Forecasting Exchange Rates

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Forecasting Exchange Rates
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Last Topic Market Efficiency

• A capital market is said to be efficient if
  prices in the market fully reflect available
  information.
• Weak, semi-strong, strong
• How to test for market efficiency
• Evidence for Stocks Not very clear

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Thats Stocks, how about Forecasting Exchange
Rates?

• Exchange Rates are a factor in almost every
  international financial market decision
• For most countries, the exchange rate is the
  single most important price in the country
• Academic economists have studied exchange rates
  intensely for the last 30 years.
• Economists at banks, securities firms, and
  elsewhere are also devoted to analyzing the
  variables that might impact foreign exchange
  rates. Recall daily trading is almost US2
  trillion.

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Exchange Rate Forecasting

• First off Who would want to forecast exchange
  rates?
• Investors, corporations, government officials,
  etc.
• Forecasts play a fundamental role in nearly all
  of international finance
• The big debate Can we do it? (forecast FX rates)
• While many business and financial decisions
  depend on FX forecasts, there is considerable
  debate about the possibility of making accurate
  or useful forecasts.
• Lets see what you think.

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The 3 options to Forecast Exchange Rates

• Use the Forward Rate
• If markets are efficient, the Forward Rate
  incorporates all relevant information. That is,
  U.I.P holds

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Use the Forward Rate

• Advantages
• Easy to obtain
• Cheap (free, just call a bank)
• Disadvantages
• Most empirical evidence is against the Forward
  Rate Unbiased Parity Condition
• Even if it is good, you cant profit from it.

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Evaluation of the Forward Rate Performance

• One popular measure, the absolute forecast error
  as a percentage of the realized value, is defined
  as
• forecasted value realized value
• realized value
• If the forecast errors are consistently positive
  or negative over time, then there is a bias in
  the forecasting procedure.

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Absolute Forecast Errors over TimeUsing the
Forward Rate as a Forecast for the British Pound
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Forecast Bias over Timefor the British Pound
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Forecast Bias

• The following regression model can be used to
  test for forecast bias
• realized value a0 a1 Ft 1 m

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Graphic Evaluation of Forecast Performance
Region of downward bias (underestimation)
Region of upward bias (overestimation)
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Graphic Evaluationof Forecast Performance

• If the points appear to be scattered evenly on
  both sides of the perfect forecast line, then the
  forecasts are said to be unbiased.
• Note that a more thorough assessment can be
  conducted by separating the entire period into
  subperiods.
• In general, most evidence is against the forward
  rate as a good predictor of the future spot rate.
  

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Forecast Bias in Different Subperiodsfor the
British Pound
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The 3 options to Forecast Exchange Rates

• Use Econometric Models (Fundamental Approach)
• Example A Supply and Demand Model

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• Where
• S log of the spot rate (US/FC)
• M US and Foreign Money Supply
• Y US and Foreign Real Incomes
• i US and Foreign nominal interest rate

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• The Model Predicts
• Recall S(US/FC)
• As US money supply increases, the
• As US income increases, the

depreciates
appreciates
If US interest rate gt Foreign interest rate, then
the dollar
depreciates
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Econometric Models

• Other variables have been found to indicate the
  direction in a currency
• Balance of Payments
• Size of Reserves
• These could be added to the model

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Econometric Models Drawbacks

• They Assume Stationary!
• Often structural breaks interrupt the stability
  and stationary of exchange rates Changes in
  exchange rate pegs, changes government
  intervention policy, realignments (Euro,
  East-West Germany unification).
• Independent variables are forecasts!
• May be as hard to forecast as S
• Parameters (bs) are measured with imprecision
  (standard errors), which may affect forecasts of
  S.
• So. How good are they?

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Econometric Models Testing

• Meese and Rogoff (1983) find that even with full
  knowledge of future independent variables, their
  models perform worse than a simple random walk
  model!

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Meese and Rogoff (1983)

• Economists do not yet understand the
  determinants of short- to medium-rum movements in
  exchange rates. models of exchange rates base
  on macroeconomic fundamentals cannot explain
  exchange rate movements better than a naïve
  alternative such as a random walk . Worse yet,
  exchange rates are hard to explain after the
  fact, even with the knowledge of actual
  fundamental variables.

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Frankel and Froot (1990) (Two Famous Economists)
also note

• It is widely accepted that standard observable
  macroeconomic variables are not capable of
  explaining, much less predicting ex ante, the
  majority of short-term changes in the exchange
  rate.

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Econometric Models Testing

• However,
• More sophisticated models exist
• VARs, Bayesian
• Most importantly, the really good models never
  get published!

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The 3 options to Forecast Exchange Rates

• Technical Analysis
• Technical Analysis is the science/art of of
  recognizing systematic patterns in historical
  exchange rates
• According to technical analysts, these patters
  will occur again (history will repeat itself)
• When you see a pattern emerge, you know what to
  do (buy or sell)
• The trend is my friend.

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Technical Analysis Cont.

• Based solely on historical prices
• Extrapolates past trends in prices (i.e.
  technical), does not use fundamentals
• Creates buy/sell signals rather than an exchange
  rate forecasts
• Techniques employed range from the simple to very
  complex

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Technical Analysis Signals

• When there is a buy signal, you revert your
  position to a long
• Buy to even out short position and buy even more
  to get a long position
• When there is a sell signal, you revert your long
  position to a short
• Sell long position and go short
• When there is no signal you hold

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Technical Analysis Filter Rules

• Based on changes in Spot Rates since the last
  local minimum or maximum
• When rates increase by more than X, signal to
  buy
• When rates decrease by more than Y, signal to
  sell

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/Euro
-Y
The rule works here BltS
S
B
X
Time
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/Euro
The Whipsaw! Buy high Sell low
-Y
B
S
X
Time
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Technical Analysis Other Types

• Moving Average Crossovers
• Buy currency when SRMA crosses LRMA going up
• Sell currency when SRMA crosses LRMA going down

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Head and Shoulders
From the sales pitch The "head and shoulders"
pattern is bearish because it often indicates the
end of an uptrend by forming a "lower high" on
the right shoulder. After the neckline is broken,
the projected downward move of ICF is typically
equal to the distance from the top of the head
down to the neckline. In this case, that equates
to a projected downside target of around 63 (7
points below the neckline of 70). Obviously, it
could easily take several weeks or more for this
to occur, but patient traders will be rewarded if
the pattern follows through to the downside
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More examples
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Empirical Evidence

• Sweeney (1986) uses 1975 to 1980 data
• Rule is to buy FX if filter rules give a signal
  in, otherwise stay in dollars

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Empirical Evidence

• The filter rules generate about 1-2 profit, even
  after transactions costs
• The 1 filter rule appears to generate
  statistically significant profits
• Other studies confirm this for other types of
  technical analysis in currencies (not stocks)
• However, have to worry about data mining

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Data Mining?

• AKA He who mines data may strike fool's gold !
• Its always possible to explain the past using
  technical analysis (sunspots, miniskirts, etc)
• An infamous example, David Leinweber went
  searching for random correlations to the SP 500.
  He sifted through a United Nations CD-ROM and
  discovered that historically, the single best
  predictor of the Standard Poor's 500-stock
  index was butter production in Bangladesh.
• What is the hard part is picking the rule that
  will work in the future.

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Fancy Mathematical Models

• Many companies offer fancy mathematical models
  that can forecast exchange rates
• They offer the modes for a price
• Is it worth paying the price?
• No!
• Lets think about this

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Would YOU Sell?

• Suppose you invent a model that can forecast
  exchange rates correctly
• Suppose further that these models work Make a
  profit
• Would You sell the model?
• No Way You could make a lot more by keeping it a
  secret and speculating in the foreign exchange
  market

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You should Not Buy

• Once a model is sold, it becomes public knowledge
  and investors revise their expectations
  accordingly
• This will cause prices to adjust in a way that
  profit opportunities disappear
• If someone wants to sell a model, it must be
  because it cant be used to make a profit
• You should not buy
• http//www.forecastingsystems.com/2003/Forecaster.
  2.1.htm

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In Reality

• More and more technical analysts appear every day
• A survey revealed that in 1990 almost 90 of all
  participants in the London forex market used some
  kind of technical model in forming short run
  expectations
• As the horizon increases, traders put more weight
  on economic fundamentals
• In the long run, everyone seems to agree that
  economic forces determine exchange rates

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How about Professional Forecasts?

• Lets see the track record of professional
  forecasters
• Before we do, we need some tools

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Forecast Performance Evaluation

• The traditional econometric approach begins with
  the forecast error made at time t

Where is the j-period ahead
forecast made at time t is the actual spot
rate at time t j
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Forecast Performance Evaluation
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Forecast Performance Evaluation
The mean squared error (MSE) and the root mean
squared error, are commonly used to estimate the
average error size. Why squared?
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Forecast Performance Evaluation

• The MSE of the forecaster is compared to the MSE
  of a naive model (the Homer Simpson Forecaster)
• For example, the forward rate
• The model with the lowest MSE wins

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Forecast Performance EvaluationAccurate versus
Useful Forecasts

• It is important to distinguish between accurate
  forecasts and useful forecasts.
• Accurate forecasts have small forecasting errors
  gauged by traditional statistical measures (MSE),
  while
• Useful forecasts are those on the right side of
  the market, leading to profitable speculative
  positions and correct hedging decisions.
• What about a forecast that is relatively
  accurate, but not useful?
• Leads to to incorrect decisions

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Forecast Performance EvaluationAccurate versus
Useful Forecasts

• In the absence of a currency risk premium, the
  right side of the market implies the right
  side of the forward rate.

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Forecast Performance EvaluationAccurate versus
Useful Forecasts

• In the absence of a currency risk premium, the
  right side of the market implies the right
  side of the forward rate.

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Forecast Performance EvaluationAccurate versus
Useful Forecasts

• If, in fact, the forward rate reflects a risk
  premium, then we expect an advisory service
  forecast to outperform the forward rate

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Forecast Performance EvaluationAccurate versus
Useful Forecasts

• To measure usefulness, let

• Then, the test for usefulness is ?

• According to the binomial distribution

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Accurate versus Useful Forecasts Intuition

• Suppose you examine 8 different advisory services
  and see that, in fact, one of the eight has done
  a great job (three quarterly forecasts in a row)
  at making correct forecasts.
• Does this tell you to go with this forecaster?
• Another way, suppose you get eight Monkeys to
  flip a coin, what is the chance that one will
  flip heads three times in a row?
• Each one has a 1/8 chance, so changes are good
  one will get it right three times in a row.

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Forecast Performance EvaluationAccurate versus
Useful Forecasts

• So to evaluate forecasters, we look at both
  accuracy and usefulness

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The Professionals

• Levich (1982) evaluated the track record
  forecasters over 1977-1980, using monthly
  forecasts
• The analysis covers 13 forecasters, nine
  currencies, four horizons and 48 separate monthly
  forecasts, generating over 11,000 individual
  forecasts to examine.
• More recent updates give similar results
• http//faculty.cox.smu.edu/dmiller/F6214/6214_cla
  ss_files/Levich1982.pdf

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Professional Forecasters Review

• Some firms appear to do better that others, but
  this could be due to chance and/or the large
  sample
• Even if some were to firms display skill, this
  may not persist over time (people move, models
  change)

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Professional Forecasters Review

• Overall Performance
• Most firms had accuracy score above 1, which is
  poor.
• In fact, only 30 do better than forward rate!
• Many had correctness score below 50, which is
  poor (Professionals worse than coin flip!)

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The Final Word We have learned some of the most
popular ways to forecast exchange rates
Using the Forward Rate
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• Using Technical Analysis

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Using Econometric Models
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The Final Word We have learned some of the most
popular ways to forecast exchange rates and how
to evaluate them
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Good forecasting methods may exist, but would you
expect them to be for sale?
Not surprisingly, most professional FX services
do a poor job
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