premium is high is a good time to enter covered call positions.
Some explanations for the effect are very complex but, very
simply, stock markets have tended to go up and volatility rises
during drops, so, a high-variance premium is correlated with
temporary dips.
Short Put Spread
We sell the 1-year ATM put and buy the 20-delta put (the 81
strike). The PL distribution from a simulation of 10,000 paths is
shown in Figure 8.8 and summary statistics are shown in Table
8.7. The initial value of the spread is $8.11.
Unfortunately, in most products the long put will have a
significantly higher implied volatility than the short ATM option.
For example, the S&P 500 20-delta put currently has an implied
volatility of about 1.36 times that of the ATM. So, if the ATM
volatility is 30%, we would be paying 40.8% for the long 20-delta
put. This doesn't greatly change the shape of the distribution but
will be a significant drag on profits. This is shown in Table 8.8.
For many definitions of conservative, the short spread is the most
conservative directional strategy. It has a high winning
percentage, a high median, and a capped downside.
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FIGURE 8.8 The PL distribution for a short 1-year ATM/20-delta put spread on a $100 stock with a 20% return. Both implied
and realized volatilities are 30% and rates are zero.
TABLE 8.7 Summary Statistics of the PL Distribution for a Short 1-Year ATM/20-Delta Put Spread on a $100 Stock
with a 20% Return (Both implied and realized volatilities
are 30% and rates are zero.)
Average
$422
Standard
deviation
$680
Skewness
−1.42
Excess kurtosis
0.43
Median
$811
90th percentile
$811
Maximum
$811
10th percentile
−$1,072
Minimum
−
$1,089
Percent profitable
78%
159
TABLE 8.8 Summary Statistics of the PL Distribution for a Short 1-Year ATM/20-Delta Put Spread on a $100 Stock
with a 20% Return (The ATM-implied volatility is 30%
and the implied volatility of the 20-delta put is 40.8%.
Realized volatilities are 30% and rates are zero.)
Average
$216
Standard
deviation
$720
Skewness
−1.52
Excess kurtosis
0.62
Median
$634
90th percentile
$634
Maximum
$634
10th percentile
−
$1,404
Minimum
−
$1,666
Percent profitable
76%
Risk Reversal
We sell the 1-year 20-delta put and buy the 20-delta call. The PL
distribution from a simulation of 10,000 paths is shown in Figure
8.9 and summary statistics are shown in Table 8.9. The initial
value of the position is a credit of $93.
160
FIGURE 8.9 The PL distribution for a 1-year 20-delta risk reversal on a $100 stock with a 20% return. Both implied and
realized volatilities are 30% and rates are zero.
TABLE 8.9 Summary Statistics of the PL Distribution for a 1-Year 20-Delta Risk Reversal on a $100 Stock with a
20% Return (Both implied and realized volatilities are
30% and rates are zero.)
Average
$948
Standard
deviation
$2,140
Skewness
2.69
Excess kurtosis
9.00
Median
$79
90th percentile
$3,666
Maximum
$22,68
0
10th percentile
−$251
Minimum
−
$3,802
Percent profitable
85%
Although this position has an initial delta of 40, as the stock
moves the delta changes. This is reflected in the fact that the
maximum profit and losses are practically the same as for a long
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stock position. In exceptionally large moves the 20-delta options
become 100 delta and the risk reversal mimics a stock position.
However, the risk reversal has lower average and median than the
stock position. There will be times when the long calls expire
worthless even when the stock rallies. The reason the median
value is positive is that the position was entered into at a credit.
In most markets, we will be benefiting from selling the 20-delta
put at an inflated volatility and, at least for indices, we will be
buying the 20-delta call at a volatility under that of the ATM. For
the S&P 500, the 20-delta call currently has a volatility of about
0.77 of the ATM volatility. Assuming this, the effect on summary
statistics is shown in Table 8.10. The fact the position performs better when there is a skew is entirely due to the extra premium
we collect. The initial value of this position is a credit of $330.
Because we can collect a reasonable premium from this position,
we can still buy a teeny put to hedge the downside risk. For
example, the implied volatility of a 5-delta index put is usually
about 1.7 times the ATM volatility. In this case that gives an
implied volatility of 51% and a premium of $1.28 for this teeny
put. That reduces the initial credit to $202 and lowers the average
and percentile numbers by the same amount.
This downside hedged risk reversal is my personal favorite bullish
directional position.
It has limited downside risk.
TABLE 8.10 Summary Statistics of the PL Distribution
for a 1-Year 20-Delta Risk Reversal on a $100 Stock
with a 20% Return (The call implied volatility is 23.1%
and the implied volatility of the 20-delta put is 40.8%.
Realized volatility is 30% and rates are zero.)
Average
$1,430
Standard
deviation
$2,320
Skewness
2.69
Excess kurtosis
10.2
Median
$366
90th percentile
$4,448
Maximum
$27,262
162
10th percentile
$85
Minimum
−
$3,205
Percent profitable
91%
It has the potential for large wins.
It takes advantage of the skewness premium.
Aside: The Risk Reversal as a Skew Trade
As demonstrated, the risk reversal is an effective way to profit
from the implied skewness premium. However, despite many
views to the contrary, it isn't particularly useful for speculating on
the movement of the implied skew itself. Although the implied
skew does fluctuate, the size of its moves is dwarfed by the effects
of the stock movement and the level of implied volatility.
Consider the risk-reversal just discussed. Imagine we are selling
the put and buying the call because we think the slope of the skew
will flatten. If we think the put volatility ratio to the ATM volatility
will drop and the call ratio will increase, we will make a profit of
(8.1)
Consider a 1-month risk reversal on a $100 stock. The 20-delta
put (91 strike) has an implied volatility of 40.8% and the 20-delta
call has an implied volatility of 23.1%. We sell the put and buy the
call because we expect the skew to flatten. Table 8.11 shows the
profits we make on the position for various degrees of flattening.
However, the expected daily move of a $100 stock with a volatility
of 30% is $1.50. If the stock drops to $98.5, the risk reversal loses
$94, and if the stock rallies to $101.5, the risk reversal will make
$16. So, an average daily P/L due to the stock's random
fluctuations is $55. Even if the implied curve flattens by three
volatility points on both the calls and the puts on one day, the
skew-related profit will still only be of the order of the
delta/gamma P/L. It is exceptionally unlikely that a move will
occur on the day after the trade is initiated. This analysis also
ignores changes in the level of the volatility curve and the effect of
correlations between stock returns and implied skewness. Long-
163
dated options will have less gamma to cause problems and more
vega to make money off implied volatility changes. However, the
long-dated implied volatility curves are much more stable than
short-dated ones.
TABLE 8.11 Results for a Short Put–Long Call 20-Delta Risk Reversal for Various Amounts of Implied Volatility
Curve Flattening
Put volatility
0.40
8
0.398 0.388
0.378
Call volatility
0.231 0.241 0.251
0.261
Risk reversal
value
0.43
0.25 0.08 −0.09
Profit ($)
0 18 35
52
It is possible to make money with this trade. The idea of taking
advantage of reversion of the implied skew is a sensible one. But
the edge from this prediction is likely to be overwhelmed by noise.
Ratio Spreads
Although all directional option positions are dependent on
volatility, some have a higher dependence than others. Ratio
spreads are an extreme example. Although they are often used to
speculate on direction, their primary exposure is to volatility. They
have the payoff of a broken wing butterfly, something we always
think of as primarily a volatility position.
We buy the 1-year ATM call and sell two of the 20-delta calls. The
PL distribution from a simulation of 10,000 paths is shown in
Figure 8.10 and summary statistics are shown in Table 8.12. The initial value of the position is a debit of $749.
164
FIGURE 8.10 The PL distribution for a 1-year ATM/20-delta risk
one-by-two call spread on a $100 stock with a 20% return. Both
implied and realized volatilities are 30% and rates are zero.
TABLE 8.12 Summary Statistics of the PL Distribution for a 1-Year 20-Delta Risk Reversal on a $100 Stock with
a 20% Return (Both implied and realized volatilities are
30% and rates are zero.)
Average
$381
Standard
deviation
$1780
Skewness
−1.10
Excess kurtosis
5.20
Median
$190
90th percentile
$2,670
Maximum
$3,140
10th percentile
−$749
Minimum
−
$15,230
Percent profitable
52%
As I have emphasized, there are few hard-and-fast rules in option
trading, but the version of the ratio spread that is long the one
option and short the second is generally best avoided. In terms of
finding edge, the trader needs a good prediction of both volatility
165
and direction. It is difficult to predict either, let alone both. There are better alternatives for both directional and volatility
speculation. It is tempting to use the sale of the two options to
“finance” the purchase of the one, but this is only done by taking
on unlimited risk. If a trader has enough edge (either in volatility
or direction) to do a trade at all, she shouldn't be afraid to pay the
option premium. There are no free lunches and there are no free
option positions.
Another reason that is often given for trading a ratio is to short a
high implied skew. This is usually done with puts because puts
usually have a more pronounced implied skew. By selling the two
farther-out-of-the-money options, the trader can short volatility at
the higher implied volatility and mitigate the risk with the single
long option. This trade has all of the same problems mentioned in
the section on trading risk reversals to capture skew, but ratio
spreads are an even worse vehicle for trading an idea that isn't
very good to start with.
If a trader wants to collect the skew premium, the safest way is to
sell a put spread rather than possibly offset this by purchasing a
call spread. The long put will almost certainly be the option with
the highest implied volatility in the structure, but because the
short put will still be trading at a volatility premium to the ATM
this position is still short implied skew.
An effective way to use a ratio spread is to buy the two options and
sell the one as a relatively cheap catastrophe hedge. If the options
are struck far enough out of the money, the hope is they will only
come into play in a huge crash and we will then end up being long
vega and net options (the most robust risk control number). This
trade is still not a free lunch. If instead of a crash we have a slow
move downwards, we can end up short gamma and paying theta,
but the bad scenarios are ones that occur slowly so at least we can
rebalance. This incurs transaction costs but at least we have a
chance to trade.
As an example, with SPY 299 on October 23, 2019, we can sell the
November 15 266 put for 0.16 and buy two of the 258 puts for 0.10
each. For the same outlay of 0.04 we could have bought the 241
put. Obviously, in almost all situations we will lose the 0.04
premium. The important thing in evaluating these positions isn't
the overall probability distribution; it is how we look in the event
of a crash. The risk slides for these two positions are shown in
166
Tables 8.13 and 8.14. On October 23 the ATM volatility was 11.4%.
To estimate the relevant implied volatilities for each underlying
price level I could use a regression model to find the historical
relationship between price and volatility moves. Such a model is
useful for normal trading purposes but for estimating tail event
parameters it is at best useless and possibly dangerous if it gives a
false sense of certainty. Instead I'm going to assign what I think
are possible and I ho
pe overly pessimistic volatility numbers.
TABLE 8.13 The Risk Slide for the Single 241 Put
SPY price
change
−30% −20% −10%
Postulated IV
120% 80% 30%
Delta
−0.61 −0.47 −0.07
Vega
$2120 $2515 $965
P/L
$465 $207
0
0 $65
TABLE 8.14 The Risk Slide for the 258/266 One-By-Two Put Spread
SPY price
change
−30% −20% −10%
Postulated IV
120% 80% 30%
Delta
−0.68 −0.53 0.14
Vega
$205 $255 −
0
6
$410
P/L
$530 $256
0
0
$42
One could argue than in a “small” crash the single teeny put
behaves better because it leaves us short delta and long vega,
although the P/L superiority is small. However, in severe crashes
the ratio spread gives significantly better protection.
Conclusion
As with volatility position selection, there is no one “best” strategy
when using options to speculate directionally. The most important
consideration is probably whether the variance premium is low or
167
high. This, more than risk preferences, is paramount in deciding
to be long or short options. Then the trader can decide on the
structure based on preference for winning percentage, maximum
profit, and maximum loss, and so on. Finally, strikes can be
chosen by considering the risk characteristics discussed in Chapter
Seven.
Summary
Variance and skew premia are the most important factors even
when trading options directionally.
Single options have the best correlation between a profit and a
successful prediction.
Spreads are useful for mitigating the dependency of the trade
on the variance premium. The fact they also create a stop (or
profit target) is useful as a risk management tool but
predicting an underlying's range is probably too hard to do
consistently.
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CHAPTER 9
Trade Sizing
It certainly is not true that good risk management can turn a
strategy with no positive expectation into a winner. Risk
management can change the return distribution of a strategy with
Positional Option Trading (Wiley Trading) Page 18
