**Introduction**

In testing the weak form version of the Efficient Markets Hypothesis (EMH), much of the empirical research has focused on the random walk hypothesis and on various econometric tests, including the like of variance ratio tests, serial correlation tests, runs test, unit root tests and spectral analysis. Moreover, different factors affecting the EMH have been considered, such as financial crises. However, only a small group of researchers considered the Global Financial Crisis of 2007-2008. This research tries to fill the gap in the existing literature. In particular, the aim is twofold: (I) investigating the *worldwide* effect of the GFC on the weak form market efficiency using the Variance Ratio test and (ii) describing how the tests respond to different data frequency, using weekly and monthly data. Lo & MacKinlay's variance ratio test is used for random walk 1 (RW1), random walk 2 (RW2) and random walk 3 (RW3). Three worldwide indices are examined, such as SPX Index, Stoxx Europe 600 and Stoxx Asia/Pacific, considering the time frame 21/12/2001 to 26/12/2014 and a pre-crisis and a post-crisis subsample.

**Brief Literature Review**

The literature on this topic is so large that a full review is impossible and is not attempted here. However, in a few words, past studies shows mixed results. On one hand, according to Fama's (1970) survey, the vast majority of research studies were unable to reject the efficient market hypothesis for common stocks. Moreover, also Jensen (1978a) and Malkiel (1999) showed supporting evidence of the EMH. On the other hand, other researchers have rejected the random walk hypothesis. Lo & MacKinlay (1988) and Lo and MacKinlay (1999) provide evidence that stock prices do not follow a random walks by using a test based on variance estimator and finding positive serial correlation in stock returns. However, as Leroy (1973) and Lucas (1978) have shown, their results do not necessarily imply that the stock markets are inefficient and therefore predictable. As a stated above, crises have the power of affecting market efficiency. For instance, Lim et al (2008) and Hoque et al (2006) investigate the effects of the 1997 financial crisis on the efficiency of eight Asian stock markets, finding mixed results. However, as far as the GFC is concerned, the literature shows a clear gap and only a small group of researchers investigated this filed. Some [Grantham (2009) & Fox (2009)] claimed that the EMH was responsible for the GFC because of its underestimation of the dangers of asset bubbles, whereas others (Ball (2009) & Malkiel (2011)) believe that it is too exaggerated to blame the EMH for the global meltdown of 2008.

**Methodology**

Although there are different ways to test the random walk hypothesis (RWH), I opted for the Lo & MacKinlay's variance ratio test (Lo & MacKinlay (1988). This test relays on the important property of the RWH, for which the variance of the increments must be a linear function of the time interval. So, the idea of the variance ratio test is to compare the variances of differently aggregated returns, checking whether their ratio is statistically indistinguishable from one. Consider r_{t} = X_{t} - X_{t-1} as the log return of the index at time t (where X_{t} = ln P_{t} is the log price process). Moreover, define

as a q-period aggregated return. The variance ratio test is defined as:

where ρ_{k} denotes the autocorrelation of order k. Note that the variance ratio may be considered as a weighted average of the first (q-1) autocorrelation coefficients with declining weights. In this research, q ranges from 2 to 16.

Under the RW1, the VR (Q) test statistic is asymptotically normal distributed:

and for convenience, the test statistic is scaled to the standard normal as follows.

On the other hand, under RW2 and RW3, returns can reveal conditional heteroskedasticity. Lo and MacKinlay (1988) derive a heteroskedasticity-consistent variance ratio test and under general forms of heteroskedasticity. The following equality holds asymptotically:

In particular, the VR test statistic becomes:

where

is an estimator for the variance of VR and

is a heteroskedasticity consistent estimator of the variance of the autocorrelation coefficients ρ_{k}.

**Data**

To test for random walks in stock market returns, I focus on the 679-week and 157- month time span from 21/12/2001 to 26/12/2014. In particular, I chose both weekly and monthly returns of three worldwide indices, including SPX Index, Stoxx Europe 600 and Stoxx Asia/Pacific 600. Then, I divided the sample in two subsamples from 21/12/2001 to 15/09/2008 and from 16/09/2008 to 26/12/2014 (for convenience, I identify the beginning of the crisis with the bankruptcy declaration of Lehman Brothers, 15 Sep 2008).

**Results**

As far as weekly returns are concerned, table 1 reports the variance ratios and the test statistics for each index, relative to RW1. In particular, the sample rows show the result for the entire sample, while the rows below for the pre-post crisis subsamples. It is clear that the RW1 is never rejected for each index and for each period at 5% level of significance. Moreover, table 2 reports the results for RW2 and RW3, where t-statistics are heteroskedasticity robust. Similarly, also RW2 and RW3 are not rejected for each index and for each period at 5% level of significance.

On the other hand, tables 4.3 and 4.4 report results for monthly data. Apart from isolated cases, RW1, RW2 and RW3 are not rejected for each index and for each period at 5% level of significance.

By and large, the variance ratios decrease with q, as opposed in Lo & MacKinlay (1988) where the variance ratios increase with q. Furthermore, t-statistics seems to be larger for monthly returns compared to the weekly returns.

**Discussion**

The above results confirm that the worldwide stock market weak form efficiency was not affected by the GFC, both for weekly and monthly returns. Hence, neither the EMH is to be blamed for the GFC nor the GFC had a devastating effect on the EMH.

These results are consistent with the previous literature for several *quantitative* and *qualitative* reasons.

Firstly, the indices taken in consideration in this paper are only value-weighted. Lo & MacKinlay (1988) and Campbel, Lo & MacKinlay (1997) state that the rejection of the random walk hypothesis was much weaker (sometimes impossible) for the value-weighted CRSP index compared to equally-weighted.

The main reason is due to the way these kinds of indices are constructed. Indeed, value-weighted indices give more weight to companies with larger capitalization and therefore more frequently traded. Thus, they are not affected by the infrequent or nonsynchronous trading characterizing small stocks, which may induce significant spurious correlation in stock returns, as happens in equal-weighted indices.

Moreover, a plausible qualitative explanation for these results may be found in the Grossman & Stiglitz (1980) argument. Indeed, markets are not efficient *per se,* but become efficient when *investors* exploit market inefficiencies, in order to make extra-profits. In particular, it is worth looking at a particular kind of investors, called hedge funds.

Chordia et al (2014) illustrate that the growth of the hedge fund industry has led to a decline in the anomaly-based profits, making the market more efficient. Hence, it is possible to find plausible explanations for the above results studying the hedge fund industry.

According to Preqin (2014), the hedge fund industry has faced a sharp reshaping from the crisis onwards. In fact, regulation increased and a strong reformulation of out-of-date business practices took place. However, the number of hedge funds sharply increased. In fact, 5165 are the currently active funds launched before or during 2008, against 5882 launched after 2008. Moreover, the industry AUM increased from $2.3 to $2.9 trillion and the industry capital invested by institutions increased from 45% to 63%. Hence, despite of the tighter regulation, the number and the activity of the so-called "smart guys" notably increased and in turn, market efficiency did not suffered all over the world.

However, these empirical results ought to be considered *cum granu salis* for various reasons. Firstly, the techniques adopted here are not highly advanced, as it would have been possible to show the empirical results of the Ljung-Box test for RW3 or of more advanced variance ratio tests, such as Wright (2000) and Whang and Kim (2003).

Moreover, the Lo & MacKinlay (1988) variance ratio test used in this paper does not take in consideration the refinements suggested by Campbel, Lo & MacKinlay (1997), namely using overlapping q-period returns, in order to improve the finite sample properties of the test.

Finally, as in Lim et al (2007), the application of the rolling bicorrelation test statistic could have been another approach (Hinich (1996)). In particular, this approach allows for the detection of nonlinear serial dependencies in time series data and a nonlinearity test would have been better, since it has good sample properties over short horizons of data.

**Conclusions**

This study appears to confirm that the worldwide stock market weak form efficiency was not affected by the GFC, both for weekly and monthly returns.

Even during a period of profound uncertainty and destabilization such as the Global Financial Crisis, market appeared to remain efficient and therefore NOT predictable.

*Keeping in mind all the limitations of this research*, I would conclude that investors should not *just* rely on exploiting market inefficiencies, even during periods of profound turmoil, as the following brief story demonstrates.

"An economist accompanied by a companion strolls down thestreet when they come upon a $100 bill lying on the ground.As the companion reaches down to pick it up, the economistsays: Don't bother - if it were a real $100 bill, someone wouldhave already picked it up."- Lo -

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.