frank musella junior paper

8/13/2019 Frank Musella Junior Paper

1/33

1

Frank Musella

Valentin Haddad

Junior Paper

24 April 2013

The Effect of Price Limits on Market Volatility: A Case Study

This paper represents my own work in accordance with University regulations


2/33

2

Abstract

Price limits are a controversial method of limiting the volatility of markets. By

preventing traders from buying or selling equities outside of a certain range of prices, price

limits are supposed to prevent wild swings in price that could be caused by trader irrationality,

thus reducing volatility. But do they actually achieve this goal? Economists have yet to reach a

consensus about the effectiveness of price limits.

In this paper, I examine the effectiveness of price limits using data from RuneScape, an

online roleplaying game with its own centralized exchange. I look at several different measures

of volatility, both before and after the removal of price limits in 2011. Using OLS, fixed-effects

models, and Chow tests, I reach a clear conclusion: the removal of price limits caused an

increase in volatility. This finding could have major policy implications for financial exchanges

across the world, particularly those considering adopting a price limits regime.


3/33

3

Introduction

On October 19, 1987, a day known as Black Monday, global financial markets

experienced their largest single-day loss in world history. Various stock indexes experienced

losses between 22% and 45%, and trillions of dollars of equity was wiped out. In the wake of

Black Monday, stock exchanges devised methods of preventing such large price fluctuations

from occurring again. In the United States, this took the form of circuit breakers: mandatory

halts in trading that take place whenever the market moves by more than 10%.

Many other stock exchanges, most notably the Tokyo Stock Exchange, have chosen a

different approach for limiting volatility. These exchanges have implemented price limits:

maximum and minimum values for orders based on the previous days closing price. These

limits are dependent on price, and generally prices cannot move in excess of 14-50% per day. 1

The stated purpose of these limits is to protect investors from excessively volatile markets .2

But is this purpose being fulfilled?

This paper will examine the effects of price limits on the volatility of markets in

RuneScape, a massively multiplayer online role playing game created by Jagex Ltd. in 2001.

RuneScape has its own self-contained economy, complete with an automated, long-only

commodities exchange known as the Grand Exchange. RuneScape has over 10 million active

users. 3 The 28 trillion units of game currency have a real-world value of roughly 10.64 million

USD; while the total value of all in-game items is unknown, it likely exceeds 100 million USD.4

From the time of its creation on November 26, 2007, until an update on February 1, 2011, the

1 Tokyo Stock Exchange2 Ibid3 Saltzman, 20124 Jagex, Ltd. Per Sythe.org, 1 million units of currency trade for roughly 38 cents US.


4/33

4

Grand Exchange had strict price limits of plus or minus 5%. After February 1, 2011, buyers and

sellers could place offers at any price of their choosing. 5 I chose RuneScape because it is the

only example I could find of a major market moving from a price limits regime to a free trade

regime in one fell swoop. This paper will attempt to determine what impact, if any, the removal

of price limits had on the volatility of prices. Since the stated intention of price limits is to

reduce volatility, I will hypothesize that removing the price limits regime will cause an increase

in volatility.

Literature

There exists extensive academic literature about the impact of price limits on volatility.

Kim and Rhee (1997) tested three different hypotheses, using data from the Tokyo Stock

Exchange. The first, volatility spillover hypothesis, states that stocks will experience significantly

more volatility after hitting a price limit than they would otherwise. 6 The second, delayed price

discovery hypothesis, states that price limits prevent market participants from determining the

true equilibrium price of a stock, since hitting a price limit implies markets are unable to clear. 7

The third, trading interference hypothesis, states that price limits are inefficient because

trading volume spikes dramatically in the days following a limit hit, implying that rational

investors refuse to trade at price limits that do not represent equilibrium prices. 8 Their analysis

upheld all three hypotheses, implying that price limits hurt market efficiency and increase price

volatility.

5 Grand Exchange History6 Kim and Rhee, pp. 8877 Ibid, pp. 8938 Ibid, pp. 897


5/33

5

Kim and Park (2010) attempt to explain price limits as a mechanism designed to fight

market manipulation. According to Kim and Park, Large or otherwise influential shareholders

can spread false rumors to falsely convey positive information to the markets. If and when the

stock price increases as a result of this false signal, these shareholders can then sell their stocks

at artificially high prices. 9 By giving market participants more time to evaluate new

information, price limits keep prices closer to their true equilibrium values.

While other methods of deterring market manipulators exist, price limits can be

maintained at minimal cost to regulators. Kim and Park find that nations with stronger

regulatory systems are less likely to implement price limits than nations with weak regulatory

systems. 10 This is because regulation increases the costs of manipulation, helping align the

incentives of manipulators with those of the general public. Since RuneScape lacks a central

regulatory agency like the Securities and Exchange Commission, price limits present a

convenient alternative method of limiting manipulation. If my analysis finds that price limits

help moderate volatility, then limiting manipulation may be the mechanism through which this

occurs.

Kim contradicts his earlier work in a 2012 working paper, which examines the Shanghai

Stock Exchange and the Shenzhen Stock Exchange. He studies volatility in 1997, the year before

a 10% price limit was implemented, and 1999, the year after a 10% price limit was

implemented.11

Kims conclusion states that price limits help moderate transitory volatility.12

However, his methodology is slightly different from mine: he measures intraday volatility, while

9 Kim and Park (2010), pp. 210 Ibid, pp. 1811 Kim et al. (2012), pp. 1212 Ibid, pp. 19


6/33

6

I measure volatility intertemporally and cross-sectionally. (Intraday trade prices are not

observable for RuneScape items.) I cannot anticipate whether or not this difference in

methodology will dramatically impact the result.

The standard methodology used to evaluate the efficacy of price limits is to examine

intraday volatility, trading volume, and returns in the days before and after a price limit hit.

However, this methodology is of limited utility. The vast majority of studies about price limits

focuses solely on price limited regimes, and do not compare markets with price limits to those

without them. This single-diff approach fails to account for myriad factors that can influence

the results either way. Indeed, different studies by the same author using the same

methodology have yielded completely different results, most of them statistically significant.

I believe my methodology will improve upon the methodology most commonly used in

the existing literature. Instead of using time-series data and confidence intervals, I will perform

multiple regression on a variety of variables, including the existence of price limits. I will also

use difference-in-difference models to separate the impact of price limits from background

market conditions. This allows me to dramatically reduce the omitted variable bias that plagues

the existing academic literature.

Data

I will use daily pricing data from the RuneScape Wiki. Each price represents the

weighted average of the previous days actual trade prices; as such, these prices may differ

from closing prices. Using a Python script, I gathered price data on 3,531 items from January 1,

2009 to March 29, 2013. Data from January 1, 2009 until November 30, 2010 will demonstrate


7/33

7

the variability of prices before the price limits were removed. My event window will be from

December 1, 2010 through March 31, 2011, representing 60 days before and after the February

1, 2011 removal of price limits. I will use data for April 1, 2011 until March 29, 2013 to

demonstrate the volatility of returns after the price limits were removed. This gap of two

months before and after the change is designed to isolate any excess volatility produced by the

announcement itself, and thus should help minimize time-fixed effects not captured by the

removal of price limits. This approach mimics the one taken by Kim et al. (2012). 13 These data

form an unbalanced panel with roughly 3 million observations.

For each observation, I also recorded the items name, the quantity limit, and the

value. Quantity limit L is the 4-hour buying limit imposed on items, which ranges from 1 to

25,000. (In an effort to prevent price manipulation, the Grand Exchange blocks players from

buying more than L of a given item in any 4-hour period. Quantity limit also serves as a rough

proxy for trade volume. ) Value is an integer between 1 and 2 million, representing an items

intrinsic value. Value is not necessarily correlated to price. Each item can be alchemized for

60% of its value. This is analogous to a perpetual put option. Since buying an item for less than

60% of its value is an easy arbitrage, prices do not fall well below 60% of their value in practice.

However, just as in real life, there may be advantages to not exercising the put option, even if it

is in the money. I generated a dummy variable, Alchable , for items that have ever traded

below the 60% of value threshold. Items in this category should not exhibit high levels of

volatility, so this will serve as a control group in my difference-in-difference analysis.

13 Ibid, pp. 12


8/33


9/33

9

data do not include information about daily trading volume, I cannot test the trading

interference hypothesis. (Summary statistics of my data can be found in Table 9 in the

appendix.)

Methodology

My first regression will measure the impact of price limits on cross-sectional volatility.

Vol it = 1*post + 2*eventwindow + + it. (1)

This regression will determine whether market-wide volatility was impacted by the

announcement of the end of the price limit regime, and whether volatility was impacted by the

regime itself. Eventwindow is a dummy variable for observations occurring within 60 days of

February 1, 2011. Post is a dummy variable for observations occurring after April 1, 2011. is

the constant, and it is the error term. Because this measure of volatility is cross-sectional, I

cannot account for the characteristics of different items, nor can I include interaction terms.

Since Vol does not vary across observations, I will cluster my standard errors by date to correct

the model.

Second, I will test the impact of price limits on idiosyncratic volatility with a series of ten

regressions. The first five regressions will use standard OLS techniques:

Variance it = 1*post + 2*eventwindow + + it. (2)

Variance it = 1* post + 2*eventwindow + 3*logprice +

4*logprice*post + 5*logprice*eventwindow + + it. (3)

Variance it = 1* post + 2*eventwindow + 3*logprice + 4*logprice * post + 5*logprice*

eventwindow + 6*alchable + 7*alchable*post + 8*alchable*eventwindow + + it (4)


10/33

10

Variance it = 1* post + 2*eventwindow + 3*logprice + 4*logprice*post +

5*logprice*eventwindow + 6*alchable + 7*alchable*post + 8*alchable*eventwindow +

9*lowtrade + 10*lowtrade*post + 11*lowtrade*eventwindow + + it (5)

Variance it = 1* post + 2*eventwindow + 3*logprice + 4*logprice * post +

5*logprice*eventwindow + 6*alchable + 7*alchable * post + 8*alchable*eventwindow +

9*lowtrade + 10*lowtrade *post + 11*lowtrade*eventwindow + 12*cheap + 13*cheap*post +

14*expensive + 15*expensive*post + + it (6)

Logprice is simply the natural logarithm of the price. Alchable is a dummy variable equaling 1

for items that have ever traded below 60% of their intrinsic value. Lowtrade is a dummy

variable equal to 1 for items whose 4-hour trading limit, L, is less than 10. Cheap is a dummy

variable equal to 1 for items with a mean price below the 10 th percentile. Expensive is a dummy

variable equal to 1 for items with a mean price above the 90 th percentile. The other variables

are interaction terms with the time dummy variables, designed to extract the difference-in-

difference. A positive coefficient on an interaction term means that price limits are better at

controlling the volatility of an item with that characteristic.

My next 5 regressions use a fixed-effects model to account for individual item

characteristics. As such, any variables which vary across items but not across time will drop out

of the regressions. Nevertheless, I can still include interaction terms to extract the diff-in-diff:

Variance it = 1*post + 2*eventwindow + i + it. (7)


5*logprice*eventwindow + 6*alchable*post + 7*alchable*eventwindow + i + it. (8)

Variance it = 1* post + 2*logprice + 3*logprice*post +


11/33

11

4*alchable*post + 5*lowtrade*post + i + it. (9)

Variance it = 1*eventwindow + 2*logprice + 3*logprice*eventwindow +

4*alchable*eventwindow + 5*lowtrade*eventwindow + i + it. (10)


5*logprice*eventwindow + 6*alchable*post + 7*alchable*eventwindow + 8*lowtrade*post

+ 9*lowtrade*eventwindow + i + it. (11)

Accounting for fixed effects will increase the standard errors, and may affect the significance of

some coefficients. The impact on the values of the coefficients is ambiguous. The coefficient on

the interaction terms can be interpreted as differences-in-differences. Note: I exclude 11 outlier

observations for which Variance it>1, since these are almost certainly caused by measurement

error.

To measure the impact of price limits on intertemporal volatility, I will repeat the

previous ten regressions, replacing variance with the RolVol variable I defined earlier. The

standard deviation of a rolling window of returns is a commonly used risk assessment, and is

used to generate technical indicators like Bollinger bands. The OLS specifications are:

RolVol it = 1*post + 2*eventwindow + + it. (12)

RolVol it = 1* post + 2*eventwindow + 3*logprice +

4*logprice*post + 5*logprice*eventwindow + + it. (13)

RolVol it = 1* post + 2*eventwindow + 3*logprice + 4*logprice * post + 5*logprice*

eventwindow + 6*alchable + 7*alchable*post + 8*alchable*eventwindow + + it (14)


12/33

12

RolVol it = 1* post + 2*eventwindow + 3*logprice + 4*logprice*post +

5*logprice*eventwindow + 6*alchable + 7*alchable*post + 8*alchable*eventwindow +

9*lowtrade + 10*lowtrade*post + 11*lowtrade*eventwindow + + it (15)

RolVol it = 1* post + 2*eventwindow + 3*logprice + 4*logprice * post +

5*logprice*eventwindow + 6*alchable + 7*alchable * post + 8*alchable*eventwindow +

9*lowtrade + 10*lowtrade *post + 11*lowtrade*eventwindow + 12*cheap + 13*cheap*post +

14*expensive + 15*expensive*post + + it (16)

The fixed-effects specifications are:

RolVol it = 1*post + 2*eventwindow + i + it. (17)


5*logprice*eventwindow + 6*alchable*post + 7*alchable*eventwindow + i + it. (18)

RolVol it = 1* post + 2*logprice + 3*logprice*post +

4*alchable*post + 5*lowtrade*post + i + it. (19)

RolVol it = 1*eventwindow + 2*logprice + 3*logprice*eventwindow +

4*alchable*eventwindow + 5*lowtrade*eventwindow + i + it. (20)


5*logprice*eventwindow + 6*alchable*post + 7*alchable*eventwindow + 8*lowtrade*post

+ 9*lowtrade*eventwindow + i + it. (21)

Additionally, I opted to run a Chow test on the cross-sectional Vol variable. I used

February 1, 2011, as a potential break date, since this was the day the price limits regime was

removed. Because the Chow test does not directly address my research questions, I leave the

details in Appendix 2.


13/33

13

To test the spillover volatility hypothesis, I modeled Variance with an AR-1 process. My

regression is:

F1.Variance it = 1*Variance it + 2*break + 3*break*Variance it + i + it. (22)

Where F1.Variance it is the idiosyncratic variance at time t+1, Variance it is the idiosyncratic

variance at time t, break is a dummy variable for dates after the removal of price limits , break*

Variance it is the interaction term, i is an entity fixed effect, and it is the error term. Price limit

advocates would argue that price limits reduce spillover volatility, and would expect the

coefficient on the interaction term to be positive. Price limit opponents would argue that price

limits increase spillover volatility, and would expect the coefficient to be negative.

Finally, I will test the delayed price discovery hypothesis, using a similar AR(1) fixed-

effects model. My regressions will be:

F1.Limitup it = 1*Limitup it + 2*break + 3*break*limitup it + i + it. (23)

F1.Limitdown it = 1*Limitdown it + 2*break + 3*break*limitdown it + i + it. (24)

Limitup is a dummy variable equal to 1 when the upper price limit is hit, or would have

been hit under a price limits regime. Limitdown is the corresponding dummy variable for items

hitting the lower price limit. The predicted variables, F1.limitup and F1.limitdown , can be

interpreted as the probability that a limit hit occurs immediately after one has occurred. If the

delayed price discovery hypothesis were true, we would expect strings of consecutive limit hits

to be relatively common under a price limits regime. This would show up in the model as a

negative value of 3, since removing price limits would reduce the probability of consecutive

limit hits. If the value of 3 is positive, this would negate the hypothesis and be a victory for

price limit enthusiasts.


14/33


15/33

15

Table 2

Estimated effects of price limits on idiosyncratic variance ( Variance it ), simple OLS regression

(2) (3) (4) (5) (6)Post 0.15***

(0.02)1.55***(0.08)

1.17***(0.08)

1.44***(0.08)

1.27***(0.08)

Event window 0.30***(0.04)

1.57***(0.20)

1.35***(0.18)

1.57***(0.21)

1.53***(0.20)

Ln(price) - -0.10***(0.005)

-0.10***(0.006)

-0.10***(0.007)

-0.08***(0.006)

Ln(price)*post - -0.19***(0.009)

-0.17***(0.009)

-0.22***(0.01)

-0.23***(0.01)

Ln(price)*eventwindow

- -0.16***(0.02)

-0.15***(0.02)

-0.19***(0.03)

-0.19***(0.02)

Alchable - - 0.18***(0.02)

0.18***(0.23)

0.09***(0.02)

Alchable*post - - 0.64***(0.04)

0.64***(0.04)

0.52***(0.03)

Alchable*eventwindow

- - 0.35***(0.07)

0.37***(0.07)

0.36***(0.07)

Lowtrade - - - 0.15***(0.03)

-0.05**(0.02)

Lowtrade*post - - - 1.11***(0.04)

0.81***(0.03)

Lowtrade*event

window

- - - 0.81***

(0.11)

0.78***

(0.11)Cheap - - - - 1.72***

(0.09)Expensive - - - - 0.81***

(0.04)Cheap*post - - - - 1.01***

(0.13)Expensive*post - - - - 1.37***

(0.07)Constant 0.68***

(0.009)

1.46***

(0.05)

1.36***

(0.05)

1.39***

(0.06)

1.10***

(0.05)Increase involatility post

22%***(3%)

106%***(5%)

86%***(6%)

104%***(6%)

115%***(7%)

R-squared p>0.05, ** denotes 0.05>p>0.01, *** denotes 0.01>p

All coefficient values multiplies by 1000


16/33

16

With respect to idiosyncratic volatility, every single one of my OLS regressions found a

coefficient on post that was positive and significant at the 1% confidence level. In other words,

the removal of price limits caused a significant increase in volatility, suggesting that price limits

were effective. The coefficient on eventwindow was also positive and significant at the 1% level,

suggesting that the transition period away from price limits was also marked by excess

volatility. Contrary to my expectations, the coefficient on alchable was also positive and

significant at the 1% level, an effect that increased with the removal of price limits and during

the transition period. Items trading near their alchemy values are thus more volatile than their

counterparts, and price limits are better at controlling the volatility of alchable items.

Volatility appears to be decreasing in price, an effect that became stronger during the

transition period and after the removal of price limits. The relative volatility of illiquid items is

ambiguous under the price limits regime, with one regression finding a positive coefficient and

another finding a negative coefficient. Nevertheless, illiquid items appear to have become

relatively more volatile in the transition period and post-price limits era. Finally, both cheap and

expensive items were more volatile than items in the middle 80% of the price distribution, an

effect that increased in the post-price limits era.

While the controls did not behave exactly as expected, they did help separate out the

impact of price limits on volatility from the impact of other factors. Without the control

variables, the removal of price limits causes an increase in volatility of 22%, exactly the same

figure as in regression 1. When controls are added, the increase in volatility is in the range of

86% to 115%, a much more dramatic effect.


17/33

17

Table 3

Estimated effects of price limits on idiosyncratic variance ( Variance it ), with item fixed effects

(7) (8) (9) (10) (11)Post 0.17**

(0.09)1.11***(0.33)

0.93***(0.34)

- 1.21***(0.35)

Event window 0.37***(0.06)

1.37***(0.24)

- 0.68**(0.29)

1.52***(0.27)

Ln(price) - -0.86***(0.16)

-0.87***(0.16)

-0.97***(0.19)

-0.84***(0.16)

Ln(price)*post - -0.16***(0.04)

-0.15***(0.04)

- -0.18***(0.04)


- -0.14***(0.03)

- -0.04(0.04)

-0.17***(0.03)

Alchable*post - 0.32*(0.17)

0.26*(0.15)

- 0.33**(0.17)


- 0.32***(0.12)

- 0.09(0.11)

0.43***(0.15)

Lowtrade*post - - 0.31**(0.14)

- 0.43***(0.15)

Lowtrade*eventwindow

- - - 0.33**(0.15)

0.59***(0.16)

Constant 0.66***(0.06)

7.32***(1.19)

7.50***(1.19)

8.15***(1.41)

7.15***(1.17)

Increase in

volatility post

26%**

(14%)

15%***

(5%)

12%***

(5%)

- 17%***

(5%)R-squared p>0.05, ** denotes 0.05>p>0.01, *** denotes 0.01>p

All coefficients multiplied by 1000


18/33

18

In the simplest possible fixed effects regression, featuring only dummy variables for the

event window and the post-price limits regime, the coefficient on post is positive and significant

at the 5% confidence level. In the other regression specifications, the coefficient on post was

positive and significant at the 1% confidence level. The positive value means that volatility

increased in the post-price limits regime, implying that price limits were effective in moderating

idiosyncratic volatility. (The coefficient on eventwindow was also positive at the 1% or 5% level

in every regression, meaning that the transition period was marked by increased volatility.)

The other coefficients behave the same way they did in the OLS regressions. Volatility

decreases as items become more expensive, an effect that becomes stronger in the post-price

limits era. Alchable items become relatively more volatile when the price limit regime ends, just

as they did before. Illiquid items also become more volatile relative to liquid items.

As we would expect, controlling for item fixed-effects appears to moderate the huge

impact on volatility that price limits had in the OLS specifications. Removing price limits still

causes an increase in volatility, but the increase is in the more modest range of 12% to 26%.


19/33

19

Table 4

Impact of price limits on intertemporal volatility ( RolVol ), OLS specifications

(12) (13) (14) (15) (16)Post 0.058%***

(0.003%)0.710%***(0.014%)

0.639%***(0.013%)

0.756%***(0.014%)

0.467%***(0.013%)

Event window 0.133%***(0.006%)

0.592%***(0.025%)

0.600%***(0.024%)

0.629%***(0.025%)

0.626%***(0.025%)

Ln(price) - -0.046%***(0.001%)

-0.043%***(0.001%)

-0.022%***(0.001%)

-0.047%***(0.001%)

Ln(price)*post - -0.086%***(0.001%)

-0.080%***(0.001%)

-0.107%***(0.002%)

-0.086%***(0.002%)


- -0.056%***(0.003%)

-0.055%***(0.002%)

-0.061%***(0.003%)

-0.060%***(0.003%)

Alchable - - 0.137%***(0.005%)

0.096%***(0.005%)

0.103%***(0.005%)

Alchable*post - - 0.102%***(0.007%)

0.151%***(0.007%)

0.008%(0.007%)


- - -0.025**(0.012%)

-0.017%(0.013%)

-0.024%*(0.013%)

Lowtrade - - - -0.641%***(0.006%)

-0.604%***(0.006%)

Lowtrade*post - - - 0.742%***(0.008%)

0.556%***(0.007%)

Lowtrade*event

window

- - - 0.286%***

(0.016%)

0.269%***

(0.016%)Cheap - - - - 0.210%***

(0.016%)Expensive - - - - 0.564%***

(0.009%)Cheap*post - - - - 1.331%***

(0.025%)Expensive*post - - - - 0.659%***

(0.013%)Constant 1.38%***

(0.002%)

1.74%***

(0.003%)

1.67%***

(0.008%)

1.57%***

(0.008%)

1.70%***

(0.009%)Increase involatility post

4%***(0.2%)

41%***(1%)

38%***(1%)

48%***(1%)

27%***(1%)

R-squared 0.0003 0.0427 0.0452 0.0475 0.1017Robust standard errors in parentheses

* denotes 0.1>p>0.05, ** denotes 0.05>p>0.01, *** denotes 0.01>p


20/33

20

In every OLS regression involving intertemporal volatility, the coefficient on post is

positive and significant at the 1% confidence level. In the simplest model, the increase in

volatility is a modest 4%; this number jumps to the 27% to 48% range when various control

variables are added. The removal of price limits thus caused a clear increase in intertemporal

volatility.

The coefficients on the control variables are similar to those from the regressions in

Table 2. Volatility decreases as price increases, an effect that becomes stronger in the post-

price limit era. Items that have traded below their alchemy value are significantly more volatile

than those that have not, an effect that also strengthens in the post-price limit era. Illiquid

items are significantly less volatile than liquid items during the price limit era, but this effect

largely disappears when price limits are removed. Both cheap and expensive items are more

volatile than items in the middle of the price distribution, an effect that becomes much

stronger when price limits are removed.

For the record, the coefficient on eventwindow is also positive and significant at the 1%

level in every regression. As we would expect, the transition period away from price limits was

marked by excess volatility. During the event window, the effect of price on volatility became

stronger, the effect of being considered alchable became weaker, and the effect of being

illiquid also became weaker.


21/33

21

Table 5

Estimated effects of price limits on intertemporal volatility ( RolVol ), with item fixed effects

(17) (18) (19) (20) (21)Post 0.144%***

(0.021%)0.433%***(0.065%)

0.406%***(0.061%)

- 0.482%***(0.067%)

Event window 0.145%***(0.019%)

0.401%***(0.062%)

- 0.086%**(0.051%)

0.420%***(0.064%)

Ln(price) - 0.010%(0.019%)

0.019%(0.019%)

-0.020%(0.019%)

0.024%(0.020%)

Ln(price)*post - -0.029%***(0.007%)

-0.034%***(0.007%)

- -0.040%***(0.008%)


- -0.028%***(0.006%)

- -0.004%(0.006%)

-0.032%***(0.007%)

Alchable*post - -0.168%***(0.044%)

-0.133%***(0.040%)

- -0.147%***(0.044%)


- -0.086%**(0.044%)

- 0.019%(0.033%)

-0.079%*(0.040%)

Lowtrade*post - - 0.268%**(0.046%)

- 0.317%***(0.052%)

Lowtrade*eventwindow

- - - -0.091%**(0.037%)

0.163%***(0.050%)

Constant 1.22%***(0.015%)

1.14%***(0.148%)

1.09%***(0.151%)

1.47%***(0.149%)

1.02%***(0.153%)

Increase in

volatility post

12%***

(2%)

38%***

(5%)

37%***

(6%)

- 47%***

(7%)R-squared 0.0004 0.0001 0.0086 0.0246 0.0074

Robust standard errors in parentheses* denotes 0.1>p>0.05, ** denotes 0.05>p>0.01, *** denotes 0.01>p

The story is largely the same when I use a fixed-effects model. Once again, the

coefficient on post is positive and significant at the 1% level in every regression. The

relationship between price and volatility disappears in these models, though price does seem to

negatively affect volatility more in the post-price limits era. Alchable items became less volatile

relative to other items when price limits were abolished, while illiquid items became more

volatile. Overall, the increase in volatility attributable to the removal of price limits is in the

range of 12% to 47%.


22/33

22

Table 6

Testing the spillover volatility hypothesis with a fixed-effects AR(1) model (22)

Price limit regime No price limit regimeFuture volatility as a % oflagged volatility

19.57%***(5.13%)

3.02%***(0.94%)

Constant 0.001676***(0.000181)

0.000933***(0.000041)

Difference-in-difference -16.55%***(5.17%)

R-squared 0.0010Robust standard errors in parentheses


To determine the effect of price limits on spillover volatility, we are most interested in

analyzing the difference-in-difference, which is the coefficient on the interaction term between

the post-price limits dummy variable and the variance variable. In the price limit regime, the

AR(1) process has a high rate of decay, but there remains significant spillover volatility. In other

words, a spike in volatility is likely to persist for a few days. In the post-price limits era, the rate

of decay is much higher: 1 minus the coefficient on the lagged variable, or roughly 97%. A

volatility shock is not likely to persist for long. The difference-in-difference is the impact on the

persistence of volatility shocks caused by the removal of the price limits regime. In this case,

the coefficient is negative and significant at the 1% confidence level. This means that removing

price limits significantly reduced spillover volatility. Price limits thus appear to cause spillover

volatility, validating the spillover volatility hypothesis and vindicating the opponents of price

limits.


23/33

23

Table 7

Testing the delayed price discovery hypothesis with a fixed-effects AR(1) model (23)

Price limit regime No price limit regimeProbability of upper limit hitday after upper limit hit

11.82%***(0.37%)

19.84%***(0.63%)

Probability of upper limit hitday after no upper limit hit

1.01%***(0.02%)

0.95%***(0.02%)

Difference-in-difference 8.09%***(0.705%)



Table 8

Testing the delayed price discovery hypothesis with a fixed-effects AR(1) model (24)

Price limit regime No price limit regimeProbability of lower limit hitday after lower limit hit

16.80%***(0.44%)

25.64%***(0.65%)

Probability of lower limit hitday after no lower limit hit

1.00%***(0.01%)

0.90%***(0.01%)

Difference-in-difference 8.94%***(0.786%)



Tables 7 and 8 demonstrate the change in the autoregressive nature of limit hits. If price

limits actually prevent price discovery, then we would expect to see large strings of consecutive

limit hits in a price limits regime, with relatively few consecutive limit hits in a market without

price limits. To put it another way, in a world with perfect price discovery, tomorrows expected

return is always zero, regardless of what todays return was.

According to the data, this is not the case. For both the upper and lower limits, the

positive value of the difference-in-difference means that consecutive limit hits were much more


24/33

24

likely to occur after the removal of price limits than during the price limits regime. It would

appear that price limits positively contribute to price discovery by giving traders more time to

evaluate new information, thus decreasing the incidence of market manipulation.

Conclusion

My results clearly demonstrate that price limits are an effective way to moderate

volatility in all forms. Out of 19 regressions measuring the impact of price limits on volatility, 18

found that removing price limits significantly increased volatility at the 1% confidence level,

with the final regression demonstrating an increase in volatility at the 5% confidence level. In

terms of cross-sectional market volatility, my linear regression model showed that the removal

of price limits caused a significant increase in the dispersion of market returns. I also found a

significant increase in idiosyncratic and intertemporal volatility, using both OLS and fixed-

effects regressions. This suggests that price limits are indeed effective in moderating volatility. I

also examined the delayed price discovery hypothesis, and found no evidence to support it. I

did find that price limits increase the decay time of volatility shocks, but if they also prevent

those shocks from occurring in the first place, then they are probably beneficial on balance.

Price limits represent a common solution to the problems of market volatility and price

manipulation. Although they are not used for US equities, price limits are ubiquitous in Asian

stock exchanges. But the discipline of economics still has not reached a consensus about their

efficacy. On the one hand, price limits may indeed limit market manipulation by decreasing the

capacity and motivation for investors to do so. They may also prevent traders from making

irrational decisions by giving them time to reevaluate their trading strategies. On the other


25/33

25

hand, some economists believe that price limits prevent prices from reaching their true

equilibrium, limit the daily trading volume, and may actually contribute to volatility instead of

mitigating it. There are costs and benefits to adopting any policy, and price limits are no

exception. However, when it comes to limiting volatility, it appears that price limits work

exactly as advertised.

Past studies have tended to focus on day-to-day happenings within markets with price

limits. But there are very few markets with robust data that have experienced periods both

with and without price limits. To quote Kenneth Kim, A major shortcoming of all existing price

limit studies is they inherently study markets with price limits, but in doing so they cannot

possibly ascertain if those markets would be better off without price limits. 15 While some

exchanges have adopted new limits, there is not a single real-world example of an exchange

eliminating price limits it had already implemented. By examining the RuneScape market, I help

bridge this gap in the existing academic literature. The policy implications of my findings are

clear: exchanges that already employ price limits should maintain them.

Inevitably, the utility of my results is limited by a few factors. One major factor is the

lack of a regulatory agency. A nation like the United States, with regulators capable of putting

market manipulators in prison, might not benefit from price limits as much as nations with

weaker institutions would, or as much as the unregulated RuneScape economy has.

Additionally, the total value of goods in the RuneScape economy is orders of magnitude below

the total value of equities traded on major exchanges. As a result, it is likely much easier to

manipulate and corner individual markets in RuneScape than in the real world.

15 Kim et al. (2012), pp. 1


26/33

26

There is also the possibility of measurement error in my data, which were mostly

compiled by human observers, instead of computer programs. Several data requests to Jagex

went unanswered, so I was forced to use data from a secondary source. I made every effort to

account for measurement error, and the enormous sample size should mitigate the effects of

data entry errors, but the possibility for bias in the coefficients due to measurement error still

exists. In the future, one possible way I could mitigate measurement error is by gathering a

second dataset from a second source, and using one dataset to instrument the other via two-

stage least squares.

Despite my paper s weaknesses, I believe I have clearly demonstrated that the removal

of price limits causes an increase in market volatility, regardless of how volatility is measured. I

would not necessarily interpret this to mean the converse: that the addition of price limits to a

market that lacks them causes a drop in volatility. 16 I would, however, let my paper serve as a

cautionary tale to any nations that might consider dropping their price limits regime. Plenty of

economists have argued quite successfully against price limits in the past. We need only

examine the recent Reinhardt and Rogoff fiasco to see that even the best economists can be

wrong, and that there are two sides to every economic story.

16 While I don t have a dataset to test this hypothesis, Kim et al. (2012) argue quite well that this is the case.


27/33

27

References

Jagex Ltd. 2012. 200 Million players since launch. Infographic.

http://www.runescape.com/200million/infographics.ws (accessed on March 29, 2013).

Kim, Kenneth A., and Jungsoo Park . 2010. Why Do Price Limits Exist in Stock Markets?

A Manipulation-Based Explanation. European Financial Management, Vol. 16, pp. 296-

318.

Kim, Kenneth A., Haixiao Liu, and J. Jimmy Yang . 2012. Reconsidering Price Limit

Effectiveness. State University of New York at Buffalo Working Paper. Accessed on 21

November 2012. http://www.asb.unsw.edu.au/schools/bankingandfinance/

Documents/J.%20Yang%20-%20Reconsidering%20Price%20Limit%20Effectiveness.pdf

Kim, Kenneth A., and S. Ghon Rhee . Price Limit Performance: Evidence from the

Tokyo Stock Exchange. The Journal of Finance , Vol. 52, No. 2 (June, 1997), pp. 885-901

RuneScape Wiki . Grand Exchange History. Accessed on 21 November 2012.

http://runescape.wikia.com/wiki/Grand_Exchange/History

RuneScape Wiki . 2009- 2012. Grand Exchange Market Watch. Wikia.

http://runescape.wikia.com/wiki/Grand_Exchange_Market_Watch (accessed December

12, 2012).

Saltzman, Mark. Five things you didnt know about RuneScape. USA Today , July 27, 2012.

http://usatoday30.usatoday.com/tech/columnist/marcsaltzman/story/2012-07-

29/runescape-fun-facts/56542606/1 (accessed March 29, 2013).


28/33

28

Tokyo Stock Exchange . What are the daily price limits? Tokyo Stock Exchange Group, Inc. 4

January 2010. http://www.tse.or.jp/english/faq/list/stockprice/p_g.html (accessed on

November 21, 2012).


29/33

29

Appendix 1

The chart above is a time series of the coefficient of variation for the RuneScape Wikis

Common Trade Index. The Common Trade Index is a weighted average price of a basket of

commonly-traded goods, and is functionally similar to the S&P 500. 17 The coefficient of

variation is equal to the standard deviation of prices divided by the mean of prices, and is

analogous to the standard deviation of returns. In this case, the coefficient of variation is

intertemporal, measuring the dispersion of prices (and returns) for the trailing 45 days.

The average CV for the period from February 14, 2009 through November 30, 2010 is

0.024062 (Price-limit regime). The average CV for the period from April 1, 2011 through

December 10, 2012 is 0.045968, or 0.039475 if we exclude the anomalous 45-day spike in

volatility in November 2011. The data in the middle is of greatest interest; it demonstrates a

spike in volatility after the removal of price limits, with volatility settling back down after a few

months. While not conclusive, these data imply that the removal of price limits contributed to

an overall increase in market volatility.

17 A list of component items and historical index values can be found athttp://runescape.wikia.com/wiki/Grand_Exchange_Market_Watch/Common_Trade_Index

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

2/14/2009 2/14/2010 2/14/2011 2/14/2012

CV45

CV45


30/33

30

Appendix 2

I ran a Chow test to determine if the removal of price limits caused a structural break in

volatility. Running the Chow test required the following AR(1) specification:

Vol it = 1*L1.Vol it + 2*L1.date + 3*break + 4*break*L1.Vol it + it. (25)

(25)L1.vol -14.99%**

(5.99%)L1.date 1.82X10 -6***

(9.06X10 -8)Break -0.6029%***

(0.2149%)

Break*L1.vol 14.38%*(7.36%)Chow statistic(P-value)

5.47***(0.0043)

R-squared 0.8883

We are most interested in the interaction term, which represents the change in the AR(1)

process caused by the removal of price limits. The coefficient on Break*L1.vol is positive and

significant at the 10% level (T-statistic=1.95, P-value=0.051). The Chow test is simply an F-test

on the hypothesis that the coefficients on Break and Break*L1.vol are both zero. The Chow test

has a test statistic of 5.47 and a P-value of 0.0043. At the 1% confidence level, we can reject the

null hypothesis that no break occurred, and conclude that the abolition of the price limits

regime caused a structural change in volatility. Note the very high R-squared of 0.8883,

reinforcing the validity of this model.


31/33

31

Figure 1

The kernel density of log prices resembles a normal distribution, so we can say that prices are

distributed roughly lognormally. This means that it is safe to use OLS on the coefficient of

ln(price) and related variables.


32/33

32

Figure 2

This graph depicts the distribution of daily returns. The anomalous spikes at -5% and 5% are

due to the effects of the price limit regime. If not for price limits, those spikes would be

redistributed to the tails of the density function, which would more closely resemble a normal

distribution.

Table 9

Summary statistics

Variable Mean St. DeviationReturn 0.008% 1.77%Ln(price) 7.6 3.5Vol 2.61% 1.22%

Variance 0.0008 0.16RolVol 1.16% 1.84%# of observations 2,889,588


33/33

Table 10

Time path of mean returns following an upper price limit hit

Day PL regime No PL regime-1 1.19% 1.99%0 7.82% 8.13%1 1.20% 1.77%2 0.86% 1.68%3 0.72% 1.36%4 0.46% 1.12%5 0.29% 0.90%Number of observations 25,111 28,867

Table 11

Time path of mean returns following a lower price limit hit

Day PL regime No PL regime-1 -1.48% -2.03%0 -7.63% -8.20%1 -1.52% -2.05%2 -0.94% -1.46%3 -0.77% -1.14%4 -0.59% -0.90%5 -0.47% -0.68%Number of observations 25,643 30,583

These tables more closely match Kenneth Kims methodology of choice. Here, I examine how

mean returns evolve before and after a price limit hit. Day 0 represents the day of a price limit

hit. In the price limits regime, mean returns converge back to their expected value of 0 much

faster than in the non-price limits regime. We can conclude that price limits help restore normaltrading activity, and do not delay price discovery. 18

18 Per Kim et al. (2012), pp. 23, Kim uses median returns instead of mean returns. However, since many of hisresults are exactly 0, I suspect there are gaps in his data. As a linear variable, returns are not particularly

tibl t bi f t l I f l f t bl i g i t d f di