the discrepancy of rationality between the options and

The discrepancy of rationality between the options and equity markets: Evidence from price pressure driven by “Mad Money”

Carl Chen* University of Dayton

David Diltz

University of Texas - Arlington

Ying Huang

Northern Kentucky University

Peter Lung University of Texas - Arlington

Abstract This paper examines the discrepancy of rationality between the options and equity markets based on the price pressure driven by a popular CNBC show, Mad Money. Literature has intensively tested the information contained in the stock and options trading activities in terms of cause-effect relations and price discovery processes. However, the difference between investors’ rationality in these two markets has never been explored. This paper uses the effect of a short-lived analyst’s recommendations on stock prices to study this issue. We find that the stock market experiences a transient price pressure effect from Mad Money, while the effect is absent in the options market. Our results also reveal that informed investors tend to use short-term in-the-money put options to trade against the stock market naïve crowd. We conclude that the options market behaves more rationally than the stock market. Furthermore, informed traders could benefit from this discrepancy of rationality.

JEL Classification: G1, G13, G14

Keywords: Contingent Pricing; Information and Market Efficiency; Price Pressure, Options.

* Contact author: Carl R. Chen, Department of Economics and Finance, University of Dayton, 300 College Park, Dayton, OH 45469-2251. Tel: (937)-229-2418, Fax: (937)-229-2477, E-mail: [email protected].

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Abstract This paper examines the discrepancy of rationality between the options and equity markets based on the price pressure driven by a popular CNBC show, Mad Money. Literature has intensively tested the information contained in the stock and options trading activities in terms of cause-effect relations and price discovery processes. However, the difference between investors’ rationality in these two markets has never been explored. This paper uses the effect of a short-lived analyst’s recommendations on stock prices to study this issue. We find that the stock market experiences a transient price pressure effect from Mad Money, while the effect is absent in the options market. Our results also reveal that informed investors tend to use short-term in-the-money put options to trade against the stock market naïve crowd. We conclude that the options market behaves more rationally than the stock market. Furthermore, informed traders could benefit from this discrepancy of rationality.

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I. Introduction

This paper examines the discrepancy of rationality between the options and equity

markets in terms of the price pressure driven by stock analysts’ recommendations. The

theoretical research on the informational role of options markets usually focuses on the

impact of option trading on the equilibrium dynamics of stock and options prices.1 This

strand of literature has tested the information contained in the stock and options trading

activities based on cause-effect relationships and price discovery processes. However, a

mystery regarding the information content in options markets still remain unanswered,

i.e., do options markets behave more rationally than stock markets? This study intends

to address this question by focusing on the effect of a short-lived analyst’s

recommendation. When the stock and options markets respond to noise information

differently, the one with stronger response would be less rational, and vice versa. If

difference in rationality exists between these markets, it is also of our interest to

investigate whether the difference could yield abnormal returns for informed investors.

We conduct these tests using the recommendations of Jim Cramer from the popular

CNBC show Mad Money. The show’s animated host, Jim Cramer, draws more than

398,000 viewers daily according to Philadelphia Inquirer.2

Research on the information content of options markets has a long history. Given

the high leverage achievable with options, absence of short-sale constraints, and the built-

in downside protection, the options market would be an ideal venue for informed trading

and thus contain information about underlying asset prices in the future.3 A substantial

body of empirical research has investigated which market leads (or lags) in terms of

information arrival through Granger lead-lag regression and similar techniques.4 While

these studies come to conflicting conclusions as to whether the stock market leads the

1 See, for example, Back (1993), Kraus and Smith (1996), Brennan and Cao (1996), and Grossman (1988). 2 January 8, 2006. The show airs three times a day during weekdays at 6:00 p.m., 9:00 p.m., and 12:00 midnight. 3 See, for example, Black (1975), and Cox and Rubinstein (1985), and Chakravarty, Gulen, and Mayhew (2004). 4 See, for example, Manster and Rendleman (1982), Stephen and Whaley (1990), Vijh (1990), Chan et al (1993), Finucane (1999), Chan et al (2002), Cao et al (2000), Easley et al (1998), and Pan and Poteshman (2003).

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options market, they consistently find no significant lead for the options market. Some

find that certain options trades could contain information about future stock price

movements, but they could not directly show that informed traders do trade in the options

markets. Using Hasbrouck’s (1995) information-share approach, Chakravarty, Gulen and

Mayhew (2004) document that about seventeen percent of price discovery occurs in the

options market. It indicates that some new information about the stock price is reflected

in option prices first. However, no paper in the literature has yet explored the rationality

of trading behaviors in the stock and options markets.

Many researchers have emphasized on the normal situation that the stock and

options markets move in the same direction with different speed, but they seldom

examine the unusual situation when these two markets diverge. If the stock and options

market do not converge under certain circumstances, it is intriguing to understand which

market behaves more rationally. The examination of rationality of a market’s trading

behavior has two important implications. First, it measures the quality of trades in a

market and reveals where informed traders are more likely to trade when the stock and

options markets move differently. As the deviation of the two markets’ reactions to

information occurs, it signals that two groups of trading crowds have different opinions.

The examination of rationality could show which group is smart money and which

market is driven by noise. Second, if the discrepancy of rationality between stock and

options markets exists, it could create excess trading profits for informed investors and/or

market makers. Given one market’s price is affected by irrelevant information and

deviates from the informational efficient value, informed investors could trade in the

other market to take advantage of the mispricing. The test of rationality will reveal which

market is more vulnerable to the mispricing due to their different reactions to noise

information.

This paper carries out the test of rationality based on the price pressure effect

proposed by Scholes (1972). The notion of price pressure effect asserts that prices could

temporarily diverge from their information-efficient values with uninformed shifts in

excess demand to compensate those that provide liquidity. Mechanically, this occurs

when prices return to their information-efficient values, presumably over a short horizon.

Literature has provided compelling evidence of price pressure effect — abnormal returns

4

and trading volumes around the arrival of irrelevant information are mainly driven by

noise trading from naïve investors; abnormal returns are reversed soon after the arrival of

the information.5 If a market behaves less rationally than others, it should experience a

stronger price pressure effect and respond more to irrelevant information. This paper uses

the effect of a short-lived analyst’s recommendations from Mad Money show to examine

the discrepancy of rationality in the stock and options markets.

Engelberg, Sassville, and Williams (2006), and Balcarcel and Chen (2007) find

that CNBC’s Mad Money spreads irrelevant information and exerts a short-lived price

pressure effect on the stock market. Although the Mad Money is a very popular program

among investors, it also disseminates noise information known among some

professionals. Thus, it constitutes a natural and ideal platform for examining the

discrepancy of rationality between markets. If the options market’s response to the short-

lived analyst’s recommendation is similar to or even stronger than that of the stock

market, it suggests that the options market is no more rational than the stock market. On

the other hand, if the options market does not show any temporary price pressure effect

while the stock market does, it suggests that the options market behaves more rationally

than the stock market.

Black (1975), Cox and Rubinstein (1985), and Chakravarty et al. (2004), among

others, suggest that the options market would be an ideal venue for informed trading. If

informed traders are more likely to trade options and uninformed trading crowds are

more likely to appear in the stock market under certain circumstances, the options and

stock markets should respond to noise or irrelevant information with distinct patterns.

The options market, therefore, should not witness any temporary abnormal price change

in the direction of the recommendation and experience no price reversal. Moreover, if

informed traders would like to take advantage of noise trading crowds, they might leave

alone the irrationality in the stock market purposely and trade against the crowds in the

options market. If it turns out to be the case, the implied price in the options market could

move in the opposite direction from the price pressure effect in the stock market.

5 See, for example, Harris and Gurel (1986), Lynch and Mendenhall (1997), and Wurgler and Zhuravskaya (2002), Mitchell, Pulvino, and Stafford (2004), Coval and Stafford (2004), Corwin (2003), and Liang (1999), Carhart et al. (2002), Cohen, Gompers, and Vuolteenaho (2002), and Hotchkiss and Strickland (2003), Engelberg, Sassville, and Williams (2006), and Balcarcel and Chen (2007).

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Consequently, the implied price derived in the options market may deviate from the

underlying asset’s price in the stock market, since stock markets are more exposed to the

price pressure effect.

This paper estimates the pseudo-price or implied price movement in the options

market based on the sequential approach (i.e., Stephan and Whaley (1990), and

Chakravarty et al (2004)) and the option boundary approach (see, for example, Bodurtha

and Courtadon (1986), and Finucane (1991)). We employ these two approaches because

both methods have their own merits and they complement each other. One can serve as a

robust check for the other.6 Using the standard event study procedure in Mikkelson and

Partch (1988), this study examines the rationality of trading behaviors in the stock and

options markets. Our sample consists of 368 buy and 358 sell recommendations made by

Mr. Cramer during the months of August and September 2005. We analyze both buy and

sell recommendations because literature suggests that analysts are more reluctant to make

sell recommendations, hence they are more credible than buy recommendations.

According to the test results, we document three major findings. First, the options

market behaves in a more rational fashion than the stock market. Consistent with

previous studies on Mad Money show, the price pressure effect in the stock market exists

for small-cap stocks Mr. Cramer recommended to buy. It scores a positive 1.9% return

around the event date. Higher share turnover and larger bid-ask spreads are also detected

for the small-cap stocks. However, this announcement effect is soon reversed during the

two weeks after the recommendation. More interestingly, the abnormal return sinks into

the negative territory, a -5.66% within a month. On the other hand, the options market

does not exhibit any positive abnormal changes for all options categories around the

event date as buy recommendation is made. It is interpreted as evidence that the stock

market is more likely to be driven by naïve investors and behaves less rationally than the

options market. For the sell recommendations, we do not detect a negative price effect on

the announcement date for both the stock and options markets.

Second, the test results show that some informed investors in the options market

may trade against the naïve trading crowd in the stock market. For the small-cap stocks

Mr. Cramer recommended to buy, we find that short-term options with high strike prices

6 A detailed description is presented in Section III.2 of this paper.

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behave in opposition to the recommendation on the following day. The abnormal price

changes are negative and significant. It reveals that some informed investors may be

aware of the short-lived price run-up and buy short-term in-the-money puts in

anticipation of price reversal soon after. This finding indicates that informed traders

could profit from the trade against the uninformed crowds. Additionally, the bid-ask

spread for the short-term in-the-money put options decreases significantly during the day

following the recommendation, as the put option trading volume increases. It suggests

that the options market makers may also expect a price reversal and are confident about

the movement in the near future.

Third, the discrepancy of rationality between the stock and options markets could

produce abnormal trading profits for informed investors around the event date. As an

individual investor buys short-term in-the-money put options on the day following the

recommendation and hold the position till maturity, the trading strategy could generate a

return as high as 26.24%, much higher than normal trades. It indicates that the price

pressure effect on the stock market could become a profitable opportunity for informed

traders. Moreover, this paper shows that informed traders choose different options to

maximize their profits under distinct conditions. When informed traders are aware of a

price pressure effect and expect the price to reverse shortly, they may speculate on the

direction of price movement and care more about the delta and market frictions of the

options instead of financial leverage or liquidity. This study also demonstrates that

informed traders tend to use put options with shorter maturity and higher strike price. We

empirically show that the trading profits around the announcement date are higher than

those on a regular trading day. Given the speculation risk is the same for all trading days,

the excess profits around the event date should be attributed to the discrepancy of

rationality. It is still unknown whether an individual investor could seize any risk-free

arbitrage opportunity from the short-lived price pressure effect. This is beyond the scope

of this study.

The rest of this paper is organized as follows. Section II reviews related

literature. Section III presents the methodologies. Section IV describes the data.

Empirical findings regarding the effects of Mad Money on the stock and options markets

are discussed in Section V. Section VI provides the conclusions.

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II. Background

The informational role of options markets has long been debated. In a frictionless,

dynamically complete market, options would be redundant securities. Options’ premiums

should depend unilaterally on the underlying assets because premiums are a function of

the underlying assets’ prices as well as other factors. Thus, the options market cannot

contain more information than the stock market. However, given the built-in downside

protection and the high leverage achievable with options, one might think the options

market would be an ideal venue for informed trading. If informed investors do trade in

the options market, we would expect at least some new information about the stock price

to be reflected in option prices first.

The use of option prices as predictors of equilibrium prices was first introduced

by Manaster and Rendleman (1982) among others. They suggest that the implied price

derived based on an option pricing model should be the options market’s assessment of

the equilibrium value of underlying asset. Using daily stock options data from 1973

through 1976, they find that implied prices contain information that is not fully reflected

in the observed stock prices. Tucker (1987) applies the same approach to examine

currency forwards and option markets. Kumar, Sarin, and Shastri (1992) document

abnormal option returns prior to block trading in the underlying stock. On the other

hand, based on the lead-lag relationship analysis, Stephan and Whaley (1990) find that

implied stock prices in the options market cannot predict future stock price changes.

Studies by Brenner, Eom, and Landskroner (1996), and Pan, Hocking and Rim (1996)

also find that currency option markets do not contain any additional information above

what is already in the spot market. Chan, Chung, and Johnson (1993), and others analyze

the lead-lag relation between high frequency stock and option returns, and find virtually

no evidence that price changes in options markets lead price changes in stock markets.

Similar results are also found in Diltz and Kim (1996), Krinsky and Lee (1997), Finucane

(1999), O’Connor (1999), and Chan, Chung, and Fong (2002). While these studies come

to conflicting conclusions as to whether the stock market leads the options market, they

consistently find no significant lead for the options markets. Hence informed trading may

not take place in the options markets.

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The findings emerging directly from the lead-lag analysis between stock and

option prices are mixed. However, using Hasbrouck’s (1995) information share analysis

technique, Chakravarty, Gulen, and Mahyhew (2004) document that seventeen percent of

the price discovery occurs in the options market and leverage may be the primary price

discovery driving force in the options market. Based on the “sequential-trade” models, a

number of articles also suggest that informed traders should sometimes trade in the

options market.7 For example, Easley, O’Hara, and Srinivas(1998), and Pan and

Poteshman (2003) use signed options trading volume to show that the options markets

contain information about the price changes of the underlying asset. Cao, Chen, and

Griffin (2000) and others document abnormal trading volume in the options market prior

to takeover announcements. Beyond academic research, informed trades occurring in the

options markets can also be inferred from the fact that there are many cases where

individuals have been prosecuted and convicted of illegal insider trading in the option

markets based on SEC litigation releases.

Previous findings have indicated that the options market may not lead the stock

market all the time. Nevertheless, evidence does show that the options market contribute

to the price discovery in the stock market. In sum, while most literature examines which

market reflects more and responds faster to new information, surprisingly, few papers

have directly examined the following question: Which market behaves more rationally

than the other when movements in these two markets diverge? Literature tends to be in

agreement that the stock and options markets are governed by the same set of

information, have similar trading crowds, and behave equally rationally. Thus, the price

movements in these two markets should change hand-in-hand in the same direction. This

is the primary reason that prior literature focuses on the lead-lag relationship and price

discovery process. Unlike previous studies, this article instead focuses on the rationality

of the trading behaviors in the stock and options markets when the lead-lag relationship

and price discovery are not obvious. 7 In “sequential-trade” models, informed traders can trade in either the stock or options market. These models suggest that the amount of informed trading in options markets should be related to the depth or liquidity of both the stock and options markets, and the amount of leverage achievable with the options. See, for example, Biais and Hillion (1994), Easley et al. (1998), and John et al. (2000), Mayhew et al (1995), Easeley et al, 1998, Cao et al (2000), Arnold et al (2000), Frye, Jayaraman, and Sabherwal (2001), and Pan and Poteshman (2003).

9

A number of authors have documented the price pressure effect in the stock

market when stock analysts’ recommendations are released to the trading crowds (see

Liu, Smith and Syed (1990), Barber and Loeffler (1993), Liang (1999), and Engelberg et

al. (2006), and Balcarcel and Chen (2007)). The impact of the recommendations is

found to be short-lived and the stock prices reverse shortly after the price run-up. These

event studies have received much attention because they provide empirical evidence

showing that the stock market behaves irrationally to noise or irrelevant information.

This research examines whether the options market also behaves irrationally and exhibits

the price pressure effect.

III. Methodology

To examine the rationality of trading behaviors in the stock and options markets,

we use an event study based on the stock analyst’s recommendation made by CNBC’s

Mad Money show. Although the show’s noisy, dramatic camera effect, and boisterous

host may seem silly to some, Mr. Cramer’s recommendations are found affecting stock

prices in the short run. Engelberg, Sasseville, and Williams (2006) show that Cramer’s

buy recommendations are followed by economically and statistically significant

cumulative abnormal returns, 5.19% overnight for small-cap stocks and 1.96% overnight

for the entire sample. These positive returns, however, reverse to negative within several

days. Balcarcel and Chen (2007) also find that Mad Money exerts a short-lived price

pressure effect on the stock market. These prior studies have led many to believe that the

stock market systematically errs when pricing new information. This article conducts

event studies on both the stock and options markets. Comparing the abnormal price

changes of these two markets’ responses to Mad Money show, we are able to analyze the

discrepancy of rationality between them.

If the noise traders are equally likely to trade in the stock and options markets,

both markets should exhibit abnormal price changes in the direction as recommended by

Mad Money. In the case that uninformed investors are more likely to trade in the stock

market while informed traders in the options market, one would expect to find abnormal

price changes in the stock market, but not in the options market. More importantly, when

some informed investors in the options market trade against the noise crowds in the stock

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market to take advantage of the short-lived price pressure effect, the implied price

movements and stock returns could diverge.

We use a standard event study procedure (see, for example, Mikkelson and Parch

(1988) and Liang (1999)) to test the abnormal price changes around the event date. The

stock market price changes are the daily log returns of the stock prices observed in the

stock market. The options pseudo-price movements are derived by inferring stock prices

from options premiums using two approaches — the sequential approach and the options

boundary approach. Section III.1 describes the event study procedure. Section III.2

elaborates the methodology of estimating the implied price movements in the options

market.

III.1 Event study procedure

To analyze the price change behavior around Mr. Cramer’s recommendation, we

first specify a benchmark return and define the daily abnormal price changes in the event

window as the difference between the actual return and the benchmark return. This paper

uses the market model to describe the return-generating process:

Rit=αi + βi Rmt + εit, (1)

where Rit is the rate of return for common stock i on day t, Rmt is the rate of return for the

CRSP value-weighted market index, and εit is the random error term of stock i on day t.

We define the announcement day as day 0, then estimate αi and βi from a 120-day period

from day -124 through day -5. The abnormal price changes for common stock i from day

1 to day 30 are estimated from:

ARit = Rit – (αì + βì Rmt) = εìt, t = 1, 2,…, 30. (2)

The cumulative abnormal returns for the portfolio consisting of N stocks from day t1 to

day t2 are:

CAR = ∑∑==

2

11

1 t

ttit

N

i

ARN

, (3)

Statistical tests are based on the following z-statistic corrected for serial

dependence, because serial correlation occurs when all abnormal returns are functions of

the same market model intercept and slope estimators, and events are announced around

the same time. As in Mikkelson and Parch (1988), the test statistics are:

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Z(CAR) =

∑∑∑===

2

1

2

1

/1

1

t

ttit

t

ttit

N

i

ARVARARN

, (4)

where ∑=

2

1

t

ttitARVAR =

22

2 )(/)]([2

1

⋅−++ ∑

=mm

t

ttmti RVARLRTR

L

TTσ , σi

2 is the variance

of ε`it, L is the length of the estimation period (L = 120 days), and T= t2 - t1 + 1.

We compute the abnormal share turnover, ATOt, on day t and its standard

deviation in the following equations. First, the stock turnover ratio is specified as:

itTO = it

it

SHROUT

VOL, (5)

where itVOL and itSHROUT are the daily trading volume and share outstanding for stock

i in day t, respectively. The average daily turnover for stock i is calculated using the daily

turnover in days -124 to -5:

∑−=

−=

=5

124

t

t

iti L

TOTO . (6)

The daily turnover for day t is the simple average turnover for all stocks in the sample:

tTO = ∑=

N

i i

it

TO

TO

N 1

1, (7)

where N is the number of stocks for day t. The abnormal share turnover, ATOt , is

computed as:

tATO = tTO - TO, (8)

where TO= ∑=

L

ttTO

L 1

1. The standard deviation of the abnormal turnover is:

52

124

1( ) ( )

1t tt

Var AO AO AOL

−

=−

= −− ∑ , (9)

whereAO= 1

1 L

tt

AOL =∑ .

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The abnormal spread, tASPREAD, on day t and its standard deviation are

estimated in the same manner as the abnormal share turnover, We first define the spread

as:

itSpread = )

2( itit

itit

BidAskBidAsk

+−

. (10)

where itSpread , itAsk , and itBid are the daily spread, ask, and bid for stock i and day t.

The average daily spread for stock i is calculated using the daily spread from days -124

through -5:

∑−=

−=

=5

124

t

t

iti L

SpreadSpread . (11)

The daily spread for day t is the simple average spread for all stocks in the sample:

tSpread= ∑=

N

i i

it

Spread

Spread

N 1

1, (12)

where N is the number of stocks for day t. The abnormal spread, tASPREAD, is

specified as:

tASPREAD = tSpread- Spread, (13)

where Spread= ∑=

L

ttSpread

L 1

1. The standard deviation of the abnormal spread is:

262

125

1( ) ( )

1t tt

Var ASPREAD Spread SpreadL

−

=−

= −− ∑ , (14)

where Spread= ∑=

L

ttSpread

L 1

1.

III.2 The methodology of estimating the implied price movements in the options market

We estimate the implied stock prices derived from option premiums in two

different ways — the sequential approach and the option boundary approach. The

sequential approach inserts the previous period implied volatility into an option pricing

model and solves for the implied stock price backward (see, for example, Stephan and

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Whaley (1990), Pan, Hocking, and Rim (1996), Brenner, Eom, and Landskroner (1996),

Kutner (1998), Chakravarty, Gulen, and Mahyhew (2004)). This approach estimates the

implied stock price directly, but may suffer from model-specification errors and non-

synchronous trading problem. The other approach, the option boundary approach, uses

the option boundary conditions to extract the options market’s expectation about the

direction of underlying asset price movements (see, for example, Cox and Rubinstein

(1985), Bodurtha and Courtadon (1986), Finucane (1991), El-Mekkaoui and Flood

(1998), and Lung and Nishikawa (2005)). The advantage of this approach is that it is a

model-free method and is designed for detecting the expectations from the options

market. It does not require pre-specified implied volatility and contains less measurement

errors from model misspecification. However, its estimate is merely an indicator, not a

price, helping to reflect the options market’s expectation about the stock price

movements. Thus, the boundary approach is a less direct method as opposed to the

sequential approach. By employing both approaches, we benefit from their merits as they

complement each other, with one serving as a robust check for the other.

III.2.a The sequential approach

For the sequential approach, this article uses Barone-Adesi and Whaley’s (1986)

American option pricing model for both calls and puts (shown in Appendix I). Let’s

denote the observed options premiums by O, the latent true stock price by S, the volatility

by σ, and all the other observable variables (i.e., the risk-free rate, maturity, strike price)

by R. The theoretical model f(.) could be specified as:

Ot = f(St; σt; Rt), (15)

As the previous period implied volatility, ^

1−tσ , is used as a proxy for σt, an

implied stock price is estimated by inverting the options model with respect to S. It is

stated as:

^

tS = fS

1−(Ot;

^

1−tσ ; Rt), (16)

where ^

tS is the implied stock price derived from the options premiums. Our calculation

algorithm follows the Generalized Newton Method (shown in Appendix II). To minimize

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the measurement error in estimating implied stock value, this study uses a three-step

procedure. We first calculate 1ˆ tσ − given all the observed variables at time t-1. Then, we

trace each option by its sequential series (option ID), adjust 1ˆ tσ − according to the passage

of time, and insert the adjusted 1ˆ tσ − into the option pricing model to invertˆtS at time t.8 If

there are more than one option in an option category at time t, instead of using randomly

assigned weights to various options, we pool the option observations together and

estimate the best implied stock price by minimizing the difference between the model and

market option premiums.9 ˆtS is then used in the event study from Equations (1) through

(4) and test the options market’s reaction to Mr. Cramer’s recommendations.

III.2.b The option boundary approach

For the option boundary approach, we employ American options boundary with

market frictions (see, Bodurtha and Courtadon (1986)) to extract the options market’s

expectations about the stock price movements. The procedure is delineated as follows.

With market frictions, the upper boundary for an American stock call option is:

(Pa + Sa - X τ×−re ) + (TX +TS +TP) ≥ Ca + TC ≥ Ca - TC ≥ Cb - TC (17)

where S, P, C, X, r, and τ refer to observed stock price, put premium, call premium, strike

price, risk-free rate, and time to maturity, respectively. The superscripts, “a” and “b” ,

denote ask and bid of the quotes. TX, TS, TP, and TC are the transaction costs for

exercising options, trading stocks, trading puts, and trading calls, respectively. The

inequalities imply that the value of a call is no more than the value of a synthetic call and

transaction costs. The degree of divergence of a call option from the boundary is:

DC = Cb – [(Pa + Sa - X τ×−re ) + (TX +TS +TP +TC)] (18)

A positive DC would indicate a violation of this upper boundary for call options.

The terms in the first parenthesis of Equation (18) represent the upper boundary of a call

with market frictions, and the terms in the second parenthesis of the equation are 8 The adjustment of 1ˆ tσ − according to the passage of time, based on the partial differential of vega to time

to maturity, should not be ignored, particularly when the time to maturity is short (i.e., less than fifteen days). 9 This procedure is similar to Whaley’s (1982) approach of estimating implied volatilities based on the options in a specific category. Instead of estimating the implied volatilities, this paper uses this procedure to calculate the implied stock price.

15

transaction costs. The larger the DC is, the greater the divergence, and this indicates that

the call option is relatively more expensive than the put option.

Similarly, the upper boundary for American put options is expressed as:

(Ca – Sb τ×−qe + X) + (TX +TS +TC ) ≥ Pa + TP ≥ Pa - TP ≥ Pb - TP, (19)

where q is the dividend yield. This put boundary shows that the value of a synthetic put

plus market friction should be higher than a put. The degree of divergence of a put from

its boundary is:

DP = Pb –[(Ca – Sb τ×−qe + X ) + (TX +TS +TC + TP)]. (20)

Again, a positive DP implies a violation of this upper boundary for put options.

The portfolio in the first parenthesis of Equation (20) is the upper boundary for a put with

market frictions, and the terms in the second parenthesis of the equation represent

transaction costs. The larger the DP, the higher the degree of divergence, and it means

that the put is relatively more expensive than the call option, and vice versa.

Combing DC and DP, the divergence between the implied stock price in the

options market and the stock price in the stock market can be derived as in Equation (21):

Divergence = DC - DP = (Ca + Cb - Pa – Pb) – (Sa+ Sb τ×−qe ) + X (1+ τ×−re ) (21)

The rationale for deriving Divergence to extract the option’s market expectation is

described as follows. Assume that the implied stock price, ˆtS , could equally likely lie at

any point in a range between Low and High. That is:

Prob.(^

tS =αi|Low ≤ αi ≤ Low) = Prob.(^

tS =αj|Low ≤ αj ≤ Low), for ∀ αi and αj (22)

Low and High are the lower and higher bounds for ˆtS , respectively, and α is any

real number between Low and High. If the range is asymmetrically biased to the upside

(downside) of the current stock price quotes, then the implied stock price is more likely to

be larger (smaller) than the observed stock price. Thus, it indicates that the options

market’s expectation is relatively higher (lower) than the observed stock price. The bias

of the range is indeed measured by Divergence = DC - DP. Based on Equations (18) and

(20), we obtain the following results:

Sa ≥ Cb - Pa + X τ×−re - (TX +TS +TP+TC) = Low (23)

Sb ≤ [Ca – Pb + X + (TX +TS +TP+TC)] / τ×−qe = High (24)

16

Combining inequalities (23) and (24), [Low, High] serves as a range for the implied

stock price when boundary conditions are not violated.10 DC, which equals (Low–Sa),

measures the difference between the lower bound and the observed stock price. The larger

the value of DC, the higher the call premium is relative to the put premium. DP, which is

(Sb–High)τ×−qe , determines the difference between the observed stock price and the higher

bound. The larger the value of DP, the higher the put premium is relative to the call

premium. Therefore, Divergence in Equation (21) measures the bias of the range for the

implied stock price. A positive (negative) Divergence shows that the implied stock price

has a higher probability to be larger (smaller) than the observed stock price. 11

Figure 1 illustrates the range and Divergence. If the range of Low to High is not

biased to either side, Divergence is zero and the implied stock price is equal to the

observed stock price. However, as the range of Low′ (Low′′) to High′ (High′′) is biased to

the left (right), then Divergence is less (greater) than zero and the implied stock price is

smaller (greater) than the observed stock price. Thus, Divergence measures the bias of

the range and reveals the expectations form the options market. If there is more than one

Divergence in an option category at time t, the mean of the Divergences is used in the

event study procedure from Equations (1) through (4).

<<Insert Figure 1 about here>>

IV. Data

The empirical analysis is based on three major data sources — the stock analyst’s

recommendation list, the daily stock data, and the daily options data. The

recommendation list is obtained from the website of madmoneyrecap.com, the stock

market data are retrieved from the Center of Research in Security Prices (CRSP), and

options data are provided by the Chicago Board Options Exchange (CBOE).

10 When the boundary condition holds, the difference between implied and observed stock prices cannot

exceed Max[ |Low- Sa| τ×−re , | Sb -High|τ×−re ]. On the other hand, if boundary conditions are violated, the

implied stock price will lie outside the range of [Low, High]. However, Divergence is still the measure for the bias. 11 If this argument is true, it will confirm and explain what was found in Bodurtha and Courtadon (1986) and El-Mekkaoui and Flood (1998).

17

For the event study, we follow Engelberg et al (2006) and Balcarcel and Chen

(2007), and use the stock recommendations made by Jim Cramer, host of the popular

television show Mad Money. We collect buy and sell recommendations made by Jim

Cramer from madmoneyrecap.com for the months of August and September 2005.

Madmoneyrecap.com is an independent site that is not related to Jim Cramer, CNBC, or

NBC. The site provides stock information through a recap of the daily show.

During August and September of 2005, Mr. Cramer made 661 buy

recommendations and 447 sell recommendations. Since more often than not, a company

would receive more than one buy (or sell) recommendation during our sample period, for

our analysis we consider the first time the company gets a buy or sell recommendation

during the sample period. Our final sample consists of 368 “unique” buy

recommendations and 358 “unique” sell recommendations. We study the stock and

options markets’ reaction to Mr. Cramer’s stock recommendations, because the show’s

large audience may comprise a variety of investors — naive investors, informed

investors, and even market makers. We analyze both buy and sell recommendations,

because literature suggests that analysts are more reluctant to make sell

recommendations, hence they are more credible than buy recommendations.

The CRSP daily stock returns and the value-weighted index returns are used in

Equation (1) to estimate the benchmark stock returns and to calculate CAR. The daily

trading volume and share outstanding are used to calculate the abnormal trading from

Equations (5) through (9). We use daily closing bid and ask prices to calculate the

abnormal spread from Equations (10) to (14). This study also classifies the sample stocks

into three size categories by ranking each observation by its market capitalization five

trading days prior to the recommendations. In this manner, we examine whether firm

size affects the price pressure effect. The lowest one third stocks are considered small-

cap, the next one third, mid-cap, and the highest one third are large-cap.

The daily options data are obtained from the Market Data Express (MDX)

provided by CBOE. The options records are organized by series, including symbol,

expiration month, strike price, type of options, open interest, daily trading volume, last

sale option price, bid and ask prices, and underlying stock symbol and price. Because the

options prices are recorded at 4:00 p.m. Eastern Time (3:00 p.m. Central Time), while the

18

stock prices in CRSP are booked around 4:30 p.m., our estimation of implied stock prices

could contain non-synchronous trading errors if using the CRSP data. In an effort to

minimize the non-synchronous trading problem when estimating the implied stock prices,

we match the underlying stock price recorded in MDX with the intraday stock bid and

ask quotes taken from the Trade and Quote (TAQ) database in New York Stock

Exchange (NYSE). We discard the observations if the stock price changes more than

0.5% between 4:00 to 4:30 p.m., because it may indicate that some significant

information has occurred after 4:00 p.m. when the equity options market is closed. Also,

similar to previous studies, i.e., Koraqjczyk and Sadka (2004), and Engelberg et al

(2006), we discard the observations with negative stock spread or with stock spread

greater than 10% of the stock price.

For the sequential approach, we use the last sale option price to estimate the

implied stock price, ̂ tS . The daily risk-free rate is the Treasury bill rates taken from the

Federal Reserve Bank of New York. The stock dividend yields are based on the actual

stock dividends from COMPUSTAT. We apply interpolation method for the interest

rates and dividend yields to match the time to maturity of options. For the boundary

approach, this study employs the bid and ask prices for options (from MDX) and stocks

(from TAQ) to calculate Divergence as shown in Equation (21). The dividend yields and

interest rates are computed in the same manner as for the sequential approach.

Options with maturity of 10 to 120 days are used to derive the implied stock

prices. In order to avoid term structure of volatility effect (see Xu and Taylor (1994),

Campa and Chang (1995)), we classify the overall observations into three maturity

groups — the short-term (10 to 30 days), mid-term (31 to 60 days), and long-term options

(61 to 120 days). Furthermore, to avoid the effect of volatility smile on the implied price

estimation, we partition the options into three categories by the degree of delta. This

paper defines out-of-the-money (OTM) options as options with delta between 0.02 and

0.45, at-the-money (ATM) options as options with delta between 0.45 to 0.55, and in-the-

money (ITM) options as options with delta from 0.55 to 0.98. We discard options with

delta less than 0.02 or higher than 0.98 to avoid thin trading problems which may cause

erratic implied price estimates. Based on the classification of moneyness, a Divergence

19

could be calculated based on a pair of OTM call and ITM put, a pair of ATM call and

ATM put, or a pair of ITM call and OTM put.

V. Empirical results

Table 1 reports the summary statistics for the stocks and options in this study. In

this table, we calculate the average size of a stock based on the market values from day -5

through day -1, and the spread and turnover are computed from day -124 through day -5

before the event date. Panel A shows the descriptive statistics for options and stocks Mr.

Cramer recommended to buy. The averages of market capitalization for small-caps, mid-

caps and large-caps are approximately $0.933, 4.6, and 36 billion, respectively. The size

is ranked by pooling all the recommended stocks. We find that the smaller the size, the

greater the stock spread and turnover tend to be. The stock spread for small-cap stocks

(0.16%), for instance, is more than twice the spread for the large-cap (0.06%). It

indicates that the small-cap market makers are faced with more uncertainty about the

stock value, higher inventory cost/order processing, and (or) greater information

asymmetry (see, for example, Madhavan et al., 1997, Liang, 1999, and Engelberg et al.,

2006).

The call option spreads exhibit a similar pattern to the stock spreads, but they are

much larger than those for stocks. It is not surprising to have extremely large option

spreads because of the high inventory cost and the price discreteness. For example, an

out-of-the-money option could have bid-ask price of $0.20-$0.40 and the option’s spread

is 66.7% ( 2)2.0$4.0($

2.0$4.0$+−

). These wide spreads enable the options market makers to

reveal their distinct information or expectation about the underlying asset’s value in their

quotes without violating the option boundary conditions and inviting arbitrages.

However, the implied stock prices, as discussed in Section III.2, may differ from the

actual stock market prices and reveal the market makers’ expectation. Panel A also

shows that small-cap stocks tend to have higher implied volatility ratio and option

volume ratio than others. In this study, the implied volatility ratio equals the implied

volatility divided by COBE’s volatility index (VIX), and the option volume ratio is

computed as option trading volume divided by the stock trading volume. The small-cap

20

stocks have higher risk and their options are relatively more heavily traded than other

stocks. The spread, implied volatility, and trading volume for put options display a

similar pattern to those of call options. Panel B shows the descriptive statistics of stocks

with sell recommendations and exhibits the same patterns as in Panel A.

<<Insert Table 1 about here>>

Table 2 displays the descriptive statistics for stock options in different categories.

Panel A is for call options of stocks with buy recommendations. The number of

observations for each category is not identical because some stocks may have missing

options of certain types. The call options spreads are negatively related to moneyness

and maturity. This is not unexpected because long-term ITM options should have higher

premiums than other options. For instance, for the small-cap stocks, the spread is 92.91%

for OTM calls with short maturity, while it is 51.16% for OTM calls with long maturity

and 15.28% for ITM calls with short maturity.

The implied volatility ratio tends to be negatively related to maturity, and it is

consistent with the volatility term structure (see, for example, Xu 1995). Also, we find

that ITM and OTM options have higher implied volatilities than ATM options across all

capital sizes. This is in line with the volatility smile found in many previous studies (e.g.,

Bolen and Whaley 2004). In addition, the stock size, spread, and turnover are not related

to options moneyness and maturity. They show a similar pattern to what we found in

Table 1.

Panel B reports the call options of stocks with sell recommendation. It displays a

similar pattern to Panel A. Nevertheless, the number of observations for small-cap stocks

in Panel B is more than that in Panel A, and vice versa for large-cap stocks. It shows that

Mad Money show is more likely to recommend selling small-cap stocks and buying

large-cap stocks. Panels C and D are for put options of stocks with buy and sell

recommendations, respectively. Comparing Panel C (D) with Panel A (B), we find that

their patterns are alike, but put options are less frequently traded than call options. In

sum, based on Tables 1 and 2, we find that stock spreads and trading volume are not

related to options maturity and moneyness.

21


V.1. Stock market price effect

The price effect of Mr. Cramer’s recommendations on the stock market is shown

in Table 3. This table reports the price effect for all the recommendations and includes

the daily abnormal return, AR, cumulative abnormal return, CAR, and their t-statistics for

day 1, 2, 10, and 30. Because Mr. Cramer’s recommendations are made after market is

closed, we study the effect starting from the day after the recommendation day. In

addition to the returns, we also show the t-statistics for the abnormal turnover, ATO, and

abnormal spread, ASPREAD. For the entire sample of buy recommendations, AR on day

1 is 0.41% and is not significant. On the other hand, both ATO and ASPREAD are

positive and significant. These results indicate that the stocks are more heavily traded

than usual although without a price effect. The stock spread increases marginally, which

is consistent with Engelberg et al’s (2006) finding and different from some of the

previous studies’ results (e.g., Liang (1999)). This finding could suggest that the

decrease in adverse selection effect is outweighed by the order processing cost. As we

move to day 10 and 30, AR becomes negative and significant. Also, from day 1 through

day 30, CAR is -2.54% and statistically significant. It indicates price reversal after the

buy recommendation. However, ATO and ASPREAD are not significant after day 1. It

shows that the abnormal trading activities do not last long.

As we classify the buy recommendations according to market capitalization, we

find that small-caps are driving the results. AR on day 1 for the small-cap stocks is

0.91% and statistically significant. Both ATO and ASPREAD are positive and significant

at less than one percent level. On day 2, AR is also positive and significant, and CAR,

1.44%, is significant as well. However, from day 1 through day 30, the CAR becomes -

3.76% and significant. It shows that small caps have a strong price reversal, and hence, a

strong price pressure effect from buy recommendations. For the mid-cap and large-cap

stocks, both AR and CAR are not significant. There is no evidence of the price pressure

effect on these stocks. Nevertheless, the CARs for these two groups from day 1 to day 30

are negative and marginally significant at less than ten percent level. These results

22

suggest that the buy recommendations for the mid-cap and large-cap stocks are not very

credible. Therefore, we conclude that Mr. Cramer’s recommendation has impact on

small-cap stocks, but the effect is short-lived, which is consistent with previous findings

(Engelberg et al. (2006) and Balcarcel and Chen (2007)).

For the sell recommendations, AR is only 0.11% and not significant during the

entire sample period. However, ATO is positive and significant, suggesting that even

though the sell recommendations affect the trading activities, they do not exert price

pressure on the stock market. AR is not significant across all the size categories.

Nevertheless, for the small-caps, CAR from day 1 to day 10 is -1.74% and significant. It

indicates that sell recommendations may be useful to predict the small-cap stock returns.


V.2. Options market price effect

The price effect of Mad Money on the options market is reported in Table 4. This

table only shows the effect on day 1 to save space. For other window periods, the test

results are qualitatively similar.12 Controlling for the effects of market value, moneyness,

and time to maturity, we categorize options into different groups according to three sizes

(small-cap, mid-cap, and large-cap), three classes of moneyness (OTM, ATM, and ITM),

and three maturities (short-term, mid-term, and long-term). AR of Call (Put) is the

abnormal return calculated based on the implied stock prices, ̂ ,tS from call (put) options.

Similar to the standard procedure to calculate AR, we first derive ̂ tS from calls (puts),

compute the price changes, and use the market model as specified in Equation (2) to find

the abnormal returns. AR of Divergence is calculated in a similar manner.

Panel A shows the test results for the buy recommendations. For the AR of Call

ˆtS , there is no evidence of any price pressure across all the categories. Although ARs are

positive for most short-term options, they are not statistically significant. For instance,

the AR for the small-cap OTM call options with short maturity is 0.14% with a t-statistic

12 The test results of the abnormal returns and cumulative abnormal returns for day 2 through day 30 are available upon request.

23

of 0.07. It is noted that these results are different from those in Table 3, where results are

significant for small-cap stocks. It seems to suggest that Mr. Cramer’s recommendations

have no impact on the options market at all. The test results based on the AR of Put

ˆtS are similar to the findings from the calls, no price pressure effect is found. It is also

worth noting that most of the short-term put options across different sizes and moneyness

have negative ARs. The small-cap ITM put options with short maturity, for example, on

average have the largest negative AR of -0.41% with a t-statistic of -1.61. Although not

statistically significant, it indicates that the trading behavior on short-term put options

may be contrary to the recommendations.

As we analyze the test results from the AR of Divergence, we notice that,

interestingly, most of the short-term Divergences are negative across different size and

moneyness categories. They seem to be to the opposite of the analyst’s recommendations.

In particular, for the small-cap OTM call / ITM put options with short maturity, the AR of

Divergence is -0.51% and significant at less than one percent level. It suggests that the

options market reacts in the opposite direction of Mr. Cramer’s recommendations,

expecting a stock price reversal within a short period of time. This finding corresponds

to the short-lived price effect and return reversal for the small-cap stocks found in Table

3. It is also intriguing that the significant contrary result only happens for the divergence

combining OTM call options and ITM put options. This result should not be a

coincident.

If market makers and/or informed traders in the options market are anticipating

the short-lived price pressure and the following reversal, some of them may trade against

the noise crowd. If the informed investors in the options market expect stock prices to

drop in the short term, they are more likely to buy a put option with high delta and/or

construct a synthetic short position with high strike price (selling an OTM call and

buying an ITM put at the same time). This is consistent with de Jong, Koedijk, and

Schnitzlein’s (2001) finding that informed traders favor ITM options if they are sure

about the future price movements.

The trading activities of these market makers and informed investors could be

uncovered in the options prices and bid-ask quotes. As they have different opinions

about the underlying asset’s price change, the market makers may adjust the options

24

prices and the direction of bid-ask quotes (as discussed in Section III.2.b) and drive the

implied price changes deviated from the stock returns. Because of the wide option

spread, they could incorporate their expectations without violating the rule of one price.

Thus, it is not shocking to find the significant and negative AR for the Divergence derived

from short-term ITM puts and OTM calls. This argument is also confirmed by the

negative AR of Put ˆtS , -0.41%, from the small-cap ITM put options with short maturity

as noted in the same panel. These results suggest that the options market behaves more

rationally than the stock market and informed traders in the options market may use

short-term ITM puts to trade against the noise crowd.

The test results for sell recommendations are reported in Panel B of Table 4. For

both call and put ̂tS , most of the ARs are negative but not significant. For example, the

small-cap short term options for OTM calls and ITM puts are marginally significant at

the 10% level. Comparing with Panel A, we find that the options market is more

responsive to sell recommendations than buy recommendations. For example, the AR of

the small-cap ITM options with short maturity is -0.46% with a t-statistic of -1.74. It

signals that the options market correctly responds to the sell recommendations which tend

to be more credible than the buy recommendations. The AR of Divergence displays a

similar pattern. The short-term Divergence derived from OTM call/ITM put options for

small-cap stocks has an AR of -0.64% and is significant at less than five percent level. It

indicates that the options market reaction is consistent with Mr. Cramer’s sell

recommendation expecting a stock price drop shortly.


V.3. Heterogeneous traders or measurement error

Given the test results above, we find that the stock and options markets may react

differently to the analyst’s recommendation. These findings could be attributed to two

reasons. First, the measurement errors of the implied stock prices drive the deviation

between the stock and options markets’ price changes. Second, the distinct responses to

Mr. Cramer’s recommendation are caused by two different trading crowds — naïve

investors and informed traders. When informed traders in the options market take

25

advantage of less rational investors in the stock market in the case of a short-lived price

run-up, the options market should behave more rationally than the stock market.

If the measurement errors are the cause, the relationship between the stock

abnormal returns and implied abnormal returns should be weak. Table 5 reports the

correlation among the abnormal stock returns, the implied abnormal returns from calls

and puts, and the abnormal divergence changes. These abnormal returns are aggregate

standardized returns from day -124 through day -5. We first standardize the daily

abnormal returns and compute the means for the stock and options markets, and then

calculate the correlations among those daily means. As shown in Table 5, all the

correlations are positive and significant at less than one percent level. It indicates that

these abnormal returns derived from stocks and options behave similarly on a daily basis.

The significant relationship is consistent with the previous literature about the lead-lag

relation between the stock and options markets (see Stephen and Whaley (1990), and

Chan et al (2002)). Thus, if the stock and options markets respond differently to the

analyst’s recommendations, it is not likely due to measurement errors of implied stock

prices.


Alternatively, if the market makers and/or informed traders in the options market

drive the different responses between the stock and options markets, their trading

behavior should also affect the options bid-ask spread and trading volume. Table 6

reports the event study test results on the day following Mr. Cramer’s buy

recommendation. The abnormal options spread, ASPREAD, is estimated the same

manner as the abnormal stock spread. The abnormal turnover, ATO, is calculated based

on the options turnover ratio which is the options trading volume divided by the stock

trading volume. The methodology to test ATO is the same as specified in Equations (6)

through (9) for the stock abnormal turnover. For call options in Table 6, most of the

ASPREAD and ATO are not significant. This finding suggests that the analyst’s

recommendations may not affect the trading behavior of call options. On the other hand,

the empirical results from put options are intriguing. For the mid-cap and large-cap

26

stocks, most of the ASPREAD and ATO are not significant and their signs are not

consistent. However, the small-cap stock options show different results. Particularly,

the ITM put options with short maturity show a significant decrease in the bid-ask spread

and a significant increase in the trading activities. Their ASPREAD is -0.73% and is

significant at less than one percent level, while ATO is 0.86 with a t-statistic of 2.13.

These results indicate that the market makers face less adverse selection risk or

information asymmetry and investors are trading more short-term ITM puts than usual.

Therefore, the opposite reaction to the buy recommendations could be driven by the

different opinions from the informed investors.


V.4. Trading profit

According to the findings from Tables 3 through 6, we have shown the evidence

of the discrepancy of rationality between the stock and options markets. It is also of

interest to analyze two practical questions. First, could the discrepancy create abnormal

trading profits for informed traders who take advantage of the Mad Money effect on the

stock market? To examine this question, we need to find out if selling/buying short-term

put options around Mr. Cramer’s buy recommendations generate excess trading returns.

Second, why are ITM put options favored by informed investors trading on the effect of

Mad Money? This latter result is not consistent with some of the prior studies. For

example, Lee and Yi (2001) document that options with higher financial leverage, or

OTM options, are more attractive to informed traders. This inconsistent finding could be

attributed to the difference of trading strategies under distinct situations. Dealing with

the short-lived price effect and short-term price reversal (within 30 days), informed

traders may want to buy short-term puts and hold them till maturity to avoid the huge bid-

ask spread cost in transaction. If short-term OTM puts remain out-of-the-money at

maturity, informed traders would still lose money, even though the stock prices do

decrease and OTM options have greater financial leverage. Thus, ITM options could be

preferred by these traders.

27

To investigate these two questions in more details, this paper conducts a trading

simulation. As we buy small-cap short-term puts a day after Mr. Cramer’s

recommendations and hold them to maturity, we would like to examine whether the

trading profits are higher than usual and if ITM puts perform better than others. The

trading returns are calculated as:

Options trading returns =t

tT

O

OV −, (25)

where tO is put options closing price on the trading day t obtained from Market Data

Express (MDX) provided by CBOE. TV is the value of the put options on expiration date,

which is )0,( TSXMax − , X is the strike price and TS is the stock closing price. The

average return during non-event period is calculated from day -125 through day -30.

This paper follows Bollen and Whaley (2004) and performs the modified t-test of

Johnson (1978, Equation (2.5), pp. 537), which explicitly accounts for the asymmetric

distribution.13

The test results are reported in Table 7. During the non-event period, buying

naked short-term OTM put options results in a monthly return of -41.69% with a t-

statistic of -4.31. This result is expected because short-term OTM puts usually remain

out-of-the-money when the stock market steadily grows during the sample period. ATM

and ITM puts also bring significant losses of -18.31% and -11.85%, respectively.

However, their returns are not worse than OTM put options, because ATM and ITM

options have much higher price, tO as specified in Equation (25), than OTM options.

During the event period, however, we find that short-term ITM put options generate the

highest return, 26.24% with t-statistic of 3.13, while OTM put options, the lowest,

-10.26%. In addition, all the differences in returns between the event period and non-

event period are positive and significant. This result is not surprising because of the

short-lived run-up and price reversal after Mr. Cramer’s buy recommendations. All of

13 The test statistic, tJohnson is specified as: tJohnson = [(x~ - u) + N

u23

6σ+

43

3σu

(x~ - u)2 ] [s2/N] -1/2 ,x~ is the

sample mean. µ, σ2, and µ3 are the first, second and third central moments, respectively. s2 is the sample variance. N is the sample size. In the mean tests, µ is set at zero, σ2 is estimated by the sample variance, and µ3 are estimated by the sample skewness.

28

these results are consistent with the findings in Tables 3 and 4. The informed traders

seem to favor short-term ITM puts as found in this study. It could be partially explained

by our finding that buying short-term ITM puts in the Mad Money event yields the

highest returns. Nevertheless, one should explain these trading profits with caution.

Although Table 7 suggests that the price pressure effect caused by Mad Money could

help informed investors earn higher speculation returns than usual, it does not indicate

that the excess returns are risk-free. It is because the trading strategy is to speculate on

the short-lived price effect, not arbitrage on any violation of the law of one price.


VI. Conclusions In this study, we investigate the discrepancy of trading rationality between the

stock and options markets using Mad Money recommendations. Literature has put forth

much effort to understand the lead-lag relation and price discovery process between these

two markets. However, it is still not clear if the stock and options markets behave

equally rationally. This question is intriguing because many researchers focus only on

the usual and reasonable situation that the stock and options markets move in the same

direction with different speed, but seldom examine the unusual or unreasonable situation

when these two markets deviate from each other. If the stock and options markets do

deviate from each other occasionally, it is worthwhile to find out why they move

differently and which market behaves more rationally. In searching for the answers, we

find that the short-lived price pressure effect caused by the Mad Money show provides an

ideal and natural experimental environment for this study.

We first follow the traditional event study procedure to examine the effect of Mr.

Cramer’s recommendations on the stock market. Consistent with previous studies, the

test results from small-cap stocks show a short-lived price run-up followed by a sharp

price reversal. It suggests that the stock market may react to the analyst’s

recommendation irrationally. This could be attributable to the behavior of the naïve

trading crowd in the stock market. If, as previous studies suggest (see, e.g.., Black

(1975), Cox and Rubinstein (1985), Easley et al. (1998), and Chakravarty et al. (2004)),

29

informed traders prefer to trade in the options market, we should find the options market

reacting to the recommendation more rationally than the stock market. Hence the implied

stock prices in the options market should display a less price run-up or no price pressure

effect. Moreover, if informed investors are aware of the Mad Money effect and expect a

price reversal in the short term, they may trade against the naïve investors and drive the

implied prices to the opposite direction.

Out test results indicate no price pressure effect in the options market around the

time of the analyst’s recommendations. Therefore, the options market behaves more

rationally than the stock market. Moreover, we find that, for small-cap stocks, the

implied prices derived from short-term ITM put options react to the buy recommendation

in the exact opposite direction. The abnormal price changes are negative and significant

a day following the event. The bid-ask spread of options decreases and trading volume

picks up as well. These results indicate that some informed traders, such as options

market makers, expect a price reversal shortly and reveal their expectations in their

trading behavior. We conduct a trading simulation based on a simple trading strategy

— buy short-term put options and hold to maturity. The test results point out that profits

during the event day are greater than those during the non-event day. More interestingly,

short-term ITM put options generate the highest monthly return. We suggest that the

discrepancy of rationality between the stock and options markets create abnormally

higher trading profits for the informed traders. Nevertheless, we need to be cautious that

the excess return is from speculation, not arbitrage, because informed traders speculate on

the price reversal, not arbitrage on the violation of law of one price.

30

References

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35

Appendix I:

The Option Pricing Model (Barone-Adesi-Whaley, 1986) used to derive implied stock price

C = c + A2 (S/S*)q2 if S<S*

= S-X if S≥S*

c = European Currency Call Options = e- rq ×τ S⋅N(d1) - e-rd×τ X⋅N(d2)

d1 = [ln(S/X) + (rd - rq + σ2/2) ×τ] /σ√τ d2 = [ln(S/X) + (rd - rq - σ2/2) ×τ] /σ√τ = d1 - σ√τ

A2 = S* / q2 × { 1- e-rq ×τ N[d1(S*)]}

q2= {-(N-1)+[(N-1)2 + 4M/k]1/2}/2

M=2rd/σ2

N= 2(rd-rq) /σ2

k=1-e-rd×τ

P = p + A1 (S/S**)q1 if S>S** = X-S if S≤S**

p = European Currency Put Options= e-rd×τ X ⋅ N(-d2) - e-rq×τ S ⋅ N(-d1)

A1 = -S** / q1 × { 1- e-rq ×τ N[-d1(S**)]}

q1= {-(N-1)-[(N-1)2 + 4M/k]1/2}/2

where C (P) is the American currency option premium for a call (put) option; S* (S**)

refers to the critical spot rate that triggers early exercise of a call (put) option. S is the

stock price; rd and rq are the risk-free rate and dividend yield, respectively; X stands for

the strike price of an option; N(⋅) is the standard cumulative normal distribution function,

σ2 is annualized variance of the continuously compounded return; and τ is time to

maturity.

36

Appendix II:

Description for applying the Generalized Newton Method to derive implied stock prices

The basics for the Generalized Newton Method is to choose a group of starting

values of the estimated parameters and continually improve the estimates based on an

inverse Jacobian matrix until the error sum of squares falls into a pre-specified acceptable

tolerance level.

In order to solve n unknown parameters among n nonlinear equations, the solution

procedure can be setup as:

X1 (v1, v2,…,vn) X2 (v1, v2,…,vn)

:

: (AII-1),

Xn (v1, v2,…,vn)

where X are the functions of parameters v1, v2,…,vn. vi is the ith parameter in X.

By setting a group of starting values (v1.0, v2.0,…,vn.0 ) to initiate the generalized Newton

procedure, the subsequent values are calculated repeatedly as follows:

v1.i v1.i-1 ∂X1/∂v1 ∂X1/∂v2….∂X1/∂vn −1 X1 (v1.i-1, v2..i-1,…,vn. .i-1)

v2.i v2.i-1 ∂X2/∂v1 ∂X2/∂v2….∂X2/∂vn X2 (v1.i-1, v2..i-1,…,vn. .i-1)

: : : : : : : : : (AII-2)

vn.i vn.i-1 ∂Xn/∂v1 ∂Xn/∂v2….∂Xn/∂vn Xn (v1.i-1, v2..i-1,…,vn. .i-1)

where j in equation (AII-2) refers to the jth iteration. Based on the generalized Newton

model, one may solve n unknown parameters according to n nonlinear equations

(functions). In this study, the function is Barone-Adesi-Whaley (1986) model given in

Appendix I, and the unknown parameter is the implied volatility or implied stock price.

37

Table 1: Summary statistics of the sample stocks from Cramer’s recommendations This table reports summary statistics of the sample stocks recommended by Cramer. Size is calculated based upon the market value of a stock from day -5 to -1; Stock spread, options spread, and stock turnover are calculated from day -124 to day -5; Beta is the systematic risk of the stock; IV ratio is the implied volatility ratio defined as the implied volatility divided by the VIX; option volume is the options trading volume; and option volume ratio is computed as options trading volume divided by the stock trading volume. Panel A: Stocks of Buy Recommendations

Obs. Size

($mil) Stock Spread

Stock Turnover Beta Call options Put options

Option Spread

IV Ratio

Option Volume

Option Volume Ratio

Option Spread

IV Ratio

Option Volume

Option Volume Ratio

Entire 368 16,455 0.10% 1.25% 1.39 30.25% 2.68 407 1.32% 29.71% 2.85 239 0.89% Small 91 933 0.16% 2.02% 2.24 35.29% 3.71 112 1.56% 36.58% 3.98 69 1.03% Med 130 4,644 0.09% 1.20% 1.33 30.51% 2.56 181 1.09% 31.62% 2.73 117 0.81% Large 147 36,510 0.06% 0.82% 0.91 26.89% 2.15 789 1.38% 23.84% 2.26 449 0.88%

Panel B: Stocks of Sell Recommendations

Obs. Size

($mil) Stock Spread

Stock Turnover Beta Call options Put options

Option Spread IV

Option Volume

Volume Ratio

Option Spread IV

Option Volume

Volume Ratio

Entire 358 10,825 0.12% 1.49% 1.71 36.32% 3.19 300 1.30% 32.82% 3.37 204 0.97% Small 152 828 0.16% 2.03% 2.35 40.22% 4.03 148 1.49% 36.15% 4.25 96 1.09% Med 118 3,799 0.10% 1.35% 1.47 34.41% 2.88 268 1.16% 32.57% 3.05 172 0.88% Large 88 37,516 0.07% 0.77% 0.92 32.16% 2.16 607 1.16% 27.43% 2.28 431 0.86%

38

Table 2: Summary statistics of the sample options data

This table reports descriptive statistics of options data. Underlying assets are classified into three sizes: small-cap, mid-cap, and large-cap; options moneyness are classified into three categories according to their delta value. Out-of-the-money (OTM) options with low delta value (0.02–0.45); At-the-money (ATM) options with medium delta value (0.45-0.55); and In-the-money options (ITM) with high delta value (0.55-0.98). Options are also classified into three maturity categories. Short represents short-term options (10-30 days); Mid represents mid-term options (31-60 days); and Long represents long-term options (61-120 days).

Panel A: Call Options for Buy Recommendations Buy Recommendations

Moneyness Maturity Obs. size

($mil) Option spread

IV ratio

Option Volume

Volume Ratio

Stock Spread

Stock Turnover

Small-Cap OTM Short 85 951 92.91% 3.95 146 1.97% 0.15% 1.97%

Mid 90 918 76.95% 3.78 120 1.86% 0.16% 1.98% Long 91 928 51.16% 3.47 69 1.29% 0.15% 2.02% ATM Short 85 921 27.00% 3.63 219 2.46% 0.16% 2.15% Mid 90 930 19.53% 3.59 124 1.67% 0.15% 1.91% Long 91 939 14.71% 3.51 77 1.25% 0.15% 1.96% ITM Short 85 940 15.28% 3.78 121 1.54% 0.17% 2.07% Mid 89 932 12.29% 3.89 88 1.25% 0.17% 2.06% Long 90 939 9.27% 3.82 55 0.79% 0.16% 2.09%

Mid-Cap OTM Short 122 4,713 95.45% 2.78 259 1.35% 0.09% 1.23% Mid 127 4,629 73.88% 2.53 210 1.23% 0.10% 1.16% Long 127 4,619 41.32% 2.33 107 0.73% 0.09% 1.18% ATM Short 123 4,677 20.20% 2.39 339 1.90% 0.10% 1.21% Mid 125 4,645 13.43% 2.43 213 1.33% 0.09% 1.20% Long 126 4,643 10.02% 2.40 119 0.83% 0.09% 1.20% ITM Short 127 4,641 9.73% 2.74 162 0.93% 0.09% 1.20% Mid 129 4,609 7.48% 2.71 148 0.94% 0.09% 1.21% Long 130 4,625 5.85% 2.69 84 0.63% 0.09% 1.24%

Large-Cap OTM Short 145 36,568 88.84% 2.16 1,206 1.95% 0.06% 0.82% Mid 146 36,352 69.37% 2.05 943 1.60% 0.06% 0.81% Long 147 36,205 40.79% 1.95 461 0.81% 0.06% 0.81% ATM Short 142 37,239 12.66% 1.93 1,379 2.40% 0.06% 0.85% Mid 146 36,465 9.13% 2.02 1,002 1.61% 0.06% 0.83% Long 147 36,252 6.69% 2.02 454 0.89% 0.06% 0.82% ITM Short 144 36,798 5.99% 2.47 823 1.68% 0.06% 0.81% Mid 146 36,407 4.74% 2.38 570 0.89% 0.06% 0.83% Long 147 36,332 3.72% 2.34 287 0.63% 0.06% 0.83%

39

Panel B: Call Options for Sell Recommendations Sell Recommendations


($mil) Option spread IV

Option Volume

Volume Ratio

Stock Spread

Stock Turnover




Large-Cap OTM Short 85 37,762 93.42% 2.22 847 1.87% 0.07% 0.77% Mid 88 36,821 82.81% 2.12 793 1.49% 0.08% 0.76% Long 87 37,122 58.91% 1.98 433 0.81% 0.07% 0.77% ATM Short 78 39,409 16.19% 1.91 1,083 1.96% 0.06% 0.77% Mid 87 37,170 11.26% 2.01 759 1.39% 0.07% 0.78% Long 86 37,436 7.75% 2.02 373 0.67% 0.08% 0.77% ITM Short 85 37,813 7.49% 2.43 548 1.05% 0.08% 0.75% Mid 87 37,139 5.55% 2.39 463 0.79% 0.08% 0.77% Long 87 37,186 4.35% 2.36 212 0.48% 0.07% 0.78%

40

Panel C: Put Options for Buy Recommendations Buy Recommendations



Option Volume

Volume Ratio

Stock Spread

Stock Turnover




Large-Cap OTM Short 143 37,005 77.99% 2.57 930 1.68% 0.06% 0.82% Mid 146 36,397 58.82% 2.51 760 1.48% 0.06% 0.83% Long 147 36,291 34.86% 2.47 374 0.84% 0.06% 0.83% ATM Short 142 37,029 13.12% 1.93 720 1.41% 0.06% 0.85% Mid 146 36,441 8.75% 2.04 499 0.85% 0.06% 0.84% Long 146 36,465 6.23% 2.06 179 0.39% 0.06% 0.85% ITM Short 144 36,742 6.37% 2.38 314 0.58% 0.06% 0.83% Mid 146 36,295 4.87% 2.25 199 0.38% 0.06% 0.84% Long 144 36,751 3.78% 2.10 76 0.17% 0.07% 0.84%

41

Panel D: Put Options for Sell Recommendations Sell Recommendations

Moneyness Maturity Obs. sizz


Option Volume

Volume Ratio

Stock Spread

Stock Turnover




Large-Cap OTM Short 85 37,825 83.49% 2.53 631 1.56% 0.07% 0.75% Mid 86 37,454 67.92% 2.56 727 1.41% 0.06% 0.76% Long 87 37,160 43.82% 2.49 381 0.75% 0.07% 0.78% ATM Short 78 39,350 15.84% 1.93 765 1.33% 0.07% 0.77% Mid 86 37,408 10.38% 2.05 479 0.92% 0.08% 0.79% Long 85 37,764 7.15% 2.07 234 0.46% 0.06% 0.80% ITM Short 85 37,799 7.47% 2.43 326 0.68% 0.06% 0.77% Mid 87 37,102 5.64% 2.30 222 0.43% 0.07% 0.78% Long 85 37,730 4.11% 2.15 147 0.28% 0.08% 0.80%

42

Table 3: The price pressure effect of Mad Money recommendations on the stocks This table shows the price pressure effect on recommended stocks. AR is abnormal return; CAR is cumulative abnormal return; ATO is abnormal turnover; and ASPREAD is abnormal spread.

Buy Sell Date AR% t-stat CAR% t-stat t(ATO) t(ASPREAD) AR% t-stat CAR% t-stat t(ATO) t(ASPREAD)

All 1 0.41 0.92 0.41 0.92 2.31 1.91 0.11 1.07 0.11 1.07 2.26 0.87 2 0.15 0.78 0.55 1.17 1.29 0.14 -0.30 -1.29 -0.19 -1.26 0.69 -0.46 10 -0.29 -1.73 -0.21 -1.62 0.47 1.09 0.17 1.08 -0.77 -1.41 0.58 -0.74 30 -0.17 -1.61 -2.54 -2.08 0.75 0.18 -0.30 -1.27 -1.27 -1.65 0.11 0.24

Small-Cap 1 0.91 2.15 0.91 2.15 9.55 2.68 0.28 1.21 0.28 1.21 2.77 1.31 2 0.53 1.91 1.44 2.83 5.12 1.05 -0.74 -1.59 -0.46 -1.30 1.67 -0.55 10 -0.64 -1.12 -0.21 -0.69 1.13 0.29 -0.20 -1.03 -1.74 -2.24 -1.55 -0.45 30 -0.12 -0.97 -3.76 -2.48 0.71 -0.41 -0.07 -0.15 -2.57 -1.81 -0.16 0.22

Mid-Cap 1 0.03 0.21 0.03 0.21 2.91 0.54 0.08 0.05 0.08 0.05 1.41 -0.79 2 -0.20 -0.39 -0.17 -1.32 1.03 0.61 -0.10 -0.11 -0.02 -0.63 1.51 -0.70 10 -0.02 -0.06 -0.08 -0.55 0.75 -0.18 0.04 0.85 -0.54 -1.09 0.68 -0.62 30 -0.17 -0.63 -1.75 -1.84 1.26 -0.21 -0.11 -0.61 -0.61 -0.81 0.97 -0.62

Large-Cap 1 0.13 1.01 0.13 1.01 1.24 0.15 0.03 0.23 0.03 0.23 2.09 0.54 2 0.03 0.98 0.16 1.24 1.06 -0.22 -0.20 -0.94 -0.17 -0.61 0.27 0.91 10 -0.14 -0.87 -0.41 -1.79 -0.41 0.71 -0.07 -0.78 -0.38 -1.05 0.10 -0.14 30 -0.23 -1.01 -1.38 -1.76 0.29 -0.13 0.01 -0.21 -0.73 -1.28 0.68 0.21

43

Table 4: The price pressure effect of Mad Money recommendations on the options This table shows the price pressure effect on the options of recommended stocks. AR is abnormal return; CAR is cumulative abnormal return; ATO is abnormal turnover; and ASPREAD

is abnormal spread. ˆtS is the implied stock price; Divergence proxies the difference between the

implied stock price and the observed stock price. Underlying assets are classified into three sizes: small-cap, mid-cap, and large-cap; options moneyness are classified into three categories according to their delta value. Out-of-the-money (OTM) options with low delta value (0.02–0.45); At-the-money (ATM) options with medium delta value (0.45-0.55); and In-the-money options (ITM) with high delta value (0.55-0.98). Options are also classified into three maturity categories. Short represents short-term options (10-30 days); Mid represents mid-term options (31-60 days); and Long represents long-term options (61-120 days). Panel A: Buy Recommendations

Call^

tS Put^

tS Divergence

AR t-stat AR t-stat AR t-stat Small-Cap OTM Short 0.14 0.07 -0.2 -0.48 OTM call and ITM put -0.51 -2.78

Mid -0.07 -0.28 0.47 1.26 0.04 0.52 Long 0.28 1.33 0.07 0.34 -0.23 -0.94 ATM Short 0.63 1.47 -0.09 -0.24 ATM call and ATM put -0.07 -0.33 Mid -0.09 -0.36 -0.23 -1.26 -1.35 -1.71 Long -0.16 -0.41 0.22 1.42 0.23 1.02 ITM Short 0.17 0.55 -0.41 -1.61 ITM call and ITM put 1.33 0.99 Mid 0.28 0.98 0.05 0.19 -0.46 -1.65 Long 0.36 1.23 0.05 0.27 0.16 1.11

Mid-Cap OTM Short 0.32 1.6 -0.23 -0.75 OTM call and ITM put -0.03 -0.64 Mid -0.1 -0.64 0.17 0.98 -1.95 -1.09 Long -0.14 -0.92 0.43 1.38 0.18 0.87 ATM Short -0.44 -0.95 0.12 0.53 ATM call and ATM put 0.21 0.96 Mid -1.02 -1.14 0.67 1.33 -0.02 -0.17 Long -0.1 -0.6 0.22 1.28 0.71 0.88 ITM Short -0.08 -0.45 -0.04 -0.16 ITM call and ITM put -0.37 -0.91 Mid -0.29 -1.06 0.03 0.17 0.18 1.64 Long -0.32 -1.56 0.57 1.38 -0.11 -0.66

Large-Cap OTM Short -0.02 -0.08 -0.01 -0.05 OTM call and ITM put -1.59 -0.93 Mid 0.01 0.04 -0.16 -1.27 0.15 1.48 Long -0.02 -0.16 0.04 0.26 0.06 0.58 ATM Short 0.15 0.64 -0.13 -0.22 ATM call and ATM put -0.11 -0.7 Mid -0.06 -0.36 -0.03 -0.13 0.13 0.46 Long 0.06 0.34 0.06 0.49 0.01 0.15 ITM Short 0.04 0.28 -0.16 -0.96 ITM call and ITM put 0.17 0.8 Mid -0.08 -0.46 0.03 0.22 0.08 1.07 Long -0.07 -0.43 0.01 0.07 -0.03 -0.33

44

Panel B: Sell Recommendations

Call^

tS Put^

tS Divergence

AR t-stat AR t-stat AR t-stat Small-Cap OTM Short -0.31 -1.86 -0.43 -1.17 OTM call and ITM put -0.64 -2.25

Mid -0.03 -0.15 -0.47 -1.60 -0.35 -0.88 Long -0.04 -0.24 -0.17 -0.88 1.44 1.05 ATM Short -0.57 -1.73 -0.40 -1.61 ATM call and ATM put -0.18 -1.05 Mid -0.39 -1.41 -0.43 -1.37 -0.07 -0.39 Long -0.30 -1.41 -0.35 -1.00 0.16 0.82 ITM Short -0.37 -1.27 -0.46 -1.74 ITM call and ITM put -0.16 -0.95 Mid -0.55 -1.58 -0.05 -0.15 0.22 1.44 Long -0.50 -1.44 -0.35 -1.59 -0.09 -1.12

Mid-Cap OTM Short -0.21 -0.78 -0.06 -0.43 OTM call and ITM put -0.10 -0.51 Mid -0.24 -1.66 -0.07 -0.42 0.12 1.34 Long -0.11 -0.68 -0.06 -0.41 -0.04 -0.30 ATM Short -0.31 -0.40 -0.50 -0.83 ATM call and ATM put 0.21 1.38 Mid 0.27 0.91 -0.08 -0.30 -0.18 -1.73 Long -0.26 -1.45 0.20 1.06 -0.05 -0.36 ITM Short -0.09 -0.40 -0.51 -1.55 ITM call and ITM put -0.07 -0.21 Mid -0.35 -1.67 -0.07 -0.43 0.13 1.61 Long -0.30 -1.30 -0.08 -0.40 0.01 0.05

Large-Cap OTM Short -0.37 -1.51 0.12 0.60 OTM call and ITM put -0.86 -1.00 Mid -0.26 -1.50 -0.01 -0.08 -0.54 -0.95 Long -0.23 -1.35 0.18 1.00 -0.23 -1.08 ATM Short -0.07 -0.27 0.26 0.64 ATM call and ATM put 0.49 1.75 Mid -0.64 -1.28 -0.15 -0.93 -0.04 -0.51 Long -0.58 -1.12 0.08 0.65 -0.17 -1.60 ITM Short -0.59 -1.53 0.10 0.38 ITM call and ITM put 0.50 0.95 Mid -0.61 -1.64 0.11 1.08 -0.28 -1.20 Long -0.21 -1.18 -0.03 -0.16 -0.18 -1.75

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Table 5: Correlations between the abnormal stock returns and abnormal implied price changes This table reports the simple correlations between abnormal stock returns and abnormal

implied stock price changes. AR is the stock abnormal return; ˆtS is the implied stock

price; and Divergence proxies the difference between the implied stock price and the observed stock price.

AR ^

tS from calls ^

tS from puts Divergence

AR 1 0.87 <0.001 0.83 <0.001 0.66 0.008 ^

tS from calls 1 0.91 <0.001 0.75 <0.001 ^

tS from puts 1 0.69 <0.001

Divergence 1

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Table 6: The effect of Mad Money recommendations on the options trading activities

This table reports the effect of stock recommendations on the trading activities of options. Aspread represents abnormal options spread; ATO represents abnormal options turnover. Underlying assets are classified into three sizes: small-cap, mid-cap, and large-cap; options moneyness are classified into three categories according to their delta value. Out-of-the-money (OTM) options with low delta value (0.02–0.45); At-the-money (ATM) options with medium delta value (0.45-0.55); and In-the-money options (ITM) with high delta value (0.55-0.98). Options are also classified into three maturity categories. Short represents short-term options (10-30 days); Mid represents mid-term options (31-60 days); and Long represents long-term options (61-120 days). Panel A: Buy Recommendations

Call Options Put Options

ASPREAD t-stat ATO t-stat ASPREAD t-stat ATO t-stat Small-Cap OTM Short -0.12 -0.49 -0.03 -0.19 -0.16 -0.61 1.23 0.81

Mid -0.13 -0.65 0.26 0.97 0.42 0.9 -0.11 -0.46 Long 0.05 0.14 0.75 1.09 0.26 1.26 -0.18 -0.86 ATM Short 1.33 1.68 0.09 0.26 0.37 1.51 0.56 0.82 Mid -0.29 -1.92 -0.19 -1.14 -0.09 -0.43 0.02 0.08 Long -0.15 -0.99 0.28 0.92 0.35 1.49 0.14 0.5 ITM Short -0.07 -0.19 -0.17 -0.98 -0.73 -2.67 0.86 2.17 Mid -0.3 -1.5 -0.19 -1.6 -0.04 -0.16 0.1 0.44 Long -0.24 -1.36 0.73 1.12 0.07 0.29 -0.18 -1.69

Mid-Cap OTM Short -0.11 -0.64 0.18 0.91 0.04 0.14 1.94 1.3 Mid -0.17 -1.31 2.22 1 0.13 0.94 -0.2 -1.41 Long -0.23 -1.71 0.15 0.74 -0.08 -0.43 0.27 0.88 ATM Short -0.01 -0.05 0.33 1.08 -0.39 -1.57 0.35 0.89 Mid 0.99 0.77 -0.26 -1.42 -0.27 -1.61 0.14 0.65 Long -0.48 -1.43 0.29 1.46 -0.08 -0.6 -0.03 -0.21 ITM Short -0.35 -1.08 1.08 1.58 -0.43 -2.07 0.3 0.95 Mid -0.23 -1.64 0.16 0.82 -0.27 -1.84 0.08 0.57 Long -0.14 -0.96 0.3 0.71 -0.04 -0.24 -0.1 -1.06

Large-Cap OTM Short -0.03 -0.18 0.24 1.27 0.02 0.12 0.1 0.33 Mid -0.01 -0.05 0.18 0.82 -0.04 -0.42 -0.05 -0.61 Long 0.25 0.96 0.2 1.58 0.29 1.66 0.64 1.25 ATM Short 0.02 0.09 -0.31 -1.45 -0.16 -0.73 -0.36 -1.86 Mid 0.05 0.39 0.04 0.25 -0.11 -0.69 0.78 1.21 Long 0.09 0.42 1.01 1.26 0.14 0.42 0.2 0.98 ITM Short -0.21 -1.69 -0.02 -0.17 0 0 0.26 1.09 Mid 0.01 0.07 -0.03 -0.32 -0.19 -1.49 0.55 1.63 Long -0.25 -1.44 1.14 1.69 0.15 0.38 1.08 1.33

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Panel B: Sell Recommendations

Call Options Put Options

ASPREAD t-stat ATO t-stat ASPREAD t-stat ATO t-stat Small-Cap OTM Short -0.11 -0.5 -0.06 -0.41 0.46 1.16 -0.3 -1.28

Mid 0.16 0.49 0.16 0.8 -0.11 -0.63 0.23 0.48 Long 0.38 1.43 0.29 0.93 0.36 0.98 0.02 0.11 ATM Short -0.51 -1.21 0.81 1.33 -0.11 -0.28 1.08 1.1 Mid -0.34 -1.75 0.07 0.43 -0.5 -1.69 0.73 1.68 Long 0.02 0.06 -0.07 -0.63 0.22 0.81 0.38 0.81 ITM Short 0.3 1.26 -0.21 -0.99 0.23 0.81 0.28 0.9 Mid 0.24 0.56 0.25 0.66 0.85 1.41 0 0.02 Long 0.06 0.18 -0.11 -1 0.7 1.91 1.17 1.41

Mid-Cap OTM Short -0.44 -1.07 0.16 0.44 -0.2 -0.63 -0.13 -0.93 Mid 0 -0.02 3.13 1.43 -0.32 -1.87 1.67 1.55 Long 0.13 0.79 1.06 1.81 0.26 1.09 1.3 1.79 ATM Short 0.04 0.06 0.23 0.58 -0.09 -0.26 1.78 1.22 Mid -0.31 -1.4 0.26 0.53 -0.02 -0.06 1.11 0.95 Long 0.06 0.22 1.44 1.29 -0.02 -0.1 0.4 1.55 ITM Short -0.19 -0.29 1.06 1.11 -0.21 -0.79 0.58 1.06 Mid -0.05 -0.35 0.38 0.74 0.08 0.35 0.04 0.17 Long 0.11 0.62 1.06 1 -0.07 -0.44 0.47 1.28

Large-Cap OTM Short 0.29 0.93 0.88 1.63 0.11 0.61 0.17 0.74 Mid -0.07 -0.33 0.15 1.06 -0.35 -1.3 0.11 0.45 Long 0.14 1.28 0.44 1.23 0.43 1.7 0.56 1.56 ATM Short -0.2 -0.35 0.8 1.52 -0.08 -0.23 1.2 0.97 Mid 0.57 1.64 -0.19 -1.06 -0.5 -1.69 0.24 0.59 Long -0.06 -0.35 0.03 0.1 0.13 0.3 -0.22 -1.77 ITM Short -0.22 -0.88 0.08 0.27 -0.15 -0.59 -0.28 -1.56 Mid 0.27 1.13 -0.19 -1.09 0.02 0.1 0.02 0.08 Long -0.18 -1.21 0.16 0.74 -0.12 -0.71 -0.02 -0.11

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Table 7: Summary of options trading returns

This table reports options trading profits from the trading simulation in which we buy short-term put options and hold till maturity. Out-of-the-money (OTM) options with low delta value (0.02–0.45); At-the-money (ATM) options with medium delta value (0.45-0.55); and In-the-money options (ITM) with high delta value (0.55-0.98). Speculation (buy put options and hold till maturity) Non-event period (%) t-stat Event period (%) t-stat Difference (%) t-stat

OTM -41.69 -4.31 -10.26 -2.22 31.43 4.25 ATM -18.31 -3.78 11.75 2.71 30.06 3.62 ITM -11.85 -2.92 26.24 3.13 38.09 5.08

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Figure 1

The Divergence between the implied and observed stock prices

This figure shows the divergence between the implied and actual stock prices with the presence of market frictions. When the range of L to H is not biased to either side, Divergence is zero and the implied price is around the stock price. However, as the range of L′ (L′′) to H′ (H′′) is biased to the left (right) side of market price, Divergence is less (greater) than zero and the implied price is smaller (greater) than the stock price.

|-----------------------•--------------*---------*----------- •---------------------------------| Low Sb Sa High |_______Divergence=0_______| Low′ High′ |________Divergence<0_______| Low′′ High′′ |_________ Divergence>0________|

the discrepancy of rationality between the options and

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