- Email: [email protected]
A note on the performance of foreign exchange forecasters in a portfolio framework
Journalof BANKING & ELSEVIER
Journal of Banking & Finance 20 (1996) 605-613
FINANCE
A note on the performance of foreign exchange forecasters in a portfolio framework Ian W. Marsh a,*, David M. Power b Department of Economics, University of Strathclyde, 100 Cathedral Street, Glasgow, G40LN, United Kingdom b Department of Accountancy and Business Finance, Uniuersity of Dundee, Dundee, DDI 4HN, United Kingdom
Received 15 July 1994; accepted 15 December 1994
Abstract This note investigates the ability of 22 currency forecasters to predict movements in three major exchange rates. In particular, it examines the profitability of portfolios of forward market positions constructed on the basis of the predictions of each forecaster. The key findings of the paper are that just one panel member proves significantly profitable to follow, and that investing on the basis of the naive alternative prediction of 'no change' produces high, though volatile, profits. We conclude that the majority of currency analysts have little ability to predict the future. JEL classification." F31; G l l Keywords: Survey data; Exchange rates; Portfolio performance
I. Introduction A large body of research, beginning with the seminal work of Meese and Rogoff (1983), concludes that in terms of the mean squared error criterion, a naive random walk strategy dominates more sophisticated forecasting techniques in predicting exchange rates. A number of papers have also investigated the ability of
* Corresponding author. Tel.: (0141) 5524400 ext. 3859; fax: (014l) 5525589. 0378-4266/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0378-4266(95)00007-0
606
L W. Marsh, D.M. Power/Journal of Banking & Finance 20 (1996) 605-613
market participants to forecast individual currencies (e.g. MacDonald and Marsh, 1994). In spite of the richer set of possible explanatory variables used in making these forecasts, the random walk model remains pre-eminent. Engel (1994) argues persuasively that accuracy may not be the best criterion by which to judge the value of exchange rate forecasts, and that a more appropriate approach would be to assign a specific objective to an economic agent and then to evaluate the contribution of competing predictions in terms of maximising this goal. An obvious objective would be to assess the ability of the forecasts to earn profits. For example, Boothe and Glassman (1987) employ a simple trading strategy whereby a long (short) position of a fixed number of dollars is established in a currency if the forecast rate is greater (less) than the forward rate. They conclude that some, though not all, of the models examined demonstrate significant forecasting ability. The same technique has been applied to the forecasts of market participants by MacDonald and Marsh (1994) with comparable success. Although insightful, such simple trading strategies are rather implausible first, because they assume a fixed position size irrespective of expected return, second, because they fail to incorporate any explicit analysis of risk and third, because they evaluate forecasts of individual currencies one at a time, despite the fact that a forecaster's prediction of one exchange rate is probably not independent of his prediction of another. In this note we address all three of these issues by using elementary finance theory to produce portfolios based on the exchange rate predictions of several leading forecasters that incorporate the interdependencies between an individual's predictions of different currencies.
2. Data description On the first Monday of each month beginning September 1989, economists, foreign exchange dealers and executives in over 150 companies and institutions in the Group of Seven nations (G7) completed a facsimile from Consensus Economics of London which asked for point forecasts of, inter alia, the spot exchange rate of the Deutschmark, pound sterling, and Japanese yen against the US dollar three calendar months ahead. The companies surveyed include commercial and investment banks, industrial corporations, chambers of commerce and forecasting agencies (in both the private and public sectors). For reasons of confidentiality we denote each respondent by a mnemonic comprising a letter giving the nationality of the forecasting company (C-Canada, F-France, I-Italy, J-Japan, B-Britain, U-USA and G-Germany) and a number to distinguish between respondents. The forecast data end with the August 1992 survey. In order to construct a portfolio of investments our forecasters must have supplied regular predictions for all three currencies, and we have included only those who have responded to at least 35 of the 36 surveys. This response requirement reduces our panel to 22 forecasters from six different countries. Any
L W. Marsh, D.M. Power~Journal of Banking & Finance 20 (1996) 605-613
607
missing values have been replaced with the current period spot exchange rate, since our main point of comparison is with the random walk model. We have matched this survey database with contemporaneous middle market spot and three-month forward rates prevailing at a time between 3:30 and 4:00 pm in the London market, taken from the Barclays Bank International pages on Datastream.
3. Portfolio formation We construct two portfolios for each of the 22 panel members in the sample. Both are standard in form and have been used widely in the literature. 1 If we define g2 as the covariance matrix of profits, the first portfolio is the solution to the problem of minimising the risk of the portfolio subject to the constraint that a minimum level of profit (5-) is expected each period. This objective can be stated as
minL
=q'I~q+ A ( q ' ? -
5-)
(1)
where q is a column vector whose elements are the dollar value of the forward purchases adopted, and ? is the vector of expected (dollar) profit per one dollar long forward position in each currency. Each element of ? is the difference between the spot rate of a currency forecast to hold at time t + k and the k period forward rate holding at t. The solution is given by ~ = g2- 17[ ~'g~- 1 7 ] - ' 5-.
(2)
An important implication of this model is that the efficient frontier is a ray through the origin. The conclusions arrived at in this paper are therefore not altered if a different level of target profit is specified. This first portfolio specification is discussed more fully in Bilson (1981) and in Hodrick and Srivastava (1984). Bilson (1984) and Bilson and Hsieh (1987) use a more orthodox portfolio model in which a utility function defined over expected profits and risk (the variance of profits) is maximised: U=E(Tr)-
V(~)=q'P-
(1) ~
q'~q
(3)
where 7/ represents the degree of risk tolerance of the portfolio manager. The optimal portfolio is given by q* = g2- lr1~.
(4)
1To conservespace, only the essential details of how the portfolioswere constructed are given here. Interested readers are referred to the articles cited in this section or to Marsh and Power (1994).
608
L W. Marsh, D.M. Power~Journal of Banking & Finance 20 (1996) 605-613
As with the target profit level in the previous portfolio, the positions taken are proportional to the risk tolerance parameter, and so the assumed value does not affect our conclusions. In Bilson (1981) and Bilson and Hsieh (1987) the covariance matrix ~O is computed using the forecast errors of the particular econometric model being tested. Such an approach is appealing in this paper since it allows the construction of each panellist's portfolios to depend not only on the current forecasts but also on the history of the analyst's forecast accuracy. However, the relative paucity of data restricts our ability to pursue this strategy. Finance theory suggests the more practical alternative of using a data set which predates our sample period to construct a covariance matrix of returns to forward investment in each currency. This returns-based matrix is less than ideal since previous forecast inaccuracy is excluded from the optimisation process, but this may not be too serious for our sample of forecasters: when Consensus Economics requests forecasts, panellists are given the option to decline to forecast a currency about which their knowledge of likely future movements is poor. Furthermore, in common with other authors we find that the composition of each portfolio is driven by the forecast returns rather than the covariance structures (see Solnik, 1993), indicating that any imprecisions in the determination of ~ are of second order importance. 2
4. Forecaster performance We use three alternative benchmarks in our assessment of forecaster performance. First, we examine whether the portfolio is profitable. If the forward market is efficient and speculators are risk neutral, systematic profits should not be possible. Both of these assumptions have, however, been questioned. Therefore, if trading profits can be anticipated, a second logical comparison is to investigate whether the forecasts perform well relative to the simple alternative prediction of 'no change' - the assumption of the random walk model that has proved itself to be more accurate than many forecasters. The third approach we follow which draws on the work of Cornell (1979) does not rely on a benchmark in the traditional sense. A 'superior' investor is defined as one who has the ability to earn higher profits than an 'uninformed' investor would have expected given his portfolio holding. The 'uninformed' investor's expected profit on a unit long position in a currency is defined simply as the unconditional mean profit of forward speculation in that currency (here computed over the same prior-dated period used to construct the covariance matrix). This mean value is assumed to 2 The covariance matrix is determined using non-overlappingreturns between January 1978 and June 1989. Several issues regarding the determination of the portfolios are more fully discussed in Marsh and Power (1994), including the determination of the covariancematrix.
L W. Marsh, D.M. Power/Journal of Banking & Finance 20 (1996) 605-613
609
Table 1 Portfolio performance Portfolio 1
R.W. C1 C5 FI0 F12 J2 J20 B12 BI3 BI6 BI8 B29 B35 U1 U20 G5 G8 G9 G10 G13 G14 G15 G22
Portfolio 2
Profit
Signif.
Excess profit
Signif.
Profit
Signif.
Excess profit
Signif.
118.15 -25.29 -25.86 -55.16 8.40 -41.56 -38.17 - 48.12 60.35 161.05 -13.75 12.13 - 142.79 80.88 22.34 - 83.07 - 107.44 138.06 - 17.24 6.36 79.51 -34.62 - 74.46
0.229 0.476 0.669 0.247 0.863 0.393 0.654 0.329 0.091 0.080 0.655 0.706 0.209 0.587 0.481 0.111 0.042 0.014 0.716 0.780 0.142 0.146 0.089
117.38 -25.33 -44.82 -59.06 8.59 -46.12 -43.60 - 50.53 59.85 146.69 -19.90 5.66 -152.19 61.63 31.75 - 75.78 - 118.50 145.62 -19.43 1.54 67.05 -38.47 - 80.85
0.234 0.479 0.467 0.208 0.862 0.352 0.605 0.320 0.102 0.110 0.520 0.859 0.211 0.673 0.296 0.146 0.030 0.009 0.681 0.945 0.191 0.119 0.071
114.19 -30.74 -56.61 -69.19 7.78 - 12.40 4.09 - 6.78 24.94 29.14 -32.70 -40.89 -8.53 64.86 33.47 - 14.11 -22.24 83.08 - 15.52 -4.31 - 16.57 -9.16 -46.06
0.285 0.358 0.176 0.021 0.760 0.724 0.853 0.757 0.085 0.261 0.204 0.401 0.610 0.272 0.228 0.438 0.277 0.004 0.608 0.834 0.395 0.607 0.155
110.69 -28.97 -66.62 -69.33 4.56 -10.96 1.99 - 6.40 25.02 21.34 -37.43 -43.74 - 12.03 65.63 39.45 - 10.26 -25.65 92.97 - 13.45 -6.66 - 19.00 -11.79 -50.95
0.289 0.383 0.112 0.020 0.857 0.753 0.926 0.759 0.087 0.426 0.151 0.372 0.481 0.283 0.172 0.590 0.205 0.002 0.656 0.743 0.351 0.524 0.113
See text for details.
p r o v i d e a m e a s u r e o f the r e q u i r e d p r o f i t f r o m i n v e s t m e n t in a c u r r e n c y g i v e n the risk o f so d o i n g , a n d h e n c e b y p a s s e s the n e e d for an explicit m o d e l o f asset pricing. D e f i n i n g e x c e s s p r o f i t s as the d i f f e r e n c e b e t w e e n actual p r o f i t s a n d the profit a n ' u n i n f o r m e d ' i n v e s t o r w o u l d e x p e c t f r o m the g i v e n p o r t f o l i o h o l d i n g s , w e c a n test w h e t h e r m e a n e x c e s s profits are significant. In T a b l e 1 w e r e p o r t the a v e r a g e actual a n d e x c e s s profits o f e a c h f o r e c a s t e r u s i n g b o t h p o r t f o l i o f o r m a t i o n t e c h n i q u e s , t o g e t h e r w i t h the a s s o c i a t e d m a r g i n a l s i g n i f i c a n c e l e v e l s c o m p u t e d u s i n g the G M M p r o c e d u r e , w h i c h is r o b u s t to h e t e r o s c e d a s t i c i t y a n d the serial c o r r e l a t i o n i n d u c e d b y o v e r l a p p i n g o b s e r v a t i o n s . T o aid c o m p a r i s o n , t h e a v e r a g e e x p e c t e d profits for e a c h f o r e c a s t e r h a v e b e e n set e q u a l to $ 1 0 0 f r o m b o t h portfolios. T h a t is, the target profit l e v e l ~r is set to $ 1 0 0 in p o r t f o l i o 1, a n d the risk a v e r s i o n p a r a m e t e r 77 is a d j u s t e d s u c h that the a v e r a g e ex ante e x p e c t e d profit q ' f is $ 1 0 0 in p o r t f o l i o 2. T h e profits o f the r a n d o m w a l k m o d e l are also s h o w n ( d e n o t e d b y R.W.). T h e p o r t f o l i o s b a s e d o n the p r e d i c t i o n s o f the f o r e c a s t e r s in o u r s a m p l e are m o s t l y u n p r o f i t a b l e , t h o u g h to v a s t l y d i f f e r e n t e x t e n t s a n d w i t h n o t a b l e e x c e p t i o n s .
610
L W. Marsh, D.M. Power~Journal of Banking & Finance 20 (1996) 605-613
Thirteen of the portfolios formed using the first approach produce losses, increasing to fifteen using the second. Two forecasters actually do better than they expected (i.e. average profits of more than $100), but the majority underperform expectations. Very few of the portfolios produce average profits which are statistically greater than zero at any reasonable level of confidence. There is frequently a marked disparity between the profits produced by the two different portfolio formation techniques, reflecting the introduction of endogenous gearing in portfolio 2. For the majority of profitable forecasters, fully endogenising the size of positions taken reduces the size of average profits, leaving only two (B13 and G9) with significantly positive average profits at the 10% level. The portfolios based on the spot exchange rate (R.W.) are a noticeable counterexample, producing average profits in excess of ex ante expectations irrespective of portfolio formation technique. Only two forecasters produce greater profits than this random walk model, and then only using the first portfolio method. It would appear that the random walk model is a relatively powerful alternative in a multicurrency context. Nevertheless, profits from the random walk portfolios are not statistically significant. For almost all forecasters the excess profit series are only slightly different to the unadjusted series, as can be seen by the similarity between the two pairs of Profit and Excess Profit columns. This finding indicates that the uninformed investor's expectation of profits accruing from the portfolios is small on average, 3 and therefore that the profits (and losses) made are primarily due to the forecasting (in)ability of the panellists. Furthermore, they are not merely taking long positions in currencies which have historically appreciated, and so would be expected to yield a profit by an uninformed investor, but are actively switching positions between currencies. Not surprisingly, the significance of excess profits are also low, with only those of G9 significantly greater than zero at the 5% level. Our results indicate that whilst some of these forecasters are on average profitable to follow, their forecasts imply very volatile portfolio holdings which lead to large variances in profits. These variances are sufficiently large to make average profits statistically indistinguishable from zero. However, for portfolio 2 where expected (let alone actual) profits are volatile it could be argued that the significance of average profits is not a valid test of ability. 4 For example, suppose a forecaster who has perfect forecasting ability produces profits of $10 for 35 periods and a profit of $3,250 in just one period. His average profit is $100, his average expected profit is $100, he never makes a loss and yet statistically we cannot say his average profit exceeds zero.
3 In fact, the naive expected profits of some portfolios are negative (excess profit greater than profits). 4 A test of mean averageprofit is valid for portfoliomethod 1 since the expectedprofit is the same each month.
I.W. Marsh, D.M. Power/Journal of Banking & Finance 20 (1996) 605-613
611
Bilson (1984) and Bilson and Hsieh (1987) argue that a more appropriate test is whether the cumulative total profit of portfolio 2 is significantly positive. Assuming the actual profit at time t is drawn from a normal distribution with the appropriate variance, they show that the null hypothesis of zero cumulated profits can be tested by computing T
z-
,=1
(5)
t__~lO't2
where tr, 2 is the variance of profits in period t, defined as q'Oq and algebraically equivalent to E(Tr)r/. Z has a t-distribution with T - 1 degrees of freedom. Bilson and Hsieh (1987) find that the theoretical variance, E(Tr)r/, can substantially underestimate the actual variance of profits. We therefore estimate the following regression o-t2 = ( T r - E(Tr)) 2, = a + (/3 + r/)E(Tr), + yE(Tr)~ + u,.
(6)
The null hypothesis that the empirical variance equals the theoretical variance would imply that a =/3 = y = 0. If the null hypothesis is not rejected we infer that the theoretical variance is the true variance and use E(Tr)rt in computing Z. However, if the null hypothesis is rejected, fitted values of Eq. (6) are used as empirical estimates of the variance in Eq. (5). Tests of significant cumulated profits are reported in Table 2 for the subgroup of forecasters who produce positive average profits from portfolio 2. We see that two of our forecasters (U1 and G9) and the random walk model produce
Table 2 Significance of cumulated profits Forecaster
Cum. profits
Portfolio variance Theoretical
R.W. F12 J20 B13 B16 U1 U20 G9
4,110 280 147 897 1,049 2,335 1,205 2,989
Empirical
Z-stat.
Signif.
Z-stat.
Signif.
2.339 0.502 0.220 1.602 1.262 2.118 1.563 3.425
0.025 0.619 0.827 0.118 0.215 0.041 0.127 0.002
NA NA 0.128 0.930 NA 1.320 NA 2.634
NA NA 0.899 0.359 NA 0.195 NA 0.012
See text for details. NA entries in the empirical variance columns imply that the theoretical variance cannot be rejected as the true measure.
612
L W. Marsh, D.M. Power~Journal of Banking & Finance 20 (1996) 605-613
significantly positive cumulated profits when theoretical variances are maintained, but that the theoretical variance measure is rejected for U1, whose cumulated profits are no longer significant under the alternative model. These results suggest that only one of our original 22 forecasters has any significant forecasting ability, and that the random walk is a strong competitor, returning higher but more volatile profits.
5. Conclusions This study has investigated the ability of 22 individual forecasters to predict movements in three major currencies against the dollar within a portfolio framework. The findings indicate that only one forecaster (G9) consistently outperforms. However, before dismissing currency forecasters in general it is important to point out that this study has considered the forecasting ability of a minority of the individual organisations which responded to Consensus Economics' invitation to predict exchange rates. The requirement that to be included in our sample the forecasters had to have made 35 out of 36 possible forecasts for all three currencies may have eliminated expert forecasters who specialise in predicting only one or two currencies rather than 'nonspecialists' who anticipate movements in all currencies. Nevertheless, despite this criticism we feel that this note represents a valuable contribution to the current debate on the ability of professionals within large organisations to forecast exchange rates.
Acknowledgements We would like to thank Mr. Michael Sykes of Consensus Economics for providing the forecast data used in this study, and Rebecca Driver, Alasdair Lonie, Ronnie MacDonald, Peter Spencer, and an anonymous referee for helpful comments. The first author is also pleased to acknowledge the financial support of the Nuffield Foundation and the ESRC (Grant No: R000232945). An earlier version of this paper was presented at the 14th International Symposium on Forecasting held at the Stockholm School of Economics.
References Bilson, J.F.O., 1981, The 'speculative efficiency' hypothesis, Journal of Business 54, 435-451. Bilson, J.F.O., 1984, Purchasing power as a trading strategy, Journal of Finance 39, 715-724. Bilson, J.F.O. and D.A. Hsieh, 1987, The profitability of currency speculation, International Journal of Forecasting 3, 115-130. Boothe, P. and D. Glassman, 1987, Comparing exchange rate forecasting models: Accuracy versus profitability, International Journal of Forecasting 3, 65-79.
L W. Marsh, D.M. Power/Journal of Banking & Finance 20 (1996) 605-613
613
Cornell, B., 1979, Asymmetric information and portfolio performance evaluation, Journal of Financial Economics 7, 381-391. Engel, C., 1994, Can the Markov switching model forecast exchange rates?, Journal of International Economics 36, 151-165. Hodrick, R.J. and S. Srivastava, 1984, An investigation of risk and return in forward foreign exchange, Journal of International Money and Finance 3, 1-29. MacDonald, R. and I.W. Marsh, 1994, Combining Exchange rate forecasts: What is the optimal consensus measure? Journal of Forecasting 13, 313-332. Marsh, I.W. and D.M. Power, 1994, Assessing the performance of foreign exchange forecasters in a portfolio framework, University of Dundee, Discussion Paper in Financial Markets. Meese, R.A. and K. Rogoff, 1983, Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of International Economics 14, 3-24. Solnik, B., 1993, The performance of international asset allocation strategies using conditioning information, Journal of Empirical Finance 1, 33-55.
Journal of Banking & Finance 20 (1996) 605-613
FINANCE
A note on the performance of foreign exchange forecasters in a portfolio framework Ian W. Marsh a,*, David M. Power b Department of Economics, University of Strathclyde, 100 Cathedral Street, Glasgow, G40LN, United Kingdom b Department of Accountancy and Business Finance, Uniuersity of Dundee, Dundee, DDI 4HN, United Kingdom
Received 15 July 1994; accepted 15 December 1994
Abstract This note investigates the ability of 22 currency forecasters to predict movements in three major exchange rates. In particular, it examines the profitability of portfolios of forward market positions constructed on the basis of the predictions of each forecaster. The key findings of the paper are that just one panel member proves significantly profitable to follow, and that investing on the basis of the naive alternative prediction of 'no change' produces high, though volatile, profits. We conclude that the majority of currency analysts have little ability to predict the future. JEL classification." F31; G l l Keywords: Survey data; Exchange rates; Portfolio performance
I. Introduction A large body of research, beginning with the seminal work of Meese and Rogoff (1983), concludes that in terms of the mean squared error criterion, a naive random walk strategy dominates more sophisticated forecasting techniques in predicting exchange rates. A number of papers have also investigated the ability of
* Corresponding author. Tel.: (0141) 5524400 ext. 3859; fax: (014l) 5525589. 0378-4266/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0378-4266(95)00007-0
606
L W. Marsh, D.M. Power/Journal of Banking & Finance 20 (1996) 605-613
market participants to forecast individual currencies (e.g. MacDonald and Marsh, 1994). In spite of the richer set of possible explanatory variables used in making these forecasts, the random walk model remains pre-eminent. Engel (1994) argues persuasively that accuracy may not be the best criterion by which to judge the value of exchange rate forecasts, and that a more appropriate approach would be to assign a specific objective to an economic agent and then to evaluate the contribution of competing predictions in terms of maximising this goal. An obvious objective would be to assess the ability of the forecasts to earn profits. For example, Boothe and Glassman (1987) employ a simple trading strategy whereby a long (short) position of a fixed number of dollars is established in a currency if the forecast rate is greater (less) than the forward rate. They conclude that some, though not all, of the models examined demonstrate significant forecasting ability. The same technique has been applied to the forecasts of market participants by MacDonald and Marsh (1994) with comparable success. Although insightful, such simple trading strategies are rather implausible first, because they assume a fixed position size irrespective of expected return, second, because they fail to incorporate any explicit analysis of risk and third, because they evaluate forecasts of individual currencies one at a time, despite the fact that a forecaster's prediction of one exchange rate is probably not independent of his prediction of another. In this note we address all three of these issues by using elementary finance theory to produce portfolios based on the exchange rate predictions of several leading forecasters that incorporate the interdependencies between an individual's predictions of different currencies.
2. Data description On the first Monday of each month beginning September 1989, economists, foreign exchange dealers and executives in over 150 companies and institutions in the Group of Seven nations (G7) completed a facsimile from Consensus Economics of London which asked for point forecasts of, inter alia, the spot exchange rate of the Deutschmark, pound sterling, and Japanese yen against the US dollar three calendar months ahead. The companies surveyed include commercial and investment banks, industrial corporations, chambers of commerce and forecasting agencies (in both the private and public sectors). For reasons of confidentiality we denote each respondent by a mnemonic comprising a letter giving the nationality of the forecasting company (C-Canada, F-France, I-Italy, J-Japan, B-Britain, U-USA and G-Germany) and a number to distinguish between respondents. The forecast data end with the August 1992 survey. In order to construct a portfolio of investments our forecasters must have supplied regular predictions for all three currencies, and we have included only those who have responded to at least 35 of the 36 surveys. This response requirement reduces our panel to 22 forecasters from six different countries. Any
L W. Marsh, D.M. Power~Journal of Banking & Finance 20 (1996) 605-613
607
missing values have been replaced with the current period spot exchange rate, since our main point of comparison is with the random walk model. We have matched this survey database with contemporaneous middle market spot and three-month forward rates prevailing at a time between 3:30 and 4:00 pm in the London market, taken from the Barclays Bank International pages on Datastream.
3. Portfolio formation We construct two portfolios for each of the 22 panel members in the sample. Both are standard in form and have been used widely in the literature. 1 If we define g2 as the covariance matrix of profits, the first portfolio is the solution to the problem of minimising the risk of the portfolio subject to the constraint that a minimum level of profit (5-) is expected each period. This objective can be stated as
minL
=q'I~q+ A ( q ' ? -
5-)
(1)
where q is a column vector whose elements are the dollar value of the forward purchases adopted, and ? is the vector of expected (dollar) profit per one dollar long forward position in each currency. Each element of ? is the difference between the spot rate of a currency forecast to hold at time t + k and the k period forward rate holding at t. The solution is given by ~ = g2- 17[ ~'g~- 1 7 ] - ' 5-.
(2)
An important implication of this model is that the efficient frontier is a ray through the origin. The conclusions arrived at in this paper are therefore not altered if a different level of target profit is specified. This first portfolio specification is discussed more fully in Bilson (1981) and in Hodrick and Srivastava (1984). Bilson (1984) and Bilson and Hsieh (1987) use a more orthodox portfolio model in which a utility function defined over expected profits and risk (the variance of profits) is maximised: U=E(Tr)-
V(~)=q'P-
(1) ~
q'~q
(3)
where 7/ represents the degree of risk tolerance of the portfolio manager. The optimal portfolio is given by q* = g2- lr1~.
(4)
1To conservespace, only the essential details of how the portfolioswere constructed are given here. Interested readers are referred to the articles cited in this section or to Marsh and Power (1994).
608
L W. Marsh, D.M. Power~Journal of Banking & Finance 20 (1996) 605-613
As with the target profit level in the previous portfolio, the positions taken are proportional to the risk tolerance parameter, and so the assumed value does not affect our conclusions. In Bilson (1981) and Bilson and Hsieh (1987) the covariance matrix ~O is computed using the forecast errors of the particular econometric model being tested. Such an approach is appealing in this paper since it allows the construction of each panellist's portfolios to depend not only on the current forecasts but also on the history of the analyst's forecast accuracy. However, the relative paucity of data restricts our ability to pursue this strategy. Finance theory suggests the more practical alternative of using a data set which predates our sample period to construct a covariance matrix of returns to forward investment in each currency. This returns-based matrix is less than ideal since previous forecast inaccuracy is excluded from the optimisation process, but this may not be too serious for our sample of forecasters: when Consensus Economics requests forecasts, panellists are given the option to decline to forecast a currency about which their knowledge of likely future movements is poor. Furthermore, in common with other authors we find that the composition of each portfolio is driven by the forecast returns rather than the covariance structures (see Solnik, 1993), indicating that any imprecisions in the determination of ~ are of second order importance. 2
4. Forecaster performance We use three alternative benchmarks in our assessment of forecaster performance. First, we examine whether the portfolio is profitable. If the forward market is efficient and speculators are risk neutral, systematic profits should not be possible. Both of these assumptions have, however, been questioned. Therefore, if trading profits can be anticipated, a second logical comparison is to investigate whether the forecasts perform well relative to the simple alternative prediction of 'no change' - the assumption of the random walk model that has proved itself to be more accurate than many forecasters. The third approach we follow which draws on the work of Cornell (1979) does not rely on a benchmark in the traditional sense. A 'superior' investor is defined as one who has the ability to earn higher profits than an 'uninformed' investor would have expected given his portfolio holding. The 'uninformed' investor's expected profit on a unit long position in a currency is defined simply as the unconditional mean profit of forward speculation in that currency (here computed over the same prior-dated period used to construct the covariance matrix). This mean value is assumed to 2 The covariance matrix is determined using non-overlappingreturns between January 1978 and June 1989. Several issues regarding the determination of the portfolios are more fully discussed in Marsh and Power (1994), including the determination of the covariancematrix.
L W. Marsh, D.M. Power/Journal of Banking & Finance 20 (1996) 605-613
609
Table 1 Portfolio performance Portfolio 1
R.W. C1 C5 FI0 F12 J2 J20 B12 BI3 BI6 BI8 B29 B35 U1 U20 G5 G8 G9 G10 G13 G14 G15 G22
Portfolio 2
Profit
Signif.
Excess profit
Signif.
Profit
Signif.
Excess profit
Signif.
118.15 -25.29 -25.86 -55.16 8.40 -41.56 -38.17 - 48.12 60.35 161.05 -13.75 12.13 - 142.79 80.88 22.34 - 83.07 - 107.44 138.06 - 17.24 6.36 79.51 -34.62 - 74.46
0.229 0.476 0.669 0.247 0.863 0.393 0.654 0.329 0.091 0.080 0.655 0.706 0.209 0.587 0.481 0.111 0.042 0.014 0.716 0.780 0.142 0.146 0.089
117.38 -25.33 -44.82 -59.06 8.59 -46.12 -43.60 - 50.53 59.85 146.69 -19.90 5.66 -152.19 61.63 31.75 - 75.78 - 118.50 145.62 -19.43 1.54 67.05 -38.47 - 80.85
0.234 0.479 0.467 0.208 0.862 0.352 0.605 0.320 0.102 0.110 0.520 0.859 0.211 0.673 0.296 0.146 0.030 0.009 0.681 0.945 0.191 0.119 0.071
114.19 -30.74 -56.61 -69.19 7.78 - 12.40 4.09 - 6.78 24.94 29.14 -32.70 -40.89 -8.53 64.86 33.47 - 14.11 -22.24 83.08 - 15.52 -4.31 - 16.57 -9.16 -46.06
0.285 0.358 0.176 0.021 0.760 0.724 0.853 0.757 0.085 0.261 0.204 0.401 0.610 0.272 0.228 0.438 0.277 0.004 0.608 0.834 0.395 0.607 0.155
110.69 -28.97 -66.62 -69.33 4.56 -10.96 1.99 - 6.40 25.02 21.34 -37.43 -43.74 - 12.03 65.63 39.45 - 10.26 -25.65 92.97 - 13.45 -6.66 - 19.00 -11.79 -50.95
0.289 0.383 0.112 0.020 0.857 0.753 0.926 0.759 0.087 0.426 0.151 0.372 0.481 0.283 0.172 0.590 0.205 0.002 0.656 0.743 0.351 0.524 0.113
See text for details.
p r o v i d e a m e a s u r e o f the r e q u i r e d p r o f i t f r o m i n v e s t m e n t in a c u r r e n c y g i v e n the risk o f so d o i n g , a n d h e n c e b y p a s s e s the n e e d for an explicit m o d e l o f asset pricing. D e f i n i n g e x c e s s p r o f i t s as the d i f f e r e n c e b e t w e e n actual p r o f i t s a n d the profit a n ' u n i n f o r m e d ' i n v e s t o r w o u l d e x p e c t f r o m the g i v e n p o r t f o l i o h o l d i n g s , w e c a n test w h e t h e r m e a n e x c e s s profits are significant. In T a b l e 1 w e r e p o r t the a v e r a g e actual a n d e x c e s s profits o f e a c h f o r e c a s t e r u s i n g b o t h p o r t f o l i o f o r m a t i o n t e c h n i q u e s , t o g e t h e r w i t h the a s s o c i a t e d m a r g i n a l s i g n i f i c a n c e l e v e l s c o m p u t e d u s i n g the G M M p r o c e d u r e , w h i c h is r o b u s t to h e t e r o s c e d a s t i c i t y a n d the serial c o r r e l a t i o n i n d u c e d b y o v e r l a p p i n g o b s e r v a t i o n s . T o aid c o m p a r i s o n , t h e a v e r a g e e x p e c t e d profits for e a c h f o r e c a s t e r h a v e b e e n set e q u a l to $ 1 0 0 f r o m b o t h portfolios. T h a t is, the target profit l e v e l ~r is set to $ 1 0 0 in p o r t f o l i o 1, a n d the risk a v e r s i o n p a r a m e t e r 77 is a d j u s t e d s u c h that the a v e r a g e ex ante e x p e c t e d profit q ' f is $ 1 0 0 in p o r t f o l i o 2. T h e profits o f the r a n d o m w a l k m o d e l are also s h o w n ( d e n o t e d b y R.W.). T h e p o r t f o l i o s b a s e d o n the p r e d i c t i o n s o f the f o r e c a s t e r s in o u r s a m p l e are m o s t l y u n p r o f i t a b l e , t h o u g h to v a s t l y d i f f e r e n t e x t e n t s a n d w i t h n o t a b l e e x c e p t i o n s .
610
L W. Marsh, D.M. Power~Journal of Banking & Finance 20 (1996) 605-613
Thirteen of the portfolios formed using the first approach produce losses, increasing to fifteen using the second. Two forecasters actually do better than they expected (i.e. average profits of more than $100), but the majority underperform expectations. Very few of the portfolios produce average profits which are statistically greater than zero at any reasonable level of confidence. There is frequently a marked disparity between the profits produced by the two different portfolio formation techniques, reflecting the introduction of endogenous gearing in portfolio 2. For the majority of profitable forecasters, fully endogenising the size of positions taken reduces the size of average profits, leaving only two (B13 and G9) with significantly positive average profits at the 10% level. The portfolios based on the spot exchange rate (R.W.) are a noticeable counterexample, producing average profits in excess of ex ante expectations irrespective of portfolio formation technique. Only two forecasters produce greater profits than this random walk model, and then only using the first portfolio method. It would appear that the random walk model is a relatively powerful alternative in a multicurrency context. Nevertheless, profits from the random walk portfolios are not statistically significant. For almost all forecasters the excess profit series are only slightly different to the unadjusted series, as can be seen by the similarity between the two pairs of Profit and Excess Profit columns. This finding indicates that the uninformed investor's expectation of profits accruing from the portfolios is small on average, 3 and therefore that the profits (and losses) made are primarily due to the forecasting (in)ability of the panellists. Furthermore, they are not merely taking long positions in currencies which have historically appreciated, and so would be expected to yield a profit by an uninformed investor, but are actively switching positions between currencies. Not surprisingly, the significance of excess profits are also low, with only those of G9 significantly greater than zero at the 5% level. Our results indicate that whilst some of these forecasters are on average profitable to follow, their forecasts imply very volatile portfolio holdings which lead to large variances in profits. These variances are sufficiently large to make average profits statistically indistinguishable from zero. However, for portfolio 2 where expected (let alone actual) profits are volatile it could be argued that the significance of average profits is not a valid test of ability. 4 For example, suppose a forecaster who has perfect forecasting ability produces profits of $10 for 35 periods and a profit of $3,250 in just one period. His average profit is $100, his average expected profit is $100, he never makes a loss and yet statistically we cannot say his average profit exceeds zero.
3 In fact, the naive expected profits of some portfolios are negative (excess profit greater than profits). 4 A test of mean averageprofit is valid for portfoliomethod 1 since the expectedprofit is the same each month.
I.W. Marsh, D.M. Power/Journal of Banking & Finance 20 (1996) 605-613
611
Bilson (1984) and Bilson and Hsieh (1987) argue that a more appropriate test is whether the cumulative total profit of portfolio 2 is significantly positive. Assuming the actual profit at time t is drawn from a normal distribution with the appropriate variance, they show that the null hypothesis of zero cumulated profits can be tested by computing T
z-
,=1
(5)
t__~lO't2
where tr, 2 is the variance of profits in period t, defined as q'Oq and algebraically equivalent to E(Tr)r/. Z has a t-distribution with T - 1 degrees of freedom. Bilson and Hsieh (1987) find that the theoretical variance, E(Tr)r/, can substantially underestimate the actual variance of profits. We therefore estimate the following regression o-t2 = ( T r - E(Tr)) 2, = a + (/3 + r/)E(Tr), + yE(Tr)~ + u,.
(6)
The null hypothesis that the empirical variance equals the theoretical variance would imply that a =/3 = y = 0. If the null hypothesis is not rejected we infer that the theoretical variance is the true variance and use E(Tr)rt in computing Z. However, if the null hypothesis is rejected, fitted values of Eq. (6) are used as empirical estimates of the variance in Eq. (5). Tests of significant cumulated profits are reported in Table 2 for the subgroup of forecasters who produce positive average profits from portfolio 2. We see that two of our forecasters (U1 and G9) and the random walk model produce
Table 2 Significance of cumulated profits Forecaster
Cum. profits
Portfolio variance Theoretical
R.W. F12 J20 B13 B16 U1 U20 G9
4,110 280 147 897 1,049 2,335 1,205 2,989
Empirical
Z-stat.
Signif.
Z-stat.
Signif.
2.339 0.502 0.220 1.602 1.262 2.118 1.563 3.425
0.025 0.619 0.827 0.118 0.215 0.041 0.127 0.002
NA NA 0.128 0.930 NA 1.320 NA 2.634
NA NA 0.899 0.359 NA 0.195 NA 0.012
See text for details. NA entries in the empirical variance columns imply that the theoretical variance cannot be rejected as the true measure.
612
L W. Marsh, D.M. Power~Journal of Banking & Finance 20 (1996) 605-613
significantly positive cumulated profits when theoretical variances are maintained, but that the theoretical variance measure is rejected for U1, whose cumulated profits are no longer significant under the alternative model. These results suggest that only one of our original 22 forecasters has any significant forecasting ability, and that the random walk is a strong competitor, returning higher but more volatile profits.
5. Conclusions This study has investigated the ability of 22 individual forecasters to predict movements in three major currencies against the dollar within a portfolio framework. The findings indicate that only one forecaster (G9) consistently outperforms. However, before dismissing currency forecasters in general it is important to point out that this study has considered the forecasting ability of a minority of the individual organisations which responded to Consensus Economics' invitation to predict exchange rates. The requirement that to be included in our sample the forecasters had to have made 35 out of 36 possible forecasts for all three currencies may have eliminated expert forecasters who specialise in predicting only one or two currencies rather than 'nonspecialists' who anticipate movements in all currencies. Nevertheless, despite this criticism we feel that this note represents a valuable contribution to the current debate on the ability of professionals within large organisations to forecast exchange rates.
Acknowledgements We would like to thank Mr. Michael Sykes of Consensus Economics for providing the forecast data used in this study, and Rebecca Driver, Alasdair Lonie, Ronnie MacDonald, Peter Spencer, and an anonymous referee for helpful comments. The first author is also pleased to acknowledge the financial support of the Nuffield Foundation and the ESRC (Grant No: R000232945). An earlier version of this paper was presented at the 14th International Symposium on Forecasting held at the Stockholm School of Economics.
References Bilson, J.F.O., 1981, The 'speculative efficiency' hypothesis, Journal of Business 54, 435-451. Bilson, J.F.O., 1984, Purchasing power as a trading strategy, Journal of Finance 39, 715-724. Bilson, J.F.O. and D.A. Hsieh, 1987, The profitability of currency speculation, International Journal of Forecasting 3, 115-130. Boothe, P. and D. Glassman, 1987, Comparing exchange rate forecasting models: Accuracy versus profitability, International Journal of Forecasting 3, 65-79.
L W. Marsh, D.M. Power/Journal of Banking & Finance 20 (1996) 605-613
613
Cornell, B., 1979, Asymmetric information and portfolio performance evaluation, Journal of Financial Economics 7, 381-391. Engel, C., 1994, Can the Markov switching model forecast exchange rates?, Journal of International Economics 36, 151-165. Hodrick, R.J. and S. Srivastava, 1984, An investigation of risk and return in forward foreign exchange, Journal of International Money and Finance 3, 1-29. MacDonald, R. and I.W. Marsh, 1994, Combining Exchange rate forecasts: What is the optimal consensus measure? Journal of Forecasting 13, 313-332. Marsh, I.W. and D.M. Power, 1994, Assessing the performance of foreign exchange forecasters in a portfolio framework, University of Dundee, Discussion Paper in Financial Markets. Meese, R.A. and K. Rogoff, 1983, Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of International Economics 14, 3-24. Solnik, B., 1993, The performance of international asset allocation strategies using conditioning information, Journal of Empirical Finance 1, 33-55.