5 Efficient markets – a first encounter
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The international setting
consider the important link between uncovered and covered interest parity, which involves
the concept of market efficiency.
Recall that, in introducing the idea of hedging in the forward market in Section 3.2,
the assumption was made that the forward rate on 1 January was equal to the spot rate
expected to prevail on 31 December. In order to illustrate what was meant by covered arbitrage, some value for the forward rate had to be assumed, and the expected spot rate was
certainly convenient, since it allowed us to use the same numerical examples in both cases.
Look back at the formal analysis in Equations 3.5–3.8. Nothing there required us to have
f = Δse (or F = Se). Covered interest parity could therefore still apply, even if we did not have
the forward rate equal to the expected spot rate.
None the less, it is obvious from comparing Equations 3.4 and 3.9 that the condition
f = Δse is far from arbitrary. In fact, since Equations 3.4 and 3.9 together imply that f = Δse,
it is obvious that covered and uncovered parity cannot both apply unless we also have
equality between the forward rate and the expected spot rate. Putting the matter differently, as long as we continue to assume risk neutrality, if the forward rate is not equal to the
expected spot rate, then either covered or uncovered parity has broken down, or both.
Now consider for a moment the situation of an individual market agent who, on
1 January, confidently expects the spot rate at the end of the year to be at a level different
from the one currently obtaining for forward foreign currency. Suppose, for example, that
the 12-month forward rate is $1.00 = £0.50, and the agent is quite convinced that the rate
at the end of the year will be $1.00 = £0.60.
If he is confident in his judgement, he will see himself as having the opportunity to profit
by a simple transaction in the forward market. All he need do is buy dollars forward, in
other words sign a contract to buy dollars at the end of the year at the current forward price
of £0.50 each, which he is so convinced will seem a bargain price on 31 December. If he is
correct in his forecast, then 12 months later, when he fulfils his promise under the terms of
the forward contract to buy the dollars at £0.50 each,15 he will be in a position to resell them
immediately at the end-of-year price prevailing in the spot market, £0.60 each – a profit of
£0.10, or 20% per dollar bought.
Of course, this strategy is risky, so if the investor is not risk-neutral he will require a risk
premium to persuade him to undertake the transaction, and £0.10 per dollar may not be
sufficient. However, if we maintain the fiction that investors are risk-neutral, we can say
that anyone who expects the spot exchange rate at some future period to be different from
the forward rate currently quoted for that period can profit by backing his judgement – that
is, by speculating.
If we can generalise the argument to the market as a whole, or, in other words, if we can
treat the market as if it were a single individual, then it follows that equilibrium will entail
a forward rate equal to the consensus view of the future spot rate. Otherwise, there will be
a net excess demand or supply of forward exchange, which will itself tend to move the rate
towards its equilibrium level. We shall henceforth make use of the following definition to
describe this situation:
Unbiasedness applies when the (3-, 6- or 12-) month forward rate is equal to the
spot rate that the market expects to see prevailing when the contract in question
matures.16
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Financial markets in the open economy
What we are talking about here is a particular example of a very general concept indeed:
market efficiency.17 For the moment, we shall take the opportunity to introduce the
following definition:
Efficient markets are ones where prices fully reflect all the available information.
There are, therefore, no unexploited opportunities for profit.
The definition seems a little vague, and, in a sense, so it should. What are we to understand by ‘fully reflect’ all information? That depends on the model of the market in question,
and its properties. By contrast, unbiasedness is a very clearly defined state and is in that
sense a special case of market efficiency. Unbiasedness implicitly assumes a particular market model, where the following conditions apply:
●
There are an adequate number of well-funded and well-informed agents in the currency
markets, with broadly similar views about likely future developments.18 Market prices
are well-defined.
●
There are no barriers to trade in the markets (that is, no exchange controls) and no costs
to dealing (no transaction costs).
●
Investors are risk neutral.
Unbiasedness and efficiency led to different conclusions about the potential for profiting
from arbitrage. If a market is efficient, investors cannot systematically make any profit over
and above their required compensation for bearing risk, whereas if it is unbiased they cannot even earn a risk premium. In the particular case of UIRP with no risk premium, it implies
that cross-country arbitrage will on average yield no profit.
What about the facts? Do they suggest that it is impossible to profit by interest arbitrage?
In the next section, we deal with this question.
3.6
The carry trade paradox
We take an agnostic approach and address the straightforward question: has it been possible in practice to profit from (uncovered) interest rate arbitrage? In other words, looking
back in time, has there been a way of reliably making money by moving money around the
world?
This is not quite the same thing as asking the question: does UIRP fit the facts? In order
to interpret it as a test of UIRP, we would have to add some kind of assumption about how
expectations are formed and what information was available to investors at any point in
time, and these are matters we defer until Chapter 11.
Instead, we want simply to know whether it was possible to profit from the strategy
widely followed by investors in recent years of borrowing in low interest rate currencies and
converting the proceeds into high interest rate currencies in the hope that the exchange rate
would either remain unchanged or at least not move sufficiently to neutralise their gain on
the interest differential. This sort of strategy is known in the international financial markets
as a carry trade. For example, for many years the major global financial institutions, hedge
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The international setting
Figures 3.2 (a–f) Exchange rate depreciation and lagged interest differential (US as
foreign country)
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Financial markets in the open economy
Figure 3.2 (continued)
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The international setting
funds etc. would target the Asian carry trade, raising large loans in yen and sometimes in
Hong Kong dollars and redepositing the funds in US dollars and pounds, which offered far
higher interest rates.
How well did it work?
Remember that UIRP implies that interest rates only differ because investors expect
the exchange rate to change, as we saw in Equation 3.4, so if, on average, investors’
forecasts are correct, this strategy will be unsuccessful, yielding a loss as often as a profit.
Yet the facts suggest otherwise, as we can see from Table 3.7 and Figure 3.2, which shows
exchange rate changes plotted against lagged interest rate differentials (annual averages
in each case).19
A number of points are clear from this data:
●
Exchange rates are far more volatile than interest rates. In fact, interest rates move only
slowly, and when they do move, there tends to be a high degree of international synchronisation.20 In fact, the standard deviation21 of annual exchange rate changes over the
years 1976 to 2011 is surprisingly uniform, varying from 9% for the yen to 11% for the
Canadian dollar, while for interest differentials the comparable figures are in the range
11/2 % to 3%. So on the face of it, whether or not forecasts based on interest rate differentials were right on average, it looks as though they were highly inaccurate, capturing very
little of the currency depreciation that actually occurred.
●
The carry trade was profitable to varying degrees for all six currencies considered here.
In the average year it earned an amazing 6% in New Zealand dollars, over 2% in pounds
and between 1% and 2% for the other currencies.
●
As Table 3.7 shows, these returns were very risky, however. They were associated with a
standard deviation of between 9% and 12% in every case except the Canadian dollar,
and as can be seen from columns (3) and (4), the ‘bad’ years generated extremely large
losses, sometimes larger in absolute terms than the returns in the best years. This raises
the question of whether the excess returns from this sort of arbitrage were in fact simply
a risk premium. In other words, it may be that UIRP fails to fit the facts because investors
Table 3.7 Returns to carry trade (in percent) 1975 –2012
AUSTRALIA
CANADA
JAPAN
NZ
SWITZERLAND
UK
(1)
MEAN
(2)
S.D.
(3)
MIN
(4)
MAX
(5)
>0
(6)
AVGE (> 0)
(7)
AVGE (< 0)
(8)
CUMULATIVE
1.8
1.6
1.1
6.0
1.0
2.2
9.8
5.1
11.4
11.1
11.7
9.2
−21.3
− 6.1
−30.7
−18.6
−27.8
−16.4
19.1
12.4
20.6
26.7
22.3
17.4
59
57
57
68
59
62
4.8
2.9
5.1
8.2
5.1
5.0
−3.1
−1.2
− 4.1
−2.1
− 4.2
−2.9
1.3
1.5
0.4
5.5
0.3
1.8
Notes
Cols (1), (2), (3) and (4): mean, standard deviation, minimum and maximum annual carry trade return
Col (5): percentage of years when carry trade return was positive
Cols (6), (7): mean return in years when return was positive, negative
Col (8): annualised cumulative return over data period
Source: Thomson Reuters Datastream
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Financial markets in the open economy
are not risk neutral, as the theory assumes, but in fact risk averse, in which case we
need to ask whether the risk premium was of the right magnitude. As we shall see in
Chapter 13, the answer is controversial since it depends on how we think risk is priced
in the currency markets.
●
Ultimately, the carry trade was profitable over the last 35 years because there were
substantially more good years than bad years (column (5)) and because, in spite of the
catastrophic years, the average return in good years outweighed those in bad (compare
columns (6) and (7)). The net effect for a hypothetical investor who each year took either
a short or long position in his chosen currency, depending on whether it paid a higher or
lower interest rate than the dollar, was a cumulative annual return of between 0.4% on
the yen and 5.5% on New Zealand dollars.
Allowing for higher frequency trading, resetting the arbitrage at monthly or quarterly
horizons, and permitting our hypothetical investor to choose whichever currency pair had
the widest interest rate differential would generate even greater profits than these. In fact,
an important recent paper estimated the excess returns to the carry trade at over 5% even
after carefully allowing for transaction costs.
These anomalous results explain why the carry trade has been the subject of so much
research as well as lively controversy. We shall return to it at various points in subsequent
chapters.
Exhibit 3.1 Sayonara carry trade
By Anthony Fensom
18 June 2013
For years, the so-called ‘Mrs Watanabe’ and her brigade of Japanese households sold the
low-rate yen to buy higher interest-rate currencies, such as the Australian dollar. But with the
US Federal Reserve moving to end its easy money policy and ‘commodity currencies’ such
as the Aussie under pressure from lower rates and resource prices, the days of the carry
trade could be drawing to a close.
‘That [carry] trade works until it doesn’t. And the Fed has basically just said that’s not
going to work anymore,’ Goldman Sachs Asset Management partner Michael Swell told the
Australian Financial Review.
Prior to the global financial crisis, yield-seeking Japanese investors sought currencies
ranging from Brazilian real to New Zealand dollars to gain higher returns. With total savings
of 1,500 trillion yen ($15.8 trillion) earning ultra-low returns at Japanese banks, Japanese
households have been keen buyers of ‘uridashi’ foreign currency bonds issued in Japan,
with emerging markets such as Turkey receiving some $3.5 billion in uridashi flows in 2012.
The popularity of the yen carry trade among overseas investors led to an estimated US$1
trillion being invested by early 2007. The Fed’s zero interest rate policy fostered the carry
trade, with hedge funds profiting from borrowing at low interest rates and speculating on
higher-yield investments, including corporate bonds and emerging market debt.
Yet signs that the party is over for the carry trade have sparked fears of massive unwinding by global investors.
➨
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The international setting
The Australian dollar climbed as high as US$1.10 in July 2011 partly as a result of the
carry trade, but has recently fallen to as low as US$0.94 on the back of weakening commodity prices and interest rate cuts by the Reserve Bank of Australia.
Meanwhile, the Bank of Japan’s move to unleash aggressive monetary stimulus as part
of Japanese Prime Minister Shinzo Abe’s reflationary Abenomics policies has sparked
increased volatility for both the yen and Japanese bonds. Recent yen appreciation reportedly
forced a scramble by Japanese investors to unwind the carry trade, with the effects felt
around the world.
‘Margin call’
According to UBS’ Art Cashin, the yen’s strength and recent dive into bear-market territory
for the Nikkei Stock Average sparked major losses for US hedge funds, as noted by the
Wall Street Journal:
‘A couple of months back, when Mr Abe announced Abenomics (aggressive QE, purposeful increase in inflation, etc.), hedge fund wizards around the world flocked to what they saw
as a ‘no-brainer’ carry trade – short the yen (which QE should push lower) and buy the Nikkei
(which would benefit from higher inflation and more trade from the lower yen). Scores of
hedge fund managers reached for this too easy brass ring.
‘Those are just one (most popular) of the carry trades. There are many others. And, when
the yen spikes, it is like a margin call on each of those trades. We all painfully remember
[what] forced liquidations looked like and felt like in late ’08 and early ’09. That’s what
markets fear – possible random liquidations.’
Yet US hedge funds have not been the only ones to feel the pain. Recent volatility in the
‘commodity currencies’ of Australia, Brazil and South Africa has been blamed on investors
exiting their investments in such emerging markets, forcing spikes in bond yields.
‘I am finding how much leverage the hedge fund community has. Everyone seems to be
up to their earlobes in Mexican government debt,’ Loomis Sayles co-head of fixed income,
David Rolley, told the Australian Financial Review.
As the spread between higher and lower yield currencies has shrunk, leveraged traders
have been squeezed on both sides amid the Fed’s threatened ‘tapering’ of quantitative
easing.
‘With commodity prices under pressure and with growth slowing globally, there’s
concern about the higher-yielding commodity currencies. The [carry trade’s] best days are
behind it and it’s going to be much more of a trading market,’ said Pierpont Securities
strategist Robert Sinche.
Source: http://thediplomat.com/pacific-money/2013/06/18/sayonara-carry-trade/
3.7
Purchasing power parity revisited*
We can now take the opportunity to tie up a loose end from the previous chapter relating to
the link between IRP and PPP. However, since the link is via another parity relationship, we
need first to deal with the analysis of how inflation impinges on interest rates in the domestic
economy.
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Financial markets in the open economy
3.7.1 Real interest rates and the Fisher equation
We start with an apparent digression on the mechanism underlying individual savings
decisions. Our initial standpoint is that of an individual economic agent in the setting
of his domestic market making a choice, again involving two periods – the present and
next year. In this stylised market, claims22 to future consumption baskets are exchanged
for an identical basket for immediate consumption, in a ratio that reflects demand and
supply at each date, now (period 0) and next year (period 1). The question we consider
is: how much should the individual consume this period, and how much consumption
should he be willing to defer to next year? In other words, what determines the willingness
to save?
In its most basic form, this simple question in applied consumer choice theory was settled
by Irving Fisher in the early twentieth century. The analysis shows that, subject to the standard assumptions of elementary choice theory,23 and in particular assuming that prices are
constant, the consumer will select a consumption-savings pattern that is determined, other
things being equal, by the rate at which the market allows him to exchange consumption
between the two periods. Other things being equal, the greater the future sacrifice required
per unit of present consumption, the less he will choose to consume this period and the
more next. The critical ratio24 is the number of units of future consumption offered in the
market in exchange for a unit of current consumption, which will be denoted by (1 + R).
For example, if at some point in time R is 5%, market conditions mean consumers have to
sacrifice 1.05 units of consumption next year, in period 1, in order to secure an extra unit
for immediate consumption. R is therefore the market premium current consumption commands over future consumption. (Notice that we can be more or less certain that R is always
positive.)
By now, it should be clear that R is actually an interest rate – in fact, the real interest rate.
It is real precisely because it is measured in units of consumption.
To appreciate the importance of inflation, or its absence, consider how R is determined.
Plainly, as usual in these models, the market price is the outcome of aggregating the choices
of consumers as a whole.25 If R is 5%, then it follows that it is possible to satisfy borrowers
in aggregate only if savers are offered the reward of a standard of living 5% higher next year
to compensate for the sacrifice required of them this year. If R were lower than 5%, then
there would be insufficient goods available for current consumption, i.e. unsatisfied
borrowers, because of an inadequate flow of savings. If R were higher than 5%, then there
would be too great a supply of sacrifice i.e. an excess demand for future consumption and
excess supply of current consumption by unsatisfied savers only too happy to defer satisfaction until next year.
Now consider how this constant-price scenario would be affected by inflation at the
rate of, say, 3% per annum. The answer is not entirely straightforward, because there can
be no inflation without money, and so far there has been no money in the analysis. Inflation
is by definition a rise in the price of goods relative to money, whereas the only price that
matters in this model is the price of period 0 goods in terms of period 1 goods. (Since the
whole analysis is in terms of physical units of consumption, it is often described as a barter
model.)
However, since R is determined by the preferences of individuals, there is no reason to
expect it to change simply because prices rise (or fall) – unless preferences are actually
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The international setting
affected in some way by the money units in which consumption is measured. We shall
assume here that people are immune to this particular form of irrationality, known as
money-illusion. In other words, we take for granted that agents are ultimately concerned
only with their access to real goods and services, and not with the number or denomination
of the banknotes involved in transactions.26
In order to cope with the introduction of inflation, imagine that what changes hands
between borrowers and savers in the market is not consumption goods directly, but claims
on goods – in other words, some form of money e.g. pounds. The sum of money, £P0, buys
a unit of current consumption, while £P1 buys a unit of consumption one year from today,
at period 1. How much of a premium per pound will savers need to be promised at period 1
in order to persuade them to sacrifice sufficient current consumption to satisfy borrowers?
In other words, how many more pounds will they need to be offered in order to keep their
behaviour unchanged? In physical terms, the answer remains the same: 5% more consumption, because, as has been explained already, there is no reason for the ‘exchange rate’
between current and future goods to have moved up or down. But the key point is that,
however many pounds were required to buy 1.05 units of consumption next year when we
were assuming zero inflation, the number of pounds required in the presence of inflation
will be greater by 3%. This is the case because, if P1 is 3% greater than P0, equilibrium
requires an exchange ratio of 1.05 × 1.03 = 1.0815. In other words, the premium on current
consumption in money terms, known as the nominal interest rate, must be the product of
1 plus the real rate and 1 plus the inflation rate:
1 + r = (1 + R)(1 + dp)
(3.12)
where dp denotes the inflation rate27 over the year: (P1 − P0)/P0. Again, unless the inflation
rate is extremely high,28 we can simplify the relationship to:
r = R + dp
(3.13)
which means that in the numerical example, the equilibrium nominal interest rate is
approximately 5% + 3% = 8%.
There is, however, one important modification needed to make the hypothesis realistic.
In the light of what has been said in the earlier sections of this chapter, the reader should
not need convincing that the inflation rate in Equation 3.13 ought to be replaced by the
expected inflation rate, since in practice the future price level, P1, is unknown and unknowable in the current period when the consumption-saving decision has to be made. So the
Fisher equation, as it is known to economists, can be written:
r = R + dpe
(3.14)
which says that the nominal interest rate – the only one we actually observe directly – is the
sum of the real interest rate and the market consensus expected inflation rate.
In fact, economics has seen decades of debate on the correct formulation and interpretation of the Fisher equation. We ignore most of these issues here, except to note that, once
again, the explanation given here ignores the risk premium. Once we allow for the fact that
the choice between consuming now and consuming in the future depends on expected
rather than actual inflation, there is always the risk that the decision-maker’s forecast may
turn out to be wrong. If the representative consumer is risk-averse, the Fisher equation will
have to incorporate a premium as a reward for bearing this risk. For present purposes, we
stick with the simple formulation in Equation 3.14, in other words we assume risk neutrality.
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Financial markets in the open economy
Notice that although the Fisher equation is supported by an undeniable logic, its
empirical validity is impossible to ascertain, because attempts to test it against the facts
run headlong into the joint hypothesis problem in its most acute form. Both the right-hand
side variables in Equation 3.14 are usually unobservable. Survey data have on occasion
been used as a measure of expected inflation, though they are often unsatisfactory for the
purpose,29 and there are few direct measures of the real rate.30 None the less, and perhaps
because, unlike PPP, it is so difficult to refute, the Fisher equation tends to be accepted by
default in economics.
3.7.2 Purchasing power parity and the real exchange rate
This brings the digression to an end. To see why it was worthwhile, suppose Equation 3.14
applies to the domestic economy, while a similar Fisher equation applies to the foreign
country:
r* = R* + dp*e
(3.14′)
Notice we are allowing for the possibility that any or all of the variables are different in the
foreign country. Clearly Equations 3.14 and 3.14′ imply that the interest rate differential is
given by:
r − r* = (R − R*) + (dpe − dp*e)
(3.15)
But unless there is something to prevent arbitrage between the securities markets of the two
countries, we know from UIRP in Equation 3.4 that, with risk neutrality, the observed or
nominal interest rate differential on the left-hand side of Equation 3.15 is equal to the
expected rate of depreciation. It follows that:
dse = (R − R*) + (dpe − dp*e)
(3.16)
which tells us that the rate of depreciation of, say, the dollar against the pound over any
time period (e.g. one year) is the sum of the difference between UK and US real interest
rates for one-year loans and the difference between UK and US expected inflation rates
during the 12 months.
Now consider the real interest differential. Suppose, given my (and the market’s) expecta
tions with regard to inflation rates in the UK and USA, I believe the real interest rate to be
higher in America. If I can possibly capture the higher real rate in the USA by lending to
American borrowers (buying US securities etc.), I will do so. The opposite will be the case
if I believe that real rates are higher in Britain, i.e. if R > R*. These statements can be made
with confidence because, as we have seen, for risk-neutral agents real rates are the ultimate
determinants of savings behaviour, since they measure the reward for saving in the ultimate
currency: real consumption units or standard of living.
This argument can lead to only one conclusion. In the absence of barriers to cross-border
capital movements, real rates should be the same in both countries, so that R = R* and we
are left with the proposition that:
dse = dpe – dp*e
(3.17)
This is sometimes called PPP in expectations. Its implications are straightforward. It
says that PPP applies not to actual exchange rates and relative inflation rates but to the
market’s expectations of these variables. According to this view, PPP is a relationship
between unobservables, rather than observables, so that any apparent failure to fit the
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The international setting
facts can always be interpreted as the outcome of using the wrong measure (or model) of
the expected rate of depreciation on the one hand or the expected inflation differential on
the other.
Note that we can rewrite Equation 3.17 in terms of the (log of the) expected real
exchange rate. By definition, since d(log Q) = dq = ds + dp* − dp, Equation 3.17 implies
dqe = 0
(3.18)
so that the change in the expected real exchange rate is zero, or q is expected to remain
constant. In time series terms, Equation 3.18 obviously means that:31
e
qt+1
= qt
(3.19)
so the typical agent in the market expects tomorrow’s real exchange rate to be the same as
today’s. This conclusion is more dramatic than it might look at first glance.32
In terms of time series statistics, there is a whole class of models consistent with Equa
tion 3.19, in particular the so-called random walk process mentioned in Section 2.7. This
argument persuaded a number of researchers that the apparently random nature of the
real exchange rate movements they observed was not such a gloomy conclusion after all,
but simply a consequence of UIRP on the one hand and real interest rate parity on the other.
An alternative rationalisation of Equations 3.17 and 3.19 would be to say that if trade in
goods takes time, then arbitrageurs will operate not on the basis of actual price differentials
but on the basis of their forecasts of price differentials when they complete their trades.
There are two apparent weaknesses in this argument. First, deviations from PPP have far
too long a life to be rationalised in this way. As we have seen, recent research suggests a
half-life of three or four years, which is long even by the standards of physical capital, let
alone consumption goods. Second, for reasons too far removed from the subject of this book
to be covered here, real interest rates are likely to be determined by more than simply consumer tastes, such as the return on capital in each country, and all the many factors that
affect it.33 The process by which real interest rates are equated is therefore likely to be more
complex than is suggested here, and almost certainly anything but instantaneous. In fact, it
is not at all obvious that it will be any faster in practice than the process of arbitrage in the
goods market, and it may be substantially slower.
Finally, it is to be hoped that by this stage the relationship between IRP, PPP and the
Fisher equation is clear in one respect at least. Suppose, as a benchmark case, all economic
agents know the future price levels in the two countries and next year’s exchange rate with
absolute accuracy. Then, in this unlikely scenario, the two Fisher equations mean we can
replace Equation 3.15 with:
r − r* = (R − R*) + (dp − dp*)
(3.20)
and using UIRP (for this reason often called the open Fisher equation) gives, in place of
Equation 3.16:
ds = (R − R*) + (dp − dp*)
(3.21)
dq = R − R*
(3.22)
or:
from which we can see that movements in the real exchange rate reflect changes in the real
interest rate differential. If we are happy to rely on real interest rates being driven into
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