Equity LEAPS Calls vs. Stocks: An Empirical Study for Long ... · PDF fileEquity LEAPS Calls vs. Stocks: An Empirical Study for Long-Term ... An Empirical Study for Long-Term Speculation

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Equity LEAPS Calls vs. Stocks: An Empirical Study

for Long-Term Speculation

S. LEILA BEHESHTI SHIRAZI, Graduate School of business, University of Malaya, 50603

Kuala Lumpur, MALAYSIA

Mobile no: 00989121999142

Email: [email protected]

AND

IZLIN ISMAIL, Senior Lecturer of finance, Graduate School of business, University of Malaya,

50603 Kuala Lumpur, MALAYSIA

Mobile No: 0060122687157

Email: [email protected]

mailto:[email protected]

Equity LEAPS Calls vs. Stocks: An Empirical Study for Long-Term Speculation

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ABSTRACT

Long-Term Equity Anticipation Security or LEAPS is a call option introduced as a more

conservative security that can replicate a common stock position. This study’s objective is to

examine the effect of applying the strategy of “Buying In-The-Money LEAPS Calls vs.

Purchasing Stocks” proposed by CBOE on the performance of traders in terms of risk and

return trade-off and the risk-adjusted performance in practice, using a sample of 54 common

stocks listed on NYSE and NASDAQ and 54 LEAPS calls on the same underlying stocks listed

on CBOE during 2008-2010. The results indicate that LEAPS calls are not a preferred

financial instrument to replace common stocks for risk-averse traders. When the stock market

experiences a progressive downturn trend, the portfolios of LEAPS calls provide much higher

negative returns, significant loss and poor performance as well as higher levels of volatility

relative to the portfolios of common stocks. The results of this study also suggest that risk-

seeking traders, who can tolerate the higher level of risk in compensation for higher returns,

choose the portfolio of LEAPS calls with high Book-To-Market (BTM) ratio assets. This

portfolio is less volatile relative to the portfolio of LEAPS with low BTM ratio and provides

higher rates of return in comparison to the portfolios of common stocks in favorable market

conditions.

JEL Classification: G11, F39

Keywords: Equity LEAPS call, common stock, long-term speculation, return, volatility, mean,

variance, risk-adjusted performance, Sharpe ratio, Treynor ratio, Jenson Alpha.

I. Introduction

Over the last four decades, many studies have conducted on derivatives (e.g. , Sears and

Trennepol, 1982; Lapan et al. ,1991; Jarrow and Turnbull , 1995; Wilmot et al.,1997; Mc

Millan, 2002, Farhi and Borgi, 2009) and a large body of the literature has been concentrated

on studying the hedging function of derivatives (see Warner, 1977; Mayers and Smith, 1982;

Smith and Stulz, 1985; Zimmerman, 1988; Blanchet-Scalliet and Jeanblanc, 2001; Lotz,

1999). However, there is limited study on the speculative use of these securities (e.g. Bauer,

Cosemans & Eichholtz, 2008), whereas many traders in the marketplace speculate on price

movements of the underlying assets (Kumar, 2007). Thus, this paper look at speculative use


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of derivatives in one of the largest and most volatile option exchange, Chicago Board Option

Exchange (CBOE).

Speculation on derivatives is usually carried out in a short-term and entails running the risk of

loss in the expectation of high reward (Farhi & Borghi, 2009). Bauer, Cosemans & Eichholtz

(2008) found evidence that most individual investors who trade short-term options to

speculate on stock price movements have incurred substantial losses on their investments.

They concluded that the poor market timing was the main determinant of their worse

performance. However, it is believed that a longer maturity derivative like Long-Term Equity

Anticipation Security (LEAPS)1 can reduce the risk of speculating on derivatives when there

is no need to time the market precisely (Apostolou et al., 2005; Thomsett, 2009). At the same

time, LEAPS provide the opportunity of gaining leverage in the stock market and speculate

on favorable price moves of the underlying assets in a long-term2. The leverage inherent in

this type of option can magnify the returns on investment, whereas investors only pay a

fraction of total capital required for the securities (Apostolou et al., 2005; Lasher, 2007).

Since, due to the effect of leverage, small changes in the value of the underlying assets

generate great changes in the value of the options (Wilmott, Howison & Dewynne, 1997).

1 LEAPS is a long-term option with the expiration date of up to three years (Lasher, 2007). LEAPS were introduced by

Chicago Board Option Exchange (CBOE) in 1990 as a new investment tool (Roth, 1994; Allaire & Kearney, 2002). It

provide a longer time frame for option traders to benefit from favorable price moves in the market (Apostolou et al., 2005).

2 Usually it is believed that the term speculation refers to a short-term financial action and the term investment to a long-term

one (Brandes, 2003; Hiriyappa, 2008). However, Nagarajan & Jayabal (2011) avoid distinguishing them based on their

holding period and explain that the distinctions between speculation and investment are the degree of risk involved and the

motives of traders. The element of risk involved in speculation is significantly higher than that of investment. A speculator

tends to take a higher level of risk when anticipates a higher level of return in future. Also, an investor’s motive is to increase

his/her income from the securities whereas a speculator’s motive is the capital appreciation. Thus, even those who buy and

hold securities for decades, may be classified as speculators, except only the rare few who are primarily motivated by

income or safety of principal rather than selling at profit. Thus, in this paper the term investors and long-term speculators are

used interchangeably when the motives of both investors and long-term speculators are earning profit from price fluctuation

in the future.


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According to Lasher (2007), gains from LEAPS calls can be sometimes 4-5 times greater

than those of the underlying stocks).

Recently, many financial advisors and option specialists (Finnegan, 1977; McMillan, 2002;

Taylor, 2008; Rahemtulla, 2009, Zigler, 2010) suggest traders and long-term speculators to

purchase LEAPS calls instead of stocks or replace the existing stocks in their portfolio of

assets with LEAPS calls. Moreover, CBOE has introduced a new investment strategy which

is called “Buying In-The-Money LEAPS Calls vs. Purchasing Stocks” to inspire investors to

buy LEAPS calls rather than underlying stocks. Therefore, the new generations of market

participants who are more risk takers have been encouraged to purchase LEAPS calls instead

of common stocks in order to obtain greater returns from the favorable price moves of the

underlying over a longer period of time (Allaire & Kearney, 2002; Kolb & Overdahl , 2007).

According to Thomsett, (2009) buying LEAPS calls can be a more conservative approach

relative to purchasing common stocks outrights in a volatile stock market because investors

will not put their whole capital at risk and just limit the risk to the premium amount paid.

However, it is significant to note that the leverage effect can also magnify the risk of

investment on LEAPS (Lasher, 2007). We were unable to find a study in literature

representing the performance of the long-term speculators by applying this strategy in

practice. So, the risk and return tradeoff as well as the risk-adjusted performance of LEAPS

calls in comparison with underlying stocks are still under question. Investors are unaware of

the actual level of returns and risks that they will experience through adopting this strategy in

order to ensure the preference of LEAPS calls over Equity stocks.

According to McMillan (2002) LEAPS calls can be used to construct a long-term portfolio

of stocks but with less capital outlay. Consistently, Taylor (2008) suggests investors can


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create a portfolio of stocks with LEAPS because LEAPS can provide them greater

diversification, manageable risk, and higher return. Thus, this study attempts to measure the

risks, returns and risk-adjusted performances of equity LEAPS calls and those of the

underlying stocks in the context of portfolios of assets in order to compare them together and

explore any preference of each. The risk-adjusted performance of these portfolios would be

measured through Sharpe, Treynor and Jenson. Also this study tries to increase the

understanding of investors or long-term speculators about their success or failure in the

market by buying LEAPS calls instead of common stocks.

The results of this study can help those investors or long-term speculators who do not have

sufficient capital to purchase various expensive stocks in the stock market and instead are

willing to buy LEAPS calls in the derivative market to enjoy from favorable price moves.

This study also would make a contribution to the literature in the area of speculating in

options, specifically LEAPS calls. It is also anticipated that this study will motivate others to

conduct further research on speculating in LEAPS calls within different periods of time and

investigate the performance of investors or long-term speculators adopted this investment

strategy in the financial markets.

This paper proceeds as follows. Section II discusses the previous studies on the return and

risk of options as well as the performance of the traders holding options for speculation.

Section III, describes data collected for this study. This is followed by the methodology

employed in the study to measure the monthly returns, risk and risk-adjusted performance of

the portfolios of LEAPS calls and the portfolios of the underlying stocks in the section IV.

Section V, presents our empirical results and discusses our findings. Section VI discusses the

conclusion, limitation of the study and a few suggestions for further research.


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II. Literature Review

A. Speculation on Options and LEAPS

Many investors, nowadays, prefer to trade options rather than stocks to save transaction

costs, to avoid tax exposure and to bypass stock market restrictive rules (Kolb & Overdahl,

2007). On the other hand, the values of options depend on the price of the underlying stock

and buying options is regarded as a substitute for direct purchase or sale of stocks (Bodi,

Kane & Marcus, 2009). Thus, some investors trade options to speculate on the price

movement of the underlying stock and obtain larger gains (Kolb & Overdahl, 2007).

According to Roth (1994) educated traders with speculative motives have moved toward

trading LEAPS rather than short-term options. Since Longer expiration period of LEAPS

overcomes the ongoing struggle of option traders with time. Moreover, LEAPS provides less

leverage for investors because the buyers of LEAPS have less time premium erosion to fight

against than the buyers of short-term options (CBOE, 2001). The fact can make the LEAPS

less volatile and risky comparing to short-term options (Holland & Wingender, 1997; Weiyu

Guo, 2003).

There are limited numbers of studies on LEAPS in literature. Among the few existing

studies on LEAPS, there are some empirical explorations concerning the pricing of SPX

LEAPS (Bakshi et al., 2000) and Equity LEAPS (weiyu guo, 2003) through Black-Scholes

model, the volatility dynamics of LEAPS on S&P 500 stock market index (Bollerslev &

Mikkelsen, 1999), trading volume of LEAPS (weiyu guo, 2003), and the relationship between

the introductions of LEAPS and changes in the value of underlying stocks (Lundstrum &

Walker, 2005). However there are a few studies on the levels of returns and risk of these

securities.


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B. Returns and Risk of the Options and the LEAPS Calls

Options, due to their inherited leverage, generate magnified returns on the investment

(Apostolou et al., 2005; Kolb & Overdahl, 2007; Gurusaour, 2009). Evidence on S&P index

shows that the returns of call options are significantly larger than those of the underlying

stocks; by average two per cent per week (Coval & Shumway, 2001). Since options have a

convex payoff (Begley & Feltham, 1999; Guy, 1999; Bryan, Hwang & Lilien, 2000) while

the payoff of stocks is linear.

According to Allaire and Kearney (2002), the implied volatility of LEAPS calls is very

high that is the great concern of traders intending to invest on these securities. The volatility

sometimes prevents the traders to invest on LEAPS calls. It implies that LEAPS calls are

more volatile and risky in comparison with underlying stocks. On the other hand, the

volatility factors can create a significant variation in a portfolio returns (Coval and Shumway,

2001). Banerjee et al. (2007) finds evidence that VIX3 variables (volatility) significantly

affect excess returns for most portfolios and this relationship is stronger for portfolios that

have higher beta values (like a portfolio of options).

Crouhy, Galai & Mark (2002) and MacMilan (2002) postulate that an options portfolio

has higher beta and risk profile comparing to a stocks portfolio. The high beta of an option

portfolio makes its returns significantly volatile. Sears and Trennepohl (1982) find evidence

that systematic risk or market variance for an options portfolio is significantly greater than

that of stocks portfolio. They conclude that the systematic risk can be reduced with the

greater chance of diversification and elimination of unsystematic risk in a portfolio.

3 VIX or volatility index is introduced by Chicago Board Option Exchange in 1993. This index is calculated

from the S&P 100 (OEX) stock index options and originally computed on a minute-by-minute basis from the

implied volatility of eight OEX option series.


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Moreover, Lowel (2009) explains that Deep-In-The Money (DITM) call strategy is the

best way to artificially own a stock with half money outlay and less risk. DITM LEAPS calls

have more potential to earn significantly huge returns in comparison with ATM LEAPS calls

because they have higher delta.

C. Speculative Performance on Derivatives and LEAPS calls

Studies over different time periods suggest that the most speculators have made net trading

losses in future market (e.g. Steward, 1949; Ross, 1975; Hieronymus,1977) as well as in the

stock market (see Barber et al. ,2004). Teweles and Jones (1987) argue that traders

mistakenly believe they can forecast prices and obtain profits, but they forget the possibility

of losses as well. Dusak (1973) finds that the average holding period returns over the period

1952 to 1967 on the future contracts over the same period were closed to zero for speculators.

Moreover, Chapman (2010) investigates the risk and return of a strategy in which speculators

use credit to maximize the probability of achieving gains. He finds that adopting such a

strategy would eventually lead to large losses and negative expected profits for the

speculator. Consistently, Clark et al. (2008) represents that a portfolio of derivative

speculators underperform a portfolio of hedgers, specifically when separated by credit risk

exposure.

In contrast, Hodrick and Srivastava (1984) examines the risk-return trade-off of speculating

in forward currency markets and finds that the strategy was profitable. They indicate that to

earn profit speculator’s willingness to absorb a substantial variance of profits is required.

Also, Changyun (2003) examines the behavior and performance of speculators and hedgers in

15 U.S. futures markets and observes that speculation (hedging) is positively (negatively)

correlated with subsequent abnormal returns after controlling for market risk. He concludes


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that speculators can outperform hedgers and speculation is significantly profitable in future

markets comparing to hedging.

Bharadwaj and Wiggins (2001) in their study investigate if the market for LEAPS written

on the S&P 500 index is efficient enough to preclude violations of put-call parity and the box

spread pricing relationship. They find that LEAPS puts are overpriced relative to calls about

80% of the time, but the discrepancy is seldom enough to produce a reliable arbitrage profit

after transaction costs.

III. Data

The sample underlying stocks are selected among the stocks listed on New York Stock

Exchange (NYSE) and NASDAQ stock market. Also the sample equity LEAPS calls have

been chosen from the listed LEAPS calls on CBOE. As S&P 500 EWI closely mirrors the

sample underlying stocks and the sample LEAPS calls, it is considered as our benchmark in

this study.

The samples are not selected randomly this study and several criteria are considered in the

sampling. First, we have picked the sample securities from different industries to meet the

diversification principle of MPT model and remove the unsystematic risk of the portfolios.

Second, we have chosen the samples based on their book-to-market (MTB) ratios because

several studies have represented a strong relationship between the assets returns and their

Book-to-Market ratios (see Rosnberg, Reid and Lanstein, 1985; Davis, 1994; Chan, Hamao,

and Lakonishok,1991; Capaul, Rowley and Sharpe, 1993). Also, Fama and French (1995)

observed that two classes of stocks tend to do better than the market as a whole: small caps

stocks and stocks with a high book-to-market ratio. Following this study, Barber, Lehavy,

and Trueman (2007) designed two portfolios of high BTM and low BTM and measured their


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returns. This issue, hence, has also taken into consideration in this study and we have

constructed two portfolios of stocks and two portfolios of equity LEAPS calls, one with high

BTM ratio and another with low BTM ratio (totally 4 portfolios of assets). Third, among

equity LEAPS calls written on the underlying stocks, only DITM equity LEAPS calls are

selected to examine the strategy proposed by CBOE.

With regard to the number of assets in a portfolio, Statman (1987) shows that a portfolio

including 30-40 stocks can effectively achieve efficient diversification. Chung (2000)

indicates a well-diversified portfolio include at least 27 securities. Consistently, Wang and

Yang (2007) based on the ordinary least square method (OLS) and GARCH Model find that

the optimal portfolio size in terms of the number of stock holdings is between 21 and 28 with

portfolio returns maximized and volatility minimized. Therefore, we have decided about the

sample size of 27 securities in each of the four equally weighted portfolios in this study.

We roll over LEAPS calls in the portfolios over through a process of selling the old option

and then purchasing a new one with the same strike price but a later expiry date (Allaire &

Kearney, 2002). This enables us to examine if a long-term speculation on LEAPS calls allows

the underlying assets to appreciate over the time and create profit for the speculators. Thus,

LEAPS calls with 2 year expiration date traded in January 2008 are rolled over in Aug 2009

at the same strike price but later expiry date (i.e. January 2011). Moreover, these portfolios

are rebalanced in August 2009 to be equally-weighted.

As equity LEAPS calls are good investment strategy when the market is bullish and The Wall

Journal reported in April 2008 that the economy of USA was expected to flourish in the

middle of the year 2008, we have decided on the three year period for the study from January

2008 to December 2011.


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IV. Method

As the strategy of Buying In-The-Money LEAPS Calls vs. Purchasing Stocks is going to be

examined in the context of portfolios of assets, we have employed the Modern Portfolio

Theory (MPT) of Markowitz (1952) in this study. Moreover, we use the strategy of buy and

hold to measure the returns, risks and risk-adjusted performance of these portfolios. Since

this strategy is a very popular investment strategy in the financial markets because most of

investors believe good assets usually grow over a long period of time, even if they seem to

decline at some points. Moreover, small investors prefer this type of investment strategy

because they are willing to find a way to minimize their transaction costs.

A. Measuring Investor Return and Risk

We define investor return as the monthly changes in the price of all stocks and LEAPS calls

in this study. In a fashion similar to the studies of stock returns by Fisher and Lorie (1968),

and stock and bond returns by Ibbotson and Sinquefield (1976), we measure monthly returns

of investment over the period of this study. Like the prior studies, we have not taken into

consideration the costs associated with commission, tax, and transactions for the sake of

simplicity. Thus, we calculate the monthly returns of common stocks as

R i,t = [(P i,t + D i,t) / P i,t-1] -1, (1)

Where Ri,t is the return of the common stock i at the end of the time t; Pi,t is the closing price

of the stock i at the end of time t; and Di,t is the dividend received from the stock i during the

time t and reinvested at the end of time t.

We obtain the returns of LEAPS calls in accordance with the study of Xiaoyan Ni (2007) on

the returns of short-term call options. So, the returns of an individual LEAPS call from one

expiration date to next is calculated as


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R i,t = [Max(S t - K, 0) / P] -1, (2)

Where Ri,t is the return of the equity LEAPS call of the stock i at the end of time t; S t is the

closing price of the stock i at the end of time t; K is the strike price of the LEAPS calls at its

expiration date; and P is the premium amount paid to buy the equity LEAPS Call of the stock

i.

Since this study is conducted in the context of portfolio, we consequently have to measure the

returns of the portfolios of assets, rather than those of the individual assets. Based on MPT,

the returns on each portfolio is calculated as the weighted sum of the returns of the securities

within the portfolios:

R P,t = ∑27

i=1 wi,t . Ri,t (3)

Where R P,t is the return of each portfolio of asset at the end of time t; w i,t is the weight of

asset i in the portfolio at the end of time t; R i,t is the return of the asset i at the end of time t.

Investor risk is defined as the standard deviation of the monthly returns on each portfolio.

That is, we measure the volatility of each portfolio by calculating the standard deviation of

the portfolio’s returns. To measure the risk of each portfolio, we also estimate the beta or

systematic risk of these portfolios. We calculate the Beta (β) of each portfolios through

regression the portfolio’s returns against the market returns.

B. Measuring Investor risk adjusted Performance

Pilotte and Sterbenz (2006) investigate the risk-returns characteristics of two equally

weighted portfolios of bills and bonds by applying both Ex-ante and Ex-post Sharpe and

Treynor Ratios. We follow the same methodology in this study to measure the risk-adjusted

performance of these portfolios. However, we only apply Ex-post Sharpe and Ex-post

Treynor Ratios. Since, we intend to evaluate the past investment performance of these

portfolios unconditionally.


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Generally, Sharpe ratio is defined as the ratio of the excess return to standard deviation of

return. We define the excess return (XRt) on the portfolios as the difference between 1-month

holding period return on each portfolio and the return on a U.S. government bond expiring in

3 years. Thus, the Ex-post Sharpe Ratio is

EX Post Sharpe Ratio= 1/T Ʃt t=1 XRp,t ,

SD (XRp,t)

Where XRt is the excess return on the portfolio p and SD (XRp,t) is the standard deviation of

XRt. Hereby, I rewrite the equation as

EX Post Sharpe Ratio= 1/TƩtt=1(Rp,t – Rf,t) , (4)

Also we use the Treynor ratio to measure the excess return per unit of market risk in the

portfolio of assets. Since this ratio is more appropriate measure when an investor holds a

well-diversified portfolio and the unsystematic risk of investment is diversified away. The

Traynor ratio is defined as:

EX Post Treynor Ratio= 1/TƩt t=1(Rp,t – Rf,t) , (5)

βp,t

Where RP,t is the return of the portfolio p at the end of time t, Rf,t is the return on T-bond at

the time t, and βP is the beta or systematic risk of a portfolio of assets.

Jenson’s alpha as another risk-adjusted measure is used in this study to determine the

abnormal returns of these portfolios over the study period. Jenson’s Approach is based on the

Capital Asset Pricing Model (CAPM) which its coefficient is the measure of performance. By

applying a regression model, we intend to find the intercept term (α) and measure the

abnormal return of each portfolio as

Rp,t - Rf = αp + βp (Rm,t – Rf)+ ept , (6)

P,t ,t


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Where RP,t is the return on the portfolio p at the end of time t, Rf, is the return on T-bond

during the time t, and βP is the beta or systematic risk of the portfolio, Rm is the return on the

equally weighted market index (S&P 500 EWI) at the time t, ept is error term.

As CAPM uses only one variable beta to describe the returns on a portfolio of assets with

return of the market as a whole, we also use the three-factor model developed by Fama and

French (1993) to measure the performance of these portfolios. Like Barber et al (2007), we

estimate the abnormal returns of the portfolios by following monthly time-series regression

for each portfolio p

Rp,t - Rf,t = αp + βp (Rm,t – Rf,t)+ bs SMBt+ bv HMLt + ept , (7)

Where SMBt is the return on an equally-weighted portfolio of small-cap stocks at the time t

minus the return on an equally-weighted portfolio of big-cap stocks at the time t, and HMLt is

the return on an equally weighted portfolio of high BTM stocks at the time t minus the return

on an equally weighted portfolio of low BTM stocks at the time t. The regression yields

parameter estimates of αp, βp, bs, and bv, where the intercept αp represent the abnormal return

on the p.

V. Research Results

A. Risk and return tradeoff

Table I provides descriptive statistics for the risk and return tradeoff on all the four

hypothetical portfolios as well as that of the S&P500 EWI. During the January 2008-

December 2011 period, the means on the returns of all the four portfolios are negative and

also that of the market index is negative. That is, the long-term speculators holding each of

these portfolios incur loss within the period of the study. However, the means on the returns


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of the LEAPS call portfolios are negatively greater negative than those of the stock

portfolios. The long-term speculators holding the portfolios of LEAPS calls experience

significantly greater negative rates of return and consequently much more losses relative to

the long-term speculators holding the portfolios of stocks. The greater negative rates of

return on the portfolios of LEAPS calls are consistent with the theoretical prediction that

leverage magnified the rates of return.

Table I. Monthly Returns on the Portfolios, Jan 2008 –Dec 2010

Stock portfolio

with HBTM

Stock portfolio

with LBTM

LEAPS Call

portfolio with

HBTM

LEAPS call

portfolio with

LBTM

S&P 500

EWI

Mean -0.201802494 -0.215923601 -1.235422759 -2.811359586 -0.183125236

Standard Error 0.026766961 0.030016351 0.129285051 0.406720552 0.02420025

Median -0.174138737 -0.184084924 -1.090235309 -1.590298701 -0.150206902

Sample Variance 0.025792927 0.032435328 0.60172648 5.95517786 0.021083476

Standard Deviation 0.160601764 0.180098106 0.775710307 2.440323311 0.145201502

Beta 1.083251327 1.167457889 0.871171190 -1.015977203 1.07387653

Skewness -0.376937597 -0.266347776 -0.617176252 -0.849119265 -0.36246228

Kurtosis 0.4024833263 0.360557358 -0.398825966 -0.437582559 0.489478238

Range 0.557287644 0.804700174 2.921221297 8.357676167 0.54188886

Minimum

(lowest return) -0.495430456 -0.58378258 -3.083731169 -8.043450536 -0.511184533

Maximum

(highest return) 0.061857188 0.220917593 -0.162509871 0.314225631 0.030704327

Sum -7.264889791 -7.773249639 -44.47521934 -101.2089451 -6.592508489

Count 36 36 36 36 36

Confidence Level

(95.0%) 0.054339819 0.060936432 0.262462606 0.825686611 0.04912912

Note. The table represents the mean on the monthly rates of return and the volatilities of the four portfolios

of stocks and LEAPS calls as well as those of S&P EWI within a three year period.

Moreover, the betas of the stock portfolios indicate that the portfolios move in the same

direction as the market. The stock portfolio with low BTM ratio, due to its greater beta, is

more volatile in comparison with the stock portfolio with high BTM ratio. The low beta of

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the LEAPS call portfolio with high BTM ratio implies that it is less volatile than the stock

portfolios and the market index. However, the negative beta of the LEAPS call portfolio with

low BTM ratio implies that the portfolio moves in the opposite direction to the market, but it

is roughly as risky as the S&P 500 EWI.

The negative values of Skewness, in table I, show that the distribution of data is not

normal and they are skewed toward left. The distribution of returns on the portfolio of stocks

is moderately skewed whereas the distribution of returns on the portfolio of LEAPS call is

highly skewed. Also the negative values of kurtosis demonstrate flatness of the peak of the

LEAPS calls portfolios and the positive values of kurtosis indicate the sharpness of the peak

of the stock portfolios and market index.

It is significant to note that the mean on the returns of the LEAPS calls portfolio with

low BTM ratio is significantly less negative than that of the LEAPS calls portfolio with high

BTM ratio. In the other words, the portfolio of LEAPS calls with low BTM ratio generates

the greatest negative rates of return and loss in comparison to the other portfolios.

The table reveals that the LEAPS call portfolios, due to their significantly higher standard

deviation, are more volatile and risky than the portfolios of stock and the market index. Our

expectations in this study on the fact that the higher level of risk yields the higher level of

returns is not realized with the portfolios of LEAPS calls; i.e. the long-term speculators

holding the portfolios of LEAPS calls experience the higher levels of risk for the lower levels

of returns. The volatility of LEAPS calls portfolio with low BTM ratio is even significantly

than the LEAPS calls portfolio with high BTM ratio.

The Figure1 illustrates that the average returns of the portfolios of stocks and LEAPS

calls as well as S&P EWI are not normally distributed and they are negatively skewed toward


17

left. It represents that the variation in the returns for the portfolios of stocks and that of the

S&P500 EWI are approximately in the same range, but the variation in the returns of the

portfolios of LEAPS call are significantly great. In general, the portfolios of LEAPS calls

have showed worse performance within the period of the study with the low level of returns

and the high level of volatility. In fact, the long-term speculators holding the portfolio of

LEAPS calls would acquire a larger amount of risk and lower level of return.

Figure1. Returns Distribution of the Portfolios of Assets

Note. No transaction cost, tax cost and reinvestmentrisk are considered into the calculations.

The Pearson unpaired two-sample T-test is also used to determine whether there is a

significant difference between the mean values of the monthly returns on each of the two

portfolios of assets. Table II indicates that the null hypotheses are rejected and there are

statistically significant differences between the means of the stock portfolios and those of the

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2

Pro

ba

bil

ity

Return (%)

Stock portfolio

with High BTM

LEAPS

portfolio with

High BTM

Stock portfolio

with low BTM

LEAPS

portfolio with

low BTM

Stock portfolio

of S&P 500

EWI


18

LEAPS call portfolios. Also the difference between the means of the LEAPS call portfolios

with high BTM ratio and low BTM ratio are statistically significant. However the results

reveal that the difference between the means of two stocks with high BTM ratio and low

BTM ratio is not statistically significant, due to the p-value of greater than 0.05. difference

between the means of two portfolios of stocks are not significantly different when the P-value

is greater than 0.05.

Table II – The Result of Pearson unpaired Two-sample T-test

Variables Difference in

means

Difference in

Standard error T-value P-value

hbtmsp

hbtmleapsp 1.033621 0.1320268 7.8289 0.0000

lbtmsp

lbtmleapsp 2.595437 0.4078267 6.3641 0.0000

hbtmsp

lbtmsp 0. 0141206 0.402174 0.351l 0.7266

hbtmleapsp

lbtmleapsp 1.575937 0.4267742 3.6927 0.0004

Hbtmsp

lbtmleapsp 2.609557 0.4076004 6.4022 0.0000

lbtmsp

Hbtmleapsp 1.0195 0.1327237 7.6814

0.0000

Note. The confidence level chosen for t-test is 95%. This level of confidence corresponds to α = .05. Since

we have tested the null hypothesis that the two means are equal, a two-tailed test is used. Also, the degree of

freedom is selected 70.

B. Risk-adjusted performance of the portfolios

The means of the sharpe ratios for all the four portfolios and that of the S&P 500 EWI are

negative because the portfolios generate negative excess returns within the period of the

study. However, the negative values of sharpe ratios are difficult to interpret. Israelsen (2004)

proposed a modification to the sharpe ratio when the excess returns are negative. He

introduced an exponent to the denominator. This exponent is made up of the excess return

divided by its absolute value. The equation of the modified Sharpe Ratio is as


19

Smod = RP - Rf (9)

σP^((R

p - R

f)/abs(R

p - R

f))

Table III represents that portfolios of LEAPS calls with the lower (or more negative)

modified Sharpe ratios are worse investment alternatives in comparison with the portfolios of

stocks with higher (or less negative) modified Sharpe ratios for the long-term speculators in

the terms of reward per unit of total risk. Moreover, the portfolio of LEAPS call with low

BTM ratio performs significantly poorer than the portfolio of LEAPS call with high BTM.

On the other hand, the results of the modified Sharpe ratios reveal that when the market is

down a stock portfolio with low BTM ratio can even perform better than the market portfolio

for long-term speculation.

Table III. Monthly Ex-Post Sharpe Ratio of the portfolios, Jan 2008 – Dec 2010

Stock portfolio

with High BTM

Stock portfolio

with Low BTM

LEAPS portfolio

with High BTM

LEAPS portfolio

with Low BTM S&P 500 EWI

Normal Modified Normal Modified Normal Modified Normal Modified Normal Modified

Mean -0.35809 -0.03025 -0.35529 -0.00851 -1.62499 -0.97780 -1.16233 -6.93819 -1.45438 -0.02875

Standard

Error 0.02677 0.00847 0.03002 0.03246 0.16667 0.10029 0.16667 0.98908 0.16903 0.00387

Median -0.33043 -0.03200 -0.32345 -0.03767 -1.43782 -0.86518 -0.66196 -3.94209 -1.22446 -0.0251

Standard

Deviation 0.16060 0.05085 0.18010 0.19475 1 0.60173 1 5.93446 1.01418 0.02324

Sample

Variance 0.02579 0.00259 0.03243 0.03793 1 0.36207 1 35.2178 1.02857 0.00054

Kurtosis -1.02483 19.7892 0.16056 30.7869 -0.39882 -0.39883 -0.43758 -0.43381 -0.48948 1.01058

Skewness -0.37694 3.84131 -0.26635 5.40859 -0.61718 -0.61718 -0.84912 -0.86303 -0.73625 0.04845

Minimum -0.65172 -0.08360 -0.72315 -0.10966 -4.00772 -2.4115 -3.30634 -19.6899 -3.74577 -0.07678

Maximum -0.09443 0.22887 0.08155 1.08728 -0.24185 -0.14553 0.11848 0.11848 0.03914 0.03914

Sum -12.8912 -1.08890 -12.7905 -0.30644 -58.4997 -35.20082 -41.8438 -249.775 -52.3579 -1.03488

Largest(1) -0.09443 0.22887 0.08155 1.08728 -0.24185 -0.14553 0.11848 0.11848 0.03914 0.03914

Smallest(1) -0.65172 -0.08360 -0.72315 -0.10966 -4.00772 -2.41155 -3.30634 -19.6899 -3.74577 -0.07678

Confidence

Level(95.0%) 0.05434 0.01720 0.06094 0.06589 0.33835 0.20359 0.33835 2.00793 0.34315 0.00786

Note. The ex-post Sharpe ratio for the portfolios is calculated by dividing the ex post premiums on those

portfolios by the corresponding standard deviation of their returns . The ex- post premium is the difference

between the mean of the monthly rates of return of the portfolios taken from table 1 and the rate of return on 3-

year US government bond.


20

As illustrated in Table IV, the means of the monthly Treynor ratios for the three

portfolios of stocks with high BTM, stocks with low BTM, and LEAPS call with high BTM

ratios have taken negative values because of their negative excess returns. However, the

mean of the monthly Treynor ratio for the portfolio of LEAPS call with low BTM ratio has

wrongly taken a positive value. Since the negative excess return and the negative beta of the

portfolio has resulted in the positive value of Traynor ratio. The fact makes it impossible to

interpret the values of Treynor ratios and rank the performance of the portfolios accordingly.

Table IV. Monthly Ex-Post Treynor Ratio of the portfolios, Jan 2008 – Dec 2010

Stock

portfolio with

High BTM

Stock

portfolio with

Low BTM

LEAPS

portfolio with

High BTM

LEAPS

portfolio with

Low BTM

S&P 500 EWI

Mean -0.209464312 -0.237423306 -1.446928885 2.7918536 -0.194058934

Standard Error 0.024709834 0.030016351 0.148403726 0.4003245 0.022553821

Median -0.183926603 -0.205584629 -1.280271112 1.589995 -0.163380151

Standard

Deviation 0.148259005 0.180098106 0.890422359 2.4019469 0.135322928

Sample Variance 0.021980733 0.032435328 0.792851977 5.769349 0.018312295

Kurtosis -1.024833263 0.160557358 -0.398825966 -0.4375826 -0.489478238

Skewness -0.376937597 -0.266347776 -0.617176252 0.8491193 -0.736246228

Minimum -0.480526027 -0.605282285 -3.568565171 -0.2845789 -0.499799192

Maximum 0.033932281 0.199417889 -0.215353622 7.9416649 0.005223045

Sum -7.540715244 -8.547239013 -52.08943986 100.50673 -6.986121611

Largest(1) 0.033932281 0.199417889 -0.215353622 7.9416649 0.005223045

Smallest(1) -0.480526027 -0.605282285 -3.568565171 -0.2845789 -0.499799192

Confidence

Level(95.0%) 0.05016363 0.060936432 0.30127558 0.8127019 0.045786691

Note. The Ex-post Treynor ratio for the portfolios is also calculated by dividing the ex post premiums on

those portfolios by the corresponding Beta or systematic risk.

To address this issue, Kothari and Warner (2001) use Jenson Alpha in their study to

examine the performance of the mutual funds when the excess return is negative.

Consistently, we measure the performance of these portfolios and their abnormal return

through the coefficient α which is obtained from our regression analysis. It is significant to


21

mention that the time-series regression is conducted for each portfolio of asset separately to

find the coefficient α.

Table V. indicates that the abnormal return or the performances of the portfolios stocks

are roughly the same within the period of the study. The values of α for both of these

portfolios are equally 0.00029. It means that they perform similarly the same and no one is

better off the other. In consistent with the results of the Sharpe ratio, the values of α for the

portfolios of LEAPS calls are very smaller (or greater negative) comparing to those of the

portfolios of stocks. It implies that their performances and the abnormal returns they can earn

are significantly poorer than the portfolios of stocks.

Table V. The Results of Time-series Regression on the Portfolios of Stocks, Jan 2008 – Dec 2010

Regression result for the portfolio of stocks with HBTM

Regression result for the portfolio of stocks with LBTM

_cons -.0002917 .0113744 -0.03 0.980 -.0234606 .0228771 hml .2414776 .0679007 3.56 0.001 .1031684 .3797868 smb -.002656 .0893912 -0.03 0.976 -.18474 .179428 mmrf 1.103969 .0362171 30.48 0.000 1.030197 1.177741 hbtmspmrf Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total .902751885 35 .025792911 Root MSE = .02872 Adj R-squared = 0.9680 Residual .026392104 32 .000824753 R-squared = 0.9708 Model .876359781 3 .292119927 Prob > F = 0.0000 F( 3, 32) = 354.19 Source SS df MS Number of obs = 36

. regress hbtmspmrf mmrf smb hml if tin(3421m1,3509m10)

_cons -.0002916 .0113744 -0.03 0.980 -.0234604 .0228772 hml -.7585224 .0679007 -11.17 0.000 -.8968315 -.6202132 smb -.0026551 .0893912 -0.03 0.976 -.184739 .1794287 mmrf 1.10397 .0362171 30.48 0.000 1.030198 1.177742 lbtmspmrf Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 1.13523638 35 .032435325 Root MSE = .02872 Adj R-squared = 0.9746 Residual .026392069 32 .000824752 R-squared = 0.9768 Model 1.10884431 3 .36961477 Prob > F = 0.0000 F( 3, 32) = 448.15 Source SS df MS Number of obs = 36

. regress lbtmspmrf mmrf smb hml if tin(3421m1,3509m10)


22

Table VI. The Results of Time-series Regression on the Portfolios of LEAPS Calls, Jan 2008 –

Dec 2010

Regression result for the portfolio of LEAPS calls with HBTM

Regression result for the portfolio of LEAPS calls with LBTM

The value of Alpha for the LEAPS call portfolio with HBTM is -0.5859, whereas this

value is about 3 times smaller (i.e. -1.6681) for the LEAPS call portfolio with LBTM ratio.

It implies that the the LEAPS call portfolio with HBTM ratio is better off the LEAPS call

portfolio with LBTM and it is a better investment alternative for long-term speculators

intending to replace their stocks with LEAPS calls.

In the other hand, the values of R square for the portfolios of LEAPS calls are

subsequently 0.27 and 0.18 which is very low. It indicates that the three-factor model of

Fama and French (1993) can not perfectly predict the return on a portfolio of option,

particularly LEAPS calls. However the result of our study with the R squares of 0.97 and

_cons -.5859263 .2751935 -2.13 0.041 -1.146477 -.0253755 hml 2.929713 1.642802 1.78 0.084 -.4165652 6.275992 smb -5.666539 2.162748 -2.62 0.013 -10.07191 -1.261165 mmrf 1.938632 .8762434 2.21 0.034 .1537827 3.723482 hbtmleapsp~f Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 21.0604231 35 .601726375 Root MSE = .69482 Adj R-squared = 0.1977 Residual 15.4488456 32 .482776424 R-squared = 0.2665 Model 5.61157754 3 1.87052585 Prob > F = 0.0180 F( 3, 32) = 3.87 Source SS df MS Number of obs = 36

. regress hbtmleapspmrf mmrf smb hml if tin(3421m1,3509m10)

_cons -1.668079 .9162128 -1.82 0.078 -3.534343 .1981856 hml 7.078108 5.469448 1.29 0.205 -4.062794 18.21901 smb -15.8994 7.200526 -2.21 0.035 -30.5664 -1.232413 mmrf 1.882966 2.917313 0.65 0.523 -4.059406 7.825338 lbtmleapsp~f Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 208.431234 35 5.95517812 Root MSE = 2.3133 Adj R-squared = 0.1014 Residual 171.242878 32 5.35133994 R-squared = 0.1784 Model 37.188356 3 12.3961187 Prob > F = 0.0943 F( 3, 32) = 2.32 Source SS df MS Number of obs = 36

regress lbtmleapspmrf mmrf smb hml if tin(3421m1,3509m10)


23

0.98 subsequently for the stock portfolio with HBTM and the stock portfolio with LBTM are

consistant with the findings of Fama and French (1993)

C. Findings of the Research

The results of the study show that the returns on the portfolios of LEAPS call are

significantly lower than those of the portfolios of underlying stock, while these portfolios

have possess higher level of volatility. It is significant to note that during the given period of

the study, the higher levels of risk or volatility of the LEAPS call portfolios are not

compensated with the higher levels of returns. Adversely, these portfolios have provided

greater loss for the long-term speculators. The results of the ex-post Sharpe ratio and Jenson

Alpha also indicate significant poor performance for the portfolios of LEAPS calls, especially

for the LEAPS call portfolio with LBTM ratio. That is the portfolios of LEAPS calls have

less abnormal returns (or higher negative excess return) comparing to the portfolios of stocks.

Unlike the prior study conducted by Bauer et al. (2008) on the main reason of substantial

loss on short-term, this study reveals that the poor market timing is not involved and in the

absence of requiring to timing the market, the only reason of substantial loss is leverage. On

the other hand, the better performance of the LEAPS call portfolio with HBTM relative to the

LEAPS call portfolio with LBTM ratio is consistant with the study of Fama and French

(1995) about the outperformance of stocks with high book-to-market ratio.

VI. Conclusion and Recommendation

In the last 2007, many financial analysts and stock market experts had expected the US stock

market to move up and boom in the following year. Based on the technical analysis, they

were looking for a bullish trend in the US stock market in 2008. They were anticipating the

future prices in the stock market would increase and market participants would obtain capital


24

gains. According to Business News Journal in the 20th December 2007, seven market

analysts suggested investors to put their money in US stock markets in 2008 to enjoy high

profitability. Based on these recommendations we constructed the portfolios of assets for the

beginning of 2008 in order to examine the strategy of "Buying In-The-Money LEAPS Calls

vs. Purchasing Stocks" in practice rather than in theory. Since the best time to purchase

LEAPS calls is when the underlying market is expected to move upward, it was anticipated

high performance for those who following this strategy within this period of time. However,

unlike what had been expected by the stock market analysts, the year 2008 was a terrible year

for most equity investors. In fact, the financial/credit crisis caused a downturn in consumer

and business spending in the year which subsequently reflected in equity markets as well.

The sudden fall in stock prices in 2008 resulted in significant losses for the markets

participants. This downward trend of US stock market even continued in the years 2009 and

2010.

The results of this study represent that all the four portfolios and S&P500EWI have

experienced significantly negative rates of return and poor performance within the given

period of study for their holders. Apart from the last observation (in December 2010) when

the stock portfolios and S&P 500 EWI turned to yield positive rates of return, the other prior

observations of the study showed significant negative rates of return and performance for the

portfolios. The fact is the result of the worse general economy of US during the period and

abrupt downturn of stock markets.

Within the period, the portfolios of LEAPS calls have had significantly lower rates of

return and higher risk and worse performances relative to the portfolios of common stock. It

implies that investing on LEAPS calls instead of the underlying stocks is not a good strategy,


25

even when it is predicted the market moves favorable to practice the strategy. There are

situations in the market when everyone predicts the general economy is providing positive

signal about the future prospects of the market and the market will improve, but everything

turns out adversely and the market moves downward. In such situations, the long-term

speculators who had expected obtaining significant gains and earning huge profits would

incur much more losses by purchasing LEAPS calls instead of common stocks.

Therefore this strategy is highly risky to involve in, because speculators cannot exactly

ensure the doom or gloom of the market. The market sometimes follows some irrational

patterns which cannot be predicted through the existing technical market analysis. So, it is

suggested to the risk-averse investors or risk-averse long-term speculators with low level of

risk tolerance to avoid this strategy and not replace LEAPS calls with common stocks in their

portfolio of investment. In other words, it would be better for risk-adverse speculators to put

their money into common stocks rather than LEAPS calls to avoid the risk of making their

funds worthless in the market downturn.

However, it would be recommended for that group of investors or long-term speculators

who are ready to take higher level of risk while making investments and are risk-seekers to

hold the portfolios of LEAPS calls with HBTM ratio in order to enjoy from favorable market

movement in the future. Since the portfolio of LEAPS calls with HBTM ratio is less volatile

than the portfolio of LEAPS calls with LBTM ratio and it generates smaller negative rates of

return when the market turns downward. At the same time, the portfolio of LEAPS calls with

HBTM is more volatile than the portfolio of stocks and it can earn higher rates of returns

relative to a stock portfolio when the market turns upward. Therefore, risk seekers can bet on

these portfolios and earn higher profit when the market moves up.


26

A. Limitation of the Study

As with all research, the current study has certain limitations. The major constraint of this

study is that we could not investigate both market upturn and market downturn

simultaneously within the period of the study to get a comprehensive and conclusive result

from applying the strategy of "Buying In-The-Money LEAPS Calls vs. Purchasing Stocks" in

both patterns of the market. Based on the behavior of the US stock market during the

investigation period, the study is only limited to the market downturn or the bearish market,

nor bullish one.

Data constraint is another limitation of the study. The primary data on LEAPS is not

distinctively available on Bloomberg and many other financial data providers. Although the

financial databases provide data on options, they do not differentiate the LEAPS from

standard or short-term options. The fact makes it impossible to distinguish between LEAPS

and short-term options and consequently find the required data on LEAPS calls. The only

database possessing the historical data on LEAPS in a classified manner is the historical

option database of CBOE. However, this database also does not provide customized data on

LEAPS to customers for different requirements. The historical data on LEAPS are offered to

all individuals in a uniform format. As it is not certain that the data is extracting would be

exactly the ones can be used in the study, the matter makes working with this database and

extracting data from it more challenging. The database provides the trading data associated

with LEAPS for each symbol but it does not offer any information about the issuance date,

expiry date and strike prices of LEAPS before purchasing the data. As the data cannot be

customized before purchasing, the risk of collecting wrong data and spending money in vain

is high.


27

Moreover, gathering and processing data from the historical option database of CBOE is

very expensive and has caused budgetary constraints for the study. Considering all the

challenges of dealing with this database and associated costs of collecting the required

primary data, we could not extend the duration of the study more than three years.

Another limitation of this study is ignoring transaction costs for the calculation of rates of

return. As the transaction cost has only happened one time in the period of study for rolling the

LEAPS Calls over and the strategy of buy and hold is applied, so transaction costs are not taken

into consideration in this study. However for any extension of the study using longer period of

time, for instance 5-10 years, the transaction costs should be included into the calculations.

B. Suggestions for further research

Areas that this study is not able to explore may provide fruitful avenues for future

researches. This study is the first step in investigating the integrity of replacing LEAPS calls

with stocks in practice. As this study could only capture the market downturn, further studies

can accomplish the results of this study by providing a comprehensive insight from both

market upturn and market downturn. So, it is highly recommended to repeat the similar study

in another time frame and also repeat it within a longer period of time. Then, through

comparing the results of this study with those of new researches, we can ensure about the

precision of adopting or preventing this investment strategy in practice rather than in theory.

C. Implications

The results of this study will give the investors, long-term speculators and funds managers a

practical insight about the performance of LEAPS calls against common stocks and the

possible gains or losses that they will likely experience in the financial markets. The findings

of this study show that investors or long-term speculators have to be very careful about

trading LEAPS calls and replacing them with common stocks. Although Roth, 1994; CBOE,


28

2001; McMillan, 2002; OIC, 2008 suggest buying equity LEAPS calls rather than common

stocks as a good substitutes for the underlying common stocks in the market and Thomsett

(2009) call it wise and a more conservative approach to buy LEAPS calls as an alternative to

simply buying common stock in a volatile stock market, this study empirically represents

opposite results. If investors or long-term speculators buy LEAPS calls in the situations when

the market suddenly moves downwards, they will incur lots of losses.

Also against the claims of many financial advisors and option specialists (Finnegan,

1977; McMillan, 2002; Taylor, 2008; Rahemtulla, 2009, Zigler, 2010) as well as that of the

CBOE about the ability to earn higher returns and lower risk relative to the underlying stocks

by constructing the portfolio of investment with LEAPS calls rather than stocks, the LEAPS

call portfolios can generate lower average rates of returns in the market. Thus, the long-term

expiration of them could not afford a conservative nature to them and they are still high risky

securities to be traded.

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