Robert Merton and the effect of time on portfolio choice

A Nobel prizewinner on when investment horizons matter

FINANCE THEORISTS are, as everybody knows, unworldly people who can scarcely tie their shoelaces, still less change a car tyre. Robert Merton confounds this stereotype. As he talks amiably at the London office of Dimensional Fund Advisors (he is the firm’s “resident scientist”), you sense that here is a man who could fix a flat in no time. He would probably deliver a cheerful lecture on the importance of the correct tyre pressure while he was tightening the wheel nuts.

Mr Merton has always had a bent for engineering, whether financial or mechanical. He bought his first stock aged ten and completed a risk-arbitrage trade (on a takeover by Singer, a maker of sewing-machines) aged 11. He rebuilt his first car aged 15. In 1997 he won the Nobel prize for economics aged 53—a career high. A year later, a career low: LTCM, the hedge fund he co-founded, imploded. These markers of the passing years matter. For Mr Merton’s specialism is the mathematics of time applied to finance

His first paper on the subject was published almost exactly 50 years ago. Its title—“Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case”—is forbidding. The ten pages of equations that follow are daunting. But for Mr Merton, the equations are tools, no different from a car jack. They allowed him and subsequent researchers to clarify an important question: when does time horizon matter in investing and when does it not?

To start to understand the paper’s importance, go back more than half a century to the birth of modern portfolio theory. Finance theory had been mostly a collection of stories and rules of thumb. Some was useful (“sell down to the sleeping point”). Little was rigorous. A new generation of scholars changed this. Their first step was to assume that investors seek the highest returns for a given amount of risk. Stocks are riskier than bonds. The issue for portfolio choice is how much of this risk to bear. That will vary. Each person should indeed hold as much as is compatible with sound sleep.

In this new, formalised set-up, investors decide once and for ever how to divide their financial wealth. But real-life investing is a movie, not a snapshot. Time is a factor, on top of risk appetite. Mr Merton wanted to go further and discover how investors, faced with an uncertain future, should decide at each moment on their mix of risky and safe assets. The folk wisdom of the time said that young people should hold a riskier portfolio than older ones, because the passing of time makes stocks less risky. That turned out to be wrong—or, at least, it was not quite right.

In two papers published in August 1969, Mr Merton and his mentor, Paul Samuelson, showed that time horizon should make no difference to portfolio choice. But the result holds only if risk appetite is unchanging and stock prices are unpredictable. Alter these assumptions, as future researchers would, and the results change. Mr Merton’s use of continuous-time mathematics created a valuable template. Finance theorists were able to apply the same toolkit to solve related problems, says Hugues Langlois of HEC Paris, a business school. The best example is the Black-Scholes model for pricing financial options, for which Mr Merton was awarded the Nobel prize, along with Myron Scholes.

A lot of finance theory that came later would tease out the circumstances in which time horizon really does matter. The reckoning changes, for instance, when wealth is looked at in the round to include non-tradable human capital—knowledge, skills and abilities. Sitting in a London office, Mr Merton gives an illustrative example.

Say, a young person’s human capital, which determines his future earnings, is 90% of his lifetime wealth, with the balance in stocks. And say that for an almost-retired person the proportions are reversed. If the stockmarket crashes by 40%, the young person has lost only 4% of his wealth. But the nearly retired person has lost 36%, which is much more serious. For older people, having all their financial wealth in stocks is not a sensible risk to take, says Mr Merton. Human capital is low-risk. If you have lots of it, you can take more financial risk.

The best lifetime strategy is a complex problem to solve, even for brainy people such as Mr Merton. But he hopes that, with the passage of time, the pension industry will create more user-friendly products. Cars are easy for their users; the complex work is done by designers and engineers. Pensions should be the same. Needs drive innovation, says Mr Merton. “That is why I’m an optimist.”

Ambitious reforms in Germany are long overdue

The grand coalition formula has reached the end of the road

Tony Barber

Like a married couple who stay together for fear that separation would be too costly, Germany’s ruling “grand coalition” of Christian Democrats and Social Democrats is a partnership empty of love and purpose.

Tensions are rising in and between the two parties that restored German democracy after 1945 and gave the country a prosperity and political stability unmatched in its history.

The frictions are symptomatic of a deeper trend — namely, the fragmentation of the German party political landscape. It is now a six-party system, or one of seven parties if the Christian Social Union, the CDU’s Bavarian sister party, is counted separately.

The impasse demands new, untested types of coalition at national level, especially if the CDU-SPD government were to fall apart. Early elections might produce yet another fall in combined support for the two mass parties of the postwar era.

Such a solution will not be easily found. The system’s unusual feature is that it contains two parties, the rightwing populist Alternative for Germany and the radical leftist Die Linke, each of which is treated like a polecat by the parties of the centre.

In a recent YouGov survey, the first preference of respondents was for a left-of-centre coalition bringing together the SPD, the Greens — whom some polls now make Germany’s most popular party — and Die Linke. However, the latter’s roots in former East Germany and its hostility to German membership of Nato are difficult for its potential coalition partners to swallow.

Germany’s 20th-century history and modern political culture, not to mention the recent sobering experience of watching the behaviour in power of Austria’s far-right Freedom party, completely rule out any role in government for the AfD. Yet the moderate option of a three-way coalition, uniting the CDU with the Greens and liberal Free Democrats, was explored to no avail after the Bundestag elections of September 2017.

Something different, including the option of Germany’s first Green-led government, with a Green chancellor, must be tried. Since Angela Merkel became CDU chancellor in 2005, three of Germany’s four governments have been grand coalitions. This formula has reached the end of the road. Successive grand coalitions have had the effect of sustaining parties at each extreme of the spectrum, just as the former West Germany’s 1966-1969 grand coalition, the first of its kind, drove up support for the student protest movement.

At the same time, Ms Merkel’s unshakeable devotion to consensual centrism has upset CDU conservatives, annoyed SPD leftwingers and made German business ask in frustration what, if anything, the grand coalition stands for.

One telling sign was the sharp exchange at this month’s annual meeting of the BDI, Germany’s powerful industrialists’ group. After Dieter Kempf, the association’s head, accused the grand coalition of losing the confidence of business, Ms Merkel retorted that the industrialists had lost society’s confidence thanks to the car sector’s diesel emissions scandal.

The larger point is that the grand coalition has lost the will to pursue serious economic reforms just when risks to Germany’s business model are rising. These include a Chinese economic slowdown, potential US tariffs on EU car exports, a no-deal Brexit and the outbreak of geopolitical crises around the world.

An ambitious reform programme could start with a shake-up of Germany’s tax systems. For almost 30 years, the government has levied a “solidarity surcharge” on income tax to pay for eastern Germany’s reconstruction after reunification. Like some medieval salt tax enforced long after its original rationale has gone, the surcharge continues to be collected from Germans, even though the funds are no longer allocated specifically to the east.

Germany’s lack of reform is reflected in the erosion of infrastructure, caused by years of under-investment, and high energy prices that damage the competitiveness of companies. Low unemployment disguises the fact that many service sector jobs are poorly paid, making it harder for some Germans to make ends meet than outsiders appreciate.

Ms Merkel stepped down as CDU leader last year, but says she intends to serve a full, four-year term as chancellor before bowing out in 2021. For years she has been all but untouchable, on account of her high international reputation and consistent success in national elections. Yet the CDU’s transfer of power is not going according to plan.

Annegret Kramp-Karrenbauer, the party’s new leader, has made one ­stumble after another. The more German voters see of her, the less impressed they are. CDU rivals, fearing the worst in the next Bundestag elections, do not want her to be the party’s pick for chancellor.

The SPD may pull the plug on the grand coalition if, as seems likely, the party suffers bad results in September and October in three eastern German state elections. However, a snap national election may simply confirm that voters’ support for the SPD is collapsing around the party’s ears.

Outsiders should not gloat about these difficulties. Germany is Europe’s indispensable pillar of stability, and no one except the west’s adversaries gains from trouble there. But renewal and a change of direction are sorely needed.

Feeding the World Along the New Silk Roads

“A decentralized approach towards global agriculture may ensure that supply meets growing demand requirements, while also encouraging equitable participation regardless of geography,” write the authors of this opinion piece. They are Michael Ferrari, managing partner of Atlas Research Innovations , who is also on the faculty advisory committee for the Wharton Initiative for Global Environmental Leadership. His work focuses on the technology-environment-infrastructure nexus, emphasizing global commodity strategy, and data science and analytics. Parag Khanna is managing partner of FutureMap. He is the author of the new book The Future is Asian. Part 1 of this two-part series looked at how the Belt and Road Initiative (BRI) portends significant shifts in the dynamics of the global agricultural trade.

Here in Part 2 they examine some of the physical risks that will accompany BRI expansion, and offer thoughts on the future agricultural supply chain.

The expanding agricultural commodity complex promises to include more buyers and sellers and with new trade routes re-opened that have long been dormant. While this is fertile ground for emerging market opportunities, there are also risks — both acute and subtle — to this expanding agriculture trade. Here we examine some of those risks in greater detail.

Consumption Risk

The first supply side risk is largely behavioral and in turn magnifies other risks. Overconsumption, and the resultant byproduct food waste, is perhaps the most important risk as it is predicated upon choice. Having a seemingly infinite selection of choices, year-round, seems like a positive byproduct associated with financial security. But being able to purchase pineapples in New York in February carries a cost: A large number of resources, chief among them water and fossil fuels, are utilized to attain a food-on-demand world. Further, this conveyor belt of continuous supply depletes soil, water, and biological resources at an unsustainable pace. Efficiency gains resulting from growing technologies and infrastructure expansion and improvements will help, but they may actually exacerbate the problem when the consumer demands continue unabated.

This also does not even begin to address the important but oft-overlooked distinction between food security and nutrition security. Today, we may have the technology network in place so that we are able to feed the population (some argue that hunger is more of an access issue than a production one), but for much of the world the calories consumed are empty. In other words, access to cheap mass-produced food with refined grains as the staple ingredient is not providing the adequate nutritional benefit commensurate with daily calorie consumption. If we are to look at food sustainability seriously, as population centers in the east are growing at a faster rate than their western counterparts, the provider community should be looking to develop affordable food products that carry and retain the nutrition present when the crops were harvested.

Physical-Climate Risks

Weather-crop disruption is the first climate related consequence. Extreme and acute examples come to mind first: widespread drought decimating the Brazil coffee crop in 2016, U.S. corn in 2011 (see price chart below), and Australian wheat in 2016. Excess precipitation can be equally devastating as the global grains complex is currently coping with the effects of flooding in the U.S. Midwest, Brazil, Central Europe and several former Soviet republics. Less publicized but equally damaging can be the slower insidious risks that develop over decades, including a lowering of the water table, the trend of increasing evening temperatures, and multiple consecutive days of triple digit temperatures.

All of these culminate in reduced supply and lower yields. Regardless of the causes, climate change and variability will alter the way commodity products are grown, how they are distributed, and even consumed against the backdrop of a growing and more affluent global population. With changes in climate, there will be winners and losers with respect to growing origins. While we can use long range models as a guide, many of the significant changes important to agriculture are expected to continue to occur between latitudes of 30 degrees north and 30 degrees south, as noted on the map above depicting projected global mean temperature anomalies changes for 2015 to 2022 versus the 1971-2000 reference period. New varieties and new origins will likely need to be developed or converted for production, and much of this potential expansion in farmable land will benefit producers operating along the transect of Belt and Road Initiative (BRI) participating countries in the East where projected temperature rises may not be as extreme.

Water and Climate Risks

Perhaps more important than changes in temperature will be how temperature shifts manifest the movement, availability and distribution of fresh water across the continents. Decadal climate models project a continuation of ongoing trends: Typically wet areas will get wetter, and moisture-deficient areas will get progressively drier. Water, and more appropriately the lack of water, is a tricky problem to anticipate. Unlike other environmental resource issues where there is often times an acute trigger before a collapse, water deficiencies can have multiple competing factors, and the onset of a problem is somewhat masked; that is until it becomes an ‘event’ and there are no viable supply alternatives.

Changing water dynamics will alter not only the varieties of annual crops that can be supported in certain geographic regions, but will also impact the investment cycles around longer maturing assets such as tree crops. These perennial biological assets, once planted, are expected to produce commercially viable yield quantities for decades. Beverage plants are another example of physical assets with a longer time horizon underlying ROI. A change in water availability one or two decades after a capital expenditure in these industries complicates the calculus of risk and return.

The water dynamic needs to consider not only the food production component, but also what happens when a ‘commons’ resource is depleted and the surrounding population suffers the effects. This issue was highlighted most dramatically in recent years when bottling plants affiliated with The Coca-Cola Company (Coke) were held largely responsible for a reduction in freshwater supplies across India and Latin America. Since then, Coke has taken ownership of this issue and started to implement a series of precautionary measures to ensure that this situation is not repeated. Further, they have pledged to ensure that communities in regions where they operate are provided with a more favorable water balance situation than they had prior to their arrival. How this unfolds in the decades to come in the face of accelerated climate change, however, remains to be seen.

Financial Climate Risks

Financial Climate RisksAccompanying climate driven changes in the supply side will be another big risk in the liquidity of commodities: Foreign exchange. Using the U.S. dollar as the global commodity benchmark, the ‘typical’ relationship between currency and commodities has been inverse: A stronger dollar tends to correlate with a suppression of food prices. The chart above shows a high level relationship between U.S. dollar and the global Food Price Index as determined by the United Nations Food and Agriculture Organization (FAO). Analysts typically look for this foreign exchange relationship to signal price reversals. While this is a generalized rule, it does not always hold true, and it is likely to erode further as Asian nations become more important players on the global agriculture stage. A growing number of regional exchanges around the world have started to offer liquid futures and options contracts for commodities, decentralizing the risk and in the process reducing the importance of contracts which originate in New York, Chicago or London.

As more regional exchanges appear, two things follow. First there is the availability of a decentralized liquid market, which is the necessary fuel for price discovery. Many market transactions work on paper, then fall apart when faced with real world risk. As markets need buyers and sellers, liquidity brings more participants to the table and lowers the barrier to entry for new-origin participants. Second, once liquidity reaches a critical mass, well-functioning markets offer financial instruments such as futures and options, which in turn attracts additional capital liquidity and more market entrants. As price transparency starts to emerge, a more equitable platform for buyers and sellers results. As more BRI participant companies grow to become major commercial supply-side players, we should expect to see the U.S. dollar relationship as the global benchmark diminish in prominence as new commodity-currency relationships emerge.

Disease Climate Risks

Changing climate patterns may also enable or suppress the conditions that lead directly to plant or cultivar disease. Moreover, these mechanisms indirectly alter the biomes that disease transmitting vectors call home. Both scenarios can lead to an increase in risk to the food system. There is already evidence over the last few decades documenting the expansion or migration of biogeographical parameters related to certain species’ survivability ranges. As temperature shifts, this can lead to the forced migration into/out of traditional biogeographic delineations. As non-endemic species travel into new ecosystems, existing flora and fauna comprised of plants, pollinators and parasites, all are subject to new evolutionary pressures they are not equipped to handle.

Evolutionary ‘fitness’ is tested within one or two generations. Technology can help to protect against some of the stresses, but in the biological arms race, traditional monoculture, the de facto method for most commercial agriculture, is increasingly at risk of collapse. Monoculture cropping is efficient at producing large quantities of food and fiber, with limited diversity, at scale, and this seems to make good sense. Biology tells us otherwise. Limiting genetic diversity on the supply side leads to susceptibility to disease – particularly those diseases whose vectors have roots in rapidly changing environmental conditions. Biomes in tropical regions where expanding temperature habitability ranges are attractive to microbial invaders immediately come to mind.

Further, climate change will only exacerbate this potential problem on a global scale.

Contagion Climate Risks

This cursory overview of the risks described above should highlight the precarious nature of the global food supply network. However, while each of these individual risks carries significance, when one or more of these factors occur in a short duration, we potentially move into threat-multiplier territory. The cascading effects from supply disruption in one market can easily spill over into several other markets, and this in turn reintroduces additional pressure on underlying foreign exchange risk.

When supply origins are in an unfavorable currency position, and physical material and product decisions for delivery several months forward are shifting in near-real time, the fallout can be severe. Again, low-margin producers get squeezed and bear the brunt of the losses. We have seen this play out numerous times on a smaller scale with Latin American and East African origins, and with BRI opening up avenues for new trade partners, the likelihood of increased risk, and the subsequent effects of contagion will surely heighten.

For a reminder of potential contagion risk, recall the Arab Spring protests from 2011. While this was undoubtedly the consequence of myriad contributing factors, one of the key catalysts for this event was tied to the ability of citizens to access ingredients to make or purchase bread, namely milled wheat. By 2010, numerous Arab countries had Russia as their largest wheat supplier, but Russia’s heat wave and drought that summer forced Moscow to ban wheat exports, leading to a significant spike in prices for which Arab governments were unprepared to respond. We of course cannot say for sure that having access to additional supply markets would have prevented the Arab Spring. Again, if we apply a blend of the precautionary principle with basic functioning of biological systems via evolutionary fitness, we could argue that redundancy (expanded supply) favors the prepared when faced with stress, and monoculture (limited supply or resources) is the precursor to bottlenecks, adaptations and collapse.

The (Belt and) Road Ahead

It is no secret that traditional agricultural commodity traders have experienced a difficult time maintaining an edge in the hyper-competitive market space in recent years. The BRI will change that. As more data has become available to an ever -increasing number of market participants, longstanding commodity corporations that once dictated physical and financial stocks and flows no longer have eminent domain with respect to market-moving information.

As a result, funds have closed, banks have sold off entire commodity units, asset managers have literally become a commodity themselves, and high frequency traders are picking up the financial crumbs. But this in no way supports the notion that the commodity complex does not have massive opportunity, particularly with more decentralized and inclusive global trade.

With BRI and other evolving network partners operating with one another, countries that had no previous relationships can become trading partners within months. Further, many models that were built and quantified on historical trade partnerships no longer have merit. As an increasing number of supply-side entrants will now be contributing physical agricultural supply to a world market which demands more products with greater diversity, suddenly any given country’s currency is now exposed to that of every other country in the world. It is not just the strength of the dollar versus the real/renminbi/rupee, but rather the dollar versus any country of choice.

Being able to navigate through this new interconnected world where borders are less important than regions is where the smart money should be placed. The BRI, and other forthcoming initiatives that might choose to replicate this example, may hold the potential to serve as the only viable means to sustainably feed the world. We maintain that the expansion or the diversity with respect to supply-side sources in commodity networks coupled with lower-cost and low latency technological solutions, can dissolve barriers to entry for emerging market participants, while at the same time providing opportunity and hedging risk.

Global infrastructure connectivity and integrated markets further propel us towards a supply-demand world of more decentralized service providers and equal access to resources, essential conditions for our collective survival and stability in an unpredictable world. A decentralized approach towards global agriculture may ensure that global supply meets growing demand requirements, while also encouraging equitable participation regardless of geography. Bringing food and fiber to the world while minimizing origin control by a few large players may be the only way that these challenges can be met.

Michael Ferrari is the managing partner of Atlas Research Innovations, and is on the faculty advisory committee at the Wharton Initiative for Global Environmental Leadership. His work focuses on the technology-environment-infrastructure nexus emphasizing global commodity strategy and data science & analytics.

Parag Khanna is the managing partner of FutureMap. He is the author of the new book The Future is Asian.

Halting Latin America’s Economic Slide

Economic growth in Latin America has decelerated, living standards have stagnated, and a return to poverty is a real possibility for much of the region’s emerging middle class. To avoid this worrisome scenario, the region urgently needs to increase investment in three priority áreas.

Mauricio Cárdenas


BOGOTÁ – “Nobody’s backyard: The rise of Latin America” was the headline on the cover of The Economist on September 11, 2010. Inside was a special report that presented an optimistic view of the region’s future. And little wonder, given that high commodity prices were enabling most Latin American countries to expand social programs and significantly reduce poverty and inequality.

Governments across the region managed to improve living standards, regardless of whether they were led by left-leaning presidents such as Luiz Inácio Lula da Silva in Brazil and Néstor Kirchner in Argentina, or by those on the right such as President Álvaro Uribe in Colombia.

China’s rapid growth and rising demand for Latin America’s minerals, soybeans, and oil created jobs and boosted tax revenues. In addition, quantitative easing by central banks in developed economies boosted global liquidity, making large amounts of capital available for investment.

But those days are long gone. Today, Latin America is at a crossroads. Economic growth has decelerated, living standards have stagnated, and the region’s social progress is at risk. The emerging middle class is now vulnerable, and a return to poverty is a real possibility for many.

To avoid this worrisome scenario, Latin America urgently needs to increase investment in infrastructure, technology, and human capital.

The International Monetary Fund expects Latin America to grow at an average annual rate of just 2.5% over the next five years, making it the slowest-growing region in the emerging and developing world, well behind Sub-Saharan Africa, Asia, and the Middle East and North Africa. Moreover, average growth of 2.5% would be about half the pace of Latin American growth in the five years leading up to the 2008 global financial crisis. As a result, unemployment and poverty are likely to increase throughout the region.

Worse, this does not seem to be a cyclical downturn. Various estimates indicate that the potential growth rate for most Latin American economies is now a full percentage point lower than it was in 2010. For example, Colombia and Peru can no longer sustain a growth rate of 4.5%, as they did a decade ago. These days, their central banks assume that 3.5% is closer to potential. Using time series, I estimate Brazil’s potential growth rate to have fallen from 3% a decade ago to 2% today, and this month, Chile’s central bank will release a new revision of potential growth, which the market expects fell from 4% to 3%.

Although the Latin American slowdown reflects lower commodity prices, this is not the only factor. True, oil and copper prices are well below their peaks in the early part of this decade.

Yet they remain far above their average level in the 1990s, when the region grew at a much faster pace than today. And although China’s slower growth – and the even faster deceleration in its imports – is of course having an impact, the main reason for Latin America’s sluggishness is a lack of investment.

As a result of austerity measures across the region during the past few years, investment rates have fallen and not recovered. This is partly the result of budgetary rigidities. Because current expenditures, such as pensions and salaries,are often constitutionally protected, the burden of fiscal adjustment tends to fall on more flexible capital spending. For example, investment rates (as a share of GDP) fell by four percentage points in Peru and Argentina as a result of the recent shock.

Increasing the level of investment across the region must therefore be a high priority. There is also a need to raise productivity and narrow the significant gap with advanced economies in this regard. But, crucially, measures to increase investment can produce faster results.

The shortfall in investment concerns not only public infrastructure, but also technology and human capital. For starters, Latin America is not investing enough in the technologies that could integrate the region into global value chains. This reflects the absence of a shared regional vision, barriers to entrepreneurship, and inadequate financing, especially for small- and medium-size enterprises. Making matters worse, the region is underinvesting just when its relatively abundant unskilled labor is coming under threat from rapid advances in artificial intelligence and robotization.

Latin America’s need for more investment is not a right- or left-wing issue, but simply a matter of urgency. Although the region’s policymakers may differ on the details, they need to agree to increase investment in the three priority areas: infrastructure, technology, and human capital.

Moreover, this investment should come from all sources – public spending, private financing, crowdfunding, global markets, and multilateral institutions.

Latin America has not invested enough in the past few years, and it is not investing enough today. This must change quickly if the region is to prevent low growth and rising poverty from becoming its new normal.

Mauricio Cárdenas, a former Minister of Finance of Colombia, is a visiting professor at Columbia University.