Purchasing Power Parity in the Long Run

This paper re-examines the evidence on Purchasing Power Parity (PPP) in the long run. Previous studies have generally been unable to reject the hypothesis that the real exchange rate follows a random walk. If true, this implies that PPP does not hold. In contrast, this paper casts serious doubt on this random walk hypothesis. The results follow from more powerful estimation techniques, applied in a multilateral framework. Deviations from PPP, while substantial in the short run, appear to take about three years to be reduced in half.     

Does the exchange rate follow a random walk? A Monte Carlo study of four tests for a random walk

Several authors have urged that real and nominal exchange rates follow a random walk. Conditions under which the exchange rate follows a random walk are reviewed in this paper. Many of these do not appear to hold. Therefore, the empirical evidence presents a puzzle : some evidence suggets the exchange rate follows a random walk, while other evidence suggests the opposite should be true. This paper attempts to reconcile the evidence. It is argued that the tests for a random walk have low power. Monte Carlo evidence on four tests for a random walk, is presented that suppors this claim.     

Variance ratio tests of the random walk hypothesis for European emerging stock markets

The hypothesis that stock market price indices follow a random walk is tested for five European emerging markets, Greece, Hungary, Poland, Portugal and Turkey, using the multiple variance ratio test. In four of the markets, the random walk hypothesis is rejected because of autocorrelation in returns. For the Istanbul market, which had markedly higher turnover than the other markets in the 1990s, the stock price index follows a random walk. This contrasts with the results of earlier research, carried out for periods of lower turnover, which rejected the random walk hypothesis.     

Investment intensity of currencies and the random walk hypothesis: Cross-currency evidence

This paper studies the cross-currency and temporal variations in the random walk behavior in exchange rates. We characterize currencies with relatively large investment flows as investment intensive and conjecture that the more investment intensive a currency is, the closer its exchange rate adheres to random walk. Using 29 floating bilateral USD exchange rates, we find that the higher the investment intensity, the less likely it is to reject random walk and the smaller the deviation from random walk is. However, the effect of investment intensity is non-monotonic. Application of threshold models shows that after investment intensity reaches the estimated thresholds, the level of investment intensity has no further effect on the deviation from random walk. These findings help reconcile the previous conflicting results on the random walk in exchange rates by focusing on the effect of cross-currency and temporal variations in investment intensity.     

Using Daily High/Low Time to Test for Intraday Random Walk in Two Index Futures Markets

This paper investigates the time of the daily high/low price in the Hang Seng and S&P 500 index futures and uses it to test for deviation from the predictive behavior of an intraday random walk model. Theoretical distributions of the daily high/low time under the random walk model are derived assuming either uniform or time-varying intraday trading speed. We show that under a random walk model, daily high/low time is more likely to occur near market open/close than in the middle of the trading day. Empirical distributions of the daily high/low time are compared with its theoretical distributions to test for the random walk model. It is found that for the intraday movement of the S&P 500 futures, the random walk hypothesis cannot be rejected. However, it is discovered that in the Hong Kong market, daily high/low time tends to appear significantly more often than is predicted by the random walk model in the first 15-minute time interval when the market opens in the morning or in the afternoon. The results remain valid even after we have taken the time-varying trading speed into account. By comparing the price behavior across markets, we can better understand the microstructure of the futures market.     

The Information Content of Cash Flows and the Random Walk: Evidence from the Helsinki Stock Exchange

Using a sample from the Helsinki Stock Exchange, this paper examines whether observed market reactions to unexpected cash flows are sensitive to the random walk assumption of cash flow behaviour. We consider the random walk (with drift) model commonly used in related literature, and we consider cash flow expectations generated with individually estimated parsimonious univariate time series models and an index model. Market reactions to unexpected cash flows are indiscernible under the random walk assumption, while significant market reactions are found when expectations of cash flows are measured with models which better capture their time series properties. Prior studies that rely on the random walk assumption have probably been biased against finding a significant market reaction to cash flow information.     

Unifractality and multifractality in the Italian stock market

Tests for random walk behaviour in the Italian stock market are presented, based on an investigation of the fractal properties of the log return series for the Mibtel index. The random walk hypothesis is evaluated against alternatives accommodating either unifractality or multifractality. Critical values for the test statistics are generated using Monte Carlo simulations of random Gaussian innovations. Evidence is reported of multifractality, and the departure from random walk behaviour is statistically significant on standard criteria. The observed pattern is attributed primarily to fat tails in the return probability distribution, associated with volatility clustering in returns measured over various time scales.     

Deviations from Purchasing Power Parity

This study uses univariate and multivariate unit root tests to analyze the random walk behavior of real exchange rates for the period 1979–1989. The univariate test fails to reject the random walk model, but the multivariate test indicates that part of the real exchange rates is predictable, a result supporting purchasing power parity. Further analysis of the random walk component in real exchange rates shows that it is quite persistent: for all currencies it takes about five to eight years for this shock to diminish to half its size.     

Rule of thumb for the determination of a sufficient risk reserve

Abstract

A particle starts a random walk from the point U on the χaxis. Each step it takes during its random walk along the χaxis is a random variable with mean value λ, standard deviation a and coefficient of skewness γ.     

Are Stock Returns Predictable? A Test Using Markov Chains

This paper uses a Markov chain model to test the random walk hypothesis of stock prices. Given a time series of returns, a Markov chain is defined by letting one state represent high returns and the other represent low returns. The random walk hypothesis restricts the transition probabilities of the Markov chain to be equal irrespective of the prior years. Annual real returns are shown to exhibit significant nonrandom walk behavior in the sense that low (high) returns tend to follow runs of high (low) returns in the postwar period.     

The influence of the forecast horizon on judgemental probability forecasts of exchange rate movements

An experiment is reported which compares directional forecasting performance of experts, novices and simple statistical models over three time horizons on a task involving probabilistic forecasts of exchange rate movements. Probability-judgement accuracy analyses illustrated no clear overall performance differences between experts and novices, but significant differences between the groups on various important components of judgement suggested that the groups obtained their similar overall scores using different cognitive strategies. Striking horizon effects and expertize–horizon interactions were also observed. The subjects performed better than a random walk forecaster, but worse than the random walk with constant drift and first-order autoregressive models. Composite human judgement, however, not only improved on individual judgement but, also, surpassed the simple statistical models in many instances. Possible explanations are offered for these results, suggestions are made for future research, and practical implications are emphasized.     

Structural models of exchange rate determination

This study compares the forecasting accuracy of state space techniques based on the monetary models of exchange rate with univariate and random walk models for four countries. It is found that these structural models outperform ARIMA and random walk models for all four countries. A state space vector that contains variables based on the monetary model easily outperforms random walk as well as ARIMA models for France, Germany, UK, and Japan during the sample period of this study.     

Random walk theory and the weak-form efficiency of the US art auction prices

We perform variance ratio tests based on non-parametric methods to detect the size of the random walk component of the US art auction prices. The past 134 years of the US art prices exhibit large transitory component (72%) and based on this, the random walk hypothesis does not hold. However, possibly due to sparse data before 1935 or due to institutional changes of the art market after World War II, we detect structural breakpoints and find that the random walk hypothesis and the weak-form efficiency of the US art market cannot be rejected at least for the past 64 years.     

Stock market prices do not follow random walks: evidence from a simple specification test

In this article we test the random walk hypothesis for weeklystock market returns by comparing variance estimators derivedfrom data sampled at different frequencies. The random walkmodel is strongly rejected for the entire sample period (1962-1985)and for all subperiods for a variety of aggregate returns indexesand size-sorted portfolios. Although the rejections are duelargely to the behavior of small stocks, they cannot be attributedcompletely to the effects of infrequent trading or time-varyingvolatilities. Moreover, the rejection of the random walk forweekly returns does not support a mean-reverting model of assetprices.     

Efficient exchange rate forecasts: Lagged models better than the random walk

The evidence of Meese amd Rogoff (1983) on the out-of-sample forecasting performance of structural exchange rate models in comparison to the random walk model portrays a disappointing picture of structural models. This paper re-considers the issue for the German mark for an updated period to include a larger set of structural models and lagged adjustment. Besides out-of-sample evidence, in-sample evidence is also examined. We conclude that while some stuctural models dominate the random walk, a lagged adjustment consideration can contribute towards better performance.     

Trends,random walks,and tests of the permanent income hypothesis

Recent studies find that consumption is excessively sensitive to income. These studies assume that income is stationary around a deterministic trend. The data, however, do not reject the hypothesis that disposable personal income is a random walk with drift. If income is indeed a random walk, then the standard testing procedure is greatly biased toward finding excess sensitivity. Moreover, if income follows either a more general non-stationary process or a borderline stationary process, this procedure is also seriously biased.     

TESTS OF RANDOM WALK AND MARKET EFFICIENCY FOR LATIN AMERICAN EMERGING EQUITY MARKETS

Variance-ratio methodology is used to test the hypothesis that Latin American emerging equity market prices follow a random walk. The data are monthly index prices in local currency from December 1975 to March 1991 for Argentina, Brazil, Chile, and Mexico. The variance-ratio tests reject the random walk hypothesis. However, runs tests indicate that Latin American equity markets are weak-form efficient. These empirical findings suggest that domestic investors might not be able to develop trading strategies that would allow them to earn excess returns.     

Exchange Rates and Fundamentals: A General Equilibrium Exploration

Engel and West (2005) show that the observed near random‐walk behavior of nominal exchange rates is an equilibrium outcome of a partial equilibrium asset approach when economic fundamentals follow exogenous first‐order integrated processes and the discount factor approaches one. In this paper, I argue that the unit market discount factor creates a theoretical trade‐off within a two‐country general equilibrium model. The unit discount factor generates near random‐walk nominal exchange rates, but it counterfactually implies perfect consumption risk sharing and flat money demand. Bayesian posterior simulation exercises, based on post‐Bretton Woods data from Canada and the United States, reveal difficulties in reconciling the equilibrium random‐walk proposition within the canonical model; in particular, the market discount factor is identified as being much smaller than one. A relative money demand shock is identified as the main driver of nominal exchange rates.     

A new perspective on post‐earnings‐announcement‐drift: Using a relative drift measure

Prior research finds that there is a delayed reaction to both analyst‐based earnings surprises and random‐walk‐based earnings surprises. Focusing on the market reaction from the post‐announcement window, prior studies show that analyst‐based drift is larger than random walk‐based drift. This finding is counter‐intuitive if we believe large, sophisticated investors tend to trade on analysts’ forecast earnings news and thus react faster and more completely than smaller and less sophisticated investors react to random walk earnings news. In this study, we construct a relative measure of post‐earnings‐announcement drift (PEAD) (i.e., drift as a proportion of total market reaction to earnings news) which we refer to as the ‘drift ratio’, and we provide evidence, consistent with our intuition, that analyst‐based drift ratio is smaller (not greater) than random‐walk‐based drift ratio. We find that this difference is more pronounced in more recent periods and for firms with more sophisticated investors. Our approach to measure the PEAD is more intuitive than that in traditional PEAD literature. Our results thus complement existing research findings by utilizing the drift ratio measure to generate new insights about the drift phenomenon.     

The Nature and Persistence of Initial Public Offering Aftermarket Returns Predictability

This paper examines the predictability of monthly aftermarket returns of initial public offerings during the first six years of trading. Predictability is tested under the null hypothesis of random walk using a Markov chain analysis. The evidence shows that excess returns of IPOs (adjusted for the return on the equally weighted NASDAQ index) demonstrate non-random walk behavior through the first five years of trading and random walk behavior in the sixth year. This is accompanied by predictability of monthly excess returns conditioned on the two previous months' excess returns. A trading strategy is offered to capitalize on the predictability patterns. Implementing the trading strategy is not possible due to institutional barriers, providing additional explanation for why IPOs do not reach their intrinsic values for extended periods of time.