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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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2
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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5
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
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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)
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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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13
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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14
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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15
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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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.
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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 0.01 level.
** Significant at the 0.05 level.
* Significant at the 0.10 level.
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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)†
Out-of-Moneyness range: 0% to 5%
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)†
Out-of-Moneyness range: 0% to 15%
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)†
Out-of-Moneyness range: 5% to 15%
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 0.01 level.
** Significant at the 0.05 level.
* 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
Out-of-Moneyness range: 0% to 2%
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)†
Out-of-Moneyness range: 0% to 5%
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)†
Out-of-Moneyness range: 0% to 15%
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)†
Out-of-Moneyness range: 5% to 15%
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)†
*** Significant at the 0.01 level.
** Significant at the 0.05 level.
* Significant at the 0.10 level. †
F-statistics for the difference in standard deviation
-
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
Out-of-Moneyness range: 0% to 2%
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)†
Out-of-Moneyness range: 0% to 5%
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)†
Out-of-Moneyness range: 0% to 15%
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)†
Out-of-Moneyness range: 5% to 15%
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)†
*** Significant at the 0.01 level.
** Significant at the 0.05 level.
* Significant at the 0.10 level. †
F-statistics for the difference in standard deviation
-
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
Mean Standard Deviation
Mean Standard Deviation
Out-of-Moneyness range: 0% to 2%
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)
†
Out-of-Moneyness range: 0% to 5%
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)
†
Out-of-Moneyness range: 0% to 15%
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)
†
Out-of-Moneyness range: 5% to 15%
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)
†
*** Significant at the 0.01 level.
** Significant at the 0.05 level.
* Significant at the 0.10 level. †
F-statistics for the difference in standard deviation
-
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
Monthly Rebalancing Intervals
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)
Quarterly Rebalancing Intervals
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)
Yearly Rebalancing Intervals
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
Monthly Rebalancing Intervals
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%
Quarterly Rebalancing Intervals
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)
Yearly Rebalancing Intervals
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
gy P
ort
folio
s S
tan
dard
Devi
ati
on
Monthly Quarterly Yearly