Predicting nine of the last five recessions

The equity market white knuckle ride continued this week as tech stocks came into the line of fire. At the start of this year I suggested that global stock markets would end the year higher than they began and wrote “I’ll stick my neck out by predicting a rise of 5-10% in the major US and European indices.” That call is not looking good at the present time with European equities well into negative territory and US markets also now in the red, having held up well until this week. However I did point out that “it might pay to reduce the degree of risk exposure – perhaps by switching the top 10% of risky assets in the portfolio for something less risky” and that “a market which is so dependent on tech stocks is clearly vulnerable to a shift in sentiment.”

Despite my apparent over-optimism, I have generally been pretty cautious on stock markets in recent years particularly since the 10-year trailing P/E ratio on the S&P500, as popularised by Robert Shiller, continued to point to a market that was running out of line with fundamentals (chart above). And the higher tech stocks drove up the market, so it was inevitable they would also lead it down. As the chart below (taken from Bloomberg) shows, over the last 12 months the so-called FAANG stocks have outperformed the S&P500 by 14% and have contributed all the increase in the index market cap. At mid-year, the outperformance index was at 37% and it has been hard for some time to avoid the sense that tech stocks have been somewhat bubbly given their stellar rise. Yet the valuations of tech stocks have not been too far out of line. Apple, for example, is trading at a P/E multiple of just below 20x earnings and the Alphabet ratio (the company formerly known as Google) of around 26x is high, but not crazy. This is testimony to the extent to which the FAANG companies have been able to generate exceptional earnings growth.

But some cracks in the façade are beginning to show. Amazon’s narrow miss relative to Q3 expectations, and guidance suggesting that the Q4 earnings season may be weaker than the consensus currently expects, have dampened enthusiasm. Yet Amazon and Alphabet recorded earnings numbers that were 30% and 21% higher respectively than a year ago. So maybe things are not as bad as painted but when they are seen as invulnerable to bad news, any negatives can have a bigger-than-expected impact. I thus tend to view the moves in tech stocks as a catalyst for selling in a market that has become rattled by other issues in the global economy.

The number one concern is the ongoing trade spat between the US and China which is now beginning to impact on corporate America if this week’s Beige Book evidence is anything to go by. We also have to add the fact that the tax cuts implemented at the beginning of this year have given corporate earnings a big lift which will not be repeated next year. As investors look ahead to 2019, they see an earnings outlook that is far less rosy. Looking further afield, Brexit issues; the ongoing dispute between the Italian government and the European Commission, and the diplomatic spat between Turkey and Saudi Arabia add to the sense that all is not well in the wider macro world. Global investors have good reasons to be nervous. 

Then there is the Fed’s rates policy, which looks set to drive interest rates still higher. There are those who believe that the recent market wobble is a good reason for the Fed to pause. I do not see why. After all, if low interest rates were responsible for driving the market up, so higher rates might be necessary to get it back into line with fair value. In any case, it has been slightly puzzling that the market has continued to go up despite the Fed’s tightening, which can only be attributable to the one-off tax cut. A pause that refreshes can only be a good thing. Putting all the pieces together and it is hard to escape the suspicion that in the equity world at least this is as good as it is going to get. This does not mean to say that it is all over. As was the case in autumn 1999, when US markets also wobbled badly, it is possible that there may be a rebound before the final reckoning. 

Yet it does not feel like a rerun of the late-1990s. For one thing, the tech companies are delivering real products that generate earnings rather than the hype which characterised the tech bubble. The global economy is far less frothy – particularly in Europe – and investors are a lot more cautious. Nonetheless, many people I speak to are concerned that the US is setting itself up for a recession on an 18-24 month horizon. Maybe! Or there again maybe not! At times like this, it is always worth recalling Paul Samuelson’s famous phrase that the stock market has predicted nine of the last five recessions.

A house divided against itself cannot stand

The weekend march in London in favour of a second Brexit referendum sent a signal that parliament would be wise not to ignore. According to the organisers, around 700,000 people ventured out onto the streets to demonstrate their support for a vote on the final terms of the Brexit deal. Unlike in 2003, when they estimated that 750,000 people took to the streets to protest against Britain’s involvement in the Iraq War, police refused to put a figure on Saturday’s crowd. Suffice to say, however, the People’s Vote march was one of the biggest popular rallies on the streets of the UK’s capital city.

I don’t wish to be a spoilsport, but it is unlikely to succeed in its objective if past history is anything to go by. In the early 1960s, popular marches against the deployment of nuclear weapons attracted crowds of up to 150,000 – pretty good going in pre-social media days – yet the UK still continued to deploy them. The violent poll tax riots in early-1990 did not prevent the government from going ahead with the introduction of a local flat tax, although it perhaps did undermine Margaret Thatcher’s position as prime minister and she was forced to resign later that same year. And as we all know, the UK soon became embroiled in the Iraq War despite significant opposition at home.

So how should we interpret major expressions of public support? It is difficult to argue with certainty that the weekend protests represent a significant shift in wider public opinion as the 2003 experience shows. Although people recall the anti-Iraq War protests as suggesting that the majority of the electorate was opposed to military action, YouGov conducted a series of 21 polls between March and December 2003 which showed that 54% of respondents believed it was right to take military action against Iraq. What is even more interesting is that polls conducted in 2015 suggested that only 37% of respondents say they believed military action was right at the time. This is a form of cognitive bias best described as consistency bias in which past attitudes are incorrectly remembered as resembling today’s attitudes.

Perhaps it is more accurate to say that big demonstrations such as those against Brexit or military involvement in Iraq represent a commitment by a passionate minority on a topic where society is genuinely split. It could, of course, be the case that public opinion has shifted on Brexit: After all, the opinion polls clearly suggest that those believing the UK made the wrong decision two years ago now outstrip those who believe it to be the right decision by a good five percentage points. But that does not mean the government will change its mind. Indeed, as I noted here, it is almost impossible to conceive of a second referendum any time soon on the grounds of democratic legitimacy.

Moreover, we have less than five months before the government is due to leave the EU, and Christmas is coming up fast. It is logistically difficult to imagine that the government will be able to pass the necessary parliamentary legislation and conduct any form of information campaign before the UK leaves the EU on 29 March 2019. As the lawyer David Allen Green has pointed out, “referendums on a UK-wide basis sit badly with the UK constitution” because while a mandate derived from a general election is a weak one (parties can simply ignore their manifesto commitments) a mandate derived from a referendum is a different beast. A second referendum merely gives us a second opinion. Which one should we choose? In Allen Green’s words, “what if the further referendum is on a lower turn-out?  Or a different majority? Which mandate takes precedence?” And as I have noted previously a second referendum would take place in an divided country which would exacerbate already-inflamed tensions.

Much as it pains me to say it, I cannot see a second referendum as being the answer to Brexit divisions. So how should they be dealt with? Perhaps the best option is for the government to push for the softest possible Brexit and dare the hardliners to challenge them: Keep the UK as closely tied to the EU as practicably possible in the hope of minimising the economic damage. Indeed, to all intents and purposes keep kicking the can down the road by finding ways to delay a full Brexit. It would, of course, provoke a dreadful row within the Conservative Party. But it was Abraham Lincoln in his famous 1858 speech, quoting from St Matthew’s Gospel, who asserted that a house divided against itself cannot stand. Brexit is really an internal Tory party matter which is never going to be resolved by compromise. This particular divided house may need some bloodletting.

Brexity McBrexface

They do say that many a true word is spoken in jest. I was thus highly amused by the Tweet in the attached graphic which pointed out that the Boaty McBoatface episode is an example of how open democracy can lead to stupid outcomes which can subsequently be reversed.

For those not familiar with the story, in 2016 the UK Natural Environment Research Council obtained a new boat to conduct research in the polar regions. In a burst of enthusiasm for open democracy the NERC set up an online poll allowing the public to choose a name. By an overwhelming margin, the most popular choice was Boaty McBoatface – a facetious choice derived from a throwaway line by a radio presenter which was made in jest. This placed the NERC in an invidious position: Either it risked the credibility of the organisation by bowing to public opinion or it could override public opinion and choose the name itself. In the end, it opted for the latter with the new boat subsequently named after the respected naturalist Sir David Attenborough.

Apart from raising a question of what the UK public was thinking in 2016, as it followed up this episode by voting for Brexit three months later, it raises all sorts of issues regarding engaging the public in open democracy and how to minimise the cost of polls giving undesirable outcomes. It is not as though this sort of thing has not happened before. One of the most infamous examples occurred in 2012 when the soft drinks company Mountain Dew created a new flavour and held an online poll to choose a name. The top suggestion, which earned the most votes by a landslide, was "Hitler Did Nothing Wrong." Not surprisingly that suggestion did not go down well with PepsiCo which eventually shut the contest down.

The Brexit debate was taken much more seriously but, like the Boaty McBoatface case, it was not a binding referendum – government is not legally bound by the snapshot of public opinion on 23 June 2016 to implement the result. But one of the key principles required of participatory democracy is that it has to be seen as legitimate. Encouraging people to participate, only for their vote to be ignored, undermines the credibility of the process. It is for this reason that I have a lot of sympathy with the prime minister when she argues that a second referendum cannot be permitted. If blame for the one time nature of the referendum is to be apportioned anywhere, look no further than  her predecessor, David Cameron, who deserves all the opprobrium he has so far received – and more – for he it was who failed to properly set the parameters, and ran a campaign of spectacular awfulness by assuming that people were broadly happy with the status quo.

One of the key lessons that has emerged from the rash of recent poll outcomes is that public engagement is vital. Participants in the Mountain Dew and McBoatface polls had no skin in the game. They had nothing to lose by making a ridiculous choice, and they knew it, hence the outcomes. Arguably, even a vote for Trump will have relatively limited consequences – in two years’ time the American electorate will have another chance to have its say. But the Brexit vote is different in that it is a one-time for all-time choice. 

We can question the extent to which the electorate was properly engaged, particularly in view of complaints around the time of the referendum – and subsequently – that many people did not understand what they were voting for. There are also many questions surrounding the legitimacy of the Leave campaign which has called its validity into question. And as it becomes clear just what Brexit entails, there is a sense that the views of the electorate are beginning to shift (as I noted here). But politicians are fixated on the notion that the vote two years ago is sacrosanct. For Brexit supporting politicians, they are at least partially motivated by the fear that they may not be able to replicate the 2016 vote if a second plebiscite is held (though I would not bet the house on that). Consequently, it is a perfectly rational strategy for them to oppose another referendum.

But with demographic trends not running in the Brexiteers’ favour (here) and signs that many MPs do indeed understand the costs of Brexit, we should perhaps view Theresa May’s attempt this week to extend the transition period as a ploy to buy more time until there is clear water between the Remain and Leave camps. At that point, a second referendum may make sense as the terms and conditions under which Brexit are to be implemented become more clear.

Ardent Brexiteers who fear that the UK may never fully leave the EU probably have a point. But the fact that large swathes of the population were not properly informed about the choices on the table in 2016 means that the final outcome of the referendum may not be known until some years after the event as the Brexity McBrexface farce unfolds.

Electric vehicles: Still in need of economic support

One of the less publicised stories of recent days was last week’s decision by the UK Department for Transport (DfT) to cut the subsidies granted to buyers of electric vehicles (EVs). From 9 November, the grants for new plug-in hybrids will be scrapped, while discounts on all-electric cars will be cut from £4,500 to £3,500. Coming in the same week as the IPCC issued a report suggesting that we have until 2030 to limit the rise in global temperatures to 1.5^oC, beyond which irreparable damage will be done to the global environment, the timing of the decision looks truly abysmal – not to mention amateurish. It certainly does not make good economic sense.

According to the DfT, the grant for plug-in vehicles was designed to help establish a market for them and having succeeded in this aim it is time to focus support on zero-emission models such as pure electric and hydrogen fuel cell cars. I would suggest that this is wrong – and industry specialists were horrified by the decision. The market is far from established in the UK (and indeed in most other European countries bar Norway): Sales of plug-in hybrid vehicles accounted for just 1.2% of total sales last year – not exactly an established market. According to Mike Hawes, chief executive of the SMMT motor manufacturers body, “prematurely removing up-front purchase grants can have a devastating impact on demand.”

All the evidence suggests that carbon emissions measured over the full lifecycle of EVs are far lower than for vehicles powered by fossil fuels. This report by the International Council on Clean Transportation calculates that even after we factor in the costs of emissions generated during the production of the vehicle battery, which are pretty high, “a typical electric car today produces just half of the greenhouse gas emissions of an average European passenger car.”

It thus makes sense from an environmental perspective to encourage the switch to electric vehicles of one kind or another. But one of the biggest deterrents to buyers is that the purchase price of electric vehicles is higher than their conventional counterparts. However, the running costs of an EV are generally lower, so consumers have to figure out how many miles (or km) they must drive in order that the lower operating costs offset the higher purchase price. In order to do this, I calculated the costs of running a Ford Focus in the US using a petrol-driven version and the electric equivalent. It currently costs around USD10 to travel 100 miles in a 30 MPG Ford Focus (assuming petrol prices at USD3 per gallon) but with US electricity costs currently averaging around 12 cents per kWh, it costs just USD3.72 to cover 100 miles in a Ford Focus Electric. Given these inputs, we can calculate the breakeven mileage based upon a range of prices for the conventional car and the markup for the electric vehicle.

According to my calculations, if the petrol vehicle costs USD15k and the EV is sold at a 10% premium, the breakeven mileage is  around 24,000 (38,000 km) which is just less than two years of driving by the average US motorist (13,474 per year). But if the EV premium rises to 20%, the breakeven mileage increases to almost 48,000 (3.5 years of driving). As the EV premium rises, so does the breakeven mileage. Similarly if the conventional vehicle is more expensive in the first place this also drives up the breakeven point. We can plot the various breakeven points in chart 1.

But what happens when a subsidy is introduced? As you might expect, it lowers the initial purchase price and as a result the mileage at which the EV becomes an economic proposition (chart 2). For a conventional vehicle costing USD15k, a USD 4k subsidy always makes it worthwhile to choose an electric equivalent for any markup below 30%. Even a 35% markup implies that the breakeven point will be achieved after 18 months of driving for the average motorist. Clearly, the more costly are EVs, the higher are the breakeven points but they are considerably lower than in the no-subsidy case (chart 2).

Obviously these are only illustrative examples – they are based on US figures and will differ according to local petrol prices and electricity costs. Nor do they include factors such as repair and other maintenance costs. But the point is made: Subsidies do significantly enhance the attractiveness of EVs over the fossil fuel equivalent and it strikes me as a remarkably short-sighted policy to begin phasing out the subsidies already, particularly when battery-powered hybrids still account for such a small market share. Over time, we would hope that the costs of EVs will decline relative to their fossil fuel equivalent, which will make them more economically attractive. But the DfT appears to be relying on the moral argument for buying EVs, rather than the economics. Of course, it would not be the first time that the UK government has launched a policy that flies in the face of the economic evidence. I think there is one that begins with a “B” …

Blink and think

In Jeremy Corbyn’s words this afternoon, this really is beginning to feel like Groundhog Day. The UK and EU27 continue to seek a resolution to the Irish border problem but are unable to find one because the British government is hemmed in by the contradictory positions of the hardline Brexiteers; remain-supporting MPs and the DUP. It is an unholy mess, and hopes that a border agreement would be thrashed out in time for this week’s Brussels summit appear to be receding. Having initially expected that both sides would agree the final outline of the Irish border agreement in October, the best that can be hoped for is that the EU will this week give a green light to hold a summit in November. European Council President Tusk has already said that if a plausible Irish border strategy cannot be agreed this week, the chances of scheduling a November summit are remote.

Increasingly, I do wonder how close to the fire politicians’ feet have to be held before they realise that playing with matches is dangerous. Theresa May’s statement to the House of Commons this afternoon was billed as an update of the state of play, but was in reality yet another blizzard of obfuscation. The prime minister’s statement reiterated that any backstop arrangement with the EU regarding the Irish border can only be temporary. But to the extent that a backstop represents the default position to which both sides revert in the event that the preferred solutions do not materialise, it can only work if it is a permanent arrangement. Nor does she concede in public that the EU simply will not accept a temporary solution. I am reminded of the line from the film The Battle of Britain, delivered by Sir Ralph Richardson who played the British Ambassador to Switzerland: “We're on our own. We've been playing for time. And it's running out!”

Not only did the PM argue for a temporary arrangement, contrary to the EU’s wishes, but she refused to be drawn on how temporary it would prove to be. A year? Two years? Longer? Quite clearly, this was Theresa May trying to square the demands of the DUP, who want to prevent Northern Ireland from being carved out from the UK, against the Brexiteers who want to break free from the EU customs union. And it is an impossible circle to square.

I had hoped that rationality would start to kick in by now, but as I noted a couple of weeks ago (here) it is entirely possible that all sides have adopted such entrenched positions that they are unable to back down and that irrational outcomes are increasingly baked in. But it is not about the UK versus the EU: The real problems lie closer to home, with the domestic positions of the respective UK parties showing no signs of moving. Perhaps even more worrying is that ideological rather than rational politics holds sway across many countries. The very fact that the sky has not (yet) fallen in suggests that those contemplating radical solutions might be tempted to pursue them in the belief that the downsides are limited. One day someone is going to make a big miscalculation, and if we continue down our present path it might just be Brexit that demonstrates where the limits of populism lie.

But there is an additional issue that politicians have to bear in mind. Although the government repeatedly tells us that it is intent on delivering the will of the people in accordance with the mandate given by the referendum, the winds may have shifted against them. Polling evidence suggests that those believing the UK made the wrong decision to leave the EU now hold a lead of at least five percentage points over those who believe it was the right decision (chart). If the government does get it wrong by triggering a hard Brexit, with all the attendant adverse economic consequences, the electorate will hold them to account. Arlene Foster, the DUP leader, memorably said yesterday in the context of Brexit that “This is a battle of who blinks first, and we’ve cut off our eyelids.” I rather suspect that an unforgiving electorate will want to cut off more than politicians’ eyelids.

Italy's budget issues: A problem of the EU's own making

Italy’s populist government has upset the European Commission with the release of its budget plans for the next three years, and the IMF has now got in on the act by warning that they risk upsetting markets. The whole furore is based on the fact that the current budget plans are higher than those outlined by the previous government. But by continuing to criticise the Italian government’s plans in public, the EC risks the very thing it is concerned about by driving bond yields higher, thereby raising debt servicing costs and exacerbating the debt problem. Whilst the EC’s criticisms of the Italian budget targets may have some validity, the fact is that EMU fiscal procedures are not fit for purpose – and perhaps never were.

To put it into perspective, the previous government targeted a deficit ratio of 1.6% of GDP which the EC deemed acceptable in order to help keep Italy’s high debt-to-GDP ratio in check. But the new government, a coalition between M5S and the League, pushed for a much higher deficit in order to fund some of its more populist schemes. Finance Minister Giovanni Tria, who is not a member of either party, initially tried to hold to the previous government’s plans but appears to have lost the domestic political battle. In late September, the budget plan envisaged a deficit-to-GDP ratio of 2.4% of GDP for the next three years but following concerns that this was too high, and despite claims by the Deputy Prime Minister that “we will not backtrack by a millimetre”, the government is now targeting deficit ratios of 2.4%, 2.2% and 2% in 2019, 2020 and 2021 respectively. 

Strictly speaking this is not an excessive deficit, which is broadly defined as 3% of GDP, and is the benchmark against which the Italian government judges its plans. But the EC’s fiscal rules are a lot more complex than they were prior to the financial crisis and it is the devil in the detail that has resulted in Rome and Brussels having very different opinions regarding the budget plans. In 2011, the EC introduced a series of reforms known as the “six pack”, one of which is designed to limit the growth rate of government spending to no more than the medium-term potential GDP growth rate. In addition, governments are now subject to Medium-Term Budgetary Objectives (MTOs), which in Italy’s case requires it to reduce the structural budget deficit to zero.

Of course the reason that the EC is so concerned about the Italian fiscal position is that it has very high debt levels (131.8% of GDP in 2017 versus a Maastricht Treaty reference value of 60%). But Italy has never even come close to meeting this threshold and was allowed into the single currency area despite a debt ratio that was way out of line with the entry requirements. Indeed, in November 2003 I wrote the following:

It is now far too late to impose on Italy the kind of fiscal austerity required to get the debt ratio down. The damage was done twenty years ago.

Italy’s problem now is that the EC’s concerns have spooked the markets and forced 10-year bond yields to their highest since early 2014 which will further raise budgetary pressures. Technically, the EC’s fiscal rules allow it to levy fines on Italy for failing to comply with its MTOs, which would be to add insult to injury. But this would be inadvisable. For one thing, Italy’s proposed 2.4% deficit ratio next year is below that of France (2.8%). Moreover, Italy is a net contributor to the EU budget to the tune of around 0.2% of GDP. And it is also the world’s third largest bond market. 

Unlike Greece, Italy will not be so easy to push around. The EC can huff and puff as much as it wishes but there are limits as to how much leverage it can exert if the Italian government is not prepared to cooperate. Perhaps more importantly, the very fact the EC is still talking about austerity after a decade of hard economic slog suggests there is a lot wrong with the rules. In any case, a couple of tenths on the deficit ratio does not mean much when the debt ratio is above 130%. By making an issue of it the EC risks exacerbating the problem, prompting a market reassessment of the whole euro zone bond sector, especially in view of the imminent end to ECB purchases. And as a final thought, two-thirds of Italy’s €2.3 trillion of outstanding debt is held by domestic residents (the ECB holds around 15%). Somehow, I can’t see the prospect of higher returns on these holdings being a great problem for yield-starved domestic investors.

Auction stations

A few days ago I heard someone describe the Brexit process in terms of the dollar auction problem and was immediately struck by how accurately it described the current state of affairs. The dollar auction problem was formulated by the late economist Martin Shubik, as a non-zero sum sequential game to illustrate how a series of rational choices can still lead to irrational outcomes.

In the original thought experiment, an auctioneer sells a dollar bill with two participants engaged in the bidding process. The caveat is that the person making the second highest bid must pay a penalty equivalent to the amount that they bid – unlike a real auction where there is no penalty for a failed bid. Suppose that bids increase in increments of 5 cents. If the first participant bids 5 cents for the dollar bill, a discount of 95% relative to the face value, the second person has an incentive to raise the bid to 10 cents because they still obtain the banknote at a 90% discount. Player One rebids because they can still make a significant notional gain and so it goes on. By the time Player One bids 95 cents, Player Two has to raise their bid to the face value of the dollar bill. They clearly make no profit but at least they avoid the 90 cents penalty from their failed bid. But Player One is facing a 95 cents penalty so it is in their interests to raise their bid to 105 on the basis that if they win, they will only lose 5 cents versus 95 cents if they do not bid. But Player Two has an incentive to bid again and the bidding round continues. In theory, it could continue forever so long as both players remain committed to winning.

Shubik designed this game to demonstrate how people can become obsessed with the idea of avoiding losing, even though the cost of winning can be so great as to leave them worse off – in effect, they lose whatever happens. This strikes me as a brilliant exposition of the underlying problems facing the two sides in the Brexit debate. We can think of the EU27 as the auctioneer determining the nature of the UK’s relationship with the EU, whilst the Leavers and Remainers bid against each other to ensure that their plan is accepted. Just as the bidding actions in the dollar auction game are determined by the action of the previous bidder, so the Leavers and Remainers have reacted to the plans made by the other side over the past two years.

We are now at the stage where Theresa May’s Chequers Plan represents the one dollar bid. It will not make the UK any better off but it will minimise the damage to the UK if accepted. But so committed are the Brexiteers to not losing the right to “take back control” that they are prepared to vote down any such plan. In their eyes, the economic losses are offset by the right (in the words of Dominic Raab) to take back control of “our borders, our money and our laws.”

Over the coming days and weeks, we will see whether the prime minister is willing to amend her plan in order to satisfy  the auctioneer’s requirement that a solution be found to the Irish border problem. Latest leaked reports suggest the government is prepared to back down on its opposition to new checks on goods moving between the British mainland and Northern Ireland. In exchange, May’s team would ask the EU to permit the whole of the UK including Northern Ireland to stay in the bloc’s customs regime (as I suggested here). At that point the Brexiteers may respond with another crazy bid, arguing that remaining in the customs union is to ignore the “will of the people” (it isn’t!)

The dollar auction game teaches us three lessons about escalation strategies: 

1. Perhaps the most obvious lesson is not to enter in the first place. But if you do, make sure you cut your losses early (too late for that I fear). 
2. It is possible to game the auction via cooperation. In the dollar auction,  the best outcome is derived if one person bids 5 cents and the second player refrains from bidding on the understanding that they will receive an equal share of the profits, in which case both end up better off. Again, it might be possible to achieve a smooth Brexit if all sides are prepared to compromise. 
3. The auctioneer is the only winner, especially as the stakes are raised.

Unfortunately, the dollar auction game can go on forever but the Brexit auction game can now only run for less than six months. Time, perhaps, to look again at option (2)
.