On the Predictability of Stock Prices - Swiss National Bank
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2011-11 Swiss National Bank Working Papers On the Predictability of Stock Prices: a Case for High and Low Prices Massimiliano Caporin, Angelo Ranaldo and Paolo Santucci de Magistris
Transcript of On the Predictability of Stock Prices - Swiss National Bank
2011
-11
Swis
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On the Predictability of Stock Prices: a Case for Highand Low Prices
Massimiliano Caporin, Angelo Ranaldo and Paolo Santucci de Magistris
The views expressed in this paper are those of the author(s) and do not necessarily represent those of the Swiss National Bank. Working Papers describe research in progress. Their aim is to elicit comments and to further debate.
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On the Predictability of Stock Prices: a Case for High and Low
Prices∗
Massimiliano Caporin † Angelo Ranaldo‡ Paolo Santucci de Magistris §
Abstract
Contrary to the common wisdom that asset prices are hardly possible to forecast, weshow that high and low prices of equity shares are largely predictable. We propose to modelthem using a simple implementation of a fractional vector autoregressive model with errorcorrection (FVECM). This model captures two fundamental patterns of high and low prices:their cointegrating relationship and the long memory of their difference (i.e. the range),which is a measure of realized volatility. Investment strategies based on FVECM predictionsof high/low US equity prices as exit/entry signals deliver a superior performance even on arisk-adjusted basis.
Keywords. high and low prices; predictability of asset prices; range; fractional cointegration;exit/entry trading signals; chart/technical analysis.
JEL Classifications: G11; G17; C53; C58.
∗The views expressed herein are those of the authors and not necessarily those of the Swiss National Bank,which does not accept any responsibility for the contents and opinions expressed in this paper. We are verygrateful to Adrian Trapletti and Guido Hachler for their support. I also thank Emmanuel Acar, Tim Bollerslev,Fulvio Corsi, Freddy Delbaen, Andreas Fischer and Andrea Silvestrini for their comments. All errors remain ourresponsibility.
†Dipartimento di scienze economiche ’Marco Fanno’, Via del Santo 22, Padua, Italy, Tel: +39 049/8274258.Fax: +39 049/8274211. Email: [email protected].
‡Angelo Ranaldo, Swiss National Bank, Research, Borsenstrasse 15, P.O. Box 2800, Zurich, Switzerland. E-mail: [email protected], Phone: Phone: +41 44 6313826, Fax: +41 44 6313901.
§Dipartimento di scienze economiche ’Marco Fanno’, University of Padua, Italy. Tel.: Tel: +39 049/8273848.Fax: +39 049/8274211. E-mail: [email protected].
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1 Introduction
The common wisdom in the financial literature is that asset prices are barely predictable (e.g.Fama, 1970, 1991). The rationale for this idea is the Efficient Market Hypothesis (EMH) inwhich asset prices evolve according to a random walk process. In this paper, we argue thatthis principle does not hold for the so-called ”high” and ”low” prices, i.e. the maximum andminimum price of an asset during a given period. By focusing on asset price predictability ratherthan assessing the EMH paradigm, we address three main questions in this paper: are high andlow prices of equity shares predictable? How can we model them? Do forecasts of high and lowprices provide useful information for asset and risk management?
There are three respects in which high and low prices can provide valuable information fortheir predictability. First, they inform people’s thinking. Kahneman and Tversky (1979) showthat when forming estimates, people start with an initial arbitrary value, and then adjust itin a slow process. In more general terms, behavioral finance studies have shown that agents’behavior generally depends on reference levels. As in a self-reinforcing mechanism, these formsof mental accounting and framing plus previous highs and lows typically represent the referencevalues for future resistance and support levels.
Second, high and low prices actually shape the decisions of many kinds of market partici-pants, in particular technical analysts.1 More generally, any investor using a path-dependentstrategy typically tracks the past history of extreme prices. Thus, limit prices in pending stop-loss orders often match the most extreme prices in a previous representative period. Moreover,as highlighted in the literature on market microstructure, high and low prices also convey infor-mation about liquidity provision and the price discovery process.2
Finally, extreme prices are highly informative as a measure of dispersion. The linear differ-ence between high and low prices is known as the range. Since Feller (1951), there have beenmany studies on the range, starting from the contribution of Parkinson (1980) and Garmanand Klass (1980) among many others.3 The literature shows that the range-based estimation ofvolatility is highly statistically efficient and robust with respect to many microstructure frictions(see e.g. Alizadeh, Brandt, and Diebold, 2002).
In order to answer the question of why high and low prices of equity shares are predictable, wepresent a simple implementation of a fractional vector autoregressive model with error correction(hereafter referred to as FVECM ) between high and low prices. The rationale for this modelingstrategy is twofold. First, it captures the cointegrating relationship between high and lowprices, i.e. they may temporarily diverge but they have an embedded convergent path in thelong run. This motivates the error correction mechanism between high and low prices. Second,the difference between the high and low prices, i.e. the range, displays long memory that can bewell captured by the fractional autoregressive technique. Combining the cointegration betweenhighs and lows with the long memory of the range naturally leads to model high and low pricesin an FVECM framework.
The long-memory feature of the range is consistent with many empirical studies on thepredictability of the daily range, a proxy of the integrated volatility, see for example Gallant,
1Recently, academics documented that technical analysis strategies may succeed in extracting valuable infor-mation from typical chartist indicators, such as candlesticks and bar charts based on past high, low, and closingprices (e.g. Lo, Mamaysky, and Wang, 2000), and that support and resistance levels coincide with liquidity clus-tering ( Kavajecz and Odders-White (2004)). The widespread use of technical analysis especially for short timehorizons (intraday to one week) is documented in, e.g., Allen and Taylor (1990). Other papers on resistance levelsare Curcio and Goodhart (1992), DeGrauwe and Decupere (1992), and Osler (2000).
2For instance, Menkhoff (1998) shows that high and low prices are very informative when it comes to analyzingthe order flow in foreign exchange markets.
3See also Beckers (1983), Ball and Torous (1984), Rogers and Satchell (1991), Kunitomo (1992), and morerecently Andersen and Bollerslev (1998), Yang and Zhang (2000), Alizadeh, Brandt, and Diebold (2002), Brandtand Diebold (2006),Christensen and Podolskij (2007), Martens and van Dijk (2007), Christensen, Zhu, and Nielsen(2009).
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Hsu, and Tauchen (1999) which fits a three-factor model to the daily range series to mimicthe long-memory feature in volatility, or Rossi and Santucci de Magistris (2009) which findsfractional cointegration between the daily range computed on futures and spot prices. Thisevidence allows the predictability of variances to be embedded in a model for the mean dynamicof extreme prices. The model we propose thus captures the predictability of extreme pricesby means of the predictability of second-order moments, which is a widely accepted fact sincethe seminal contribution of Engle (1982) and following the ARCH models literature. We thusprovide an affirmative answer to the first and second questions initially posed: first, there iscompelling evidence of the predictability of high and low prices; second, it suffices to apply alinear model that captures the fractional cointegration between the past time series of highs andlows.
To answer our third question, i.e. do forecasts of high and low prices provide useful infor-mation for asset management, we analyze intraday data of the stocks forming the Dow JonesIndustrial Average index over a sample period of eight years. The sample period is pretty rep-resentative since it covers calm and liquid markets as well as the recent financial crisis. Wefind strong support for the forecasting ability of FVECM, which outperforms any reasonablebenchmark model. We then use the out-of-sample forecasts of high and low prices to implementsome simple trading strategies. The main idea is to use high and low forecasts to determineentry and exit signals. Overall, the investment strategies based on FVECM predictions delivera superior performance even on a risk-adjusted basis.
The present paper is structured as follows. Section 2 discusses the integration and cointe-gration properties of high and low daily prices in a non-parametric setting. At this stage, ouranalysis is purely non-parametric and employs the most recent contributions of the literature(such as Shimotsu and Phillips (2005), Robinson and Yajima (2002), and Nielsen and Shimotsu(2007)). Section 3 presents the FVECM that is an econometric specification consistent with thefindings of the previous section, i.e. the fractional cointegration relationship between high andlow prices. After reporting the estimation outputs, Section 4 provides an empirical applicationof the model forecast in a framework similar to the technical analysis. Section 5 concludes thepaper.
2 Integration and Cointegration of Daily High and Low Prices
Under the EMH, the daily closing prices embed all the available information. As a result, the bestforecast we could make for the next day’s closing price is today’s closing price. This translatesinto the commonly accepted assumption of non-stationarity for the closing prices or, equiva-lently, the hypothesis that the price evolution is governed by a random walk process (which isalso referred to as an integrated process of order 1, or a unit-root process). Consequently, pricemovements are due only to unpredictable shocks.4 Furthermore, the random walk hypothesis isalso theoretically consistent with the assumption that price dynamics are driven by a geometricBrownian motion, which implies normally distributed daily log-returns. Finally, the EMH im-plies that the prices are not affected by some short-term dynamics such as autoregressive (AR)or moving average (MA) patterns.5
However, it is also commonly accepted that daily log-returns strongly deviate from the hy-pothesis of log-normality, thus casting some doubts on the law of motion hypothesis, in particularwith respect to the distributional assumption. In fact, extreme events are more likely to occurcompared with the Gaussian case, and returns are asymmetric, with a density shifted to the
4In more general terms, if the EMH holds, future prices cannot be predicted using past prices as well as usingpast values of some covariates. We do not consider here the effects of the introduction of covariates, but focus onthe informative content of the price sequence. As a result, we focus on the ”weak-form efficiency” as presented inFama (1970).
5The short-term dynamic could co-exist with the random walk within an ARIMA structure, where autoregres-sive (AR) and moving average (MA) terms are coupled with unit root (integrated) components.
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left (negative asymmetry). Many studies analyze market efficiency by testing the stationarityof daily closing prices or market values at given points of time, see Lim and Brooks (2011).6
Although market efficiency should hold for any price, by their very nature high/low pricesdiffer from closing prices in two main respects. First, liquidity issues are more relevant for highand low prices. Intuitively, high (low) prices are more likely to correspond to ask (bid) quotes,thus transaction costs and other frictions such as price discreteness, the tick size (i.e. the minimalincrements) or stale prices might represent disturbing factors. Second, highs and lows are morelikely to be affected by unexpected shocks such as (unanticipated) public news announcements.Then, some aspects such as market resiliency and quality of the market infrastructure can bedeterminant. In view of these considerations, we pursue a conservative approach by consideringthe predictability of highs and lows per se as weak evidence of market inefficiency. A morerigorous test is the analysis of the economic implications arising from the predictability of highsand lows. More specifically, we assess whether their prediction provides superior information torun outperforming trading rules.
We should also stress that this attempt will be limited to the evaluation of the serial cor-relation properties of those series, without the inclusion of the information content of othercovariates. Our first research question is thus to analyze the stationarity properties of dailyhigh and daily low prices in order to verify whether the unpredictability hypothesis is valid ifapplied separately to the two series. If the unpredictability hypothesis holds true, both high andlow prices should be driven by random walk processes, and should not have relevant short-termdynamic components (they should not be governed by ARIMA processes). To tackle this issuewe take a purely empirical perspective: at this stage we do not make assumptions either onthe dynamic process governing the evolution of daily high and low, nor on the distribution ofprices, log-prices or returns over high and low. Such a choice does not confine us within theunrealistic framework of geometric Brownian motions, and, more relevantly, does not prevent usfrom testing the previous issues. In fact, when analyzing the non-stationarity of price sequences,a hypothesis on the distribution of prices, log-prices or returns is generally not required. Giventhe absence of distributional hypotheses and of assumptions on the dynamic, we let the dataprovide some guidance. We thus start by analyzing the serial correlation and integration prop-erties of daily high and low prices. Furthermore, given the link between high and low prices andthe integrated volatility presented in the introduction, we also evaluate the serial correlation andintegration of the difference between high and low prices, the range. In the empirical analyseswe focus on the 30 stocks belonging to the Dow Jones Industrial Average index as of end ofDecember 2010.
We consider the daily high log-price, pHt = log(PH
t ), and the daily low log-price, pLt =
log(PLt ). Our sample data covers the period January 2, 2003 to December 31, 2010, for a total
of 2015 observations. The plots of the daily high and low prices show evidence of a strongserial correlation, typical of integrated processes, and the Ljung-Box test obviously stronglyrejects the null of no correlation for all lags.7 Therefore, we first test the null hypothesis ofunit root for the daily log-high, log-low and range by means of the Augmented Dickey Fuller(ADF ) test. In all cases, the ADF tests cannot reject the null of unit root for the daily log-highand log-low prices.8 This result is robust to the inclusion of the constant and trend, as wellas different choices of lag. The outcomes obtained by a standard approach suggest that thedaily high and daily low price sequences are integrated of order 1 or, equivalently, that theyare governed by random walk processes (denoted as I(1) and I(0), respectively). At first glance,this finding seems to support the efficient market hypothesis. This is further supported by theabsence of a long- and short-range dependence on the first differences of daily high and dailylow log-prices. Moreover, there is clear evidence that daily range is not an I(1) process, but
6To our knowledge, Cheung (2007) represents the only noticeable exception that analyzes high and low prices.7Results not reported but available on request.8Using standard testing procedures based on the ADF test, we also verified that the integration order is 1,
given that on differenced series the ADF test always rejects the null of a unit root.
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should be considered an I(0) process. Based on these results, one can postulate that daily highand daily low prices are cointegrated, since there exists a long-run relation between highs andlows that is an I(0) process. However, this finding must be supported by proper tests, sincethe existence of a cointegrating relation between daily high and daily low potentially allows forthe construction of a dynamic bivariate system which governs the evolution of the two series,with a possible impact on predictability. These results confirm the findings in Cheung (2007).Besides the previous result, Andersen and Bollerslev (1997) and Breidt, Crato, and de Lima(1998), among others, find evidence of long memory (also called long range dependence) in assetprice volatility. This means that shocks affecting the volatility evolution produce substantialeffects for a long time. In this case, volatility is said to be characterized by a fractional degree ofintegration, due to the link between the integration order and the memory properties of a timeseries, as we will see in the following. In our case, the autocorrelation function, ACF, in Figure1 seems to suggest that the daily range is also a fractionally integrated process, provided that itdecays at a slow hyperbolic rate. In particular, the ACF decays at a slow hyperbolic rate, whichis not compatible with the I(0) assumption made on the basis of ADF tests. Unfortunately, theADF is designated to test for the null of unit root, against the I(0) alternative, and it is alsowell known, see Diebold and Rudebusch (1991), that the ADF test has very low power againstfractional alternatives. Therefore, we must investigate the integration order of daily high andlow prices and range in a wider sense, that is in the fractional context. We also stress that thetraditional notion of cointegration is not consistent with the existence of long-memory. In orderto deeply analyze the dynamic features of the series at hand, we resort to more recent and non-standard tests for evaluating the integration and cointegration orders of our set of time series.Our study thus generalizes the work of Cheung (2007) since it does not impose the presence ofthe most traditional cointegration structure, and it also makes the evaluation consistent withthe findings of long memory in financial data.
We thus investigate the degree of integration of the daily high and low prices, and of theirdifference, namely the range, in a fractional or long-memory framework. This means that weassume that we observe a series, yt ∼ I(d), d ∈ �, for t ≥ 1, is such that
(1 − L)dyt = ut (1)
where ut ∼ I(0) and has a spectral density that is bounded away from zero at the origin.Differently from the standard setting, the integration order d might assume values over thereal line and is not confined to integer numbers. Note that if d = 1 the process collapses ona random walk, whereas if d = 0 the process is integrated of order zero, and thus stationary.The econometrics literature on long-memory processes distinguishes between type I and type IIfractional processes. These processes have been carefully examined and contrasted by Marinucciand Robinson (1999), and Davidson and Hashimzade (2009). The process yt reported aboveis a type II fractionally integrated process, which is the truncated version of the general typeI process, since the initial values, for t = 0,−1,−2, ... are supposed to be known and equal tothe unconditional mean of the process (which is equal to zero).9 In this case, the term (1−L)d
results in the truncated binomial expansion
(1 − L)d =
T−1∑i=0
Γ(i − d)
Γ(−d)Γ(i + 1)Li (2)
so that the definition in (1) is valid for all d, see Beran (1994) among others. In particular,for d < 0, the process is said to be anti-persistent, while for d > 0 it has long memory. Whendealing with high and low prices, our interest refers to the evaluation of the integration orderd for both high and low, as well as of the integration order for the range. Furthermore, if thedaily high and daily low time series have a unit root while the high-low range is a stationary
9In contrast, type I processes assume knowledge of the entire history of yt.
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but long-memory process, a further aspect must be clarified. In fact, as already mentioned, thepresence of a stationary linear combination (the high-low range) of two non-stationary seriesopens the door to the existence of a cointegrating relation. However, the traditional tests ofcointegration are not consistent with the memory properties of the high-low range. Therefore,we chose to evaluate the fractional cointegration across the daily high and daily low time series.
In the context of long-memory processes, the term fractional cointegration refers to a gen-eralization of the concept of cointegration, since it allows linear combinations of I(d) processesto be I(d − b), with 0 < b ≤ d. The term fractional cointegration underlies the idea of theexistence of a common stochastic trend, that is integrated of order d, while the short perioddepartures from the long-run equilibrium are integrated of order d−b. Furthermore, b stands forthe fractional order of reduction obtained by the linear combination of I(d) variables, which wecall cointegration gap. We first test for the presence of a unit root in the high and low prices, sothat d = 1, and, as a consequence, the fractional integration order of the range becomes 1−b. Inorder to test the null hypothesis of a unit root and of a fractional cointegration relation betweendaily high and low prices, we consider a number of approaches and methodologies. First, weestimate the fractional degree of persistence of the daily high and low prices by means of theunivariate local exact Whittle estimator of Shimotsu and Phillips (2005). Notably, their estima-tor is based on the type II fractionally integrated process. The univariate local exact Whittleestimators for high and lows (dH and dL, respectively) minimizes the following contrast function
Qmd(di, Gii) =
1
md
md∑j=1
[log(Giiλ
−2dj ) +
1
GiiIj
]i = H, L (3)
which is concentrated with respect to the diagonal element of the 2 × 2 matrix G, under thehypothesis that the spectral density of Ut = [ΔdH pH
t , ΔdLpLt ] satisfies
fU (λ) ∼ G as λ → 0. (4)
Furthermore, Ij is the coperiodogram at the Fourier frequency λj = 2πjT of the fractionally
differenced series Ut, while md is the number of frequencies used in the estimation. The matrixG is estimated as
G =1
md
md∑j=1
Re(Ij) (5)
where Re(Ij) denotes the real part of the coperiodogram. Table 1 reports the exact local Whittleestimates of dH and dL for all the stocks under analysis. As expected, the fractional orders ofintegration are high and generally close to 1. Given the estimates for the integration orders,we test for equality according to the approach proposed in Nielsen and Shimotsu (2007) that isrobust to the presence of fractional cointegration. The approach resembles that of Robinson andYajima (2002), and starts from the fact that the presence or absence of cointegration is not knownwhen the fractional integration orders are estimated. Therefore, Nielsen and Shimotsu (2007)propose a test statistic for the equality of integration orders that is informative independentlyfrom the existence of the fractional cointegration. In the bivariate case under study, the teststatistic is
T0 = md
(Sd
)′(
S1
4D−1(G G)D−1S′ + h(T )2
)−1 (Sd
)(6)
where denotes the Hadamard product, d = [dH , dL], S = [1,−1]′, h(T ) = log(T )−k for k > 0,D = diag(G11, G22). If the variables are not cointegrated, that is the cointegration rank r iszero, T0 → χ2
1, while if r ≥ 1, the variables are cointegrated and T0 → 0. A significantly
large value of T0, with respect to the null density χ21, can be taken as an evidence against the
equality of the integration orders. The estimation of the cointegration rank r is obtained bycalculating the eigenvalues of the matrix G. Since G does not have full rank when pH
t and pLt
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are cointegrated, then G is estimated following the procedure outlined in Nielsen and Shimotsu(2007, p. 382) which involves a new bandwidth parameter mL. In particular, dH and dL areobtained first, using (3) with md as bandwidth. Given d, the matrix G is then estimated, usingmL periodogram ordinates in (5), such that mL/md → 0. The table reports the estimates formd = T 0.6 and mL = T 0.5, while results are robust to all different choices of md and mL.Let δi be the ith eigenvalue of G, it is then possible to apply a model selection procedure todetermine r. In particular,
r = arg minu=0,1
L(u) (7)
where
L(u) = v(T )(2 − u) −2−u∑i=1
δi (8)
for some v(T ) > 0 such that
v(T ) +1
m1/2
L v(T )→ 0. (9)
The previous tests are concordant in suggesting that the integration order of pHt and pL
t areequal and close to unity. This is the case for 26 out of 30 equities of the DJIA index. Furthermore,Table 1 shows that L(1) < L(0) in all cases considered, and this can be taken as strong evidencein favor of fractional cointegration between pH
t and pLt , so that equation 8 is minimized in
correspondence of r = 1. The results reported are relative to the case where v(T ) = m−0.35L
and remain valid for alternative choices of v(T ) (not reported to save space). Note that, in thebivariate case, equation 8 is minimized if v(T ) > min(δi), where min(δi) is the smallest eigenvalueof G (or alternatively of the estimated correlation matrix P = D−1/2GD−1/2). Provided thatthe correlation between pH and pL is approximately 1 in all cases, then P is almost singular andthe smallest eigenvalue of P is very close to 0. Therefore v(T ) ≈ v(T ) − min(δi) > 0 and thisexplains why L(1) has a similar value across all the assets considered. As a preliminary dataanalysis, we also carry out the univariate Lagrange Multiplier (LM) test of Breitung and Hassler(2002) to verify the null hypothesis of unit roots against fractional alternatives. Unfortunately,we cannot use the extension of Nielsen (2005), since the multivariate LM test of fractionalintegration order, which is based on the type II fractionally integrated process, always rejectsthe null of d = 1, when series are fractionally cointegrated. Therefore, it is impossible to knowif the null has been rejected due to a cointegration relation or because one of the variables isI(1). Table 1 reports the p−values of the univariate LM tests of Breitung and Hassler (2002)for pL
t and pHt . In all cases the null hypothesis cannot be rejected at the 5% significance
level, meaning that the high and low log-prices can be considered unit root processes, so that[ΔpH
t , ΔpHt ] ∼ I(0). As a further check, provided that the daily range is an estimate of the daily
integrated volatility (Parkinson (1980)), and given several empirical studies showing that thedaily realized range has long-memory, we consider the evaluation of the fractional parameterof the daily range series. Note that we refer to the range, Rt = pH
t − pLt , as the rescaled root
square of the Parkinson estimator, that is RG2t = 0.361 · (pH
t − pLt )2. The Breitung and Hassler
(2002) test on Rt confirms the results of the Nielsen and Shimotsu (2007) procedure, since thelinear combination pH
t − pLt significantly reduces the integration order in almost all cases, and
the local exact Whittle estimates of dR are approximately 0.6 − 0.7 in all cases, that is in thenon-stationary region. Furthermore, the LM test for Rt rejects the null of unit root in 28 out of30 cases at 10% significance level. As expected, the range has a fractional integration order thatis significantly below 1, and in the next section we will show how to incorporate this evidence ina parametric model which exploits the long-run relationship between daily high and low prices.These results are in line with the well-known stylized fact that volatility of financial returnsis characterized by long-range dependence, or long memory, see, for instance, Baillie (1996),Bollerslev and Mikkelsen (1996), Dacorogna, Muller, Nagler, Olsen, and Pictet (1993), Ding,Granger, and Engle (1993), Granger and Ding (1996), Andersen, Bollerslev, Diebold, and Ebens
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(2001). In a recent contribution, Rossi and Santucci de Magistris (2009) find evidence of longmemory and fractional cointegration between the daily ranges of the spot and futures prices ofthe S&P 500 index.
3 Modeling Daily High and Low Prices
As we showed in the previous section, the high and low prices have an embedded convergent pathin the long run, so that they are (fractionally) cointegrated. For intuitive reasons10, we expectthat high and low prices can deviate in the short run from their long-run relation. The conceptof cointegration has been widely studied during the last three decades, since the original paperby Granger (1981). Most of the analysis has concentrated on the special case where a linear (ornonlinear) combination of two or more I(1) variables is I(0). Tests for I(1)/I(0) cointegrationare carried out in a regression setup, as proposed by Engle and Granger (1987), or investigatethe rank of the cointegration matrix in a system of equations following the Johansen (1991)procedure. A similar approach has been followed by Cheung (2007). When a cointegrationrelation exists across two variables, the bivariate system can be re-written in a Vector ErrorCorrection (VEC) form, where the first difference of the cointegrated variables is a functionof the cointegrating relation. Such a model has an interesting economic interpretation sincedeviations from the long-run equilibrium (given by the cointegrating relation) give rise to anadjustment process that influences the future values of the modeled variables. In our framework,changes in the actual high and low prices that make them inconsistent with the long-run relationwill produce an effect on future high and low prices. However, the long memory must also betaken into account, differently from what has been considered in Cheung (2007). In a recentcontribution, Johansen (2008) proposes a generalization of the VEC model to the fractionalcase. Such an extension allows for a representation (through a so-called Granger representationtheorem) which, in turn, enables us to distinguish between cofractional relations and commontrends. Johansen (2008) suggests studying the fractional cointegration relation in the followingsystem representation
ΔdXt = (1 − Δb)(Δd−bαβ′Xt − μ) +K∑
j=1
ΓjΔdLj
bXt + εt (10)
which is based on the new generalized lag operator Lb = 1 − (1 − L)b. In our set-up, thevector Xt includes the daily high and low log-prices, Xt = (pH
t , pLt )′, and εt = (εH
t , εLt )′ is
assumed to be i.i.d. with finite eight moments, mean zero and variance Ω. Furthermore, α =(αH , αL) is the vector of the loadings, while β = (1, γ) is the cointegration vector. The firstterm on the right can be represented as α(1−Δb)Δd−b(pH
t +γpLt −μ) where the core component
(1 − Δb)Δd−b(pHt + γpL
t − μ) defines the cointegration relation. Differently, the element αi inthe vector α measures the single period response of variable i to the shock on the equilibriumrelation. In the following, we restrict the cointegration parameter γ to be equal to −1, so thatthe cointegration relation can be interpreted in terms of the high-low range. We note thatin preliminary estimates where this restriction was not imposed, the estimated cointegrationparameter was generally very close to one, and we were not rejecting the null of γ = 1. Moreover,imposing the condition d = 1 in model (10) implies that, following the definition of Hualdeand Robinson (2010), in the case of strong fractional cointegration, i.e. b > 1/2, the rangewould be stationary and integrated of order d − b < 0.5. On the other hand, the case ofweak fractional cointegration, where 0 < b < 1/2 see Hualde and Robinson (2010), leads toa non-stationary fractionally integrated range. We also introduce a constant term, μ, in thecointegration relation, which represents the mean value of the range; μ must be positive, provided
10High and low prices can deviate temporarily because of information motives, liquidity factors or other mi-crostructure effects such as bid-ask spread bounces, price discreteness, trading pressure.
9
that pHt ≥ pL
t by definition. Assuming that the rank of the matrix αβ, the cointegration rank r,is known already, model (10) is estimated following the procedure outlined in Lasak (2008) andJohansen and Nielsen (2010a). In particular, model (10) is estimated via a maximum likelihoodtechnique analogous to that developed by Johansen (1991) for the standard VEC model11.The asymptotic distribution of the FVECM model estimators is studied in Lasak (2008) andJohansen and Nielsen (2010b,a), while this estimation procedure has been employed by Rossiand Santucci de Magistris (2009), which show the finite sample properties of the estimatorsthrough a Monte Carlo simulation. In a recent contribution, Johansen and Nielsen (2011) showthat the asymptotic distribution of all the FVECM model parameters is Gaussian when b < 1/2.On the other hand, when b > 1/2, the asymptotic distribution of β is mixed Gaussian, while theestimators of the remaining parameters are Gaussian. On the basis of the results in the previoussection, it seems natural to estimate model (10) on the log high and low prices for the 30 stocksunder analysis. One lag in the generalized autoregressive term is assumed to be sufficient inall cases for a good description of the short term component. Table 2 reports the estimationresults of model (10) on the 30 series. The estimated parameter b is lower than 0.5 in 27 cases,meaning that, as expected, daily range is generally non-stationary. In particular, the estimateddegree of long range dependence of daily range implied by the FVECM model is between 0.4611and 0.7467, meaning that the persistence of the range is very high, while the null hypothesisd = 1 cannot be rejected in most cases. It is noteworthy to stress that the estimated degree oflong memory of the range which is implied by the FVECM model is very close to the valuesobtained with the semiparametric estimators, in Section 2. Moreover, αH and αL are significantand with the expected signs, so that it is possible to conclude that high and low prices are tiedtogether by a common long-memory stochastic trend toward which they converge in the longrun at significant rates.
Interestingly, the deviations from the attractor (the long-run relation) have an economicinterpretation in terms of volatility proxy, that is the range. Therefore, a parametric model forthe high-low prices incorporates significant information on the degree of dispersion of the prices.Hence, we are able to exploit the long-memory feature of the price dispersion in order to obtainbetter forecasts of future high and low log-prices based on past values. Figure 1 reports thehigh and low log-prices series of IBM and the common stochastic trend constructed from theestimates of model 10 and the Granger representation theorem for fractional VAR in Johansen(2008). It is also clear that the common stochastic trend closely follows the dynamics of thehigh and low log-prices, provided that they are tied together by a strong cointegration relation.The deviations from the long run relationship, which is the high-low distance or range, are alsoplotted. The range is a highly persistent series characterized by long periods above or below theunconditional mean. For example, the recent financial crisis in 2008-2009 is characterized by alarger discrepancy between the high and low prices, that is the result of a higher market risk. Inthe next section, we will show a possible trading strategy that can benefit from better forecastsof daily high-low bands.
4 Forecasting and Trading
Given the estimates of model (10), a natural exercise would be based on the forecasts of the highand low prices, using them to implement a trading strategy based on the predicted so-calledhigh-low bands. Our focus is purely illustrative, and we provide a reasonable application ofour modeling approach, thereby extending the study of Cheung (2007) in that direction. Indoing so, we consider an expanding estimation period, which is used to evaluate the model andproduce the one-step-ahead forecasts. We base our analysis on a subset of 20 assets of the DowJones index, for which we dispose of high frequency prices (i.e. one-minute frequency) for atotal of 390 intradaily prices per day. The sample covers the period from January 2, 2003 to
11The VEC is obtained as a special case of the FVECM when d and b are fixed to be equal to 1
10
December 31, 2009, for a total of T = 1762 observations. We provide out-of-sample forecastsfor the last 251 sample data points, the year 2009. Therefore, the estimation sample lengthincludes a minimum of S = 1511 observations and a maximum of S = T − 1 data points. Ateach step, model (10) is estimated on the first S observations, and a one-step-ahead forecast ofthe high and low prices is obtained; we call these forecasts FC bands. Note that, in order toguarantee that the predicted high-low bands are robust to the overnight activity, the overnightreturn log Ot − log Ct−1 is included in model (10) as an additional explanatory variable (Ot andCt−1 are the opening and closing prices, respectively). The introduction of the overnight returnlog mimics the regular operating activity of a trader who, using the model, produces the day tforecasts for high and low, including the opening price of time t in the information set. Giventhe bands, the trader uses them within day t regular trading hours. Figure 2 plots the Japanesecandlesticks, based on the observed prices of JPM, with the corresponding predicted high-lowbands. It is clear that the FC bands provide a better out-of-sample fit of the high-low dispersionwith respect to the high-low bands based on a 5-day moving average of high and low, MA5,which represents a tool often used by technical analysts. Table 3 reports the p-values of theDiebold and Mariano (1995) test for the out-of -ample forecasts of the high and low log-prices,obtained using the FV ECM . As competing models we chose the random walk, RW , the 5-daymoving average, MA5, and the 22-day moving average, MA22, which correspond to weekly andmonthly averages respectively.12 We correct the predicted high-low bands of RW , MA5 andMA22 by adding the difference between the opening price of day t, Ot, and the closing price ofday t− 1, Ct−1. Such a choice realigns those competing forecasts with the information set usedin the FV ECM model where the opening price of time t is taken into account. The Dieboldand Mariano (1995) test for the forecasting superiority of FV ECM is carried out focusing onthe mean squared error (MSE) and on the mean absolute error (MAE) of the forecasts, wherethe error of model i at date t is defined as the difference, εi,t, between the observed high in theperiod t + 113, and the corresponding forecast provided by model i:
εHt+1,i = pH
t+1 − pHt+1,i i = FV ECM, RW, MA5, MA22 (11)
Specifically, the interest is on the measure of the relative forecasting performance of the differentmodel specifications, testing the superiority of model i over FVECM, which is the benchmark,with a t-test for the null hypothesis of a zero mean in
ε2t+1,FV ECM − ε2
t+1,i = ci + νt (12)
|εt+1,FV ECM | − |εt+1,i| = di + ξt
where negative estimates of ci and di indicate support for the FV ECM , provided that all modelsare compared to the FV ECM . The Diebold and Mariano (1995) test is the t-statistics for thenullity of the estimates of ci and di. Overall, Table 3, depicts a situation where the forecasterrors associated with the FVECM are significantly smaller than those of the competing models.As expected, the p-value of the test for MA5 and MA22 is highly significant in all cases. Thisis due to the fact that moving averages are used in practice to identify local trends in the pricesand not for a point estimate of the prices. On the other hand, for what concerns the RW model,the t-test based on MSE is always negative and the p-value is often lower than 5% for both thepH
t and pLt . This result suggests that the fractional cointegration model significantly improves
the forecasts of high and low log prices, with respect to the model that, consistently with thestrong efficiency of the markets, assumes that the best forecast of future prices is the actualprice.
We then implement two simple trading rules that make use of the model outcomes. Atfirst, we consider a trading rule based on the predicted high-low bands. We define buy and sell
12The alternative specifications all consider separately the high and low prices for the construction of high andlow bands. By contrast, our model provides the high and low forecasts within a unified framework.
13Analogously for the low log-price.
11
signals comparing the intradaily evolution of the equity price and the high-low bands. If theprice crosses the high band, we interpret it as a buy signal. Conversely, if the price crosses thelow band we have a sell signal, see Murphy (1999). This can be interpreted as a trend-following
strategy, where the upper line is used as a bull -trendline in a uptrend, while the lower line isused as a bear -trendline in a downtrend. We also implement the contrarian strategy: if the pricecrosses the high band, we interpret it as a sell signal. Conversely, if the price crosses the lowband we have a buy signal.
It is therefore possible to carry out a realistic trading strategy based on the high-low bands,as described above. In particular, the previous rules define the creation of long or short positions.Those positions created within day t can be closed or maintained in the following days. Once weenter a new position, two additional bands are created in order to guarantee a desired minimumlevel of profit or a maximum acceptable loss. These additional bands, called the stop-loss andtake-profit bands, are proportional to the high-low distance and are created as follows. Supposethat we have a trend-following strategy, and the predicted upper bound, PH
t , is crossed by theprice at a given time t < τ0 < t + 1. In this case, we open a long position and the stop-loss andtake-profit thresholds are created as SLt = PH
t − δRt and TPt = PHt + δRt, respectively, where
δ determines the size of the new bands and Rt = PHt − PL
t is the predicted daily range. If theprice crosses the SLt or TPt in τ0 < τ < t + 1, then the long position is closed. On the otherhand, if an open position is not closed during day t, then it is maintained until t+1. By design,positions can also be closed at the opening price for two possible reasons: first, during the marketclosing period, relevant news might be released with a potentially elevating impact on prices;second, the FVECM model does not guarantee that the opening price at time t + 1 is inside thehigh/low bands of time t+1. Suppose that at time t we have an opened long position in a trendfollowing strategy. At the beginning of t + 1, the position is closed if Ot+1 < max([PL
t+1; SLt])
or if Ot+1 > min([PHt+1; TPt]). Such a choice allows us to avoid too risky strategies which might
be taken in case of large variations of the prices over two consecutive days. If a position isnot closed during the market opening, then PL
t+1 and PHt+1 are used as predicted H-L bands for
t + 1. Similarly we can define stop-loss and take-profit bands for the short positions and for thecontrarian strategy. The payoffs of this trading system, based on two couples of high-low bands,are reported in Table 4. In order to consider a realistic trading strategy, it is assumed that aninitial amount, A0, of 20,000 US dollars can be invested in the strategy. A fixed cost of 5 dollarsis charged on each transaction. During day t, the investor can buy or sell an amount of stocksthat is equal to Nt = [At/Pτ0 ], where [x] indicates the nearest integer less than or equal to xand τ0 is the time in which the price crosses the bands.
It is immediately evident that the strategies are symmetric, so that when the trend-following
strategy produces a positive payoff, then in most cases the corresponding payoff of the contrarian
strategy is lower than 20000 dollars. We notice in general that, across the strategies considered,the payoff from the contrarian strategy is generally higher than the payoff obtained with trend
following. This is probably due to the fact that, when the price exceeds a given threshold, thereis a higher probability that it will revert, tending to move toward the initial value, rather thanmoving further toward more extreme values. The reverting behavior of the extremes has alsobeen noted by Cheung (2007).
Relatively to the other bands employed, the FC bands have similar performances in termsof final outcome. The FC bands provide less frequently the worst performance with respect tothe alternative choices. Moreover, when the contrarian strategy is employed with the FC bands,we observe 12 and 11 positive outcomes with δ = 0.25 and δ = 0.5. In particular, the strategybased on the FC bands has good relative performances when the contrarian strategy is appliedwith δ = 0.5, which increases the probability of maintaining the position opened until t + 1. Inthat case, the FC bands have the best performances in 7 cases. Except for the case of BACand JPM , the profits and losses associated with FC are rarely above 3000 dollars (or less than-3000), so we can conclude that in general it seems that the payoff variability associated with
12
FC is lower than the variability associated with the other strategies.An alternative trading system could be based on a different construction of the bands. Now
we focus on the predictions of the model (10) as a possible way of recovering a forecast of therange, Rt. This is automatically obtained by the difference between the predicted high and lowprices. Therefore a range-based strategy can be employed. For MA5 and MA22, these are theaverages of the daily range with different horizons, while RW simply takes the range at timet−1 as the predicted range at time t. In this case, the daily H-L bands for day t, are centered onthe open price, so that the upper band is equal to Ot +Rt and Ot−Rt. Therefore, the size of theband is 2Rt. Once the bands have been created, the trend-following (or the contrarian) strategycould be implemented similarly to as described above, with the corresponding SL and TP bandswhich are constructed with δ = 0.5. In this case, the position, eventually opened during day t,is not maintained until t + 1 and must be closed before (or in correspondence of) the last tradeof day t. Table 5 reports the results of a contrarian strategy based on the daily range bands.Table 5 reports the value of the investment at the end of the sample, say on December 31, 2009.In 12 out of 20 cases the strategy based on the range, obtained from model (10), reports positiveprofits, while the strategy based on buy and hold, fifth column, has positive profits in 11 outof 20 cases. With respect to the other strategies, the FC bands perform generally better thanRW and MA5, while having similar performances to MA22. This is due to the fact that MA22
is able to well approximate the long-run dependence of the range series and, in this particularstrategy, the difference in terms of profits is not relevant. This evidence can be well understoodfrom Figure 3 which plots the forecasts of the range based on different model specifications. It isclear that RW provides a very noisy forecast of the range, while MA22 is extremely smooth andit is close to the forecast of the FV ECM that is based on the maximum likelihood estimatesof b, which governs the persistence of the range. Relative to the other strategies, the strategybased on FV ECM has a lower number of days of trading, that is approximately 40, comparedto RW and MA5, which trade more frequently. Moreover, the variance associated with thedaily payoff of the various strategies is the lowest for the FV ECM in 12 out of 20 cases. Thevariance of the buy & hold strategy, B&H, is always greater than the variance of the strategiesbased on intradaily trading. Finally, the Sharpe ratio associated with the FC strategy oftentakes the highest value. This means that, when the returns of the strategies are adjusted bytheir riskiness, the FC strategy outperforms the others. This is probably due to the fact thatthe FVECM is able to provide good forecasts of the range, and therefore more precise timingfor investments.
5 Conclusion
The main contribution of this paper is to show that high and low prices of equity shares arepartially predictable and that future extreme prices can be forecast simply by using past highand low prices that are readily available. Apparently, their predictability is at odds with thedifficulty of forecasting asset returns when prices are taken at a fixed point in time (at closing,say) and with a long tradition of empirical work (e.g. Fama (1970 and 1991)) supporting theefficient market hypothesis.
We propose to model high and low prices using a simple implementation of a fractional vectorautoregressive model with error correction (FVECM). This modeling strategy is consistent withtwo main stylized patterns documented in this paper: first, high and low prices are cointegrated,i.e. they may temporarily diverge but they have an embedded convergent path in the long run.Second, the difference between them, i.e. the range, displays a long persistence that can be wellcaptured by the fractional autoregressive technique.
The analysis of some simple trading strategies shows that the use of predicted high andlow prices as entry and exit signals improves the investment performance. More specifically,we find that out-of-sample trading strategies based on FVECM model forecasts outperform any
13
reasonable benchmark model, even on a risk-adjusted basis.Future research might extend our work in many respects. An interesting question to address
is how good predictions of high and low prices can enhance risk analysis and management.
14
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0.9
645
0.9
619
0.3
197
0.6
862
-1.2
991
-1.6
444
0.2
269
0.2
252
0.0
000
0.7
260
0.3
328
0.0
532
0.5
480
0.1
356
GE
1.0
880
0.9
651
0.4
989
0.6
104
-1.2
991
-1.6
439
0.5
884
0.5
573
0.0
000
0.3
391
0.3
984
0.0
195
0.3
375
0.3
933
HD
0.9
284
1.0
163
0.2
995
0.6
913
-1.2
991
-1.6
441
0.8
446
0.8
474
0.0
000
0.3
364
0.1
888
0.0
169
0.1
114
0.3
143
HP
Q0.9
452
0.9
877
0.0
243
0.5
963
-1.2
991
-1.6
440
0.5
117
0.4
852
0.0
000
0.2
433
0.2
144
0.0
324
0.2
017
0.0
732
IB
M1.0
808
1.0
018
2.6
934
0.6
623
-1.2
991
-1.6
440
0.8
250
0.7
689
0.0
000
0.7
496
0.3
154
0.0
150
0.5
617
0.3
417
IN
TC
1.0
784
1.0
290
0.2
405
0.6
488
-1.2
991
-1.6
460
0.7
680
0.7
687
0.0
000
0.6
995
0.7
717
0.0
334
0.6
168
0.6
883
JN
J0.9
426
0.9
450
0.3
649
0.5
684
-1.2
991
-1.6
406
0.3
885
0.3
074
0.0
000
0.7
268
0.4
298
0.0
402
0.8
001
0.4
969
JP
M1.0
021
0.8
836
4.0
912
0.5
837
-1.2
991
-1.6
374
0.0
226
0.0
068
0.0
000
0.1
176
0.2
276
0.0
402
0.1
117
0.2
051
KF
T0.8
719
0.9
699
0.3
984
0.5
472
-1.2
991
-1.6
437
0.6
771
0.6
770
0.0
000
0.1
382
0.7
410
0.0
158
0.3
522
0.9
141
KO
1.0
685
1.0
098
0.0
809
0.6
524
-1.2
991
-1.6
422
0.9
368
0.9
242
0.0
000
0.3
775
0.1
756
0.0
177
0.3
055
0.1
499
MC
D0.9
238
0.9
946
0.1
789
0.5
451
-1.2
991
-1.6
435
0.5
975
0.5
990
0.0
000
0.3
930
0.1
961
0.0
108
0.1
248
0.6
076
MM
M0.8
719
0.9
699
0.3
984
0.5
472
-1.2
991
-1.6
437
0.2
188
0.1
782
0.0
000
0.2
930
0.1
466
0.0
143
0.2
640
0.1
362
MR
K1.0
639
0.9
716
1.2
338
0.5
397
-1.2
991
-1.6
428
0.2
260
0.1
866
0.0
000
0.5
058
0.9
536
0.0
164
0.4
936
0.2
856
MS
FT
1.0
163
0.9
729
1.5
089
0.5
581
-1.2
991
-1.6
432
0.1
189
0.1
121
0.0
000
0.1
844
0.2
010
0.0
436
0.1
800
0.1
962
PF
E0.9
626
0.9
120
0.0
034
0.5
221
-1.2
991
-1.6
448
0.3
415
0.3
029
0.0
000
0.2
156
0.1
942
0.0
141
0.0
961
0.1
937
PG
0.9
439
1.0
036
5.1
116
0.4
385
-1.2
991
-1.6
363
0.3
527
0.2
142
0.0
000
0.2
087
0.2
184
0.0
057
0.7
931
0.1
609
T1.0
061
0.9
731
4.4
517
0.6
318
-1.2
991
-1.6
390
0.5
508
0.4
881
0.0
000
0.3
233
0.3
027
0.0
128
0.2
979
0.2
811
TR
V0.8
134
0.8
893
0.1
183
0.7
296
-1.2
991
-1.6
233
0.3
598
0.3
376
0.0
000
0.2
446
0.1
160
0.1
137
0.2
072
0.1
035
UT
X0.9
708
0.9
769
0.2
015
0.6
304
-1.2
991
-1.6
433
0.3
999
0.3
807
0.0
000
0.5
784
0.4
849
0.0
477
0.5
443
0.2
838
VZ
0.9
093
0.8
937
0.3
750
0.6
228
-1.2
991
-1.6
430
0.2
418
0.1
657
0.0
000
0.7
232
0.1
651
0.0
118
0.3
188
0.1
189
WM
T0.8
327
0.8
767
1.2
432
0.5
688
-1.2
991
-1.6
401
0.7
634
0.7
711
0.0
000
0.0
895
0.0
684
0.0
197
0.0
888
0.0
676
XO
M0.8
810
0.8
968
0.2
200
0.5
532
-1.2
991
-1.6
353
0.3
639
0.3
612
0.0
000
0.5
522
0.6
749
0.0
473
0.5
922
0.4
737
Table
1:
Long
mem
ory
and
fract
ional
coin
tegra
tion
esti
mati
on.
Table
report
sth
elo
ng
mem
ory
esti
mate
sof
dof
pH
and
pL
base
don
the
exact
loca
lW
hit
tle
esti
mato
rof
Phillips
and
Shim
ots
u(2
005).
The
T0
isth
ete
stst
ati
stic
for
the
equality
of
the
inte
gra
tion
ord
eras
inN
iels
enand
Shim
ost
u(2
007).
L(0
)and
L(1
)is
the
valu
eof
loss
funct
ion
of
Nie
lsen
and
Shim
ost
u(2
007),
evalu
ate
din
corr
esponden
ceof
aco
inte
gra
tion
rank
equal
to0
and
1,
resp
ecti
vel
y.A
DF
H,
AD
FL
and
AD
FR
are
the
p-v
alu
esof
the
augm
ente
dD
ickey
-Fuller
test
of
unit
root
for
pH
,p
Land
pR.
Table
als
ore
port
sth
ep-v
alu
eof
the
Bre
itung
and
Hass
ler
(2002)
test
,B
H,fo
runit
root
again
stfr
act
ionalalt
ernati
ves
,fo
rp
H t,p
L tand
Rt.
The
last
two
colu
mns
report
sth
eB
reit
ung
and
Hass
ler
(2002)
test
for
the
null
hypoth
esis
that
Δp
H tand
Δp
L tare
I(0),
again
stfr
act
ionalalt
ernati
ves
.
20
01−11 01−12 01−0136
37
38
39
40
41
42
43
44Japanese CandleStick and High−Low Bands
|open−close|open<closeopen>close
pHFC
pLFC
(a) FC bands
01−11 01−12 01−0136
37
38
39
40
41
42
43
44Japanese CandleStick and High−Low Bands
|open−close|open<closeopen>close
pHMA
5
pLMA
5
(b) MA5 bands
Figure 2: Japanese CandleStick with predicted high-low bands. Panel a), the red lines are the
high-low band based on model (10). Panel b) the red lines are the high-low bands based on the
5 days moving average. The sample covers the period from November 1, 2010 to December 31,
2010.
21
Januar
yMa
rchMa
yJul
ySe
ptemb
erNo
vember
024681012Pre
dicted
Range
for IB
M from
FVEC
M
(a)
FV
EC
M
Januar
yMa
rchMa
yJul
ySe
petem
berNo
vember
024681012Pre
dicted
Range
for IB
M from
RW
(b)
RW
Januar
yMa
rchMa
yJul
ySe
petem
berNo
vember
024681012Pre
dicted
Range
for IB
M from
MA5
(c)
MA
5
Januar
yMa
rchMa
yJul
ySe
ptemb
erNo
vember
024681012Pre
dicted
Range
for IB
M from
MA22
(d)
MA
22
Fig
ure
3:
Fore
cast
sofdaily
range
base
don
diff
eren
tm
odel
s.
22
bα
Hα
Lμ
γ11
γ12
γ21
γ22
R2 H
R2 L
d=
1
AA
0.3
802
-0.7
876
1.9
877
0.0
291
0.1
187
0.8
603
0.3
370
1.3
752
0.0
782
0.0
590
0.0
795
AX
P0.3
502
-0.7
125
1.8
281
0.0
393
0.2
689
0.1
149
-0.0
569
0.4
921
0.0
298
0.1
560
0.5
162
BA
0.3
375
-1.0
255
2.4
771
0.0
306
0.2
686
-0.8
925
0.0
422
1.4
337
0.0
577
0.0
873
0.3
629
BA
C0.3
844
0.2
369
2.2
214
0.0
372
-0.2
898
-0.5
099
0.6
056
1.1
072
0.0
330
0.1
097
0.0
852
CA
T0.2
697
-2.3
315
2.4
985
0.0
467
1.2
326
-0.5
665
-0.9
508
1.1
358
0.0
547
0.0
777
0.1
407
CS
CO
0.4
275
-0.6
787
1.4
959
0.0
229
0.1
058
-0.3
997
0.2
773
0.7
573
0.0
612
0.0
662
0.0
905
CV
X0.3
575
-0.5
380
1.9
635
0.0
469
0.0
715
-0.4
240
0.1
927
0.9
602
0.0
382
0.0
829
0.8
450
DD
0.3
777
-0.8
042
1.8
971
0.0
268
-0.0
255
-0.6
022
0.2
900
1.1
052
0.0
832
0.0
772
0.2
250
DIS
0.3
063
-1.5
021
2.1
362
0.0
354
1.0
623
-0.1
047
-0.8
818
0.7
130
0.0
212
0.1
153
0.0
058
GE
0.3
147
-0.8
360
2.2
335
0.0
266
0.0
995
-0.6
979
0.2
625
1.3
624
0.0
721
0.0
842
0.0
516
HD
0.2
948
-1.1
819
2.9
520
0.0
281
0.7
487
-0.6
773
-0.4
761
03550
0.0
242
0.1
580
0.0
682
HP
Q0.5
045
-0.5
667
1.1
586
0.0
245
0.0
301
-0.0
405
0.1
366
0.4
246
0.0
579
0.0
899
0.2
885
IB
M0.2
716
-1.0
091
3.6
272
0.0
375
0.2
703
-1.2
317
0.0
306
2.0
732
0.0
420
0.1
185
0.2
019
IN
TC
0.3
111
-0.7
790
3.3
368
0.0
199
-0.0
398
-1.5
638
0.3
408
2.0
540
0.0
498
0.0
838
0.0
193
JN
J0.3
511
-0.4
001
2.1
323
0.0
187
-0.1
219
-0.5
973
0.2
461
1.0
202
0.0
265
0.0
945
0.9
027
JP
M0.4
055
0.6
632
2.3
961
0.0
365
-0.9
959
-1.0
623
1.1
665
1.6
600
0.0
404
0.1
285
0.3
737
KF
T0.3
837
-1.1
606
2.1
448
0.0
190
0.6
585
-0.5
196
-0.4
301
1.0
009
0.0
433
0.1
368
0.8
407
KO
0.4
179
-0.7
837
1.2
345
0.0
187
0.1
014
0.0
076
0.0
849
0.4
602
0.0
657
0.0
921
0.4
340
MC
D0.2
533
-1.5
769
4.2
245
0.0
238
0.5
656
-1.9
158
-0.4
243
2.3
400
0.0
404
0.1
090
0.7
580
MM
M0.3
837
-1.1
606
2.1
448
0.0
190
0.6
585
-0.5
196
-0.4
301
1.0
009
0.0
433
0.1
368
0.1
370
MR
K0.3
772
-0.9
899
1.9
819
0.0
236
0.2
362
-0.6
770
-0.0
323
1.0
499
0.0
708
0.0
784
0.2
805
MS
FT
0.2
948
-2.3
810
1.9
808
0.0
230
1.3
380
-0.3
381
-1.2
334
0.7
385
0.0
464
0.0
817
0.2
973
PF
E0.5
044
-0.6
663
1.1
935
0.0
197
0.1
622
-0.2
072
0.0
241
0.4
410
0.0
726
0.0
796
0.0
810
PG
0.5
389
-0.1
512
1.8
463
0.0
179
-0.0
526
-0.3
057
0.0
960
0.4
942
0.0
431
0.3
229
0.9
057
T0.2
686
-1.4
082
3.4
427
0.0
420
0.1
897
-1.8
229
-0.0
263
2.2
960
0.0
738
0.0
783
0.3
577
TR
V0.2
631
-1.7
507
1.7
828
0.0
475
0.6
894
-0.0
560
-0.5
969
0.4
932
0.0
567
0.0
876
0.6
518
UT
X0.3
402
-0.6
000
2.3
287
0.0
318
0.1
768
-0.2
775
0.0
241
0.8
860
0.0
257
0.1
457
0.1
235
VZ
0.3
611
-0.3
482
2.4
522
0.0
210
-0.0
092
-0.6
247
0.2
592
1.1
408
0.0
324
0.1
306
0.6
763
WM
T0.4
395
-0.7
569
1.1
748
0.0
167
0.4
527
0.2
228
-0.2
677
0.1
232
0.0
296
0.1
328
0.9
219
XO
M0.4
183
-0.0
364
1.6
712
0.0
309
-0.6
596
-0.6
936
0.6
496
0.9
401
0.0
471
0.0
576
0.3
069
Table
2:
FV
EC
Mes
tim
ati
on.
Bold
mea
ns
signifi
cance
at
5%
.
23
pH t
pL t
MS
EM
AE
ME
SM
AE
RW
MA
5M
A22
RW
MA
5M
A22
RW
MA
5M
A22
RW
MA
5M
A22
AX
P0.0
089
0.0
000
0.0
000
0.0
076
0.0
000
0.0
000
0.0
042
0.0
000
0.0
000
0.1
359
0.0
000
0.0
000
BA
0.0
111
0.0
000
0.0
000
0.3
395
0.0
000
0.0
000
0.0
021
0.0
000
0.0
000
0.0
442
0.0
000
0.0
000
BA
C0.3
427
0.0
000
0.0
000
0.7
831
0.0
000
0.0
000
0.6
205
0.0
000
0.0
000
0.6
517
0.0
000
0.0
000
CA
T0.0
032
0.0
000
0.0
000
0.0
442
0.0
000
0.0
000
0.0
022
0.0
000
0.0
000
0.0
015
0.0
000
0.0
000
CV
X0.1
224
0.0
000
0.0
000
0.9
611
0.0
000
0.0
000
0.0
012
0.0
000
0.0
000
0.0
077
0.0
000
0.0
000
DD
0.0
041
0.0
000
0.0
000
0.0
858
0.0
000
0.0
000
0.0
025
0.0
000
0.0
000
0.0
456
0.0
000
0.0
000
GE
0.0
695
0.0
000
0.0
000
0.6
094
0.0
000
0.0
000
0.7
163
0.0
000
0.0
000
0.4
283
0.0
000
0.0
000
HD
0.2
005
0.0
000
0.0
000
0.7
307
0.0
000
0.0
000
0.1
004
0.0
000
0.0
000
0.4
059
0.0
000
0.0
000
HP
Q0.0
009
0.0
000
0.0
000
0.0
028
0.0
000
0.0
000
0.0
006
0.0
000
0.0
000
0.0
305
0.0
000
0.0
000
IB
M0.0
146
0.0
000
0.0
000
0.0
042
0.0
000
0.0
000
0.0
000
0.0
000
0.0
000
0.0
000
0.0
000
0.0
000
JN
J0.0
051
0.0
000
0.0
000
0.0
031
0.0
000
0.0
000
0.0
003
0.0
000
0.0
000
0.0
045
0.0
000
0.0
000
JP
M0.2
140
0.0
000
0.0
000
0.1
722
0.0
000
0.0
000
0.0
372
0.0
000
0.0
000
0.1
714
0.0
000
0.0
000
KF
T0.0
198
0.0
000
0.0
000
0.2
294
0.0
000
0.0
000
0.0
095
0.0
000
0.0
000
0.1
471
0.0
000
0.0
000
MC
D0.4
937
0.0
000
0.0
000
0.5
012
0.0
000
0.0
000
0.0
455
0.0
000
0.0
000
0.1
225
0.0
000
0.0
000
PF
E0.0
141
0.0
000
0.0
000
0.0
102
0.0
000
0.0
000
0.0
149
0.0
000
0.0
000
0.0
577
0.0
000
0.0
000
PG
0.3
179
0.0
000
0.0
000
0.5
565
0.0
000
0.0
000
0.3
134
0.0
000
0.0
000
0.7
674
0.0
000
0.0
000
T0.0
017
0.0
000
0.0
000
0.0
005
0.0
000
0.0
000
0.0
160
0.0
000
0.0
000
0.2
384
0.0
000
0.0
000
VZ
0.1
094
0.0
000
0.0
000
0.0
822
0.0
000
0.0
000
0.2
841
0.0
000
0.0
000
0.8
604
0.0
000
0.0
000
WM
T0.3
155
0.0
000
0.0
000
0.3
800
0.0
000
0.0
000
0.0
400
0.0
000
0.0
000
0.0
624
0.0
000
0.0
000
XO
M0.1
278
0.0
000
0.0
000
0.4
371
0.0
000
0.0
000
0.0
033
0.0
000
0.0
000
0.0
043
0.0
000
0.0
000
Table
3:
Die
bold
Mari
ano
test
for
out-
of-sa
mple
fore
cast
:ta
ble
report
sth
ep-v
alu
eofth
eD
iebold
-Mari
ano
test
base
don
the
mea
n-s
quare
der
ror,
ME
S,and
on
the
mea
n-a
bso
lute
erro
r,M
AE
.T
he
fore
cast
per
iod
incl
udes
the
last
yea
roftr
ansa
ctio
ns.
24
Str
ate
gy
Per
fom
ance
s
Tre
nd-F
ollow
ing
Contr
ari
an
δ=
0.2
5δ
=0.5
δ=
0.2
5δ
=0.5
FC
RW
MA
5M
A22
FC
RW
MA
5M
A22
FC
RW
MA
5M
A22
FC
RW
MA
5M
A22
AX
P25131
16588
17674
18503
17923
12414
15299
21831
15248
22947
21737
21248
19080
27421
22381
17224
BA
21226
19832
20419
19640
24645
18318
19458
19030
18534
19807
19378
20148
15247
20610
19639
20535
BA
C14049
13672
10429
24399
44110
15439
7462
31268
25074
25887
34157
15891
5880
17548
40545
11860
CA
T22955
20843
21467
18215
15541
23830
28227
15391
16840
18540
18273
21752
23311
15337
13106
25040
CV
X19395
18710
21198
18612
15705
19643
24690
18091
20387
21052
18726
21374
24470
19497
15650
21559
DD
17100
18106
20874
20320
18250
18158
25736
23411
22736
21592
18920
19543
20736
20664
14794
16589
GE
18010
21738
17975
20522
20217
23109
15309
22454
21244
17758
21691
19350
17639
15427
23566
17416
HD
14890
15643
19447
18480
21882
18362
25504
21302
26321
25120
20304
21465
17417
20479
14939
18255
HP
Q21511
19293
20660
18471
21941
19839
21858
16823
18348
20416
19137
21487
17535
19333
17711
23278
IB
M21316
18705
18596
19086
21316
18705
18596
19086
18597
21214
21372
20849
19901
22475
22487
19146
JN
J17094
17339
18506
19346
19378
17857
20782
18470
23268
22905
21479
20577
20260
21938
18797
21278
JP
M19921
21708
21107
21474
10448
10405
23608
22750
19067
17633
18454
18210
31943
31478
14993
16698
KF
T21035
21168
18663
19253
14538
19193
16864
15867
18820
18697
21242
20712
26583
20303
23136
24705
MC
D19460
18583
20061
18597
15650
18297
14424
19379
20422
21357
19828
21410
24973
21317
26891
20206
PF
E19563
19134
20492
19309
22410
17043
21907
18161
20175
20560
19346
20569
17227
22676
17576
21549
PG
19809
18606
19826
20003
21055
21417
20475
23351
20043
21319
20037
19901
18560
18259
19064
16933
T19857
18122
17307
19198
19029
15849
14312
19530
19842
21769
22860
20750
20214
24236
26879
20055
VZ
19806
19125
19277
19521
18869
17834
18982
21297
19998
20674
20501
20407
20583
21664
20425
21335
WM
T20832
21853
18713
18719
21603
20154
19523
18363
19038
18173
21207
21239
18074
19414
19891
18454
XO
M19373
18018
20499
18900
16942
17960
17787
15145
20405
21955
19407
21062
22877
21490
21642
25861
Table
4:
Sto
p-loss
and
Conta
rian
Str
ate
gy
per
form
ance
sbase
don
diff
eren
tH
-Lbands.
FC
refe
rsto
the
stra
tegy
base
don
the
pre
dic
ted
hig
h-low
bands
from
model
(10).
RW
refe
rsto
the
stra
tegy
base
don
the
pre
dic
ted
hig
h-low
bands
from
ara
ndom
walk
model
.M
A5
and
MA
22
refe
rsto
the
stra
tegy
base
don
the
pre
dic
ted
hig
h-low
bands
from
am
ovin
gaver
age
model
ofth
ela
st5
and
22
days,
resp
ecti
vel
y.T
he
init
ialm
onet
ary
am
ount
is20000
dollars
.
25
Payoff
Num
ber
ofTra
nsa
cti
ons
Payoff
Vari
ance
Sharp
eR
ati
o
FC
RW
MA
5M
A22
B&
HF
CR
WM
A5
MA
22
FC
RW
MA
5M
A22
B&
HF
CR
WM
A5
MA
22
B&
H
AX
P17780
15819
19214
19331
42408
41
61
53
46
2.3
969
2.1
412
1.9
014
2.6
758
104.1
2–
––
–8.2
698
BA
23240
21797
22891
23499
23776
48
66
52
48
1.1
327
1.2
431
1.3
403
1.3
340
21.5
38
12.0
54
7.7
032
10.2
57
12.0
31
3.7
596
BA
C15139
17081
12649
12912
21015
36
55
49
39
10.6
00
3.3
298
6.3
379
3.4
755
75.3
67
––
––
–
CA
T19281
18857
20792
20158
24343
43
65
49
41
1.8
900
2.1
414
1.8
975
1.9
650
26.0
83
––
2.6
885
0.7
994
4.2
094
CV
X20082
19441
19446
19322
20207
39
52
40
38
0.3
049
0.3
441
0.2
215
0.2
622
10.4
81
0.7
207
––
–0.9
740
DD
17847
15881
17101
19177
25828
43
62
50
43
0.8
208
0.6
618
0.8
267
1.1
014
31.5
42
––
––
4.8
798
GE
23825
28488
19198
22227
17625
48
62
50
51
2.1
932
4.3
626
2.0
740
3.6
149
23.1
25
10.4
06
15.2
11
–4.8
961
–
HD
24779
21998
24354
24301
24141
42
54
51
43
0.6
102
0.9
362
0.8
297
0.7
642
18.2
13
23.9
47
8.2
744
18.9
61
19.2
71
3.9
09
HP
Q19490
19273
18855
19104
28131
44
61
53
49
0.7
340
0.5
161
0.6
358
0.5
462
18.2
74
––
––
7.4
841
IBM
20195
20591
19978
19406
30263
47
65
53
43
0.4
362
0.5
118
0.4
672
0.5
858
15.5
95
4.0
053
3.2
041
––
10.2
48
JN
J20805
20955
20668
20132
21329
37
56
40
33
0.1
472
0.2
202
0.1
974
0.1
474
4.1
811
8.2
920
8.2
037
6.1
025
1.4
464
3.0
183
JP
M26914
23154
26441
27094
27111
35
59
52
38
1.9
902
3.3
331
1.7
588
2.5
489
80.7
32
16.9
82
9.0
347
18.3
34
15.1
87
5.2
394
KFT
19480
19495
18969
19568
19905
44
68
51
45
0.3
281
0.4
180
0.4
070
0.3
429
9.3
886
––
––
–
MC
D20763
20633
20418
21361
19717
44
69
51
45
0.3
839
0.4
088
0.3
934
0.3
898
6.3
828
5.0
193
4.0
59
2.7
998
8.7
672
–
PFE
19399
21330
20532
20106
19761
39
62
44
41
0.7
179
0.8
730
0.8
422
0.7
808
11.0
10
–5.7
428
2.5
382
0.6
980
–
PG
20461
19486
21021
20003
19467
42
62
48
39
0.2
706
0.4
075
0.2
840
0.2
902
6.8
057
1.5
370
1.0
763
1.0
270
1.3
817
–
T20758
18868
20217
21736
19480
39
62
50
42
0.4
013
0.4
452
0.3
493
0.4
434
8.7
918
4.9
675
1.1
209
––
–
VZ
21666
21070
19020
22260
19668
46
64
49
50
0.7
179
0.8
200
0.5
025
0.8
101
7.9
600
7.9
862
4.9
179
–10.2
46
–
WM
T20743
20076
20574
20747
18708
37
65
45
41
0.1
726
0.3
474
0.1
955
0.2
444
6.0
072
7.3
423
0.6
598
5.3
207
6.1
568
–
XO
M19381
19859
19114
19135
16770
38
59
42
44
0.2
554
0.4
162
0.3
104
0.3
344
8.2
115
––
––
–
Table
5:
Str
ate
gy
per
form
ance
sbase
don
diff
eren
tdaily
range
model
s.F
Cre
fers
toth
est
rate
gy
base
don
the
pre
dic
ted
range
from
model
(10).
RW
refe
rsto
the
stra
tegy
base
don
the
pre
dic
ted
range
from
ara
ndom
walk
model
.M
A5
and
MA
22
refe
rsto
the
stra
tegy
base
don
the
pre
dic
ted
range
from
am
ovin
gaver
age
model
of
the
last
5and
22
days,
resp
ecti
vel
y.B
&H
isth
epayoff
of
ast
rate
gy
base
don
buy
at
the
init
ialdate
and
sell
at
the
finaldate
.T
he
init
ialm
onet
ary
am
ount
is20000
dollars
.T
he
vari
ance
ofth
eport
folio
incr
emen
tsis
calc
ula
ted
as
var(
ΔA
t/100).
The
Sharp
eR
ati
ois
calc
ula
ted
as
SR
=μ σ·100,w
her
eμ
=m
ean(Δ
At/
At−
1)
and
σ=
std(Δ
At/
At−
1).
The
Sharp
era
tio
isonly
report
edfo
rposi
tive
valu
esofμ.
Swiss National Bank Working Papers published since 2004: 2004-1 Samuel Reynard: Financial Market Participation and the Apparent Instability of
Money Demand 2004-2 Urs W. Birchler and Diana Hancock: What Does the Yield on Subordinated Bank Debt Measure? 2005-1 Hasan Bakhshi, Hashmat Khan and Barbara Rudolf: The Phillips curve under state-dependent pricing 2005-2 Andreas M. Fischer: On the Inadequacy of Newswire Reports for Empirical Research on Foreign Exchange Interventions 2006-1 Andreas M. Fischer: Measuring Income Elasticity for Swiss Money Demand: What do the Cantons say about Financial Innovation? 2006-2 Charlotte Christiansen and Angelo Ranaldo: Realized Bond-Stock Correlation:
Macroeconomic Announcement Effects 2006-3 Martin Brown and Christian Zehnder: Credit Reporting, Relationship Banking, and Loan Repayment 2006-4 Hansjörg Lehmann and Michael Manz: The Exposure of Swiss Banks to
Macroeconomic Shocks – an Empirical Investigation 2006-5 Katrin Assenmacher-Wesche and Stefan Gerlach: Money Growth, Output Gaps and
Inflation at Low and High Frequency: Spectral Estimates for Switzerland 2006-6 Marlene Amstad and Andreas M. Fischer: Time-Varying Pass-Through from Import
Prices to Consumer Prices: Evidence from an Event Study with Real-Time Data 2006-7 Samuel Reynard: Money and the Great Disinflation 2006-8 Urs W. Birchler and Matteo Facchinetti: Can bank supervisors rely on market data?
A critical assessment from a Swiss perspective 2006-9 Petra Gerlach-Kristen: A Two-Pillar Phillips Curve for Switzerland 2006-10 Kevin J. Fox and Mathias Zurlinden: On Understanding Sources of Growth and
Output Gaps for Switzerland 2006-11 Angelo Ranaldo: Intraday Market Dynamics Around Public Information Arrivals 2007-1 Andreas M. Fischer, Gulzina Isakova and Ulan Termechikov: Do FX traders in
Bishkek have similar perceptions to their London colleagues? Survey evidence of market practitioners’ views
2007-2 Ibrahim Chowdhury and Andreas Schabert: Federal Reserve Policy viewed through a Money Supply Lens
2007-3 Angelo Ranaldo: Segmentation and Time-of-Day Patterns in Foreign Exchange
Markets 2007-4 Jürg M. Blum: Why ‘Basel II’ May Need a Leverage Ratio Restriction 2007-5 Samuel Reynard: Maintaining Low Inflation: Money, Interest Rates, and Policy
Stance 2007-6 Rina Rosenblatt-Wisch: Loss Aversion in Aggregate Macroeconomic Time Series 2007-7 Martin Brown, Maria Rueda Maurer, Tamara Pak and Nurlanbek Tynaev: Banking
Sector Reform and Interest Rates in Transition Economies: Bank-Level Evidence from Kyrgyzstan
2007-8 Hans-Jürg Büttler: An Orthogonal Polynomial Approach to Estimate the Term
Structure of Interest Rates 2007-9 Raphael Auer: The Colonial Origins Of Comparative Development: Comment.
A Solution to the Settler Mortality Debate
2007-10 Franziska Bignasca and Enzo Rossi: Applying the Hirose-Kamada filter to Swiss data: Output gap and exchange rate pass-through estimates
2007-11 Angelo Ranaldo and Enzo Rossi: The reaction of asset markets to Swiss National Bank communication
2007-12 Lukas Burkhard and Andreas M. Fischer: Communicating Policy Options at the Zero
Bound 2007-13 Katrin Assenmacher-Wesche, Stefan Gerlach, and Toshitaka Sekine: Monetary
Factors and Inflation in Japan 2007-14 Jean-Marc Natal and Nicolas Stoffels: Globalization, markups and the natural rate
of interest 2007-15 Martin Brown, Tullio Jappelli and Marco Pagano: Information Sharing and Credit:
Firm-Level Evidence from Transition Countries 2007-16 Andreas M. Fischer, Matthias Lutz and Manuel Wälti: Who Prices Locally? Survey
Evidence of Swiss Exporters 2007-17 Angelo Ranaldo and Paul Söderlind: Safe Haven Currencies
2008-1 Martin Brown and Christian Zehnder: The Emergence of Information Sharing in Credit Markets
2008-2 Yvan Lengwiler and Carlos Lenz: Intelligible Factors for the Yield Curve 2008-3 Katrin Assenmacher-Wesche and M. Hashem Pesaran: Forecasting the Swiss
Economy Using VECX* Models: An Exercise in Forecast Combination Across Models and Observation Windows
2008-4 Maria Clara Rueda Maurer: Foreign bank entry, institutional development and
credit access: firm-level evidence from 22 transition countries 2008-5 Marlene Amstad and Andreas M. Fischer: Are Weekly Inflation Forecasts
Informative? 2008-6 Raphael Auer and Thomas Chaney: Cost Pass Through in a Competitive Model of
Pricing-to-Market 2008-7 Martin Brown, Armin Falk and Ernst Fehr: Competition and Relational Contracts:
The Role of Unemployment as a Disciplinary Device 2008-8 Raphael Auer: The Colonial and Geographic Origins of Comparative Development 2008-9 Andreas M. Fischer and Angelo Ranaldo: Does FOMC News Increase Global FX
Trading? 2008-10 Charlotte Christiansen and Angelo Ranaldo: Extreme Coexceedances in New EU
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2008-11 Barbara Rudolf and Mathias Zurlinden: Measuring capital stocks and capital services in Switzerland
2008-12 Philip Sauré: How to Use Industrial Policy to Sustain Trade Agreements 2008-13 Thomas Bolli and Mathias Zurlinden: Measuring growth of labour quality and the
quality-adjusted unemployment rate in Switzerland 2008-14 Samuel Reynard: What Drives the Swiss Franc? 2008-15 Daniel Kaufmann: Price-Setting Behaviour in Switzerland – Evidence from CPI
Micro Data
2008-16 Katrin Assenmacher-Wesche and Stefan Gerlach: Financial Structure and the Impact of Monetary Policy on Asset Prices
2008-17 Ernst Fehr, Martin Brown and Christian Zehnder: On Reputation: A
Microfoundation of Contract Enforcement and Price Rigidity
2008-18 Raphael Auer and Andreas M. Fischer: The Effect of Low-Wage Import Competition on U.S. Inflationary Pressure
2008-19 Christian Beer, Steven Ongena and Marcel Peter: Borrowing in Foreign Currency:
Austrian Households as Carry Traders
2009-1 Thomas Bolli and Mathias Zurlinden: Measurement of labor quality growth caused by unobservable characteristics
2009-2 Martin Brown, Steven Ongena and Pinar Ye,sin: Foreign Currency Borrowing by
Small Firms 2009-3 Matteo Bonato, Massimiliano Caporin and Angelo Ranaldo: Forecasting realized
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Uncertainty 2009-5 Christian Hott: Explaining House Price Fluctuations 2009-6 Sarah M. Lein and Eva Köberl: Capacity Utilisation, Constraints and Price
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Adjustment Decisions
2009-10 Philip Sauré: Bounded Love of Variety and Patterns of Trade 2009-11 Nicole Allenspach: Banking and Transparency: Is More Information
Always Better?
2009-12 Philip Sauré and Hosny Zoabi: Effects of Trade on Female Labor Force Participation 2009-13 Barbara Rudolf and Mathias Zurlinden: Productivity and economic growth in
Switzerland 1991-2005 2009-14 Sébastien Kraenzlin and Martin Schlegel: Bidding Behavior in the SNB's Repo
Auctions 2009-15 Martin Schlegel and Sébastien Kraenzlin: Demand for Reserves and the Central
Bank's Management of Interest Rates 2009-16 Carlos Lenz and Marcel Savioz: Monetary determinants of the Swiss franc
2010-1 Charlotte Christiansen, Angelo Ranaldo and Paul Söderlind: The Time-Varying Systematic Risk of Carry Trade Strategies
2010-2 Daniel Kaufmann: The Timing of Price Changes and the Role of Heterogeneity 2010-3 Loriano Mancini, Angelo Ranaldo and Jan Wrampelmeyer: Liquidity in the Foreign
Exchange Market: Measurement, Commonality, and Risk Premiums 2010-4 Samuel Reynard and Andreas Schabert: Modeling Monetary Policy 2010-5 Pierre Monnin and Terhi Jokipii: The Impact of Banking Sector Stability on the
Real Economy 2010-6 Sébastien Kraenzlin and Thomas Nellen: Daytime is money 2010-7 Philip Sauré: Overreporting Oil Reserves 2010-8 Elizabeth Steiner: Estimating a stock-flow model for the Swiss housing market 2010-9 Martin Brown, Steven Ongena, Alexander Popov, and Pinar Ye,sin: Who Needs
Credit and Who Gets Credit in Eastern Europe? 2010-10 Jean-Pierre Danthine and André Kurmann: The Business Cycle Implications of
Reciprocity in Labor Relations 2010-11 Thomas Nitschka: Momentum in stock market returns: Implications for risk premia
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crisis: funding liquidity constraints and covered interest parity 2010-15 Jean-Marc Natal: Monetary Policy Response to Oil Price Shocks 2010-16 Kathrin Degen and Andreas M. Fischer: Immigration and Swiss House Prices 2010-17 Andreas M. Fischer: Immigration and large banknotes 2010-18 Raphael Auer: Are Imports from Rich Nations Deskilling Emerging Economies?
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risks 2011-4 Francis Breedon and Angelo Ranaldo: Intraday patterns in FX returns and order
flow 2011-5 Basil Guggenheim, Sébastien Kraenzlin and Silvio Schumacher: Exploring an
uncharted market: Evidence on the unsecured Swiss franc money market 2011-6 Pamela Hall: Is there any evidence of a Greenspan put? 2011-7 Daniel Kaufmann and Sarah Lein: Sectoral Inflation Dynamics, Idiosyncratic
Shocks and Monetary Policy 2011-8 Iva Cecchin: Mortgage Rate Pass-Through in Switzerland 2011-9 Raphael A. Auer, Kathrin Degen and Andreas M. Fischer: Low-Wage Import
Competition, Inflationary Pressure, and Industry Dynamics in Europe 2011-10 Raphael A. Auer and Philip Sauré: Spatial Competition in Quality, Demand-Induced
Innovation, and Schumpeterian Growth 2011-11 Massimiliano Caporin , Angelo Ranaldo and Paolo Santucci de Magistris: On the
Predictability of Stock Prices: a Case for High and Low Prices
Swiss National Bank Working Papers are also available at www.snb.ch, section Publications/ResearchSubscriptions or individual issues can be ordered at Swiss National Bank, Fraumünsterstrasse 8, CH-8022 Zurich, fax +41 44 631 81 14, E-mail [email protected]
