What was the effect of the short selling ban on returns and
volatility of Japanese financial stocks?
Name: Martijn Vink
Student number: 10211063
Field: Finance
Supervisor: P.J.P.M. Versijp
Date: 30-12-2013
Abstract
In October 2008, Japan introduced a short selling ban on all stocks to protect financial stability in the country. This research focuses on two aspects of this stability: returns and volatility. Using OLS-regression and the market model, I find that there is no substantial effect on either the returns of financial or non-financial sectors. The volatility did increase substantially after the financial turmoil in the United States and the introduction of the ban helped to decrease this volatility. However, the positive effect of the ban did not outweigh the negative effect of the crisis at hand.
1. Introduction
The financial crisis of 2008 resulted in an output loss of $6 to $14 trillion so far for the U.S. economy. That amounts to $50,000 to $120,000 for every U.S. household (Lutrell, Atkinson & Rosenblum, 2013). But the United States were not the only country affected by this crisis. Practically the entire world has suffered in one way or another. Things are finally looking better now, but we are far from the point we were.
Financial institutions faced rough times in the 2007-2009 period. Bear Stearns was the first bank to fall in March 2008, which resulted in the acquisition by JP Morgan Chase for a price of 2 dollars a share (the share worth 30 dollars the day before). Lehman Brothers went to bankruptcy six months later on September 15th. That bankruptcy is the biggest bankruptcy we know till date with over 600 billion dollar of assets. The fall of Lehman Brothers affected not only the United States but the entire world as well. Financial firms were in danger; their stock price was dropping quickly and the Security Exchange Commission (SEC) was afraid that speculators would exploit this instability with selling attacks. These short-selling attacks would benefit that particular speculator but would harm the entire market eventually. The SEC introduced a ban on short selling of financial stock in the United States on September 18th to prevent this from happening. A lot of countries followed America with this ban and so did Japan.
This thesis will focus on the ban on short selling in Japan. The reasoning behind Japan is the relative long period (in comparison with for example the U.S.) between the fall of Lehman Brothers and the introduction of the ban. This long period provides an opportunity to better assess the independent effect of the ban which will be discussed later. It will answer the following research question: “What was the effect of the short selling ban on returns and volatility of Japanese financial stocks?”. The answer to this question is relevant because a crisis is not a one-time phenomenon: it is something recurring. The question is not if there will be another crisis, but, when will the next crisis be? The results of this research will make us understand what kind of tool a short selling ban really is. Does it have the effects we expect it to have and how powerful is it?
This research will follow the following structure: first, there will be a literature review where background information and existing literature regarding this subject
will be discussed. The design of the research will be discussed after that, followed by a description about the gathered data. The results will follow after that, to end with the conclusion, discussion and suggestions for further research.
2. Literature review
2.1. How does short selling work?
The short selling of a stock is the process of investor selling a stock that he does not currently own and repurchasing the same stock afterwards. This is all done with a bearish mind: the investor believes the price of the stock will decrease in the time window between initial sell and repurchase. This process can be divided into a number of subsequent steps. First of all, the investor borrows a stock of company C from a brokerage firm, pays a lending fee L and immediately sells the stock for a price of P1. After that, the price of stock changes into P2. The investor decides to buy
back the stock of company C for the new price of P2 and returns the stock to the
brokerage firm. When the initial price P1 is higher than the new price P2, the investor
will make a profit. His profit will be as following: profit = P1 – P2 - L.
It is possible that the lender of the stock is unaware about the fact that his stock is sold by the investor. When company C chooses to pay out dividend D, they will pay this dividend to the person who is the “holder of record” which is the person who the investor sold it to. However, the lender still expects the dividend. Therefore, the investor has to compensate for this “missed dividend” and his profit will eventually be as following: profit = P1 – P2 – L – D.
There are two different ways of selling short: covered short selling, which is the process as described above where the short sell is covered by a borrowed stock, and naked short selling, the process of selling short without a borrowed stock. When the investor is unable to deliver the stock to the buyer of the stock, the result is know as “failure to deliver”. Easily said: covered short selling is selling something you own and naked short selling is selling something you do not have at that particular point of time with the risk of not being able to buy it in time.
Miller (1977) stated that one of the purposes of short selling is counteracting the bidding up to higher prices of risky stocks. This because short selling is only profitable when the stock price declines with a sufficient rate with respect to the possibly paid out dividend. So, an investor is only willing to sell short when he is sure the stock will decrease in price with a significant amount.
Boehmer, Jones & Zhang (2008) found that short sellers are extremely well informed. They have come up with some fascinating conclusions in the research they have done. They found that heavily shorted stocks underperform the market in the next 20 days by a cumulative of about 1,16% (15,6% annualized). This result indicates that, on average, short sellers are important contributors to efficient stock prices. Besides that, Boehmer & Wu (2013) are concluding in their research that the discovery of prices is achieved faster when short sellers are highly active and react quickly.
Another purpose of short selling is given by Woolridge & Dickinson (1994). They state that short selling improves the liquidity of the market. The liquidity of market means the ability of the market assets to be sold without a significant drop in the price.
Short selling is proven to be an effective tool against mismanaging, fraud and other unhealthy firms as well. An example is James Chanos who owns an investment company named “Kynikos” which is Greek for cynic. This hedge fund seeks for “unhealthy” companies and subsequently sell short in those companies in order to make a profit when the stock price goes down.
Besides these more broad and economical purposes of short selling, there are a lot of more personal and financial reasons. One of them is for the pure purpose to make a personal profit. Bearish investors wish to sell short in contrast with bullish long buyers. Another purpose is hedging of your portfolio. Hedging is making an investment that offsets a potential loss. In other words: a hedge is made in order to prevent yourself from the downside of an investment.
2.3. Controversy regarding short selling
The subject of short selling has always been criticized. One of the most heard and simplistic critics about short selling is that investors who sell short are pessimists. People who want to earn money when others lose theirs.
Another critic on short selling focuses on false information. Bad news about a company does almost always result in decreasing stock prices and a negative return. It really doesn’t matter whether this bad news is true or false. Even when the firm corrects the false news and the stock prices are back up where they belong, it is already too late. The short seller made a profit in the hours, minutes or even seconds in which the price was affected by the false bad news.
Naked short selling has always been controversial as they could affect the number of shares outstanding. In the practice of naked short selling, an investor wants to sell someone a stock that the investor does not own. He creates a “phantom share”; a share that does not really exist. This phantom share increases supply and therefore decreases the price. This decrease of price could eventually harm the company.
2.4. Short selling regulations in the history
There have been regulations regarding short selling in the past as well. The SEC introduced the uptick rule in 1938. This rule made sure that an investor could only sell short when the last price of that particular stock was higher than the last different price of the stock. The uptick rule was affective until 2007. The reintroduction of this rule was widely debated in 2009 and a modified rule has been introduced in 2010.
The end of the uptick rule began with the beginning of regulation SHO. This regulation aimed to prevent abusive naked short selling. An investor was not allowed to make a short sale before he owned or at least identified (the “look out”) the stock being sold.
2.5. The link between Lehman Brothers and Japan
The financial crisis of 2008 is considered the worst financial crisis since the depression in the thirties by a lot of economists. There are a lot of factors that have played a role in the development of this crisis but one of the, if not the most important one was the housing market in the United States. Driven by the housing bubble of the beginning of this century, the house prices were increasing and increasing. With the introduction of subprime mortgages and collateral debt obligations (CDO’s) investment banks were able to buy the (risky) mortgage from the mortgage broker with borrowed money and sell it again to investors. It all changed when families with a subprime mortgage were defaulting on their payments. This results in the investment bank receiving fewer payments, which causes the CDO to become less
profitable for the investor. Besides that, defaulting on mortgage payments results in an increasing housing supply, which implies a decreasing price. This decreasing pricing results in a higher default rate and in this way it becomes a vicious circle. The result is that the investment bank has a lot of CDO’s with no demand for it. The problem behind this story is that the bank bought the mortgages with borrowed money and has to repay in somewhere in the future.
Lehman Brothers was one of those banks involved in the subprime mortgage market. The first cracks were visible in August 2007 when the firm closed their biggest subprime lender BNC Mortgage. Lehman Brothers lost 73% of its value in the first half of 2008 alone. Several banks were interested in buying the bank now its value was so drastically decreased. But despite this interest, none of the banks actually did buy the firm. So Richard Fuld, the CEO of Lehman, filed for bankruptcy on September 15. The Dow Jones dropped over 700 points that day resulting in an overall decrease of almost 8% which is still one of the largest decreases known to date.
Japan, as well as practically the entire world, was heavily affected by the bankruptcy of Lehman Brothers. It is said that Japanese banks and insurers had a combined potential loss of 2,4 billion dollars. The Financial Services Authority (FSA) stated that Japanese banks made the most lending to Lehman Brothers but that the profits could offset this loss and their financial system was stable enough to survive this shock. This shock was reflected in the rates of the Nikkei 225, they dropped 4,95% on the day of the fall and the rate of return for the month after the fall was -24,37% (Yahoo! Finance).
2.6. Existing literature
Beber and Pagano (2013) did research on the effects of different mixes of short selling bans on liquidity, price discovery and stock prices. This mix consists out of a number of different parameters. The day the ban was imposed and lifted again was one of these parameters. The number of days the ban was actually effective is the exact difference between those two. Other parameters were: the country in which the ban was imposed, the degree of the ban (financial vs. all stocks) and the stringency of the ban (naked- vs. general short-selling). They found that bans (i) are detrimental for liquidity, especially for stocks with small capitalization and no listed options; (ii) slow
down price discovery, especially in bear markets, and (iii) fail to support prices, except possibly for U.S. financial stocks (Beber & Pagano, 2013).
Saffi and Sigurdsson (2011) did research on a global data set of more than 12600 stocks form 26 countries in the timespan from 2005 to 2008. They focused on how short sale constraints affected stock price efficiency and return distributions. Their findings consist out of two different parts. One of them was that lending supply had a significant impact on the efficiency. The higher the constraint, the lower lending supply and the lower price efficiency. The second finding was that relaxing these constraints did not lead to an increase in price stability or extreme negative returns.
Boehmer, Jones and Zhang (2008) focused their research on the United States where the Security and Exchange Commission (SEC) introduced a ban on most short sales of 797 financial stocks. They found that the market quality of large-cap stock subject to the ban drastically decreased. This decrease is measured by quoted and effective spreads, price impacts and realized spreads. The reason for this decrease of market quality lays in the fact that many traders cannot act as an informal market during the ban. Furthermore, Boehmer et al (2008) discuss whether the SEC should have introduced the ban on short sales or not. They conclude that SEC should not have introduced it but that the abusive short selling could possibly harm the market at that particular point of time.
Jones and Lamont (2002) focus their research on overpricing and market efficiency using new and direct evidence on the cost of shorting. Their data set is quite remarkable because it focuses on the shorting costs of New York Stock Exchange (NYSE) stocks in the period of 1926 to 1933. They find that short selling constraints allows the stock to become overpriced. And although the research was done with an old data set, it seems that the results could be generalized to the present financial markets as well.
Battalio and Schultz (2011) focus their research of the restrictions the SEC introduced in September 2008. They examined how the confusion and regulatory uncertainty affected the equity option markets. They found that the short selling ban had dramatically increased the bid-ask spreads for options on those banned stocks. Furthermore, they find that the price of synthetic options become significantly lower than the actual prices of these options during the ban.
This research will be conducting an event study on what the effect of the naked short selling ban was on the returns and volatility of different financial sectors in Japan. Ideally, the research will be constructed in such a way that there are financial and non-financial sectors (sector difference) and sectors with and without a ban (scope difference). In this way it is possible to draw a good conclusion on what the exact effect of the ban on the financial sector was. Because the FSA introduced the ban on sectors, there is no scope difference but only sector difference (FSA, 2008). The different financial sectors will be: insurance, banking, real estate, securities and the sum of these four together. The four different non-financial sectors will be: construction, food, iron/steel and motor. These sectors are identified by their identification code on the Tokyo Stock Exchange.
There will be two different events in this research. The first is the bankruptcy of Lehman Brothers in the United States on September 15th. Lehman Brothers is till date the biggest bankruptcy in the world with assets worth of over 639 billion dollars. The second event is announced by the Japanese Minister of Finance Shoichi Nakagawa on October 24th. He stated that although Japan’s financial system was relatively stable, they had safety nets such as the ban on naked short selling on all stock that will go into effect on October 30th (FSA, 2008). This ban on naked short selling will be the second event.
By the introduction of these two subsequent events, there will be 3 different periods. These 3 periods will be addressed as follows:
Period Timespan of period Days in period
1 June 14th 2008 – September 14th 2008 93
Bankruptcy September 15th 2008 1
2 September 16th 2008 – October 29th 2008 44
Ban October 30th 2008 1
3 October 31st 2008 – January 31st 2009 93
The timespan of the periods are including the last day; so June 14th 2008 is the first observation day of period 1 and September 14th 2008 is the last. Notice that the event days itself are left out in the estimation period because they could influence the normality of the estimation (MacKinlay, 1997).
This research will consist out of two different parts: the research on the effect the ban had on returns and the effect on the volatility (variance) of the financial sector in Japan. These two different parts have their own hypotheses to test. The hypotheses for the returns-part are as follows:
𝐻𝐻0: 𝐴𝐴𝐴𝐴����� = 𝐴𝐴𝐴𝐴1 ����� 2 𝐻𝐻1: 𝐴𝐴𝐴𝐴����� ≠ 𝐴𝐴𝐴𝐴1 ����� 2 (H1)
𝐻𝐻0: 𝐴𝐴𝐴𝐴����� = 𝐴𝐴𝐴𝐴2 ����� 3 𝐻𝐻1: 𝐴𝐴𝐴𝐴����� ≠ 𝐴𝐴𝐴𝐴2 ����� 3 (H2)
𝐻𝐻0: 𝐴𝐴𝐴𝐴����� = 𝐴𝐴𝐴𝐴1 ����� 3 𝐻𝐻1: 𝐴𝐴𝐴𝐴����� ≠ 𝐴𝐴𝐴𝐴1 ����� 3 (H3)
When put to words, men could say: the null hypothesis states that the mean abnormal return will not change between different periods. These three tests will be done for every sector and will isolate the effect of the ban from the effect the bankruptcy had. The hypotheses for the volatility part will be as follows:
𝐻𝐻0: 𝑠𝑠12= 𝑠𝑠22 𝐻𝐻1: 𝑠𝑠12≠ 𝑠𝑠22 (H4)
𝐻𝐻0: 𝑠𝑠22= 𝑠𝑠32 𝐻𝐻1: 𝑠𝑠22≠ 𝑠𝑠32 (H5)
𝐻𝐻0: 𝑠𝑠12= 𝑠𝑠32 𝐻𝐻1: 𝑠𝑠12≠ 𝑠𝑠32 (H6)
So the null hypothesis states that the volatility will not change between periods. Just as for the returns part, these tests will be performed for every sector as well and will isolate the ban from the bankruptcy.
3.1. Research design for the returns part
To test the hypotheses of the returns part of this research, we will follow the event study as how MacKinlay designed it. MacKinlay (1997) based his work on event studies on the work of Fama, Fisher, Jensen & Roll (1969) and the adjustments Boehmer, Masumeci & Poulsen (1991) made on the work of Fama and others.
First of all, following MacKinlay (1997), the market model will be estimated by performing an Ordinary Least Squares (OLS) regression. This regression will be unbiased, consistent and normally distributed assuming the general conditions of an OLS regression (Stock & Watson, 2012). The market model is given by the formula
Comment [PV1]: coefficients will
be unbiased and consistent,
residuals may be normally
distributed
BTW, you will need to test if these general conditions hold. MARTIJN: How can I test these general conditions?
PV: test for heteroskedasticity using a white test or (easier in Stata) Breusch-Pagan test (estat hettest is the stata command), and for serial correlation using the Breusch-Godfrey test (estat bgodfrey). The other assumptions basically boil down to having a correct
specification, and can only be tested when you have some alternative, which isn’t really applicable here. MV: I only have access to SPSS right now, I cant get access to a computer with any other statistical software because im not enrolled in any statistics courses. Is it really necessary or can I do the same test in SPSS?
𝐴𝐴𝑖𝑖𝑖𝑖= 𝛼𝛼𝑖𝑖+ 𝛽𝛽𝑖𝑖𝑖𝑖𝐴𝐴𝑚𝑚𝑚𝑚𝑖𝑖+ 𝜀𝜀𝑖𝑖𝑖𝑖 (1)
Where Rit, the period t return on sector I, is the dependent variable and Rmkt, the
market return in that period, is the independent variable in the OLS regression. αi, βit and εit are the parameters of the market model. βit or beta is the number that indicates the co-movement from the sector with the market. The market used as benchmark is the Nikkei. The parameters of the market model will be estimated with data 2 years prior to the bankruptcy of Lehman Brothers until the day before the bankruptcy. The parameters will remain constant in the rest of the research. This choice to use the historical alpha and beta and held them constant is made in order to simplify the research.
Secondly, these parameters will be used to calculate the abnormal return ARit of a given sector i in that particular period t by the formula:
𝐴𝐴𝐴𝐴𝑖𝑖𝑖𝑖= 𝐴𝐴𝑖𝑖𝑖𝑖− 𝛼𝛼�𝑖𝑖− 𝛽𝛽̂𝑖𝑖𝑖𝑖𝐴𝐴𝑚𝑚𝑚𝑚𝑖𝑖 (2)
This abnormal return is the difference between the actual return and the expected return. Equation (1) implies that the return is equal to the expected return, equation (2) implies that the abnormal return is indeed the difference between the actual and expected return (Boehmer et al, 1991).
Thirdly, the cumulative abnormal return will be calculated by the following formula:
𝐶𝐶𝐴𝐴𝐴𝐴𝑖𝑖𝑖𝑖= ∑ 𝐴𝐴𝐴𝐴𝑖𝑖𝑖𝑖 (3)
Where CARit iscalculated by summing all the abnormal returns for a given sector and given period. Of course, the cumulative abnormal return does not say a lot by itself because the periods have different lengths.
Therefore, we introduce the mean abnormal return:
𝐴𝐴𝐴𝐴 ����𝑖𝑖𝑖𝑖= 1
𝑛𝑛𝐶𝐶𝐴𝐴𝐴𝐴𝑖𝑖𝑖𝑖= 1
The problem of different period lengths is eliminated with the introduction of this term because this mean abnormal return can be explained as the average of deviations from the return we expected.
Next step is to test whether the mean abnormal return of each sector has changed over the periods by performing a Welch’s t-test. This form of a t-test is useful in a situation where men want to compare two means when population variances are expected to be different (Keller, 2009). The formula of this t-statistic is as follows: 𝑡𝑡 = (𝐴𝐴𝐴𝐴����� − 𝐴𝐴𝐴𝐴1 �����)2 �𝑠𝑠12 𝑛𝑛1+ 𝑠𝑠22 𝑛𝑛2 ~ 𝑡𝑡[𝑑𝑑𝑑𝑑] where: 𝑑𝑑𝑑𝑑 = �𝑠𝑠 12 𝑛𝑛1+ 𝑠𝑠 22 𝑛𝑛2� 2 �𝑠𝑠12 𝑛𝑛1� 2 (𝑛𝑛1− 1) + �𝑠𝑠22 𝑛𝑛2� 2 (𝑛𝑛2− 1)
Finally, with a chosen alpha and the performed t-test, it is possible to decide if the mean abnormal return is changed over the periods. The effect of the bankruptcy of Lehman Brothers and the separate effect of the ban are both visible through the introduction of the three periods.
3.2. Research design for the volatility part
The volatility part of this research is based on the variance of the daily returns of the sectors. The variance (squared standard deviation) will be calculated by statistical software and will be used in a F-test in order to test hypotheses H4, H5 and H6. The F-statistic is as following: 𝐹𝐹 = 𝑠𝑠12 𝑠𝑠22 ~ 𝐹𝐹[𝑑𝑑𝑑𝑑] (7) where: (5) (6)
𝑑𝑑𝑑𝑑 = [𝑑𝑑𝑑𝑑𝑛𝑛𝑛𝑛𝑚𝑚𝑛𝑛𝑛𝑛𝑛𝑛𝑖𝑖𝑛𝑛𝑛𝑛= 𝑛𝑛1− 1 & 𝑑𝑑𝑑𝑑𝑑𝑑𝑛𝑛𝑛𝑛𝑛𝑛𝑚𝑚𝑖𝑖𝑛𝑛𝑛𝑛𝑖𝑖𝑛𝑛𝑛𝑛 = 𝑛𝑛2− 1] (8)
4. Data
The used data set is retrieved from the Datastream database. The export made there was from all the sectors of the Japanese Nikkei. Not every day was available because the Tokyo Stock Exchange is not open every day of the year. It is closed in the weekends and on public holidays as ‘respect for the aged-‘ and ‘emperor’s day’. The timespan of the retrieved data was from September 15th 2006 until January 30th 2009. Microsoft Excel was used in order to manipulate the data. Daily returns were calculated on basis of the number of points the entire sector had that particular day. Statistical software like IBM’s SPSSStatistics and Statacorp’s Stata were used to make the needed regressions and descriptive statistics. Following the research design as described earlier, the found parameters were put back in Microsoft Excel to calculate the needed means and test t- and F-statistics.
5. Results
This research consists out of three different parts with each part having their own results and conclusions. The first of the three parts is making the ordinary least squares regressions to compute the alphas and betas for each of the sectors. These parameters are used in the second part to test whether the abnormal return is significant or not. Notice that the second is dependent from the calculated values in the OLS-regression. The last part is testing the difference in variance across periods.
5.1. OLS-regression
The outcome of the OLS-regression is given in table 1. The constant for every sector is given in percent and is not significantly different from 0 in any of the sectors. This constant is the alpha in equation (1) and represents the risk-adjusted measure of the active return on the investment. This means that each sector has earned a return that is
adequate for the risk taken (Berk & DeMarzo, 2007). The beta of each sector is positive and varies between 0,766 for food and 1,524 for insurance. The sector food, with a beta between 0 and 1, is a sector that moves in the same direction as the benchmark (NIKKEI) but does so to a lesser extent. This outcome is expected because the food sector is not so dependent from the overall economy; everybody needs food, in good and in bad economic times. All the other included sectors have a beta greater than 1, which means those sectors move along with the market but react more strongly to economic developments.
Coefficient Value Standard error t-value
Insurance Constant (%) 0,000 0,002 0,001
Beta 1,524 0,072 21,208
Banking Constant (%) -0,045 0,001 -0,317
Beta 1,293 0,052 24,880
Real estate Constant (%) -0,018 0,002 -0,814
Beta 1,185 0,080 14,839
Securities Constant (%) -0,019 0,002 -0,993
Beta 1,358 0,071 19,029
Sum finance Constant (%) -0,008 0,001 -0,556
Beta 1,364 0,053 25,794 Construction Constant (%) 0,114 0,001 1,336 Beta 1,043 0,031 33,287 Food Constant (%) 0,036 0,001 0,405 Beta 0,766 0,033 23,416 Iron/Steel Constant (%) -0,176 0,002 -1,083 Beta 1,435 0,059 24,135 Motor Constant (%) -0,133 0,002 -0,858 Beta 1,352 0,057 23,885
Table 1 - Outcomes of the OLS-regression
5.2. Abnormal returns
The results of the second part are calculated by computing the values of the Welch’s t-test and are given in table 2. Column 2, 3 and 4 give the mean abnormal return for
respectively period 1, 2 and 3. Column 5, 6 and 7 give the t-value of the performed Welch’s t-test between two different periods. The mean abnormal return of the sectors varies between -0,24% and 0,19%. At some of the sectors the mean abnormal changes from positive to negative (or the other way around) twice. This could imply that the standard deviation is relatively high. Equation (5) shows that a high standard deviation results in a t-score closer to 0. And this is exactly what is visible in the last three columns. None of the t-values is significant, even with an alpha of 10% one-sided test. 𝑨𝑨𝑨𝑨𝟏𝟏 ������ (%) 𝑨𝑨𝑨𝑨������ (%) 𝑨𝑨𝑨𝑨𝟐𝟐 ������ (%) t 1 vs. 2 𝟑𝟑 t 2 vs. 3 t 1 vs. 3 Insurance -0,05 0,19 -0,06 -0,41 0,37 0,03 Banking -0,05 0,08 0,12 -0,23 -0,08 -0,61 Real estate 0,14 -0,09 -0,21 0,27 0,13 0,83 Securities -0,05 -0,19 -0,23 0,19 0,04 0,51 Sum finance 0,00 0,04 -0,08 -0,06 0,20 0,33 Construction -0,10 0,11 0,04 -0,81 0,26 -0,74 Food 0,12 -0,05 -0,07 0,52 0,07 1,17 Iron/Steel 0,01 -0,24 0,12 0,45 -0,66 -0,36 Motor 0,01 0,12 -0,22 -0,19 0,80 0,87
Table 2 - Outcomes of market model and Welch's t-test
Figure 1 - Abnormal return insurance -0,15 -0,1 -0,05 0 0,05 0,1 6-16-08 7-16-08 8-16-08 9-16-08 10-16-08 11-16-08 12-16-08 1-16-09
ARinsurance
Figure 2 - Abnormal return construction
5.3. Volatility
The last part is tabulated in table 3 and shows the calculated F-statistics. Given the degrees of freedom calculated by equation (8) all the found F-statistics are significant with an alpha of 5% except “Insurance, 2 vs. 3”. “Real estate, 2 vs. 3”, “Construction, 1 vs. 3” and “Motor, 2 vs. 3” are significant with an alpha of respectively 5; 5 and 2,5 percent. The remaining of the F-statistics are significant with an alpha of 1%. Increases in variance, and thus in volatility, are highlighted in red while decreases are highlighted in green. F 1 vs. 2 F 2 vs. 3 F 1 vs. 3 Insurance 7,68*** 1,64 4,81*** Banking 5,06*** 2,98*** 1,70** Real estate 5,43*** 1,77* 3,06*** Securities 6,16*** 2,30*** 2,68*** Sum finance 6,47*** 2,06*** 3,14*** Construction 6,80*** 4,42*** 1,54* Food 14,98*** 5,36*** 2,79*** Iron/Steel 7,73*** 3,23*** 2,39*** Motor 10,18*** 1,94** 5,26***
Table 3 - Outcomes of the F-test with *, ** and *** being an alpha of 5; 2,5 and 1 percent.
-0,04 -0,02 0 0,02 0,04 0,06 6-16-08 7-16-08 8-16-08 9-16-08 10-16-08 11-16-08 12-16-08 1-16-09
ARconstruction
6. Conclusion, discussion and suggestions
6.1. Conclusion
This research is focused on two different effects of the naked short selling ban in Japan. The first being the effect the ban had on the daily returns of financial stocks and the second part being the effect on the volatility of these daily returns on financial stocks.
The first part is statistically quite difficult to answer because there are no significant results. Therefore, it is not possible to reject the null hypotheses of the hypothesis pairs H1, H2 and H3: the mean abnormal return for every sector is not significantly changed over the different periods. There are a number of conclusions that we can draw from that. First of all, the fall of Lehman brothers had no significant effect on the mean abnormal return of any of the financial sectors, or on any non-financial sectors for that matter. The same conclusion can be drawn for the ban on short selling; there was no significant effect on the mean abnormal return for financial and non-financial sectors before and after the ban.
Besides that, there is not even a trend to be found in the results. As can be seen in table 2, the mean abnormal return changes from positive to negative (and the other way around) twice. Examples are “Insurance” and “Iron/steel”. This could be the result of the increased variance that will be discussed later on.
Notice that the abnormal return does not tell us anything about the actual return of the stock, it is just the deviation from what we expected as equation (2) shows us. This implies, with the use of historical data, that all sectors react on the fall of Lehman Brothers and the ban just as we have expected.
The second part is statistically easier to answer. Table 3 shows us that the volatility, between period 1 and 2, of every single sector has increased with an alpha of 1%. Therefore, the null hypotheses of hypothesis pairs H4, H5 and H6 can be rejected and we thus can conclude that the variance of daily returns has changed (increased) between period 1 and 2. This implies that the bankruptcy of Lehman Brothers indeed had a significant effect on the volatility of daily returns for financial and non-financial sectors. The F-statistics for the change in volatility between period 2 and 3 measure whether the ban on naked short selling in Japan actually had an effect on the volatility of the daily returns. For every sector there is a decrease in volatility but it is not always significant. We can therefore conclude that the ban had
no significant effect on the volatility of the sector “Insurance”. The volatility of all the other sectors, financial and non-financial, are affected positively and significantly. So, the goal that was set by the Japanese Minister of Finance, to ensure the stability of the Japanese financial market, is achieved. However, looking at the last column of table 3, the volatility between period 1 and 3 has increased significantly. This implies that the negative effect of the fall of Lehman brothers is greater than the positive effect from the ban. So the overall conclusion is as follows: the fall of neither Lehman Brothers nor the ban on naked short selling has a significant effect on the mean abnormal return. The variance however, is negatively affected by the fall of Lehman Brothers but is positively affected by the ban. The negative effect was greater than the positive resulting in a negative overall effect.
6.2. Discussion
There are a number of things to keep in mind when reading this thesis. First of all, the scope of the short selling ban in Japan. The Financial Services Agency in Japan introduced the short selling ban on all stocks on the Japanese market. It is therefore difficult to state what affect the ban on itself had; there is no control group with financial stocks in the same period without the ban.
Another aspect is the amount of data collected. Period 2, between the fall and the ban, is 44 days long but there are only 30 observations due to weekends and national holidays. This makes it more difficult to draw statistical conclusions. There is no solution to this problem when working with daily returns.
The market model in equation 1 shows us to what extent the particular stock or sector reacts to the market. This model is said to be endogenous because the return of the sector affects the return of the market. This endogeneity problem of the market model is one of the known problems of this model and is chosen to ignore in this research.
The alpha and beta of equation 1 is calculated with historical data 2 years prior to the fall of Lehman Brothers. These parameters are held constant for the remainder of this research because this would simplify the research. However, the alpha and beta of a sector changes every day.
6.3. Suggestions for further research
Suggestions for further research are primarily based on the discussion points above. This research is based on the short-term effect of the ban because period 3 is only 3 months long. As discussed before for the volatility, the positive effect the ban had, did not outweigh the negative effects of the fall of Lehman Brothers. It could be that the ban simply did not had enough time to counteract the negative effects of the fall. So a suggestion is to compare the effects from the ban over different periods of time (3 months, 6 months etc.). Another suggestion is to let the alpha and beta differ for every period. This would mean that a lot of OLS-regressions have to be made. However, it should be possible to automate this process by using Microsoft Excel with an analysis-package.
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8. Appendix -0,1 -0,05 0 0,05 0,1 6-16-08 7-16-08 8-16-08 9-16-08 10-16-08 11-16-08 12-16-08 1-16-09
ARbanking
-0,2 -0,15 -0,1 -0,05 0 0,05 0,1 6-16-08 7-16-08 8-16-08 9-16-08 10-16-08 11-16-08 12-16-08 1-16-09ARrealestate
-0,15 -0,1 -0,05 0 0,05 0,1 6-16-08 7-16-08 8-16-08 9-16-08 10-16-08 11-16-08 12-16-08 1-16-09ARsecurities
-0,15 -0,1 -0,05 0 0,05 0,1 6-16-08 7-16-08 8-16-08 9-16-08 10-16-08 11-16-08 12-16-08 1-16-09
ARfin
-0,06 -0,04 -0,02 0 0,02 0,04 6-16-08 7-16-08 8-16-08 9-16-08 10-16-08 11-16-08 12-16-08 1-16-09Arfood
-0,1 -0,05 0 0,05 0,1 6-16-08 7-16-08 8-16-08 9-16-08 10-16-08 11-16-08 12-16-08 1-16-09Ariron/steel
-0,1 -0,05 0 0,05 0,1 6-16-08 7-16-08 8-16-08 9-16-08 10-16-08 11-16-08 12-16-08 1-16-09
