A Puzzle in the Market for Foreign Exchange
by Alex Maynard
Consider Dave and Nancy, two Canadian snow-birds who are about to purchase
a fancy winter home in Florida with a closing date in one-month's time. A
payment of 100 thousand U.S. dollars (USD) is required at next month's
closing date. Dave and Nancy are the type of people that always balance
their checkbook and like to budget everything carefully ahead of time. They
are glad to have locked in a U.S. dollar price for their house but, because
they don't know where the exchange rate will be a month from now, they don't
know the Canadian dollar price of the house, which is the price that
really matters to them.
Frustrated, they call their broker. She suggests purchasing a forward
contract. This contract would commit them to purchase 100 thousand U.S.
dollars in one month's time at a rate agreed upon today. The advantage of
this approach is that they would lock in a Canadian dollar price for the
house today.
The price in Canadian dollars (CAD) that they would agree to pay in one month
for each U.S. dollar is known as the one-month forward exchange rate. It turns
out that, at 1.22 CAD/USD, this forward is rate is more expensive than the
current spot rate of exchange of 1.20 CAD/USD, the rate that they would pay
to buy U.S. dollars today.
Is this a fair price? They call their broker to ask about the discrepancy.
She explains that the forward rate is a market price that should generally
reflect the market's expectations regarding the future spot price. If the
forward rate is higher than today's spot price then this is because the
spot rate is likely to rise--all the more reason to lock in a price today.
They purchase a forward contract, agreeing to buy 100 thousand USD at a rate
of 1.22 CAD/USD in a month's time. Curious, they check the spot price a month
later. Rather than going up as predicted by the forward rate, the spot price
of the U.S. dollar has fallen from 1.20 a month ago to 1.18 today. The U.S.
dollar weakened rather than strengthened.
Upset by their bad luck they put in another call to complain to their
broker. She patiently explains that the forward rate reflects only the
market's best guess of the future spot rate and not the actual spot rate
itself. No one can out-guess the market, but even the market isn't right
every time. It might not have been correct this particular time, but the
market will get it right on average.
Still a bit skeptical, they ask their granddaughter, an aspiring economist.
She decides that the only way to convince them is to show them. She collects
27 years of historical data, spanning 1973-2000, on USD/CAD spot and forward
exchange rates and sets out to show her grandparents that on average the
forward rate really does reflect the future spot rate, just as the broker said.
To her surprise, this doesn't seem to be the case. Not only is the forward rate
wrong on average, but it turns out to be a very bad predictor of the future
spot rate. On average it actually mispredicts even the direction of change.
When the forward rate lies above the current spot rate, the spot rate is
actually more likely to fall further away from the forward rate than it is
to rise up towards it. In other words, far from being unusual, her
grandparents experience was quite common. Maybe this is just something
special to do with Canada, she thought? So she checked other major
currencies such as the Japanese Yen and British Pound but found the same
thing.
This rather surprising finding has become known as the "forward premium
puzzle". While intuition suggests that the forward exchange rate
should be a good a predictor of the future spot rate, historical experience
suggests the opposite. It seems to be a perverse predictor, predicting
exchange rate movements in the direction opposite to which they actually
occur.
What explains this perverse behavior? To this day there is no commonly
agreed upon explanation.
It is possible that the (average) discrepancy between the forward rate and
the future spot rate is simply due to a risk premium. After all, shouldn't
Nancy and Dave have to pay at least some premium in return for avoiding
the risk of exchange rate fluctuations? Since they are not charged an
explicit fee, you would expect this to built into the forward price.
However, there are difficulties with this explanation. For one thing,
a high forward rate from the Canadian perspective means a low forward rate
from the U.S. perspective and vice versa. So if residents of one country pay
a premium it implies that residents of the other country get a discount.
More importantly, economists have found that individuals have to be extremely
risk averse in order to generate risk premiums that could fully explain
the behavior of the forward premium. While nothing in principle rules out
such high levels of risk aversion, it seems inconsistent with other
aspects of human behavior in which people display substantially less risk
aversion. If investors are really so risk averse when betting on foreign
exchange, why are the casinos in Los Vegas packed with gamblers willing to
pay a premium to engage much riskier bets?
Surveys of currency forecasters provide an alternative measure of market
expectations of future exchange rate movements. Since the forecasters are
merely providing a forecast rather taking a position in the foreign
exchange market, they are unlikely to incorporate any risk premium. Yet,
the average currency forecast seems to have done just as poorly as the
forward rate.
This suggests that the markets may be doing an extremely poor job
forecasting exchange rates--so poor in fact that they get even the direction
of change wrong. Or, perhaps, it only looks like this after the fact. Maybe
investors were rationally worried about serious risks to the dollar, such as
fundamental shifts in monetary policy (or, more recently, a second terrorist
attack) that never actually occurred. These concerns may have been reflected
in the forward rate, which later looks mispriced only because the risks in
question were never realized. For example, if after 30 years your house
has never had a fire, the last 30 years of buying fire insurance might seem
to have been a waste, despite being perfectly reasonable at the time
you bought the insurance. Named after a feared devaluation of the Mexican Peso,
this phenomenon is known as a "Peso effect". When a "Peso
effect" is occurring, we never actually observe the risk that investors
are worried about. For this reason, the validity of this explanation is
impossible to either confirm or refute.
A second possibility is that markets take a while to learn how to forecast
exchange rates, especially after major policy changes that effectively
change the rules of the game. United States inflation rates dropped
substantially in the early 1980s following a more aggressive tightening of
U.S. monetary policy at the time and this marked a period during which
forward rates were especially bad in predicting future exchange rate
movements. Also somewhat supportive of this explanation is the fact that the
forward rates for some currencies have gradually improved as predictors of
future spot rates.
Obviously, this is an important area for future research--eventually we
will find answers!
Return to the Index
A Macroeconomic Forecast for Canada
by Peter Dungan, Steve Murphy and Tom Wilson
The Policy and Economic Analysis Program (PEAP) at the Institute for Policy
Analysis conducts macroeconomic forecasting and policy analysis on an
ongoing basis. At the heart of the program are computer simulation models
of the Canadian and Ontario economies. These models are built on the basis
of macroeconomic theory using econometric methods to obtain key
sensitivities and test relationships. Not surprisingly, they are thus
called "macroeconometric" models.
Macroeconometric modeling has a long history at the University
of Toronto. The program actually began in the late 1960s and has extended
to the present with major contributions by many of our distinguished
Department economists. Most notably, the program was begun and built up by
Professors John Sawyer, Greg Jump and Tom Wilson,
but many other colleagues have also contributed.
Throughout the life of the program the macroeconometric models have been
used for three major purposes--for macroeconomic forecasting (both
short-term and long-term), for macroeconomic policy analysis, and
simply to build up and develop our understanding of how the Canadian
macroeconomy works.
The economic forecasting element of the program began in the early 1970s,
originally under the Institute's own banner, and then for a time, through
Data Resources Inc.--a private economic consulting and forecasting firm
founded by Harvard Economics Professor Otto Eckstein. In 1976 the
short-term forecasting part of the program was discontinued in order to
concentrate on further model development and on policy analysis. It was
then added back to the menu of services provided by PEAP in the early 1990s
and regular short-term forecasts have been produced ever
since. One impetus to returning to short-term forecasting was the
realization that it is very difficult to track and analyze monetary and
fiscal policy without a solid and ongoing knowledge of where the economy is
and where it is heading.
It is worth noting that the University of Toronto is the only Canadian
university that provides this kind of ongoing economic analysis and
forecasting service. (There are a number of academic institutions that do
this in the U.S., including the University of Michigan, the Anderson School
of Business at UCLA and the University of Maryland). In the regular surveys
of Canadian forecasters conducted by the Department of Finance, the Ontario
Ministry of Finance, and Consensus Economics in the UK, the University of
Toronto is the only academic participant.
The ongoing development and use of macroeconometric models for policy
analysis and forecasting has also given the University, the Department and
the Institute a unique place in the eyes of Federal and Provincial
policymakers. For example, when in 1999 Finance Minister Paul Martin
decided that it would be best to use private-sector estimates of the size of
the "fiscal dividend" that was then emerging after years of
deficits, there were only four institutions in the country that had the
tools and experience to do the necessary work. The only academic institution
was the Department of Economics at the University of Toronto.
The Policy and Economic Analysis Program produces both short-term and
longer-term economic forecasts on a regular basis. Typically, short-term
forecasts are developed at least four times a year, within a week or two of
the release of the quarterly national accounts. Long-term projections are
generally developed in January and again in June/July after the
annual national accounts revisions. Forecasts are updated as needed if
additional impacts or information come to light--as, for example, after the
events of September 11th, 2001. The forecasts are distributed in detail to
members of the program and a summary is released to the press and to the
various organizations that collect surveys of forecasts.
In PEAP's experience, economic forecasting is done with the aid of the
macroeconometric model, but not by the model working on its own. Our
understanding of how the economy works, and of all the emerging factors that
can affect it in the short-term especially, is simply insufficient for it to
be possible to have a model generate a forecast "all on its own"
after the relevant data have been updated and the exogenous inputs entered.
("Exogenous" variables are those, like U.S. GDP, that are not
determined in the model.) For a number of years Professor Ray Fair at
Yale, one of the pioneers in the field of macroeconometric modeling, has
generated a series of "hands-off" model-based forecasts with no
judgemental adjustments added. The results have been mixed--the forecasts
have certainly not bested those generated by a combination of model and
judgment with any regularity, but neither have they been markedly inferior.
In any event, the PEAP forecasts for Canada depend both on the models, as
tools forcing consistency and carrying forward historical regularities, and
on judgments based on rapidly emerging current data and on knowledge of where
the model has been deficient in the recent past, given that not all such
deficiencies can be instantly fixed!
A brief summary of the PEAP forecast distributed on December 12, 2005
is presented in the following table and discussed below:
Message from the Chair---by Arthur Hosios, Chair
