Positional Option Trading (Wiley Trading)
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not what is predicted by the rational expectations hypothesis.
Rational expectations say that the futures prices are unbiased
predictors of the future value of the cash price. If this was true, the
basis would have no predictive power.
The effect also exists for VIX futures. Simon and Campasano
(2014) present evidence that the futures can be predicted by
looking at the basis. That is, if the futures are trading over the
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index, VIX, the futures will tend to fall, and if the futures are trading below the index, they will tend to rise (see Chapter Four).
The VIX term structure is usually in contango at low VIX levels
and in backwardation when the VIX is high. This means the term-
structure anomaly is often in conflict with the mean reversion of
the VIX. Mean reversion would encourage you to buy futures at
low VIX levels even in the presence of contango. However, it
seems that the term structure is usually a stronger predictor of
futures' returns. The exception would be when the VIX is at very
high levels.
This is probably why the term-structure effect fails to apply to the
cross-section of equity option returns. Vasquez (2017) found that
long straddle portfolios with high contango in the volatility term
structure outperformed straddle portfolios with low contango or
backwardation. My guess is that this is because the entire universe
of stocks contained enough examples of extreme cases for mean
reversion to dominate.
This effect has existed in commodity futures for at least as long as
we have had data to look at. This points to it being a mispriced risk
premium. Keynes's (1930) theory of normal backwardation says
that producers hold short futures positions to hedge against price
drops. They are prepared to pay a premium for this insurance.
However, you can also argue exactly the opposite side: consumers
take long futures positions in order to hedge against unexpected
future price rises. So, they should pay an insurance premium. The
debate continues.
Trading Strategy
Sell VIX futures or index options when the term structure is in
contango. Buy VIX futures or index options when the term
structure is in backwardation.
Options and Fundamental Factors
It is now well accepted that certain factors predict future stock
returns. This is the idea behind “smart beta.” Value stocks
outperform growth stocks. Small-cap stocks outperform large-cap
stocks. Low-beta stocks outperform high-beta stocks. High-
momentum stocks outperform low-momentum stocks. High-
quality stocks outperform low-quality stocks.
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Factor investing is not a new idea. Academic studies began with
the development of the capital asset pricing model (CAPM) by
Treynor (1962), Sharpe (1964), Lintner (1965), and Mossin (1966),
which suggested that individual stock returns were driven by the
broad market. Expanding this idea, the arbitrage pricing theory
(APT) of Ross (1976) modeled stock returns as driven by many
different factors. Unfortunately, the model did not say what these
factors were, but nonetheless APT gave a solid theoretical
underpinning to the idea of factor investing. Once a theoretical
basis was established its implications could be tested and
explored. This led to academics discovering a number of different
investing factors or “anomalies” (so named because they didn't fit
into the world of CAPM).
What is less well known is that similar fundamental factors also
predict volatility returns. The number of studies that relate factors
to volatility is much smaller than the literature on smart beta stock
returns and unfortunately researchers haven't studied exactly the
same factors as each other.
I did a study constructing option trading strategies based on P/E
(the price-to-earnings ratio or the current stock price divided by
the previous year's earnings per share), P/B (the price-to-book
ratio or the current stock price divided by the previous year's
balance sheet assets), RoA (the return on assets), RoE (the return
on equity or the return on assets after all liabilities have been
settled), market capitalization (the dollar value of the company's
outstanding shares), D/E (the debt-to-equity ratio), and P/CF (the
ratio of the stock price to the previous year's cash flow per share).
The universe of stocks considered was the S&P 100 after excluding
financial companies. Naive application of accounting metrics can
give a misleading picture of financial companies because their
business is based on providing loans. So, their “assets” are actually
liabilities, which makes things confusing. The time period we
looked at was from the start of 2000 through to the end of 2012.
On the Friday of each week I ranked all the stocks according to the
valuation metrics and then formed an option portfolio based on
this ranking by selling straddles on the top quartile of stocks and
buying straddles on the bottom quartile. Specifically, we traded at
the money straddles in the second monthly expiry. Each trade is
done in a notional size of $10,000. For example, on a $100 stock
we would trade one straddle (each straddle controls 100 shares
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and each share is worth $100). Correspondingly, we would trade
two straddles on a $50 stock. Under standard strategy-based
margin this sizing choice gives a margin of roughly $100,000.
Portfolio margins would be considerably smaller. This portfolio is
held for a week, then the process is repeated.
P/E Straddle Trading Results
Long options on low P/E stocks and short options on high P/E
stocks
Average weekly PL: $294
Best week: $21,111
Worst week: −$8,111
Sharpe ratio: 1.03
P/B Straddle Trading Results
Long options on high P/B stocks and short options on low P/B
stocks
Average weekly PL: $48
Best week: $12,094
Worst week: −$7,246
Sharpe ratio: 0.24
Market Capitalization Trading Results
Long options on high-cap stocks and short options on low-cap
stocks
Average weekly PL: $355
Best week: $15,532
Worst week: −$23,077
Sharpe ratio: 1.17
P/CF Straddle Trading Results
Long options on low P/CF stocks and short options on high
P/CF stocks
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Average weekly PL: $198
Best week: $22,235
Worst week: −$13,637
Sharpe ratio: 0.71
D/E Straddle Trading Results
Long options on high D/E stocks and short options on low D/E
stocks
Average weekly PL: $338
Best week: $25,382
Worst week: −$5,292
Sharpe ratio: 1.16
RoE Straddle Trading Results
Long options on high-RoE stocks and short options on low-
RoE stocks
Average weekly PL: $361
Best week: $16,922
Worst week: −$19,102
Sharpe ratio: 1.20
RoA Straddle Trading Results
Long options on high-RoA stocks and short options on low-
RoA stocks
Average weekly PL: $220
Best week: $16,539
Worst week: −$21,702
Sharpe ratio: 0.72
The results of the P/B strategy are disappointing, but the others
are good. The results can be summarized simply. Try to be long
volatility (or options) in stocks with these characteristics:
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Low P/E
Low P/CF
High market cap
High RoE
High RoA
High D/E
These are classic indicators of “value” stocks apart from the high
debt-to-equity ratio. This is a strange anomaly. High debt to
equity (or high leverage) implies a higher risk of bankruptcy. This
would clearly be a high-volatility event for the stock. However,
these are all large companies that have presumably a very low
chance of going bankrupt. Also, high leverage could imply that the
bond market sees value in the company. Disentangling this
conundrum would involve further work. Does the effect hold in
smaller companies? Does it matter how the leverage reached
current levels? It could well be that high leverage resulting from a
declining stock price is very different from high leverage from new
bond issuance. Does the creditworthiness of the debt matter more
than the absolute size of the debt?
We can combine our findings to construct a portfolio of options
that is long “value” volatility and short “growth” volatility. To do
this we first create a combined ranking consisting of one-sixth the
P/E ranking plus one-sixth the P/CF ranking and so on. This
portfolio has these results:
Portfolio Straddle Trading Results
Average weekly PL: $476
Best week: $18,963
Worst week: −$9,429
Sharpe ratio: 1.44
A similar study was done by Cao et al. (2015). They studied delta-
hedged option returns for US equity options from 1996 to 2012.
They found that long volatility positions profits increase with size,
momentum, and company profitability and decrease with cash
holding, analyst forecast dispersion, and new issuance. These
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option returns are independent of any associated underlying
predictability.
Their study showed the profitability of portfolios sorted into
deciles. The long-short 10/90 portfolios had monthly returns of
the order of 3% to 5%. (As usual this was calculated on the
notional value of the positions. This makes sense for long
positions but not for short positions, where a risk-based margin
number would be a more appropriate denominator.) Sharpe ratios
were between 0.6 and 2.0.
There is a lot more work that could be done along these lines and
this research raises a lot of questions. For example, how
independent are these various measures of value when applied to
option trading? Are these results independent of the results from
time series analysis? How do these results change across industry
groups?
As always, the phenomena are more important than the particular
implementation. The best way to trade this is probably to build a
factor portfolio instead of doing single factor sorts. Alternatively,
the fundamental factors could be used to directly forecast
volatility. Trading options based on smart beta is still a new and
unexplored idea, but it is probably a more promising avenue than
trying to improve time series–based forecasts.
Generally speaking, there are two views as to why factor returns
exist: risk and investor behavior. The risk school of thought says
that the return is simply reward for bearing some sort of risk. For
instance, the equity market premium is a result of the greater
uncertainty associated with owning stocks as opposed to bonds.
This explanation fits well with mainstream economic theory but
sometimes it is a little hard to figure out what exact risk is being
compensated for. As an example of this, volatility is usually
associated with risk, but historically low volatility stocks have
outperformed high-volatility stocks. The behavioral explanation
contends that investors systematically make decisions that cause
these anomalies. Again, these arguments seem more persuasive in
some cases than in others. Momentum, for example, has plausible
behavioral roots but in other cases trying to identify a
psychological reason for a factor seems like merely searching for a
tidy explanation, rather than doing real science and following the
data. These explanations are summarized in Table 5.1.
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Whether stock smart beta is inefficiency due to behavioral biases or risk premia is still being debated. And even if that dispute is
resolved, the corresponding volatility effect will probably still be
argued over. However, applying factor analysis to options trading
is where I will be spending most of my future research efforts. It is
a very new field so the risk and uncertainty is high, but I'm sure it
is better to deal with this than to try to scratch another tiny
improvement from a time-series method.
TABLE 5.1 Postulated Risk and Behavioral Reasons for the Smart Beta Factors
Factor
Risk Explanation
Behavioral
Explanation
Smaller firms are less able
Smaller firms are
generally poorly
Size
to weather bad periods and
have less diversified
covered by analysts,
businesses.
which leads to investor
uncertainty.
Cheap stocks tend to be
Investors pay too much
those of the companies that attention to recent stock
Value
perform worst in periods
performance and overly
when the overall economy is fear distressed
suffering.
situations.
Underreaction: new
Momentu Momentum can lead to
information is not
m
bubbles and crashes.
incorporated into prices
instantaneously.
It is harder for a high-
Quality
quality company to improve. High-quality firms may
It may only have downside. be “too good to be true.”
Post-Earnings Announcement Drift (PEAD)
Post-earnings announcement drift (PEAD) is the tendency for a
stock to continue to move in the direction caused by an earnings
surprise. The first study of this effect was by Beaver (1968), who
showed that prices react to the information content in earnings
reports. Ball and Brown (1968) found evidence that stock returns
continue to drift in the same direction as unexpected earnings.
That is, stock prices tend to increase (decrease) after earnings
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announcements with positive (negative) earnings surprises. This
wasn't greatly shocking. What was unexpected was that the
outperformance didn't happen abruptly but ac
cumulated over
three months. The stock prices did incorporate the news but did so
slowly. In fact, the prices reacted so slowly that the effect was
tradable. This effect is inconsistent with the concept of efficient
markets, where the information contained in an earnings report
should be quickly incorporated in prices, but even one of the
inventors of EMH acknowledges the existence of the anomaly
(Fama, 1998).
He wrote in the abstract, “Most long-term return anomalies tend
to disappear with reasonable changes in technique” or when
“alternative approaches are used to measure them” (p. 288), but
concluded, “Which anomalies are above suspicion? The post-
earnings announcement…has survived robustness checks,
including extension to more recent data.” He has also written that
PEAD is the only anomaly that is “above suspicion” (p. 304).
Early research focused on the change in year-over-year earnings.
But in the 1980s the consensus of analyst forecasts became
available. This enabled the magnitude of the earnings surprise to
be defined as the percentage difference between the reported EPS
and the consensus forecast. Sorting stocks on the basis of this
surprise gave the same result. Further, it seems that the effect of
the earnings report isn't limited to the headline EPS number. The
momentum created by the earnings report is a follow-through of
the initial price move based on the entire report, rather than being
due to any single accounting number.
Bernard and Thomas (1989, 1990) show that the drift is robust to
risk adjustments, cannot be attributed to market frictions, and is
not due to model misspecification, standard risk factors, or flaws
in research design. These conclusions have been verified in many
subsequent studies. PEAD seems more likely to be an inefficiency
than a risk premium.
There is some evidence that it is most pronounced in firms that
report after their direct competitors and have earnings that
outperform those firms by a surprising amount (Lee, 2017).
The effect is remarkably robust. Long-short stock portfolios based
on the size of the surprises have been shown to return 9% to 27%
annually, depending on the sorting method (deciles, quartiles,
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etc.), the definition of surprise, and whether returns are raw or adjusted with respect to sector, beta, size, value, and momentum.