greece, and the first decisions of the new Greek government to
date have not facilitated a rapprochement.
...and Russia.
At the same time, the tensions between Russia and Ukraine continue to generate uncertainty
regarding their economies, significantly weakened as a result of the armed conflict, and also
regarding the economy of the eurozone.
Growth in the US will accelerate to 3.5%.
At the macroeconomic level, in February, growth in the US should continue to be confirmed.
Improvements in employment and the real estate sector, together with the drop in oil prices,
will continue to be felt in relation to consumer spending and this year, growth is expected to
reach 3.5%, close to its potential.
The eurozone will accelerate to reach discreet growth rates.
Although Europe will exercise less fiscal restraint than in recent years and this, together with
the Juncker plan will allow for more investment in infrastructure and services, European growth
will accelerate but below its potential, at a rate of around 1.1%. High unemployment is an
obstacle for significant recovery in consumption.
Monthly Strategy Report. February 2015
The growth forecast for emerging regions is varied.
The economic outlook for emerging countries is mixed. Among the elite club –the BRICs– there
are significant differences. China is expected to lower its objective for growth to around 7%,
since authorities must prevent excessive stimulus from creating bubbles. India seems to be on
the path to increase its growth rate to 6%, while Russia will suffer a severe recession and Brazil
will only recover very gradually this year.
Growth in developed countries without inflationary pressure.
The acceleration of growth in developed countries will continue without inflationary pressures.
The weak wage growth and the drop in the price of oil since mid-2014 have created a downward
trend in prices which will remain at least until the middle of the year due to the base effect.
The Fed will raise rates gradually given the risk to the global economy.
In this context, we expect the Fed to very gradually raise interest rates this year given the
continued risk to the global economy and the danger that the dollar will become too strong,
threatening the US economy. The Bank of England could begin to raise interest rates at the end
of 2015 or at the beginning of 2016. On the other hand, the ECB will begin its massive purchase
programme in March and the Bank of Japan will continue to be committed to an ultra-expansive
monetary policy.
The dollar will continue to appreciate.
In this environment, the interest rates on US and UK bonds will trend upward over the course
of the year, while European and Japanese interest rates will remain very low. This means that
the euro will continue to depreciate this year and could approach levels close to EUR 1.1/USD
up to those levels, we continue to be committed to investing in dollars and, although to a lesser
extent, investing in pounds. For the same reasons, we will avoid exposure to the yen.
Liquid assets will continue to offer a very low return.
Investment in liquid assets –cash or cash equivalents– continues to offer a very low yield,
as returns on deposits, treasury bills and Euribor have fallen. Nevertheless, the deflationary
context being experienced in Spain and Europe will enable real returns to be good. In this
context, low-volatility absolute return funds contribute to complementing the treasury funds.
Sovereign bonds from peripheral countries will continue to be backed by the ECB.
The sovereign bond market continues to present attractive investment opportunities. US and
German bonds offer very low yields and prospects for higher interest rates during the year lead
us to fear a fall in prices not offset by the coupon. Returns on sovereign bonds from peripheral
European countries have also plummeted but they are worth holding in the portfolio because
they offer an additional yield and their valuation will continue to be backed by the ECB’s massive
purchase of sovereign bonds.
Among corporate bonds, high yield and convertible bonds provide more value.
Corporate bonds continue to be vulnerable to increases in benchmark rates, although the
economic context is favourable and the default rate is low. Bonds issued by companies with
high credit ratings which offer very low returns and do not offset the risk of potential increases
to interest rates are particularly sensitive. More value can be found in investment-grade, or high
yield, bonds since they offer more attractive yields. Furthermore, convertible bonds provide
more value, due to the fact that they have greater exposure to equity performance.
The stock market offers attractive dividend yields and profits on the rise in a context of low interest
rates and abundant liquidity.
In comparison to the limited returns offered by equities, stock markets offer an attractive
Monthly Strategy Report. February 2015
dividend yield, above all in Europe. To the above, it must be added that company profits
continue their upward trend, as can be seen in the current earnings season which began in
January. US companies are exceeding expectations despite the fact that the dollar’s strength
limits their income. European companies are improving their income and cost prospects due
to the depreciation of the euro and the drop in the price of oil. Thus, in an environment of low
interest rates and abundant liquidity provided by the central banks, equity is one of the assets
with the most potential.
We prefer the eurozone, the US and Asia Pacific.
The eurozone stock markets are attractive to us because they are improving their cost structure
and their international sales, something US companies have already done and demonstrated the
value of. Moreover, the price is attractive and they are backed by the ECB’s monetary policy.
However, we continue to be optimistic about US equities due to their strong performance
and economic prospects, despite a more adjusted price. We also believe a moderate emerging
markets weighting is reasonable, particularly in the case of the Asia-Pacific region, because of
its attractive valuation and the improved margins.
Commodity prices should recover in the second half of the year.
With respect to commodities, we believe that in the coming months they will be priced within
existing ranges: the price of gold is limited by the dollar’s appreciation and the prospect of a rise
in US interest rates. At short term, the excess supply will continue to apply downward pressure
to the price of oil, but it should return to levels close to USD 75 per barrel at medium term.
Some commodity weight in portfolios seems reasonable for diversification purposes, because
of improved global growth expectations and because supply has balanced out and no longer
seems excessive.
Monthly Strategy Report. February 2015
Euribor
Euribor 12 months (3 years)
Currencies
Government Bonds
EUR/USD (3 years)
10 years government yields
Corporate Bonds (1 year spread)
Commodities
Equity Indices
Data: Bloomberg
IBEX35 (3 years)
Monthly Strategy Report. February 2015
Equity Indices performance (3 years)
Monthly Strategy Report. February 2015
Important Remark:
This contents of this document are merely illustrative and do not pretend, are not and cannot be considered
under any circumstances as an investment recommendation towards the contracting of financial products.
This document has only been prepared to help the customer make an independent and individual decision
but does not intend to replace any type of advice needed for the contracting of such products.
The terms and conditions described in this document are to be viewed as preliminary terms only, subject
to discurssion and negotiation as well as to the agreement and final drafting of the terms affecting the
transaction, which will appear in the contract or certificate to be issued.
Consequently, March Gestión de Fondos, S.G.I.I.C., S.A.U. and its customers are not bound by this conditions
concerning the final documents to be approved. March Gestión de Fondos, S.G.I.I.C., S.A.U. does not offer
any guarantee, expressly or implicitly, in relation with the information shown in this document.
All terms, conditions and prices contained in this document are merely informative and subject to modifications
depending on the market circumstances, changes in laws, jurisprudence, administrative procedures or any
other issue which may affect them. The customer should be aware that the products mentioned in this
document may not be appropriate for his/her specific investment targets, financial situation or risk profile.
For this reason the customer must make his/her own decisions by taking into account such circumstances
and by obtaining specialized advice in tax, legal, financial, regulatoy, accounting issues or any other type of
information required.
March Gestión de Fondos, S.G.I.I.C., S.A.U. does not assume any responsibility for any direct or indirect cost
or loss which may result from the use of this document or its contents. No part of this document can be
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Please note this document has been translated for your information only. In case of any errors or
misinterpretations, the Spanish text will always prevail.