are shown in Figure 9.16.
From the figures the higher volatility of the subaccount method is
largely due to the positive upside. Summary statistics are shown in
Table 9.4.
Using a percentage-based trailing stop retains many good features
of the aggressiveness of the Kelly criterion. It does better both on
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average and in the extreme cases. The great results are those that
start well and continue well, never being affected by the stop. And
when the stop does come into play, the trailing stop idea protects
capital nearly as well as the other two, more conservative,
methods. Trading according to full Kelly on a percentage-based
subaccount seems to be the best idea no matter what criteria are
considered.
FIGURE 9.15 The distribution of the final account after 10,000
simulations of a GBM where μ=0.05 and σ=0.3 when only trading
a subaccount that begins at $43.70 at full Kelly.
FIGURE 9.16 The distribution of the final account after 10,000
simulations of a GBM where μ = 0.05 and σ = 0.3 when only trading a subaccount of 43.7% of the total at full Kelly.
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TABLE 9.4 A Comparison of Trading at Quarter Kelly and Trading Full Kelly in Subaccounts
Statistic
Quarte Subaccount with
Subaccount
r Kelly
Fixed Maximum with Trailing %
Loss
Loss
Average
$101.70
$102.20
$117.13
Minimum
$78.30
$68.75
$69.36
Maximum
$129.50
$187.60
$305.60
10th
percentile
$91.70
$86.30
$89.30
90th
percentile
$111.10
$120.90
$153.40
Average
maximum
9%
12%
12%
drawdown
Maximum
drawdown
26%
38%
30%
Conclusion
The Kelly criterion is only optimal in the sense that it maximizes
growth. There are many other things a trader could be interested
in maximizing. However, using a modified Kelly scheme that
explicitly includes higher-order moments in the return stream,
sampling errors and drawdown control is a consistent, sensible
method that is vastly preferable to either an ad-hoc strategy or one
that is based on mistaken ideas.
Summary
Adjust the Kelly ratio to account for skew. Trade negatively
(positively) skewed strategies and instruments smaller (larger)
than suggested by the standard Kelly criterion approximation.
Quantify the uncertainty in the estimate of the Kelly ratio.
Scale the raw ratio to give a prespecified chance of it being
non-negative.
Split the trading account into an untraded percentage and a
traded percentage. Apply full Kelly to the risky part of the
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portfolio.
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CHAPTER 10
Meta Risks
Most discussion of the risks related to options focuses on market
risks. Obviously, it is important to mitigate these risks, but they
can be mitigated. They are entirely under the control of the trader.
If a trader blows up because of a market move, it is due to either
ignorance or overconfidence.
There is a far more dangerous type of risk. These are risks from
outside the market. Options don't exist in a vacuum. They are
traded as part of an economic system that contains moral, legal,
and governmental risks. These are the risks that are hardest to
anticipate, but it is still important to learn as much as possible
about them and to take any precautions we can.
Currency Risk
All traders will have currency risk. You can't execute stock and
option trades with anything other than fiat currency. Even if we
ignore exchange rate risk (because your currency of determination
might be the currency of the trades), fiat currency is risky due to
inflation. For example, Zimbabwe has had a stock exchange since
1993. In the same period the inflation rate has reached up to 98%
a day. It is respectable if a trader averages 0.1% a day. No one is
good enough to keep up with hyperinflation.
The worst examples of historical inflation have been in war zones
or places experiencing massive political instability: Greece in
1944, Hungary in 1946, Yugoslavia in 1994, Germany in 1923,
China in 1949, and Venezuela in 2018. It would be simple to write,
“Avoid living in such situations.” But this is generally much easier
said than done. A lot of people would love to have left these places
but didn't have the means to do so. And even in the very stable
country of New Zealand, the inflation rate reached 17% during the
1970s. It is tempting to think that these periods are confined to the
past but that seems very unlikely. Inflation cannot generally be
avoided. The only thing traders can do is be aware of it, and when
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active trading isn't producing real returns stop and invest in
something else.
FIGURE 10.1 The price of Bitcoin in USD in 2018.
Cryptocurrencies have their own problems. Although they are not
subject to the inflationary spending of a government, they are
exceptionally volatile. In 2018, Bitcoin had a low of $3,190 and a
high of $17,700 (Figure 10.1). Average annualized volatility was
68%. Typically, major currencies have cross-rate volatilities in the
single digits. For example, in 2018 the volatility of euro/USD was
7%. And the volatility of USD/yen was 6%.
And although cryptocurrency exchanges are regulated as
businesses in their country of incorporation, they are not run with
the same degree of care and oversight that we can expect from a
traditional exchange. A good example of this occurred in 2018
when the owner of the Canadian exchange QuadrigaCX died. He
was the only person who knew the passwords to the exchange's
cold storage. As of February 2019, customers were unable to
access US$190 million.
Also, no significant exchange will let you pay for anything in
Bitcoin. Almost no one will. Bitcoin fails as a currency both
because it is far more volatile than what you will be buying with it
and because it is not a widely accepted medium of exchange. As of
January 2019, the total value of all the Bitcoin in the world was
US$64 billion. In comparison the total amount of USD was 16
trillion. To become a legitimate currency Bitcoin (and
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cryptocurrencies in general) would need to both vastly increase in
value and vastly drop in volatility.
Finally, many financial institutions want nothing to do with any
cryptocurrencies. Quoting a senior banker in the clearing division
of a major US bank, “If you have anything to do with crypto, this
conversation is over.” Part of this reluctance is due to the current
uncertainty of the regulatory
environment. Some more is because
banks are looking to develop private versions of the blockchain.
Finally, although it seems that the blockchain could eventually
help KYC (“know your customer”) due diligence, banks are
currently more worried that the verifiability of each transaction in
the blockchain can directly tie them to criminal activity.
Lessons
Currency risk is unavoidable but can be diversified.
Cryptocurrencies are speculative instruments and not currency
in the normal sense.
Theft and Fraud
Thieves steal things that are worth money. And, as nothing is
more clearly worth money than money itself, the financial
industry provides good targets for thieves, con artists, and
hucksters. It is impossible to be completely protected from this
risk. Everyone who trades or invests will rely on other people.
Even those who execute their own trades on an exchange will still
have risk associated with their custodian and clearinghouse.
The good news is that most criminals and fraudsters are not
masterminds. Many simply rely on the fact that if they are
charming, no one will do the necessary due diligence.
The first thing is to look at the people involved. Everything a fund
does is because of the people running it. You are not investing in a
fund. You are investing with people. It is important to know who
the managers are, their backgrounds, their experiences, their
levels of involvement, and the amount, both professionally and
financially they have invested. Do they have criminal convictions?
Have they been censured by regulatory bodies (leaving aside floor
traders being fined by the exchange for a fight over a spot or
something)? Do they treat your money even more respectfully
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than they treat their own? For that matter, do they have a
significant amount of their net worth invested in the fund? Do
only one or two people in the fund have access to the account
statements? Often you can get a lot of insight about a person's
character just by asking around. The trading world is a small place
and someone with a dubious reputation quickly becomes known
(even if this isn't discussed on the record).
Any legitimate organization will be pleased an investor asks these
things. For the manager, it is both understandable and makes
dealing with the customer easier. It is always better to be in
business with sensible people.
Further, any legitimate fund should have a third-party
administrator. This is a separate firm that has access to bank
statements and brokerage reports. They verify positions and
returns and generate the monthly reports sent to clients. Don't
accept an excuse such as, “We are just a startup and can't afford a
third-party administrator.” It is non-negotiable. Had Bernie
Madoff's victims insisted on the oversight of an independent body,
they would have immediately discovered that Madoff had done no
trades and held no positions.
More generally, a lot of financial disasters can be traced back to
the victims not knowing about their inventory and hence their
risk. Many of the catastrophic and infamous derivatives losses
have been caused when an institution or investor did not know
what their position was.
Example One: Baring's Bank
Baring's bank was the second oldest merchant bank in the world.
It was founded in 1762 by Sir Francis Baring. In 1990, Nick Leeson
was employed in the Singapore branch of Baring's. He was
authorized to act as a floor broker and to arb the Nikkei futures
between the Singapore and Osaka exchanges. All brokers have an
“error account.” Any trades that are in some way mistakes get put
into the error account. This is meant to be for accounting
purposes. As soon as the error is found the broker is supposed to
exit the trade by liquidating the position. Leeson had a small error
that led to a position of 20 Nikkei futures. Leeson changed the
account number so the head office didn't see reports and began to
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trade in the account to recoup a loss of £20,000, eventually
accumulating a large position in short Nikkei straddles.
On January 17, 1995, a major earthquake hit Kobe and, over the
next four days, the Nikkei dropped 16%, making the short
straddles enormous losers. Leeson started to make even bigger
trades trying to recoup losses. This didn't work. He lost £827
million (the equivalent of about US$2.5 billion in 2018). On
February 23, he absconded to Malaysia and sent a confession note
(consisting only of “I'm sorry”) to London at the same time.
Barings was insolvent and was eventually sold to ING for one
pound.
Lessons
Never let a trader or fund be both a trader and a risk manager.
A trader shouldn't have the ability to create accounts.
Don't invest in products or strategies that you don't
understand. The London office believed Leeson's falsified
profit numbers while someone familiar with the Nikkei arb
would know that the reported numbers were impossible.
Example Two: Yasumo Hamanaka, aka “Mr.
Copper”
In 1995 (a big year for rogue traders) the head copper trader at
Sumitomo bank, Yasumo Hamanaka, lost about US$1.8 billion
(roughly $3 billion in 2018 terms). Over a period of about 10
years, he accumulated about 5% of the world's copper, owning
both the actual metal and the futures. Five percent of a commodity
might not seem excessive, but copper is illiquid and has relatively
low turnover. Using his large futures position, Hamanaka kept the
price artificially high. As well as making his position look
profitable, this enabled him to earn inflated commissions on
physical copper trades, in which commission is calculated as a
percentage of the price (which is in itself ridiculous, because
brokers do no more work to sell something for $100 than they do
when it is $50).
Other traders speculated that Sumitomo was manipulating the
price, but that is weak evidence as traders are generally paranoid
and think every price is being manipulated. No one could confirm
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suspicions because the London Metal Exchange had no position
limits and didn't publish open interest statistics.
In 1995, the price of copper dropped as Chinese mining increased.
This new supply had a greater effect than Hamanaka could
counter, and liquidating his huge position only added to the price
decline. He was removed from his copper trading job and
Sumitomo liquidated the position.
Sumitomo claimed they were totally ignorant of the positions.
Although they had to keep pumping huge sums of money to
collateralize the trade, ignorance is still possible (as we saw in the
Baring's case, treasury and management don't always understand
the positions they have). They said Mr. Hamanaka hid trade
confirmations. He was later convicted of forgery. Nonetheless,
Sumitomo was either complicit, ignorant, or negligent.
Treasury and management need to be aware of how much
margin it takes to hold a position.
Beware of instruments that have limited liquidity or
transparency.
Ask, “Is it reasonable for a trader to make this much money
trading this product?” If you can't answer this, you shouldn't
invest.
Example Three: Bernie Madoff
Bernie Madoff was a very well-respected figure in the investing
world. The son of a plumber (later a stockbroker), he was
genuinely a self-made man. His early jobs included lifeguard and a
sprinkler installer. In 1960 Madoff founded a penny-stock
brokerage, which eventually grew into Bernard L. Madoff
Investment Securities. He became known as an ethical,
philanthropic businessman. He was the chairman of the NASD
board of directors and advised the SEC.
His business had two divisions. There was a broker-dealer and
there was a money management firm. In 2008, it was discovered
that the money management division was running a $50 billion
Ponzi scheme in which Madoff paid redemptions from new
investor deposits rather than any investment returns.
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Madoff claimed consistent returns of 12% a year in all market
conditions. Given that from 1950 to 2007, the S&P 500 averaged
only about 9% a year, his fund found it easy to raise money.
Unfortunately, the S&P 500 dropped over 38% in 2008. Many
people asked for their money, and there were no inflows to cover
the withdrawals.
(There were rumors that some of these reported returns were due
to the investment division front-running client orders from the
brokerage. Some investors thought they were the smart insiders in
the scam. If this is true, it suggests the phrase, “You can't cheat an
honest man.”)
Madoff's story was that he employed a split strike conversion
(more commonly called a collar) in which he was long stock, short
calls, and long puts. The fact that he told people about his strategy
should have shut him down earlier. If you tell people what you are
doing, they can more easily see if your returns are plausible.
Although it is possible for a good trader to beat a strategy
benchmark, the benchmark will still give a good baseline.
And it didn't even take an enormous amount of work to see that
Positional Option Trading (Wiley Trading) Page 21