the purported returns were implausible. The first skeptic, an
investment analyst called Harry Markopolos, claimed he could see
within five minutes that the results were suspicious and only
another four hours to prove it. He first notified the SEC in 2000
and then again in 2001, 2005, and 2007. He wrote the book No
One Would Listen (Markopolos, 2010) about the experience. A detailed analysis of the split-strike conversion was published by
Bernard and Boyle (2009).
Not only were Madoff's returns not real, most of his trades
weren't, either. From at least the 1990s, he would just create fake
trade confirmations based on idealized prices.
It is hard to quantify how much money really disappeared, given
that most of it was fictional the whole time, but by 2019 only about
$11 billion of the initially invested $17.5 billion had been returned
to investors.
Lessons
Check the plausibility of the strategy. Is the return stream
consistent with a theoretical analysis? Is there enough liquidity
to execute the claimed strategy?
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It is dangerous to rely on a superficial character assessment.
Madoff had an exceptional reputation and it still isn't at all
clear why someone as legitimately successful as he was would
run a fraudulent operation.
Only invest in funds with a separate TPA and custodian.
Index Restructuring
It is easy to forget that indices aren't real. They are just numbers
calculated according to some methodology by a third party. There
is nothing to stop the publisher changing the methodology or
composition of the index. Generally, these changes are
inconsequential (for example, most indices add and delete some
components regularly). But not always.
The EuroSTOXX 50 is an index that is composed of the 50 largest
capitalized companies in the eurozone, irrespective of what
country they are from. At least it is now. Originally it was designed
to have companies from each eurozone country. When STOXX
made this change, they reweighted the index so its value wouldn't
change. But the dividend yield, and hence the implied forward
basis to cash, changed enormously (by about 50%).
Any option trader with a forward position lost money (still my
largest 1-day loss).
A similar situation occurred in February 2018, when the volatility
ETNs spiked (see Sinclair, 2018). UVXY, the ProShares Ultra VIX
Short-Term Futures ETF, had its leverage reduced from 2 to 1.5.
This meant that the expected future volatility dropped by 25%,
which hurt any trader who was long vega. It isn't entirely clear
whether this was allowed under the terms of the prospectus, and
as of May 2019 lawsuits arguing about this have not been decided.
But it seems likely option buyers will not recoup all losses.
Lesson
Be aware of what contract specifications can be changed.
Arbitrage Counterparty Risk
Often, spread traders or arbitrageurs find they have large profits
at one institution and large losses at another. This leads to credit
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risk.
A LIFFE broker had made a lot of money on spread bet arbitrage,
buying low at some bookies and selling high at others.
Unfortunately, almost all his winning bets were held by one
bookmaker. And that person wasn't capable of paying. The simple
thing would have been for him to just default, because gambling
debts in England were not legally enforceable. But that wouldn't
have been good for business, so he did something else.
The bookie's shop was between the train station and the broker's
house. So, every evening, there were a couple of attractive, morally
malleable young women waiting at the station when the broker
disembarked. They escorted (in both senses) him to the shop
where he was entertained with alcohol and cocaine while watching
and gambling on greyhound races. Three months later the bookie
had his money back (and the broker had STDs).
Lessons
Try to stay flat counterparty risk.
Don't do anything that would make your mother cry.
Conclusion
Amateur option traders lose money due to practically every
decision they make. Professionals should be able to manage their
market risks so that no single loss will be catastrophic. The risks
that a professional should be most concerned about are those
created by political instability, contract specification changes, the
stability of financial institutions, and fraud. These can never be
totally avoided. All a trader can do is to check everything that can
be checked and avoid being completely exposed to any single
country, currency, or institution.
Summary
As much as possible, separate compliance, trading, and risk
management.
Never invest in a strategy you don't understand.
Avoid illiquid products and situations.
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Try to diversify across institutions, currencies, managers, and
countries.
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CONCLUSION
Football is like chess, but with dice.
—Peter Krawietz, assistant manager of Liverpool Football Club, from
Biermann (2019)
The same is true of option trading. Skill is essential, and the more
knowledge and experience a trader accumulates the greater her
chance of success. But there is also a tremendous amount of
randomness in any individual trade. It is quite possible to predict
realized volatility and direction correctly and still lose money as
options also depend on implied volatility, interest rates, borrow
rates, and dividends. The situation is even more complex if
options are hedged as then path dependency is introduced.
The most important concept in trading is accepting that we will be
making decisions in situations of great uncertainty. And this is not
even the comparatively tame uncertainty of Knight (1921), in
which the probabilities are unknown but are at least well defined.
Traders operate in a realm of ignorance and unknowability where
probabilities are changing, poorly defined, and the events they
measure change. We will never know more than a tiny fraction of
what can be known. And what can be known is a tiny fraction of all
that there is.
This is not a reason to stop looking for trades with edge. It is a
reason to look very hard and test ideas as rigorously as possible.
Edges exist, but they need to be very robust to withstand the
enormous amount of noise in the world. A trading strategy needs
to have valid test statistics when applied to several markets.
Ideally, it will also have a clear reason for existence. And all
strategies should be robust with respect to the details of
implementation.
When looking for ideas it is important to focus on phenomena
rather than parametrizations or models. For example, volatility is
important because it measures uncertainty and variability, not
because it is the standard deviation of returns. That is just a
mathematical
expression of the core idea, chosen largely due to its
mathematical tractability. Many other statistics could express the
idea of variability. A good trading phenomenon is one that can be
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measured, modeled, and traded in many ways. For example,
momentum investing is merely the observation that stocks tend to
continue in the direction they have been moving. This can be
studied at daily, weekly, or monthly time scales. It can be
quantified by moving average rules, returns over previous periods,
or numerous signal processing methods. The general observation
is robust. The details of the trading model are of course important.
It is possible to lose money trading a strong phenomenon by using
a poor model. But the phenomenon itself is the most important
thing.
It is important to continually search for new ideas. Max Planck
said that science progresses one funeral at a time, and trading
methods seem to as well. Although the markets are always
changing, individual traders tend not to. When the trading floors
closed, a lot of floor traders tried to apply the same techniques to
trading on the screens. They didn't adapt. They kept trying to
apply an obsolete set of methods until they retired. The most
important thing for traders is that they are in a position to trade.
So, we need to keep adapting to stay in the game.
Remember to be primarily a trader, not an option trader. Options are just a tool to express opinions. They are useful because of the
various characteristics of volatility, but they won't be the best tool
in every situation. Nietzsche (1878) (it is no coincidence that the favorite philosopher of many traders was a syphilitic maniac …)
said, “Many people are obstinate about the path once it is taken,
few people about the destination.” Remember this and don't fall
into the trap of thinking more about options than trading.
Trading will always involve uncertainty. No matter how hard we
work, we will still need luck. Both Napoleon and Eisenhower
expressed their preference for lucky generals over talented ones.
But it is important to remember that all their generals had reached
that rank because they were talented. Talent was a given. It is the
same with trading. Luck will play a part, but over a long career it
will generally separate those of equal talent and knowledge rather
than elevate the merely lucky. Learn all that you can but be
sanguine about randomness.
Good luck.
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APPENDIX 1
Traders' Adjustments to the BSM
Assumptions
The Existence of a Single, Constant Interest
Rate
The BSM model assumes a constant risk-free interest rate. There
is no such thing as an interest rate. Interest rates have a bid-ask
spread. We borrow and lend at different rates. Further, there is a
different interest rate for each maturity: the yield curve. All these
rates change over time. And no interest rate is risk free.
Before we even discuss the effects of any mispricings due to
interest rates, it is important to note that very few traders hedge
their own interest rate risk. At a large firm, this will be handled by
the risk management group, which will hedge the firm's net
exposure by aggregating the exposures of all positions
denominated in each currency. Independent traders generally
don't hedge interest rate risk at all. It is too expensive in terms of
transaction costs and ties up margin. If independent traders start
to accumulate too much rho, they will reduce it by trading options.
Market-makers will shade their rate input so they trade out of
their rho position in the same way that they shade their volatility
inputs if they want to reduce volatility risks. Positional traders will
either trade a reversal, conversion, or a box. This somewhat lax
attitude toward rho is an indication of how robust the BSM model
is with respect to interest rate inaccuracy.
Different maturity loans and bonds have different interest rates.
This forms the yield curve. In theory this is no problem at all. We
just hedge with the bond (or in practice the Eurodollar strip)
corresponding to the lifetime of the option. However, the steeper
this curve is the higher the chances are that we will be using an
incorrect interest rate. How incorrect does the rate have to be
before we develop significant price errors or, more important,
delta errors? And what size is the likely input error?
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A 1-year European call on a $100 stock that pays no dividends,
struck at 130, priced with a volatility of 30% and 5% interest rate,
has a value of $4.67 and a delta of 0.288. If we incorrectly used a
rate of 4%, we would get a value of $4.44 and a delta of 0.277. A
delta difference of 0.011 isn't totally insignificant, but the same
size error would result if we used an incorrect implied volatility of
29%, an input error that is far more likely.
Further, in the current environment a trader would need to be
extremely inattentive to have an interest rate input that is
incorrect by 1%. On March 18, 2019, the US 1-month zero coupon
rate was 2.47% and the 1-year rate was 2.52%. The effect of pricing
options off the wrong spot in the yield curve was practically zero.
Interest rates are also volatile. Although the BSM model can
handle a static yield curve, one where different maturities have
different rates but they are unchanging, stochastic interest rates
are more of an issue. When the underlying's volatility is constant,
Merton (1973) showed that the current zero-coupon bond yield
will still work, even when rates are stochastic. However, this does
not work if volatility is also stochastic. But the effects of rate
volatility are also negligible.
Just as the absolute size of rate errors is small, so is the volatility
of rates. In particular, the volatility of rates is much lower than the
volatility of volatility. The absolute daily changes of the VIX, and
the 1-year rate, are shown in Figures A1.1 and A1.2.
The standard deviation of daily VIX changes has been 1.7 points.
The standard deviation of daily changes in the 1-year rate was
0.037%.
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FIGURE A1.1 The daily VIX changes from 2000 to 2018.
FIGURE A1.2 The daily 1-year rate changes from 2000 to 2018.
Because the volatility of rates is so comparatively low, it isn't
necessary to use a model that incorporates stochastic interest
rates. This has been confirmed by several empirical studies.
Bakshi et al. (1997, 2000) showed that, after accounting for stochastic volatility, adding stochastic rates did little to improve
pricing and hedging for options, even LEAPs with up to three
years to expiration. Kim (2002) found an even stronger result:
incorporating stochastic rates into an equity option pricing model
offered no improvement over the BSM model.
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One situation in which an incorrect rate can cause problems is
when making early exercise decisions. When exercising a put on a
stock we need t
o decide if interest income on the proceeds from a
short stock position is greater than the amount of optionality value
we are losing. If rates are stochastic, we might get this calculation
wrong. There isn't a lot we can do about this. Certainly, no model
can help.
Finally, interest rates have a bid-ask spread. It is possible to
modify the BSM model to take this into account (Bergman, 1995).
The analysis is similar to the modification necessary when the
underlying has a bid-ask spread. And, as in that case, differential
interest rates imply that the option has a band of values rather
than a single price. But again, the effects are very, very small in
practice.
The Stock Pays No Dividends
The BSM model assumes the underlying stock pays no dividends.
Correcting this is trivial. We simply price the option off the stock
minus the discounted value of the dividend. So, in the case of a
single discrete dividend, D,
(A1.1)
In some cases, a continuous dividend yield, q, is a fair
approximation. In this case,
(A1.2)
A similar adjustment is needed if a stock becomes hard to borrow.
The BSM assumes that sale proceeds can be invested at the risk-
free rate but if a stock is hard to borrow, the trader receives a
lower rate, r-λ, where λ is the borrowing penalty.
Absence of Taxes
The BSM model ignores taxes. Some traders are taxed as
individuals and some as corporations. Sometimes profits will be
taxed at the short-term capital gains rate, sometimes at the long-
term capital gains rate, and sometimes at a mix of the two rates.
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Tax cheats pay no taxes. Foreign investors may have other tax
complications.
If all investors had the same tax rate, BSM could be adjusted by
using a modified interest rate. The problem isn't the difficulty of
including taxes in a pricing model; it is that different people have
different taxes. An investor's tax situation will affect his trading
strategies (Scholes, 1976), but it is impossible to construct a
pricing model that considers different, unknown tax obligations.
Options will be worth different amounts to different people, but
we can't value the effect.
Positional Option Trading (Wiley Trading) Page 22
