the efficiency of the buy-write strategy: evidence from ... annual...fundamentals like earnings per...

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The Efficiency of the Buy-Write Strategy: Evidence from Australia

Tafadzwa Mugwagwa, Vikash Ramiah and Tony Naughton

School of Economics, Finance and Marketing, RMIT University, GPO Box 2476V, Melbourne, 3001, Australia

Abstract

We examine the performance of the buy-write option strategy on the Australian Stock Exchange and

analyse whether such an investment opportunity violates the efficient market hypothesis on the basis of

its risk and returns. This study investigates the relationship between buy-write portfolios returns and past

trading volume and other fundamental financial factors including dividend yield, firm size, book to market

ratio, earnings per share (EPS), price earnings ratio and value stocks within these portfolios. We also

test the profitability of the buy-write strategy during bull and bear markets. The empirical results

demonstrate that buy-write portfolios do not outperform basic equity portfolios among the strategies

examined in Australia. Surprisingly, the buy-write strategy does not generate a lower risk investment

opportunity. Inconsistently with the bulk of the literature we find that the buy-write strategy does not

violate the efficient market hypothesis, but on the contrary, it is an inefficient strategy.

The authors wish to acknowledge the invaluable assistance and support of the Australian Stock Exchange and the Melbourne Centre for Financial Studies in data gathering. An earlier version of this paper was presented at the RMIT Finance Seminar 2008, and we also wish to thank the seminar participants, in particular Richard Heaney and Malick Sy, for their helpful comments. Any remaining errors are the responsibility of the authors.

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The Efficiency of the Buy-Write Strategy: Evidence from Australia

Abstract

We examine the performance of the buy-write option strategy on the Australian Stock Exchange and

analyse whether such an investment opportunity violates the efficient market hypothesis on the basis of

its risk and returns. This study investigates the relationship between buy-write portfolios returns and past

trading volume and other fundamental financial factors including dividend yield, firm size, book to market

ratio, earnings per share (EPS), price earnings ratio and value stocks within these portfolios. We also

test the profitability of the buy-write strategy during bull and bear markets. The empirical results

demonstrate that buy-write portfolios do not outperform basic equity portfolios among the strategies

examined in Australia. Surprisingly, the buy-write strategy does not generate a lower risk investment

opportunity. Inconsistently with the bulk of the literature we find that the buy-write strategy does not

violate the efficient market hypothesis, but on the contrary, it is an inefficient strategy.

JEL Classification: G11, G12, G14, G24, G32

Keywords: Buy-Write Strategy; Option; Equity; Portfolio Performance; Efficient Market; Market

Fundamentals; Market Conditions

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I. Introduction

A buy-write strategy is a variation of a covered call, whereby an investor buys the physical stock

and simultaneously writes an out-of-money call option contract against that same physical asset (Isakov

and Morard 2001 and Board, Sutcliffe and Patrinos, 2000). The benefits of the buy-write product are

similar to those of the physical stocks in that investors earn capital gains and dividends. The theoretical

value added of the buy-write strategy over the physical stock originates from the introduction of a call

option and the actual option premium earned. The existence of the call option acts as portfolio insurance

and hence reduces the volatility of this hybrid product, whilst the option premium acts as another source

of income that reduces the initial investment cost. Given these two attractive components, the majority of

the buy-write strategy (BWS) literature challenges the efficient market hypothesis of Fama (1970) and

shows that it is possible to earn higher returns whilst simultaneously reducing risk. For instance, Hill and

Gregory (2002), Whaley (2002), Feldman and Roy (2004), Hill, Balasubramanian and Tierens (2006),

Kapadia and Szado (2007) demonstrate the success of the buy-write strategy in the US, and similar

findings are observed in Switzerland1 and Australia2. Board, Sutcliffe and Patrinos (2000) and Lhabitant

(2002), on the other hand, argue otherwise, and Lhabitant (2000) concludes that further investigation of

this product is necessary. Hence the primary objective of this paper is to test whether the buy-write

strategy violates the efficient market hypothesis, i.e., whether this strategy offers higher returns and

concurrently a lower risk.

The risk and return profile of the BWS is dependent on the capital appreciation of the underlying

security and the call option premium. Theoretically, as the call option moves deeper out of money, the

call option premium is reduced, thus having a negative impact on the return of the BWS. Hill and

Gregory (2002) shows that the profitability of the BWS varies with the level of out-of-moneyness of the

call option. They show that as the call options within the BWS portfolios move away from at-the-

moneyness, the BWS becomes more profitable. However, as the call options become deeper out-of-

money, the benefits of the BWS are reduced as the hybrid product approximates the returns and risks of

the physical stocks. Lhabitant (2000), Hill and Gregory (2002), Hill, Balasubramanian and Tierens

1 See Isakov and Morard (2001) and Groothaert and Thomas (2003).

2 See El-Hassan, Hall and Kobarg (2004), Jarnecic (2004), Hallahan, Heaney, Naughton and Ramiah (2007) and O’Connell and

O’Grady (2007). Note the Hallahan et al. (2007) is an unpublished report from the Australian Stock Exchange.

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(2006), and Kapadia and Szado (2007) support the hypothesis that the level of out-of-moneyness affects

the return of the BWS; however, there is no general consensus on the optimal level of out-of-

moneyness. The remaining studies on BWS overlook the importance of the level of out-of-moneyness;

we therefore seek to determine the optimal level of out of moneyness.

Theoretically, the shorter the rebalancing period, the more successful the BWS will be. The

benefits of the BWS arise from the regular resetting of the exercise price, which increases the likelihood

of the call options remaining out-of-money. Another explanation for why shorter interval BWS portfolios

produce healthier returns than longer interval portfolios lies in the time value decay of call options

argument. Hill, Balasubramanian and Tierens (2006) and Figelman (2008) argue that the time value

decay of an option is larger in the months closer to the expiry date. When the BWS portfolios are

rebalanced on a shorter interval, they are exposed to these larger time value decays, which when

compounded, become significant (Feldman and Roy, 2004). The existing empirical evidence agrees that

the investment horizon affects the returns of the buy-write strategy. Consistently with the theories, the

literature shows that monthly3 buy-write portfolios yield the highest return. However, we are not aware of

any published work in this area in the Australian context. In order to determine an interval effect in the

BWS portfolios in Australia, we use the same data set and the same time period, and investigate

whether different portfolios rebalancing produce different results.

The risk and return of the BWS are directly related to the market fluctuations. The literature4

demonstrates that during periods of weak market conditions, BWS portfolios outperform equity portfolios

as investors benefit from the call option premium received, as the probability of the call option being

exercised falls. In addition, Hill and Gregory (2004) argue that the increased volatility during weak

economic conditions increases the value of the options and hence improves the performance of the

BWS. On the other hand, in periods of good financial performance, the increase in value of the

underlying security enhances the probability of the call options being exercised, which should negatively

affect the BWS. In the Australian market, El-Hassan, Hall and Kobarg (2004) support the above

hypothesis that BWS outperforms equity portfolios during weak market environments. However El-

3 See Board, Sutcliffe and Patrinos (2000), Isakov and Morard (2001), Groothaert and Thomas (2003), Feldman and Roy

(2004), Hill, Balasubramanian and Tierens ( 2006), Kapadia and Szado (2007) and Figelman (2008). 4 Groothaert and Thomas (2003), El-Hassan, Hall and Kobarg (2004), Hill and Gregory (2004) and Hill, Balasubramanian and Tierens (2006)

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Hassan, Hall and Kobarg (2004) restrict their definition of weak and strong markets to changes in

returns, with no consideration of market volatility. By including a volatility factor into the calculation of the

market performance, we provide a superior analysis of the profitability of the BWS under different market

conditions.

The BWS literature is in alignment with the value added of stock selection process of Brinson

Hood and Beebower (1986). For instance, Board, Sutcliffe and Patrinos (2000) use high and low price

earnings stocks to enhance their BWS portfolio returns, and El-Hassan, Hall and Kobarg (2004) use

large capitalisation stocks for that purpose. To the best of our knowledge, the BWS fundamental analysis

is limited to the above two variables. We extend the literature by assessing whether other market

fundamentals like earnings per share (EPS), leading price earnings, price to book value ratio, book to

market ratio, and volume can provide superior BWS returns.

O’Connell and O’Grady (2007) shows that the Australian options market is an illiquid one. As a

result of the enormous number of options and the limited number of market participants, a lot of the

options do not have a traded price, and the exchange usually records them as zero premiums. These

zero premiums, if unaccounted for, can provide misleading results; some options researchers address

this empirical issue by ignoring these options. We, on the other hand, will adopt the approach of Bollen

and Whaley (2004). They proposed the use of simulated option prices instead of excluding them. To that

end, we employ the Black-Scholes option pricing model and adjusted Black-Scholes option pricing

models. One major criticism of the entire existing body of research in this area is about the assumption

of a one out-of-money option to one stock approach and a failure to adopt a dynamic delta hedging

strategy. A dynamic delta hedging approach is expected to contribute to a further risk reduction in the

buy-write portfolios. Thus another unique contribution of this study is the application of delta hedging in

the BWS literature.

The Australian Stock Exchange provides an ideal testing ground for our arguments. In a bid to

increase market participation in the options market, the Australian Stock Exchange (ASX) has

encouraged and financed various research activities in this area. While this initiative may be good for

researchers in the field, the exchange publications may contain some positive bias. In other words, this

could lead to the exchange publishing primarily materials in favour of the strategy. We contribute to this

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debate as an independent research paper. Our analysis suggests that BWS does not provide superior

returns than a simple equity portfolio. Furthermore, there is also no apparent benefit from risk reduction.

These results are thus inconsistent with the majority of the BWS literature, but are consistent with the

EMH. Interestingly, there are other inconsistent findings when it comes to interval estimates, market

conditions and finance fundamentals. Consistently with prior studies we observe a relationship between

the level of out-of-moneyness and the performance of the BWS. This study also provide further insights

into of value construction and destruction in fundamental analysis, the performance of BWS under good

market conditions and the preferences of Australian options traders. Using simulated option prices, we

also show that the equity portfolios continue to outperform the buy-write portfolios and that the risks and

returns of the BWS are altered. Furthermore, we find additional risk reduction in the buy-write portfolios

following the adoption of the dynamic delta hedging. The rest of the paper is organised as follows: In

Section II we present the data and methods used in this paper. Section III presents the empirical

findings, and Section IV concludes the paper.

II. Data and Methodology

Data

We use equity data and exchange traded call options data for the period from January 1995 to October

2006 for our empirical analysis. Our total sample comprises 179 equity stocks that had options written on

them at the end of our sample period. The daily stock prices, total return indices, earnings per share,

price earnings, leading price earnings, book value, trading volume, number of outstanding shares,

market capitalisation, and dividend yield of these stocks were sourced from Datastream. We used the

180-day Bank Bills rate as the risk-free rate, and the S&P ASX200 as the proxy for the market. Following

Ince and Porter (2004), the data downloaded from Datastream were adjusted for company suspensions.

The volume is defined as the average daily turnover ratio, where the daily turnover ratio is obtained by

dividing the daily trading volume of a stock by the number of shares of the same stock at the end of the

day. Table 1, Panel A reports the descriptive statistics for each variable, i.e., the mean, median,

standard deviation, excess kurtosis, skewness, minimum, maximum, number of firms and JB statistic for

each variable. It can be seen from Table 1, Panel A that the average daily stock return is positive for the

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sample period, positively skewed and leptokurtic. Jarque-Bera (JB) statistics show that the daily returns

are not normally distributed, and this is consistent with Fama (1976).

The call option data was provided by the Australian Stock Exchange, and we filtered this data set

to obtain the out-of-money call options. The out-of-money call options were then categorised into four

different levels of out-of-moneyness. Table I, Panel B presents the descriptive statistics of the out-of-

money call options premium used in this study. As the data contained a significant number of zero

premiums, we exclude these zero values and report the average traded premium for the 179 companies

as well. It is clear from Table I, Panel B that the average option premium increases for all the different

classes after adjusting for the illiquid premium. For instance, the average premium for the period

investigated is $0.28, which increased to $0.62 after adjusting for the illiquid options for the 0% to 2%

out-of-money call options.

Methodology

This study begins by comparing the performance of buy-write portfolios to the performance of

purely equity portfolios. All the stocks that have options written on them are used to form the equity

portfolios, and the out-of-money call options are included in those equity portfolios to form the buy-write

portfolios. Portfolios are formed on either a monthly, quarterly or yearly basis. The stocks and options

are selected at the beginning of each period and held for the remainder of the period. For instance, at

the beginning of each year, both an equity portfolio and a buy/write portfolio are formed and are

assumed to be held for the rest of the year. The process is repeated for the entire length of the sample,

and then we compare the performance of these two portfolios on both a risk and return basis. We then

test whether the results differ with the level of out-of-moneyness in the various ranges 0% to 2%, 0% to

5%, 0% to 15% and 5% to 15%. The returns of the equity portfolios EPFitR are calculated as the average

return of the constituents SitR of the portfolios.

m

i

Sit

EPFit R

mR

1

1

(1)

The rate of return on each stock is defined as

8

1

1

it

ititSit

RI

RIRIR

, (2)

where itRI is the total return index, which includes adjustments for capitalisation changes and dividends

for the share i at time t.

As for the buy-write portfolios, we adopted and adjusted the methodology of Whaley (2002) in

the returns calculation. One characteristic of the options market is that options do not last for a long

period of time. An out-of-money call option has an average life of three months, and occasionally lasts

for over one year. Therefore for longer holding periods, a rollover of the options with lower lifetimes is

required. Hence the return for each individual BWS jBWSitR , is estimated as

11

1

1

11

,

itit

itit

it

ititit

jBWSit

CS

CCRI

RIRIS

R

, (3)

where jBWSitR, is the return on the buy-write strategy on stock i for the buy-write sub-period j within the

holding period from t-1 to t. itS is the price of the share i at time t and itC is the actual traded premium

on the options where it is available. Otherwise, this variable is proxied by the midpoint of the bid and

asking price. Thus the return on a BWS BWSitR for longer holding periods is usually made up of a

series5 of sub-period BWS jBWSitR , and, the holding period return is given as follows:

11...11 ,2,1, nBWSitBWSitBWSitBWSit RRRR(for j = 1 to n). (4)

At times, there is no out-of-money call option in the sub-periods and under these circumstances; it is

assumed that the portfolio is reinvested at the risk-free rate. Next, the return on the buy-write

portfolio BPFitR is calculated by averaging the returns of the individual BWS

BWS

itR .

m

i

BWSit

BPFit R

mR

1

1

(for i = 1 to m shares in the portfolio) (5)

Another empirical issue that we faced with the options data was the number of zero-premiums for

the call options. Two approaches were used to deal with this problem. First, we excluded all the options

with zero premiums and re-estimated the risks and returns of these portfolios. This technique eliminates

5 Given the number of rollovers that are required to perform a BWS, the transaction costs for BWS will be higher than those of

the equity portfolios, and one limitation of this work is its failure to account for this factor.

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the problem of zero-premiums but imposes an unrealistic assumption on the model, in that; it assumes

that the options market is a very liquid one. The second approach was to ignore the traded price and

estimate a fair price for these options using three different option pricing models, developed by Black

and Scholes (1973), Merton (1973) and Black (1975), respectively. The first model, developed by Black

and Scholes (1973), is based on a non-dividend paying stock, and thus does not consider payouts on

the stock. Given that buy-write investors seek to benefit from some level of dividends payout, it is

important to adjust for dividends paid to stockholders in the option pricing model. To that end, we

adopted the methods of Merton (1973) and Black (1975), which control for long-term and short-term

dividend payouts, respectively. Equations 6, 7 and 8 below depict the Black and Scholes (1973), Merton

(1973) and Black (1975) options pricing models that we used to estimate the fair price.

*1*1 tdNKedNSC lrtitBSit (6)

*2*2 tdNKedNPC lrtitMit (7)

*3*3* tdNKedNeSC lrtytitBit (8)

In these equations, itC denotes the estimated call option premium for stock i at time t. BS, M and B

stand for Black and Scholes (1973), Merton (1973) and Black (1975), respectively. itS denotes the

stock price, K the strike level, r is the risk-free interest at a continuously compounded rate, t* the term to

maturity, the estimated annualised volatility with either implied (l=1) or historical (l=2) volatility, and y

the dividend yield. Then 1d , 2d , 3d and itP are given by

*

*2

2

1t

trK

SLn

d

l

lit

(9)

*

*2

2

2t

trK

PLn

d

l

lit

(10)

10

*

*2

3

2

t

tyrK

itsLn

d

l

l

(11)

Div

nq

r

nDitSitP

1 3651 (for n = 1 to div for the stock), (12)

where Dn is the dividend paid and q is the time to dividend payment. All of the option pricing parameters

are obtained objectively, with the exception of the volatility variable. Both the implied volatility (l=1) and

historical volatility (l=2) were fitted to the above option pricing models. A three-year window was

employed to estimate the annualised historical volatility rate, and the approach of Brenner and

Subrahmanyam (1988) was used to estimate the implied volatility. We choose this approach as the

literature shows that it is more appropriate for out-of-the-money options with maturities longer than three

months. The Brenner and Subrahmanyam (1988) implied volatility is given by

*398.0

1*1

tKe

Crt

. (13)

To further reduce the risk of the buy-write strategy, we implement a dynamic hedging strategy where the

neutral ratio is estimated by

ititNR

1

, (14)

where delta it is equal to 1dN . This technique gives rise to a new dynamic hedged buy-write

portfolio, and the return of this new portfolio can be calculated by

11

11

11

,

*

ititit

itititit

ititit

jDBWSit

CNRS

CCNRRI

RIRIS

R

. (15)

After dealing with the zero-premium problem, we test the performance of the buy-write strategy

under different market conditions, namely under strong, moderate and weak market conditions. Hill and

Gregory (2002) defined a bull market as one where a positive market return is associated with low

volatility and a bear market where a negative market return is combined with volatility. A moderate

market condition was described as a state where there is average return and normal volatility. We adopt

their definitions of these three states and apply it to the Australian market. Given the small sample

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period size, this analysis was best performed for monthly portfolios. The returns and volatility of the ASX

200 index were used to identify the three market conditions. Next we estimate the performance of the

buy-write strategy and the equity portfolios over the three different market scenarios and test which of

these strategies works best under each of the different scenarios.

The next step will be to conduct a fundamental analysis of the buy-write portfolios and the equity

portfolios. For instance, if we want to test for the liquidity of these portfolios, we subcategorise the buy-

write and equity portfolios into quartiles. This gives rise to four other portfolios, where the first quartile

contains the most liquid stocks whilst the last quartile contains the most illiquid ones. We calculate the

return of the buy-write portfolios for the first quartile and compare it with the return equity portfolios. The

process is repeated for the remaining quartiles. Note that the trading volume is defined as the average

monthly turnover ratio, where the monthly turnover ratio is obtained by dividing the monthly trading

volume of a stock by the number of outstanding shares for the stock at the end of the month. Many

studies have used the turnover ratio as a consistent measure of trading volume, since the raw trading

volume is not scaled and is highly likely to be correlated with size.6 This analysis is extended to other

financial fundamentals like earnings per share, price earnings, leading price earnings, price to book

value ratio, book to market ratio, market value and dividend yield.

III. Empirical Results

This section reports the results of the five different hypotheses that we test about the BWS. In particular

the efficiency, the optimal level of out-of-moneyness, the interval estimates analysis, market conditions

and fundamental analysis of the buy-write strategy on the Australian Stock Exchange. It also contains

the results of the various robustness tests that we conducted. These results are then compared to equity

portfolios to test whether BWS is a superior strategy. Using a risk and return analysis, we find that the

BWS strategy does not violate the EMH, but on the contrary it is an inefficient strategy in the Australian

individual stock market. Our findings show that the performance of the BWS improves as the call option

moves out-of-money, and then deteriorates as the options turn deeper out-of-money. Given that

Australian options traders deal with quarterly options more regularly, we find that the most favourable

6 See Campbell, Grossman, and Wang (1993) and Lee and Swaminathan (2000).

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rebalancing period for BWS in Australia is quarterly, as opposed to the monthly preference of the US.

Surprisingly, we could not establish a statistical difference between the performance of BWS and equity

portfolios during weak market conditions. Nonetheless, we show that equity portfolios surpass BWS

portfolios in periods of good market conditions. Moreover, when these portfolios are ranked on their

financial fundamentals, we still could not uncover the superiority of the BWS. Furthermore, we find that

fundamental analysis can either add value or destroy value in the BWS.

The Buy-Write Strategy and the Efficient Market Hypothesis

Table II shows the risk and return analysis of the BWS and equity portfolios for the different levels

of out-of-moneyness and different interval estimates. Following Whaley (2002), we report the mean

return of the BWS, equity (EQTY) portfolios and the difference in the mean returns of these portfolios

(EQTY-BWS), as well as their respective t-statistics, for all the portfolios that we constructed. In other

words, we are assessing the performance of buy-write portfolios against that of their respective equity

portfolios. Theoretically, we expect to observe a difference between the returns of the equity portfolios

and those of the buy-write portfolios as a result of the additional premium obtained from writing options,

which further reduces the initial investment costs. The results reported in Table II do not support the

theoretical hypothesis, as the equity portfolios clearly and consistently outperform the BWS. For

instance, Table II Panel A illustrates that a 0% to 2% out-of-money buy-write portfolio that is rebalanced

on a monthly basis earns, on average, 7.6%, whilst its corresponding equity portfolio yields 13.7%. This

demonstrates that equity portfolio outperforms the BWS by 6.1%, and this difference is statistically

significant. The rest of the empirical findings on the mean return, in the second column of Table II, show

that equity portfolios consistently provide better returns. These empirical findings are thus consistent with

Kapadia and Szado (2002), Whaley (2002) and Feldman and Roy (2004) whereby they showed that

BWS do not outperform the equity markets. However, these studies were carried out on equity market

indexes rather than individual stocks. Kapadia and Szado (2002) assessed the profitability of the 0% to

2% BWS using monthly investment intervals on the Russell 200, and showed that the BWS

underperformed the Russell 200 index by only 0.1%. This difference is relatively small when compared

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to the Australian individual stocks market. Further, the BWS that underperformed the most in our study

was the one for monthly investment intervals and for 5% to 15% out-of-money options (see Table II,

Panel A). The statistically significant return difference is 7.8%, and such a large percentage gap is

empirically unusual. Our results also challenge a number of research papers in the area, in particular

Jarnecic (2004), El-Hassan, Hall and Kobarg (2004), Hill and Gregory (2004), Hill, Balasubramanian and

Tierens (2006), and more recently O’Connell and O’Grady (2007). These studies argue that BWS offers

superior returns, and once again a direct comparison with their results [except for El-Hassan, Hall and

Kobarg, 2004)] is not possible as they use market indices. Although it is not precisely in the BWS area,

Bollen and Whaley (2004) explained that option writing strategies on stock options are usually less

profitable than index based strategies primarily due to demand and supply forces. They show that stock

options have a higher demand than index options, thereby lowering the liquidity risk premium-profitability

of the stock options.

Furthermore, the literature highlights another benefit of buy-write strategies, namely their lower

volatility. The introduction of call options into the physical stock portfolios theoretically acts as portfolio

insurance, thereby reducing the risk. The majority of the existing literature demonstrates that buy-write

portfolios concurrently generate higher returns and lower volatility. These portfolios are regarded as the

new efficient portfolios, and their existence is a direct violation of the efficient market hypothesis (EMH).

Our next objective is to test whether buy-write portfolios breed significantly lower volatility than the equity

portfolios. The last column of Table II reports the volatility (standard deviation) of the equity portfolios,

BWS portfolios, and the difference in between these two portfolios (EQTY-BWS). We also include the F-

statistics for the difference in volatility between these two portfolios in Table II. A positive (negative)

difference in volatility indicates that the buy-write portfolios generate a lower (higher) volatility than the

equity portfolios. We test the validity of the above previous empirical findings using four different levels of

out-of-moneyness and three interval estimates. The results reported in Table II do not support the

theoretical background, as the buy-write strategies do not yield significantly lower volatility than the

equity portfolios. For instance, the volatility of a monthly buy-write portfolio with 0% to 15% out-of-

moneyness is 25.9%, whereas that of the corresponding equity portfolio is 11.5%, resulting in a

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difference in volatility of -14.4% (see Table II Panel A, column 8).This shows that the buy-write portfolio

has a higher volatility than the equity portfolio, and this difference is statistically significant. Out of twelve

portfolios studied, we find two cases where the volatility of the equity portfolios is lower than that of the

BWS. In 66% of the portfolios, we do not observe any statistical difference between the equity portfolios

and the BWS portfolios. Therefore, the results for ten of the twelve portfolios that we studied are not

consistent with the theory.

When we combine the risk and return of BWS portfolios and then compare them to equity portfolios, our

general conclusion is that BWS do not offer lower risk but pay lower returns. Markowitz (1952) refers to

portfolios with the same or higher risk and lower returns as inefficient portfolios. As such, we are not

convinced that BWS violates the EMH; on the contrary, we find that the strategy is an inefficient one. Our

findings are consistent with those of Board, Sutcliffe and Patrinos (2000), who reported that buy-write

portfolios do not dominate the underlying portfolios. However, our findings challenge the rest of the

literature in the area, which show that BWS is a dominant strategy.

Our analysis provided two exceptional cases in the yearly portfolios that warrant further discussion (see

Table II Panel C). The first portfolio is the 0% to 5% out-of-money BWS portfolio. In this particular

portfolio, BWS has a lower volatility than the equity portfolio and there is no statistical difference in

returns. The volatility of the BWS is 5.1%, whilst the volatility of the equity portfolio is 12.4%. In this

particular instance, we find both theoretical and empirical consistency. In the second instance (see 0% to

2% level of out-of-moneyness), we find that BWS offers statistically lower risk and lower returns. For

4.1% of volatility, BWS generates 9.8% returns, whilst the volatility of the equity portfolio is 12.1% with a

return of 17.4%. This portfolio is consistent with the EMH hypothesis, and depicts a positive relationship

between risk and return. At the same time, it suggests7 further discussion on the risk-adjusted

performance of these portfolios. Columns three to seven show the results of the different risk-adjusted

measures used in this study. In most cases, these results support our view on the inefficiency of the

BWS.

7 Lhabitant (2000) also argues for the need for appropriate risk-adjusted measures to evaluate the performance of BWS

portfolios.

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The Optimal Level of Out-of-Moneyness of the BWS

Theoretically, there is an inverse relationship between the profitability of the BWS and the level of

out-of-moneyness. Our findings, from Figure 1, partially support this theoretical argument. Initially, when

the call options move from 0% to 2% to 0% to 5%, the return of the BWS improves for three different

rebalancing periods. As the call options move deeper out-of-money, the returns of the BWS deteriorate

systematically. These results are thus consistent with the previous empirical findings [see Hill and

Gregory (2002), Hill, Balasubramanian and Tierens (2006), and Kapadia and Szado (2007)]. The

highest profit was achievable for the 0% to 15% out-of-moneyness level for the yearly portfolios (see

Figure 1). However, this level of out-of-moneyness does not consistently generate the highest profit for

other rebalancing periods. When we consider the 0% to 5% level of out-of-moneyness, we find that the

highest return for the remaining interval occurs within this band. Hence, we cannot clearly determine the

optimal level of out-of-moneyness for the BWS. Whilst the literature documents the relationship between

the level of out-of-moneyness and the performance of the BWS, the existing literature fails to describe

the relationship between the volatility of the strategy and the level of out-of-moneyness. As depicted in

Figure 2, as the call option moves away from 0% to 2% (until it reaches 0% to 15%), the volatility of the

BWS increases. Interestingly, for deeper out-of-money options (5% to 15%), the volatility drops.

The Favourable Portfolio Rebalancing Interval of the BWS

The current literature suggests that monthly intervals are the most favourable portfolio

rebalancing of the BWS. Our findings, however, show otherwise for the Australian market. As shown in

Figure 1, monthly portfolios produced the lowest profits when compared to quarterly and yearly intervals.

These outcomes are inconsistent with Hill, Balasubramanian and Tierens (2006) who finds that a BWS

with monthly rebalancing interval earns a higher return than a quarterly rebalancing interval strategy in

the US. One possible explanation for the difference in these findings is that the American market

participants trade more monthly options, whilst the Australian market players trade more quarterly

options. For 0% to 2% out-of-money portfolios, we observe that quarterly rebalancing offers the highest

16

returns. For deeper out-of-money call options, we find that yearly portfolios are more profitable.

Interestingly, we observe from Figure 2 that monthly portfolios generate the highest volatility, whilst the

yearly portfolios are the safest. When we combine the risk and return of the rebalancing interval, we find

that the yearly portfolios are preferable as they offer the lowest risk and the highest returns for the

deeper out-of-money call options.

BWS under different Market Conditions

According to the current literature, the performance of the BWS varies with the state of the

economy. Table III8 reports the performance of the BWS portfolios, the equity portfolios and the

difference between the equity and BWS portfolios under weak, moderate and strong market conditions.

The evidence from the last column of Table III contradicts the majority of the literature, as we find no

statistical difference between the returns of these two portfolios. For instance, under weak market

conditions, a 0% to 2% out-of-money BWS earns a mean return of 0.9% and the equity portfolio

achieves -4.6% mean return. However, the difference in mean returns is not statistically significant.

These results contradict the findings of Groothaert and Thomas (2003), El-Hassan, Hall and Kobarg

(2004), Feldman and Roy (2004), Hill and Gregory (2004) and Hill, Balasubramanian and Tierens

(2006), who illustrate the superiority of the BWS during weak market periods. This inconsistency may

arise because of our different definitions of what constitutes a weak market condition. The prior literature

defines a weak market as one with negative returns, whereas we define a weak market condition as a

state where the returns are negative and the volatility is high. Our results for the strong market

conditions, however, are consistent with the existing literature in that we find that for 0% to 2% and 0% to

5% out-of-money BWS (see column 2 of Table III), the corresponding equity portfolios outperform BWS.

Note that other than these two out-of-money levels during the strong market, we cannot find any

difference in the returns of equity portfolios and BWS portfolios.

Also reported in Table III are the standard deviations of the equity portfolios, the BWS portfolios

and the difference in the volatility of these two portfolios. In a BWS, the presence of a call option is

8 Note that we only report the findings of the monthly portfolios, as the quarterly and yearly portfolios are subject to small

sample issues.

17

meant to reduce the risk of this strategy, and these results allow us to evaluate the risk of these

portfolios during the three market conditions. In the last column of Table III, we observe that the standard

deviation of the BWS for a 0% to 2% level of out-of-moneyness is 2.5%, when the risk of the equity

portfolios is 2.7% during weak market conditions. In this instance and for the 0% to 5% level of out-of-

moneyness (for the weak market condition), we find that BWS offers a lower risk. However, we find no

statistical difference in the volatility of the equity and BWS portfolios under moderate market conditions.

Surprisingly, we document that equity portfolios are less risky for the remaining cases (i.e., for the strong

market condition and for deeper out-of-money BWS during the weak market conditions).

A Fundamental Analysis of the BWS

In this section we examine whether there is any relationship between financial fundamentals and

past portfolio returns for equities and BWS listed in the Australian market. Table 4 reports the returns for

portfolios formed on the basis of a two-way sort between returns of equity, BWS portfolios and a number

of fundamentals like EPS, PE, leading PE, price to book value, book value, volume, market value and

dividend yield. The analysis was conducted for all the levels of out-of-moneyness as well as for all the

rebalancing periods. However, for the purpose of brevity, we only report the findings for the 0% to 2%

out-of-moneyness, the first quartile and the fourth quartile. The first quartile (Q1) represents portfolios

with the highest financial fundamental values, whilst the fourth quartile (Q4) contains portfolios with the

lowest values. We then report the performance of the BWS portfolios, equity portfolios and the difference

between equity and BWS portfolios (EQTY-BWS) within these two quartiles. Thus, when BWS portfolios

perform better (worse) than equity portfolios, the EQTY-BWS portfolios result in a negative (positive)

value. Our results show mixed returns for the EQTY-BWS for the different scenarios. Hence we cannot

conclude that there is evidence that, conditional on past returns, BWS portfolios consistently outperform

equity portfolios. For instance, in the high EPS portfolios for the 0% to 2% level of out-of-moneyness

(see Table IV, fourth column), rebalanced on a monthly basis, the BWS portfolio earned on average

9.1% and the equity portfolio produced on average 22.5% (note that the t-statistic shows that the return

is statistically significant). This implies that the equity portfolio earned a return in excess of 13.4% over

the equity portfolio. In other words, in this particular example, it will be best to invest in the high EPS

18

equity portfolio. Similarly, we find that high EPS equity portfolios that are rebalanced on a yearly basis for

the 0% to 2% level of out-of-moneyness are more profitable than the BWS portfolios. However, the

remaining9 evidence for the EPS portfolios illustrates that there is no difference in the returns of BWS

and equity portfolios.

Table IV, Column V shows the results of high and low PE ratios. Interestingly, we find that equity

portfolios surpass BWS portfolios by 12.1% for low PE ratio portfolios that are rebalanced on a monthly

basis. Nevertheless, when the rebalancing periods are altered to quarterly, we find that BWS

outperforms the equity portfolios by 9.6% for portfolios with high PE values. The PE ratio (also known as

trailing PE, calculated by the stock price divided by the last known earnings dividend) is used when an

analyst cannot forecast the earnings of the company; and on the other hand, the leading PE is used

when forecasted earnings are available. In our sample, we find no major difference between the leading

PE and trailing PE, and consequently the findings in Column 6 of Table IV are similar to those of the

trailing PE.

Like the previous fundamentals, portfolios ranked on price to book value offer mixed signals. In

Table IV, we document that the returns for equity portfolios exceed the returns of BWS portfolios on two

counts for the low price to book value portfolios, whilst we find one opposite outcome for the high price to

book value portfolios. For the remaining fundamentals (like book value, volume, market value and

dividend yield), however, we find that equity portfolios provide superior returns when compared to the

BWS portfolios. So far, we have ranked the BWS and equity portfolios on financial fundamentals and

then compared their performance. Our results show that even after an extensive stock selection

analysis, we do not have strong evidence in favour of the BWS.

The next step will be to determine whether the stock selection process enhances the buy-write

strategy. Table V shows that there are instances where fundamental analysis adds value to the BWS

portfolios, but these fundamental analyses are more of a value destruction exercise for the BWS

portfolios. For example, in Table V, Columns 3 and 4, we show the return of the BWS for the entire 179

firms and the return of the high EPS buy-write portfolios, respectively. For a BWS with monthly

rebalancing intervals and a 0% to 2% level of out-of-moneyness, the return of the BWS for the 179 firms

9 This includes the other findings that we do not report.

19

is 7.6% and the return for the high EPS buy-write portfolio is 9.1%. A stock selection process on the

basis of high EPS yields a value enhancement of 1.5% for the BWS. Such results persist for the

remaining levels of out-of-moneyness and rebalancing periods. The high EPS portfolios formation leads

us to believe that there are value enhancements, and as we extend our analysis to other fundamentals,

we find that high market value and low book value portfolios offer analogous benefits (as well as high

price to book value and high dividend yield, but to a lesser degree). Conversely, investors must be

careful in generalising these findings, as other fundamental analyses, like high trailing P/E, leading P/E,

price to book value, volume and low EPS, market value and dividend yield are value destructive for the

BWS (see Table V). Our findings are thus in accordance with the study of El-Hassan, Hall and Kobarg

(2004) and Board, Sutcliffe and Patrinos (2000), who demonstrate value added in terms of large cap

stocks and value destruction respectively.

This examination was extended to the equity portfolios, and although we do not present a

separate table, the information could be gathered from Tables 2 and 4. The benefit of this exercise is

twofold. First, it allows us to have a deeper understanding of the Australian equity markets and secondly

it enables us to understand the factors that jointly affect the equity and BWS portfolios. The fundamental

factors that enhance the quality of equity returns are high EPS, book value, dividend and low price to

book value. Low PE, low volume traded and market value are other factors that had weaker positive

effects on the returns. The equity value destruction fundamental factors are low EPS, book value and

dividend yield, and high trailing P/E, leading P/E, price to book value. Not surprisingly, most of the

factors that affect the equity portfolios tend to have a similar effect on the BWS.

Robustness Tests

In this section we address two issues in this area of research, namely the illiquidity of the options and the

one-to-one hedge ratio assumption of prior studies. In order to overcome the illiquidity of the Australian

options market, we adopt the following two measures. First, we exclude all the zero premiums from the

data set, and while this method is unrealistic as it assumes that investors will always earn a premium on

out-of-money call options, it allows us to test whether the results of our study will change. It is important

to note that for the robustness tests, we only stress test our results on the risk and return relationship,

20

the level of out-of-moneyness and the interval estimate. Although we do not show the results of this

exercise, we did not uncover any major difference in our results. In other words, even if traders were to

earn the traded option premiums, our major conclusions in the earlier sections would not change.

Second, we replace all the zero premiums with fair prices. The fair prices were calculated using Black

and Scholes (1973), Merton (1973) and Black (1975) for both historical and implied volatility. Finally, we

control for delta hedging using these options pricing models. The zero premiums are substituted with the

various fair prices (including controlling for delta hedging) and we find that both the risks and returns of

the BWS are altered. Our initial conclusion that BWS is an inefficient portfolio is adjusted to say that it is

an efficient one with low risk and low return. In addition, the favourable rebalancing period is changed

from quarterly to yearly.

IV. Conclusions

This study investigates the return and volatility attributes of the buy-write strategy in the

Australian market. The study focuses on five key efficiency areas of the BWS namely, risk and

return analysis, optimal level of out-of-moneyness, favourable rebalancing intervals, performance

under different market conditions, and when a stock selection process is used in the portfolio

construction. The existing literature portrays the BWS as one that violates EMH in terms of either

superior returns or lower risk. Our paper, however, provides further evidence in favour of the

efficient market hypothesis, whereby we demonstrate that the BWS on individual stocks in Australia

is an inefficient one. Further, our outcomes reinforce the literature in terms of the desired optimal

level of out-of-moneyness. We show that initially as the options move away from at-the-moneyness,

the profitability of BWS increases, and then it decreases as the options moves deeper out of money.

Given that there is a preference for options with a maturity of around three months in Australia, we

find that quarterly rebalancing periods offer better returns for the BWS. The results comparing the

BWS and the market performance challenge the prior literature in that we did not find that BWS

outperform the equity portfolios under weak market conditions. Moreover, we find that in a good

market condition the equity portfolios surpass the BWS ones. Even when a financial fundamental

analysis is conducted, we could not prove that BWS consistently outperform equity portfolios.

21

Consequently, after an extensive analysis of this product we are not convinced of the superiority of

the buy-write strategy on individual stocks on the Australian market. Investors will be better off with a

fundamental analysis of a pure equity portfolio.

22

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Lausanne.

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24

Table I: Descriptive Statistics

Panel A: Descriptive statistics of the market returns, earnings per share (EPS), trailing price earnings (PE), leading price earnings (Leading PE), price to book value (Price to BV), book value (BV), volume, market value (MV), and dividend yield for the Australian Equity Markets, from January 1995 to October 2006.

Market Returns

EPS PE Leading

PE Price to

BV BV Volume MV

Dividend Yield

Mean 0.1% 0.37 12.23 12.51 2.50 0.89 0.00 4186865 4.3%

Median 0.1% 0.23 13.56 13.55 1.65 0.51 0.00 1601087 4.0%

Standard Deviation 0.00 0.63 16.39 16.88 3.87 4.43 0.02 8168088 0.03

Kurtosis 3.33 33.05 5.16 4.92 90.85 171.56 176.12 28 17.71

Skewness 0.56 4.50 -1.28 -1.03 8.51 13.07 13.22 5 3.27

Minimum -0.3% -0.79 -55.46 -55.48 -1.00 -0.38 0.00 3466 0.2%

Maximum 0.4% 5.81 66.21 66.55 45.63 58.72 0.29 69048895 22.3%

Count 179 179 179 179 179 179 179 179 179

JB-Statistic 92*** 8753*** 247*** 213*** 63717*** 224607*** 236551*** 6413*** 2658***

*** Significant at the 0.01 level.

** Significant at the 0.05 level.

* Significant at the 0.10 level.

25

Table I: Descriptive Statistics (Continued)

Panel B: Descriptive statistics of the actual call option premiums and traded premiums used in monthly, quarterly and yearly rebalancing buy-write strategy portfolios at different levels of out-of-moneyness from January 1995 to October 2006.

0% to 2% 0% to 5% 0% to 15% 5% to 15%

Actual

Premium Traded

Premium

Actual Premium

Traded Premium

Actual

Premium Traded

Premium

Actual Premium

Traded Premium

Monthly Rebalancing Intervals

Mean 0.28 0.62 0.31 0.58 0.37 0.61 0.31 0.59

Median 0.17 0.42 0.13 0.34 0.15 0.32 0.12 0.28 Standard Deviation 0.39 0.60 0.49 0.65 0.60 0.74 0.49 0.78

Kurtosis 8.57 2.88 7.48 4.69 8.79 4.72 6.78 7.59

Skewness 2.60 1.82 2.61 2.16 2.83 2.24 2.57 2.55

Minimum 0.00 0.01 0.00 0.01 0.00 0.01 0.00 0.01

Maximum 2.27 2.84 2.86 3.33 3.50 3.72 2.49 4.84

Count 179 179 179 179 179 179 179 179

JB-Statistic 750*** 160*** 622*** 303*** 816*** 315*** 540*** 624***

Quarterly Rebalancing Intervals

Mean 0.30 0.56 0.30 0.53 0.32 0.59 0.46 0.46

Median 0.13 0.36 0.13 0.31 0.13 0.31 0.24 0.24

Standard Deviation 0.47 0.64 0.47 0.63 0.53 0.74 0.56 0.58 Kurtosis 8.42 7.21 8.42 6.31 9.79 4.83 4.28 4.83

Skewness 2.79 2.55 2.79 2.47 2.96 2.26 2.18 2.26

Minimum 0.00 0.01 0.00 0.01 0.00 0.01 0.00 0.01

Maximum 2.80 3.63 2.80 3.52 3.23 3.84 2.78 2.98

Count 179 179 179 179 179 179 179 179

JB-Statistic 761*** 582*** 761*** 479*** 976*** 326*** 279*** 327***

Yearly Rebalancing Intervals

Mean 0.28 0.52 0.28 0.52 0.30 0.52 0.24 0.45

Median 0.12 0.30 0.11 0.28 0.09 0.24 0.08 0.22

Standard Deviation 0.43 0.61 0.46 0.68 0.52 0.67 0.41 0.57

Kurtosis 9.97 6.25 9.69 10.95 11.66 4.58 10.01 4.65

Skewness 2.92 2.33 2.90 2.90 3.14 2.20 2.95 2.17

Minimum 0.00 0.01 0.00 0.01 0.00 0.01 0.00 0.01

Maximum 2.61 4.02 2.78 4.86 3.38 3.64 2.58 2.99

Count 179 179 179 179 179 179 179 179

JB-Statistic 996*** 454*** 952*** 1145*** 1307*** 301*** 1007*** 302***



* Significant at the 0.10 level.

26

Table II: Return, Risk and Adjusted Risk-Return Performance for the Buy-Write Strategy and Equity Portfolios

Panel A: Return, risk and adjusted risk-return performance of buy-write strategy (BWS) and equity (EQTY) portfolios with monthly rebalancing intervals, from January 1995 to October 2006, for different levels of out-of-moneyness. The table also shows the difference between the equity and buy-write strategy portfolios (EQTY - BWS). The corresponding t-statistics are provided in parentheses.

Mean Jensen Alpha

Leland M

Squared Sharpe Treynor

Standard Deviation

Out-of-Moneyness range: 0% to 2%

BWS 7.6%** -0.02 0.13 3.1% 0.67*** 0.03 11.3%

(2.34) (4.77) (1.63)

EQTY 13.7%*** 0.01 0.27 2.4% 2.11*** 0.10* 9.9%

(4.80) (11.25) (2.77)

EQTY - BWS 6.1%** 0.03 0.14 -0.7% 1.44*** 0.07** -1.4%

(2.10) (49.56) (2.24) (1.31)†


BWS 10.1%** 0.00 0.26 2.4% 1.99*** 0.07*** 14.0%

(2.50) (14.35) (3.73)

EQTY 15.9%*** 0.03 0.31 2.0% 2.47*** 0.12** 14.8%

(3.72) (12.55) (3.06)

EQTY - BWS 5.8% 0.03 0.05 -0.4% 0.48*** 0.05 0.8%

(1.70) (14.18) (1.39) (1.11)†


BWS 6.5% -0.09 0.07 1.2% 0.05 0.0 25.9%

(0.86) (0.25) (0.04)

EQTY 12.7%*** -0.01 0.24 0.9% 1.73*** 0.07** 11.5%

(3.83) (8.96) (1.93)

EQTY - BWS 6.2% 0.08 0.17 -0.3% 1.68*** 0.07 -14.4%***

(1.12) (30.13) (1.26) (5.08)†


BWS 2.7% -0.11 -0.08 -4.7% -1.41*** -0.04 16.9%

(0.56) (-8.81) (-1.59)

EQTY 10.5%*** -0.01 0.18 -0.1% 1.15*** 0.06 8.3%

(4.37) (6.01) (1.70)

EQTY - BWS 7.8%** 0.10 0.26 4.6% 2.56*** 0.1** -8.6%**

(2.25) (74.02) (2.97) (4.12)†



* Significant at the 0.10 level. †

F-statistics for the difference in standard deviation

27

Table II: Return, Risk and Adjusted Risk-Return Performance for the Buy-Write Strategy and Equity Portfolios (Continued)

Panel B: Return, risk and adjusted risk-return performance of the buy-write strategy (BWS) and equity (EQTY) portfolios with quarterly rebalancing intervals, from January 1995 to October 2006, for different levels of out-of-moneyness. The table also shows the difference between the equity and buy-write strategy portfolios (EQTY - BWS). The corresponding t-statistics are provided in parentheses.

Mean Jensen Alpha

Leland M

Squared Sharpe Treynor

Standard Deviation


BWS 12.8%*** 0.04 0.31 7.4% 2.51*** 0.22*** 8.1%

(5.47) (15.63) (8.62)

EQTY 14.2%*** 0.01 0.19 2.0% 1.24*** 0.09 11.1%

(4.44) (4.93) (1.41)

EQTY - BWS 1.4% -0.03 -0.12 -5.4% -1.27*** -0.13*** 3.0%

(0.56) (-51.06) (-5.36) (1.87)†


BWS 13.0%*** 0.04 0.31 7.6% 2.47*** 0.21*** 7.9%

(5.69) (15.02) (7.87)

EQTY 13.9%*** 0.01 0.18 1.8% 1.20*** 0.09 11.0%

(4.39) (4.76) (1.39)

EQTY - BWS 0.9% -0.03 -0.13 -5.8% -1.27*** -0.12*** 3.1%

(0.35) (-50.17) (-4.93) (1.92)†


BWS 13.0%** 0.02 0.18 8.1% 1.20*** 0.11** 15.8%

(2.85) (5.11) (1.90)

EQTY 14.5%*** 0.01 0.19 2.2% 1.29*** 0.09 11.5%

(4.39) (5.14) (1.42)

EQTY - BWS 1.5% -0.01 0.01 -5.9% 0.09** -0.02 -4.3%

(0.40) (2.37) (-0.41) (1.90)†


BWS 9.0%*** 0.00 0.15 1.7% 0.87*** 0.08** 8.4%

(3.70) (4.93) (2.45)

EQTY 15.1%*** 0.01 0.20 2.4% 1.37*** 0.09 11.7%

(4.45) (5.40) (1.44)

EQTY - BWS 6.1%** 0.01 0.05 0.7% 0.50*** 0.01 3.3%

(1.86) (15.32) (0.50) (1.94)†





28

Table II: Return, Risk and Adjusted Risk-Return Performance for the Buy-Write Strategy and Equity Portfolios (Continued)

Panel C: Return, risk and adjusted risk-return performance of the buy-write strategy (BWS) and equity (EQTY) portfolios with yearly rebalancing intervals, from January 1995 to October 2006, for different levels of out-of-moneyness. The table also shows the difference between the equity and buy-write strategy portfolios (EQTY - BWS). The corresponding t-statistics are provided in parentheses

Mean

Jensen Alpha Leland

M Squared Sharpe Treynor

Standard Deviation


BWS 9.8%*** 0.05 0.15 5.6% 0.85*** -0.26*** 4.1%

(8.32) (4.22) (-6.34)

EQTY 17.4%*** 0.03 0.15 4.1% 0.92** 0.11 12.1%

(4.44) (2.64) (0.93)

EQTY – BWS 7.6%** -0.02 0.00 -1.5% 0.07 0.37*** 8.0%***

(1.86) (1.62) (8.99) (8.90)†


BWS 12.7%*** 0.06 0.19 6.8% 1.24*** 0.76*** 5.1%

(8.57) (5.49) (14.91)

EQTY 16.1%*** 0.02 0.14 1.8% 0.79** 0.1 12.4%

(4.39) (2.24) (0.81)

EQTY – BWS 3.4% -0.04 -0.05 -5.0% -0.45*** -0.66*** 7.3%***

(0.89) (-11.72) (-17.20) (5.88)†


BWS 15.1%*** 0.08 0.16 9.8% 0.96*** 2.67*** 9.2%

(5.70) (3.16) (29.21)

EQTY 16.4%*** 0.03 0.16 3.1% 0.92** 0.11 10.9%

(4.39) (2.79) (1.02)

EQTY – BWS 1.3% -0.05 0.00 -6.7% -0.04 -2.56*** 1.7%

(0.32) (-0.84) (-62.16) (1.43)†


BWS 11.0%*** 0.05 0.12 6.6% 0.55** -0.81*** 8.6%

(4.43) (1.87) (-9.34)

EQTY 16.6%*** 0.02 0.15 3.3% 0.84** 0.10 12.3%

(4.45) (2.39) (0.84)

EQTY – BWS 5.6% -0.03 0.03 -3.3% 0.29*** 0.91*** 3.7%

(1.28) (6.64) (20.69) (2.04)†





29

Table III: Buy-write Strategy Performance During Strong, Weak and Moderate Market Conditions The table shows the returns and volatility of the monthly rebalancing buy-write strategy (BWS) and equity (EQTY) portfolios during periods of strong, weak and moderate market conditions, from January 1995 to October 2006, for different levels of out-of-moneyness. The table also shows the difference between equity and buy-write strategy portfolios (EQTY - BWS). The corresponding t-statistics are provided in parentheses.

Strong Market Moderate Market Weak Market

Mean Standard Deviation




BWS 1.4% 1.0% 1.8% 1.4% 0.9% 2.5%

(1.45) (1.23) (0.35)

EQTY 4.6%*** 0.9% 2.7% 1.6% -4.6% 2.7%

(5.27) (1.70) (-1.69)

EQTY - BWS 3.1%** -0.1%*** 0.9% 0.1% -5.5% 0.3%***

(2.85) (83.92)† (0.34) (0.53)

† (-1.49) (45.71)

†


BWS 1.9% 1.2% -0.4% 5.1% -0.2% 3.1%

(1.59) (-0.08) (-0.05)

EQTY 4.4%*** 1.1% 3.4% 3.0% -4.9% 3.3%

(3.90) (1.11) (-1.49)

EQTY - BWS 2.5%** -0.1%*** 3.8% -2.1% -4.7% 0.2%***

(2.23) (33.51)† (0.46) (1.20)

† (-1.13) (24.54)

†


BWS 2.3% 2.1% 0.4% 5.2% -2.3% 3.6%

(1.11) (0.07) (-0.63)

EQTY 4.3%*** 1.1% 3.1% 2.9% -5.2%** 2.7%

(4.06) (1.07) (-1.93)

EQTY - BWS 2.0% -1.0%*** 2.8% -2.3% -2.9% -0.9%**

(1.00) (11.36)† (0.34) (0.64)

† (-0.75) (6.45)

†


BWS 1.7% 1.9% 0.5% 4.1% -2.3% 3.5%

(0.88) (0.11) (-0.65)

EQTY 3.7%** 1.8% 3.4% 2.7% -5.2%** 2.7%

(2.06) (1.26) (-1.93)

EQTY - BWS 2.0% -0.1%** 2.9% -1.5% -2.9% -0.8%**

(0.82) (8.75)† (0.44) (1.04)

† (-0.70) (6.78)

†





30

Table IV: Performance of the Buy-Write Strategy and Equity Portfolios for Different Market Fundamentals The table shows the performance of the 0% to 2% out-of-money buy-write strategy (BWS) and equity (EQTY) portfolios for monthly, quarterly and yearly rebalancing intervals, from January 1995 to October 2006. The buy-write strategy and equity portfolios are constructed based on each of the following market fundamentals: earnings per share (EPS), price earnings (PE), leading price earnings (Leading PE), price to book value (Price to BV), book value (BV), volume, market value (MV), and dividend yield. The stocks are ranked in descending order based on each of these fundamentals and then categorised into quartiles (Q1 to Q4). Stocks in each quartile are then used to construct the buy-write strategy and equity portfolios. The table shows the mean returns of the BWS equity and equity portfolios, and the difference between the equity and buy-write strategy portfolios (EQTY - BWS), for quartile 1 (Q1) and quartile 4(Q4) for each market fundamental. The corresponding t-statistics are provided in parentheses.

EPS PE Leading PE

Price to BV

BV Volume MV Dividend

Yield


Q1

BWS mean 9.1% 4.3% 4.3% 5.5% 7.4% 5.5% 7.4% 9.5%

(6.32) (5.87) (5.87) (6.03) (8.36) (5.54) (6.39) (7.32)

EQTY mean 22.5% -0.6% -0.6% 8.5% 19.6% 12.3% 14.4% 15.6%

(6.53) (-0.13) (-0.13) (2.89) (3.91) (2.80) (4.25) (4.27)

EQTY -BWS Mean 13.4%*** -4.9% -4.9% 3.0% 12.2%*** 6.8% 7.0%*** 6.1%***

(5.01) (-1.16) (-1.16) (1.33) (2.49) (1.49) (2.49) (2.43)

Q4

BWS mean 5.0% 6.2% 6.2% 7.7% 7.7% 7.2% 6.0% 4.0%

(7.83) (6.60) (6.53) (6.77) (8.67) (9.99) (6.46) (3.11)

EQTY mean 0.3% 18.3% 18.4% 18.7% 12.5% 15.0% 13.0% 8.5%

(0.07) (4.60) (4.59) (4.41) (3.66) (4.21) (2.25) (1.54)

EQTY -BWS Mean -4.7% 12.1%*** 12.2%*** 11.0%*** 4.8% 7.8%*** 7.0% 4.5%

(-0.94) (2.70) (2.70) (2.41) (1.59) (2.43) (1.26) (0.89)

31

Table IV: Performance of the Buy-Write Strategy and Equity Portfolios for Different Market Fundamentals (Continued)


Q1

BWS mean 22.2% 10.1% 10.1% 14.5% 11.5% 14.5% 21.2% 10.4%

(9.56) (6.53) (6.53) (7.84) (3.47) (4.49) (9.91) (2.54)

EQTY mean 24.9% 0.5% 0.5% 8.1% 21.1% 10.7% 15.3% 19.1%

(6.32) (0.13) (0.13) (2.12) (4.80) (2.32) (4.53) (5.78)

EQTY -BWS Mean 2.7% -9.6%*** -9.6%*** -6.4%** 9.6%** -3.8% -5.9% 8.7%**

(0.73) (-2.49) (-2.49) (-1.95) (2.32) (-1.08) (-1.44) (2.10)

Q4

BWS mean 2.6% 8.8% 8.8% 6.1% 10.2% 8.0% 5.7% 11.5%

(0.45) (1.31) (1.31) (0.99) (1.76) (2.24) (1.00) (3.64)

EQTY mean 1.5% 14.4% 14.4% 19.5% 11.3% 17.2% 13.2% 8.1%

(0.29) (2.45) (2.45) (4.47) (2.46) (5.81) (2.05) (1.32)

EQTY -BWS Mean -1.1% 5.6% 5.6% 13.4%** 1.1% 9.2%** 7.5% -3.4%

(-0.18) (0.88) (0.88) (2.23) (0.18) (2.36) (1.25) (-0.84)


Q1

BWS mean 11.7% 7.6% 7.6% 10.1% 11.2% 9.3% 11.0% 8.6%

(9.14) (5.78) (5.78) (4.03) (6.63) (4.79) (5.82) (4.49)

EQTY mean 22.9% 6.4% 6.4% 12.6% 26.7% 16.2% 15.2% 15.8%

(6.37) (1.41) (1.41) (2.99) (6.58) (3.29) (5.08) (3.42)

EQTY -BWS Mean 11.2%** -1.2% -1.2% 2.5% 15.5%*** 6.9% 4.2% 7.2%

(2.69) (-0.23) (-0.23) (0.46) (2.93) (1.22) (1.20) (1.41)

Q4

BWS mean 7.7% 9.8% 9.8% 9.2% 10.1% 9.1% 9.4% 9.4%

(3.96) (5.00) (5.00) (6.54) (5.29) (6.64) (6.52) (7.05)

EQTY mean 7.9% 17.7% 17.7% 21.8% 11.2% 21.7% 22.9% 21.0%s

(1.68) (2.94) (2.94) (6.27) (2.88) (6.12) (2.98) (5.83)

EQTY -BWS Mean 0.2% 7.9% 7.9% 12.6%*** 1.1% 12.6%*** 13.5% 11.6%***

(0.03) (1.22) (1.22) (2.82) (0.27) (2.70) (1.61) (2.49)

*** Testing whether the equity portfolio outperforms the buy-write portfolio at the 1% level of significance. ** Testing whether the equity portfolio outperforms the buy-write portfolio at the 5% level of significance. * Testing whether the equity portfolio outperforms the buy-write portfolio at the 10% level of significance.

32

Table V: Performance of the Buy-Write Strategy and Equity Portfolios for High and Low Market Fundamentals

The table shows the performance of the buy-write strategy (BWS) and equity (EQTY) portfolios for monthly, quarterly and yearly rebalancing intervals, from January 1995 to October 2006, for different levels of out-of-moneyness. The stocks are ranked in descending order and then categorised into high and low categories based on the top quartile (Q1) and bottom quartile (Q4) respectively for each market fundamentals. This process is undertaken for each of the following fundamentals: earnings per share (EPS), price earnings (PE), leading price earnings (Leading PE), price to book value (Price to BV), book value (BV), volume, market value (MV), and dividend yield. Stocks with high and low market fundamentals are then used to construct the buy-write strategy and equity portfolios.

Full Sample

EPS PE Leading

PE Price to BV

BV Volume MV Dividend

Yield


0% to 2% High 7.6% 9.1% 4.3% 4.3% 5.5% 7.4% 5.5% 7.4% 9.5%

Low 5.0% 6.2% 6.2% 7.7% 7.7% 7.2% 6.0% 4.0%

0% to 5% High 10.1% 15.5% -2.2% -2.2% 5.0% 13.1% 8.4% 16.7% 10.0%

Low 3.0% 12.5% 12.5% 11.3% 12.2% 9.0% 5.9% 6.9%

0% to 15% High 6.5% 18.8% -14.0% -14.0% -20.4% 4.6% -6.6% 14.0% 4.1%

Low -5.6% 2.7% 2.7% 2.9% 2.3% 4.8% -5.8% -0.1%

5% to 15% High 2.7% 14.5% -4.1% -4.1% 1.9% 1.3% -3.0% 9.7% 3.2%

Low -2.8% -3.7% -3.7% 0.6% 7.9% 4.4% 2.6% 2.5%


0% to 2% High 12.8% 22.2% 10.1% 10.1% 14.5% 11.5% 14.5% 21.2% 10.4%

Low 2.6% 8.8% 8.8% 6.1% 10.2% 8.0% 5.7% 11.5%

0% to 5% High 13.0% 21.4% 11.1% 11.1% 13.9% 11.7% 14.7% 21.6% 10.7%

Low 2.9% 8.5% 8.5% 5.1% 10.4% 8.8% 5.5% 10.4%

0% to 15% High 13.0% 34.7% 7.1% 7.1% 14.3% 15.5% 9.3% 31.3% 14.0%

Low -6.8% 3.6% 3.6% 1.3% 4.0% 11.7% -2.1% 7.7%

5% to 15% High 9.0% 21.6% 3.9% 3.9% 7.0% 7.8% 11.5% 18.7% 10.3%

Low -0.3% 6.4% 6.4% 6.2% 6.4% 8.4% 3.3% 3.3%

33

Table V: Performance of the Buy-Write Strategy and Equity Portfolios for High and Low Market Fundamentals (Continued)


0% to 2% High 9.8% 11.7% 7.6% 7.6% 10.1% 11.2% 9.3% 11.0% 8.6%

Low 7.7% 9.8% 9.8% 9.2% 10.1% 9.1% 9.4% 9.4%

0% to 5% High 12.7% 17.6% 8.8% 8.8% 13.1% 13.3% 14.3% 16.6% 11.2%

Low 8.6% 13.0% 13.0% 13.8% 13.1% 8.8% 9.7% 12.9%

0% to 15% High 15.1% 29.2% 12.3% 12.3% 15.7% 19.9% 20.9% 24.7% 23.6%

Low -1.3% 4.5% 4.5% 5.1% 5.7% 5.4% 2.1% 3.3%

5% to 15% High 11.0% 19.6% 9.6% 9.6% 13.5% 12.7% 14.8% 16.6% 16.0%

Low -2.5% 0.2% 0.2% 4.6% 3.8% -1.1% 0.0% 1.2%

34

Figure I: The Optimal Level of Out-of-Moneyness and Rebalancing Interval for Maximising the Mean Returns of the Buy-Write Strategy Portfolios Mean for the period January 1995 to October 2006.

0%

2%

4%

6%

8%

10%

12%

14%

16%

0% to 2% 0% to 5% 0% to 15% 5% to 15%

Out-of-Moneyness Level

Bu

y-W

rite

Str

ate

gy P

ort

folio

s M

ean

Retu

rn

Monthly Quarterly Yearly

Figure II: The Optimal Level of Out-of-Moneyness and Rebalancing Interval for Minimising the Risk of the Buy-Write Strategy Portfolios for the period January 1995 to October 2006.

0%

5%

10%

15%

20%

25%

30%

0% to 2% 0% to 5% 0% to 15% 5% to 15%

Out-of-Moneyness Level

Bu

y-W

rite

Str

ate

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s S

tan

dard

Devi

ati

on

Monthly Quarterly Yearly

the efficiency of the buy-write strategy: evidence from ... annual...fundamentals like earnings per...

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