Implied/Realized volatility arbitrage

Pretty good article of exploiting index volatility discrepancies for a statistically expected profit.

Key Concepts

Volatility arbitrage is morphing from a niche institutional

strategy to mass market, index-linked products.

Volatility arbitrage strategies attempt to take advantage of the

difference between the implied volatility of an asset and its

realized volatility.

Variance swaps are ideally suited to capturing the difference

between implied and realized volatility.

Volatility arbitrage indices, such as the S&P 500 Volatility

Arbitrage Index, measure the performance of a tradable short

variance swap strategy that is long implied volatility and short

realized volatility.

Since 1990, the S&P 500 Volatility Arbitrage Index has

outperformed the S&P 500 at an annualized rate of more than

three percentage points while having one-third of benchmark

volatility. It has never had a twelve-month negative return period.

Article Link

It's pretty clear that profit potential off this strategy lies in a deep understanding of the math involved (e.g. GARCH, cointegration, ARIMA, and etc.)

About the $100 Bill Auction

OK so I'm going through Games People Play: Game Theory in Life, Business, and Beyond, and it mentions a game involving hundreds of (allegedly elite) Wall Streeter groups that resulted disastrously. Yeah, I'm talking about the $100 Bill Auction.

Basic rules: Everyone bids for the $100 bill, and the highest bidder pays the bid, and gets the bill. The catch: the 2nd highest bidder must pay the bid, and get nothing.

The average winning bid: $400 (where the top bidder loses $300, and 2nd top bidder $395~)

Attempting to "win", these "titans of Wall Street" ended up taking huge losses. As a corollary, why are these people managing other people's money? Who the heck's managing your KiwiSaver account (New Zealand version of 401k)? The level of incompetence is scary within the industry.

837% return in 33 days (Poker)

Smasharoo, a pro poker player, documented a return of 837% within 33 days, with very little volatility (adequate bet size management), at fullcontactpoker.com. That’s pretty amazing. I have learned a few things from his much appreciated shared experience.

Minimum volatility

Position size/bankroll management and playing strategy largely optimize return volatility. Basically, understand the statistics behind your strategy and make betting size decisions with respect to it for optimization. The Kelly Formula is a pretty good reference.

High frequency of compounding

This explains why successful day traders practically always outperform those holding longer positions. I have discussed that even with a small statistical edge; higher frequency of compounding makes a HUGE difference (see Slight Edge Butterfly Effect).

Poker and financial instruments

I see a lot of similarities. They both hold inefficiencies due to varying skill levels, i.e. more informed players will consistently profit over time. So the key then lies in becoming more informed, the part that requires diligence, critical thinking, and probably guts too amidst discouragement from fixed, traditional thinkers. Kinda cool huh!

America on sale

This is In-Your-Face deflation that has not eased for a while now.
AP News, by Rachel Beck

" Prices on everything from clothes to coffee to cat food are dropping, some faster than they have in half a century. Items rarely discounted - like Tiffany engagements rings - are now. The two biggest purchases most people make - homes and new cars - are selling at steep price reductions.

Traditionally, manufacturers and retailers lowered prices to clear inventory. Today, they're cutting prices because consumers are demanding it. If it lasts, the ramifications will be wide-ranging.

Retail sales remain sluggish, and more than half of the people surveyed recently by America's Research Group and UBS said they are shopping less.

Homes in parts of Detroit are cheaper than a new car.

Overall, prices are tumbling at the fastest rate in decades. The government's Consumer Price Index, which measures the average price of goods and services purchased by households, has fallen 1.5 percent over the last 12 months. The reading for July showed a 2.1 percent annual decline, the biggest since 1950 "

The world, lead by US, remains in a credit/monetary contraction phase, while inflation has remained positive in New Zealand. This really hurts over here. People are losing jobs left and right, and everything just keeps getting more expensive (as inflation kicks in).

Stochastic Finance on Stock Returns

The stochastic calculus based interpretation of stock returns offers a glimpse of institutional perspective and indirectly reveals how buying and holding leads to a negative expectancy. While numbers and symbols may look intimidating initially, they tell a very simple story.

Variable definitions

The excerpt comes from Stochastic Calculus for Finance Vol1.

S0: Stock price at time step 0

S1: Stock price at time step 1

r: risk free interest rate (usually off treasury debt)

S1(H): Stock price at time step 1 if “heads” were to occur off a random coin toss

S1(T): Stock price at time step 1 if “tail” was to occur off a random coin toss

p: probability of H occurring

q: probability of T occurring

u: multiple applied to S if H occurs (e.g. S1(H) = 2S0)

d: multiple applied to S if T occurs (e.g. S1(T) = 0.5S0)

Note: p + q = 1, so they are collectively exhaustive

Formula 1.1.8 displays “expected” probabilities for future price moves.

Slower than actual rate of inflation

The expected returns adjust simply with r. The “risk free” (questionably) debt instruments usually offer the lowest of interest returns compared to institutional, private loans. As way more money becomes created via institutional and private borrowing, the actual rate of inflation is naturally greater than whatever return off government debt.

Credit risk ignorance makes the model impractical

The binomial pricing model assumes all listed companies to operate with infinite lifespan. Is this belief viable for actual money management? I’d say not. By the way this also invalidates general portfolio theory, sorry Markowitz!

While some revealed, many issues remain to be addressed with quantitative financial theories. Until academic ideas become aligned with empirical evidence, traders must search out personal, unique ways to remedy quantitative model weaknesses to become/remain profitable.

Yield matters

When it comes to stocks, yield hints immediate future price moves via implied professional sentiment. Keep in mind that large, price affecting orders come from institutions and high value traders who make decisions largely by economic means, not historical price charts.

Yield vs. fixed interest

The relationship is simple. When dividend yield of a stock exceeds fixed interest instruments (bonds, savings accounts, and etc.), some large investors find the said stock more desirable due to a relatively higher return over time. So naturally when yield makes a historically significant high, large buying orders come and push the price up in the immediate future, and vice versa.

Of course if we take into account of credit risk (listed company going bankrupt) or direct market directional risk, it becomes a bit more complicated. Despite that, from personal experience and empirical evidence, not all institutional investors comprehend these issues. Remember how I mentioned that 80% of hedge fund employees did not understanding the technicalities of “hedging”?

How to apply this for an edge

Yield as a time series tends to remain stationary and has a negative correlation to the underlying stock price. Consider selling short when yield gets to a historical low, look at covering when it reverts to mean value; and vice versa for buying and selling.

The chart holds last two years of McDonald’s (MCD) along with its yield. Pretty easy right?

Focus On A Few And Not "Diversify"

Many successful full time, professional traders engage entire days on one or two stocks or futures exclusively. No matter how little of an edge this practice offers, learning traders should grasp and take up whatever is available.

Floor Traders

On the exchange floors, the same traders engage in the same security day in and day out. This means that over time, their behavior could display patterns and therefore exploited by the retail trader who spends all his/her time on the associated stock or future.

Reduced Transaction Costs

This should be obvious. Operating a successful business requires expenses to remain at the absolute minimum, and so does trading on a professional level.

Reduced Mistakes

Everybody makes mistakes, and they cost money, at least in the amount of transaction fees. Volatility measure errors, fat finger mistakes like buying instead of shorting or keying in the wrong order volume become rare once the trader becomes familiar with the security.

Diversification Is Obsolete

The permanently optimistic analysts on TV or radio still scream about the well aged concept of diversification. The whole idea was created by an academic, not a professional security trader, decades ago. The highly correlated environment today, along with the credit contraction have created risks that were entirely overseen or intentionally ignored to deceive the public.

Either way, logical, profitable solutions always lie within something that the masses do not realize or engage in. At this moment, majority of the publicly uninformed still embrace the concept of “diversified portfolios” to reduce risk; didn’t turn out that way though for the past year, did it?

Using The TICK For Profitable Trading

The NYSE TICK (ticker symbol ^tick at prophet.net or $tick at stockcharts.com) gives a net difference between stocks moving up against those on the decline, and it could help provide an edge for short term traders. As this indicator moves in a mean reverting fashion, interim emotional buying and selling become easier to identify.

Applying TICK for profitable trading

Naturally, you want to buy if TICK closed at extremely low levels the previous day, and vice versa. However there is more, and I will provide an example for a buying opportunity.

Alongside a low TICK value, this usually means below -800 for me, price action also matters. If accompanied by a dip in the indexes, then an opportunity is present for a buying entry. On the open of the next day, get in ONLY if price opens below the close of the previous day.

The opposite works for short positions. This scheme provides a slight edge for the learning trader. If liquidated at the end of the days, these theoretical opened positions would have all ended profitably for the past two months on the SPY (see above graphs). Yes it takes a heck of a lot of patience to trade it, well at least it would help your trading performance in the positive while the search for high returns goes on.

About Victor Niederhoffer's Experiences

In 1979, Victor Niederhoffer turned $50K into $20Million within 18 months, and became one of the first traders known for quantitative perception. Like any other business, his performance has had ups and downs throughout the decades, and perhaps we could all learn something from the experiences.

I came across this article a few days ago, and it really begs the question of practicality concerning quantitative finance developments today. Mr. Niederhoffer had assumed that stock markets generally moved upwards, a fundamental concept behind current theories in mathematical finance, and this belief had hurt his performance.

Stock prices drift downwards, too

The assumption that stock fundamental values generally stay static while risk-free interest rate serves as an upward drift parameter, i.e. value added via inflation, simply does not apply for actual, realistic market behavior. Companies fail, and more often than not speculative bubbles become mistaken for genuine added value.

Ignoring “unlikely” risks, weaknesses of applied mathematical models, generally makes blowing up a statistical eventuality (Mr. Niederhoffer had blown several hedge funds, but had always managed to get back up and fight another day). No matter how infrequently storms occur, boats are built to withstand the heaviest of them. So should your trading strategy.

Change of paradigm

Fundamentally and statistically, it does not take much for businesses to fail, and yet it requires everything for a moment or two of success. Business and liquidity cycles all point to very dissimilar perspectives than that of Mr. Niederhoffer, or the typical public investor.

It does not matter if your convictions are right or wrong, your objective remains to come out profitable. Pride plays no part in the markets. With that, maybe it is time to take a deeper look into your risk management, so that you WILL survive the worst of times.

Stock Investments Superior To Real Estate

Several fundamental, logical grounds make long term stock investments more viable than real estate. As investments initiate with general objectives of selling later down the line for an increased amount, added value means everything.

Added Value Explained

Potential buyers in the future, especially those with rationality, would only offer higher prices for the same commodity/security/land, if they recognize additional value on top of whatever the original investors had acquired. This could mean new products, higher demand, brand name, intellectual property, land, and etc.

Real Estate Offers Little Value Growth

Aside from discovering gold, oil, or dinosaur bones in the backyard, the land itself offers absolutely no added value. The building itself actually depreciates over time, and requires additional expenses (or risks for the investor) for upkeep.

Inflation backs this illusion of consistent growth over time, and collective investor sentiment determines short term price fluctuations. Nevertheless, prices always revert to the mean, i.e. they come back down to the expected, inflation adjusted value (minus depreciation on the building). John Villareal explains this concept clearly at the Super Genius.

Businesses Operate To Increase Value

Stock investors own shares of the company. With each venture, active, determined people toil every single day with the objective of value enhancement. Therefore, despite the short term up or downside swings, companies operate to exploit every opportunity to add value for shareholders in the long run and some do it quite rapidly.

Of course even for long term investors, risk management remain crucial for success. Investing itself equates to that of a self run business where value improvement lies at the end of the road.

King of Queens (Net Prophets Episode)

In this episode, they attempt to trade a tech stock and make pretty much all the newbie mistakes in a light hearted manner, notably the lack of entry/exit strategies, and allowing emotions to take hold. The show is hilarious.

Part 1


Part 2


Part 3

Classical Arbitrage Strategies Explained

Now that I have described pair trading, the next topic of interest lies in “risk-free” arbitrage strategies. Due to generally limited literature, this subject remains heavily veiled behind institutional trading.

Classical arbitrage defined

Classical arbitrage applies to any business strategy where one exploits market inefficiencies for a risk-free, self-financed profit. Discrepancies in offered values of same underlying commodities/services present the said “market inefficiencies”.

I had provided some examples a while ago on the blog. They present some direct and practical business models or trading schemes applied by real life people.

Are they really entirely risk-free?

No, but it takes much less effort to control the risks arbitrage strategies face, as profitable trades occur regardless of market movement or volatility exposure. In other words, common risks associated with naked stock positions disappear.

Liquidity, price impact, and transaction costs (associated with transaction sizes) generally become manageable via adequate calculations. Mathematical finance helps to optimize arbitrage strategies via things like linear programming or vector space representations, but to become basically profitable (just not maximized), anyone with basic algebraic understanding can manage it.

Do you need huge capital to apply arbitrage strategies?

No. Many opportunities exist for traders of all levels of account sizes. Though of course the larger the trades, the more insignificant transaction-costs become which makes rewards more attractive.

Quick example:

A NZ company is listed on both the NZSX and ASX, and today at close you see the following prices for the stock:

(Hypothetical prices)

· At NZSX: $10.00NZD/share

· At ASX: $10.50NZD/share

You sell 300 shares short on the ASX (requires $3,150 cash in account), then buy 300 shares of the stock long on NZSX. When prices converge you close both positions.

· Total initial cash requirement: $6,300

· Total profit: $150

· Total transaction cost (at $30/trade): $120

· Total net profit: $30

At $30/trade, the brokers here charge way too much, hence making arbitraging in this manner not-so-attractive.

So, with a few thousand dollars, anyone can make money in these markets regardless of market movement.

Reasons why not all traders apply these strategies

Some simply do not understand it or never bothered looking it up. Then for others, the returns remain too low. While arbitrage strategies offer double digit returns per year with very low-risk, ambitious traders aim for much higher targets.

Exceptionally high returns require strategies of highly active management and innovation. Though once found, the mentioned arbitrage models do not look attractive anymore. I have met traders who make over 1% per day, consistently, so yes it is all possible.

Diversification Doesn't Lower Risk

“You want to reduce your portfolio risk. Diversify, diversify, diversify…” I remember hearing some stock broker ranting on TV a decade ago, as the bear market hit US in 98 along with the collapse of Long Term Capital Investments. The audience at the studio watched her intently, the pain of recent losses still apparent on their faces. They all wanted desperately a way out of the hole, and turned to this supposedly professional for advice. She kept going with the metaphors of eggs and baskets, how risk is bad... Just exactly how and why, she did not bother mentioning.

Hedging Via Diversification Limits Returns

The concept never made sense to me even before any exposure to the financial markets. You buy a stock, then you buy some more because you hope they will move against each other, does that not simply lead to low potential returns, if any, and high commission costs?

ETF’s and Hedge Funds Increase Correlations

With the advent of Exchange Traded Funds and the explosion of hedge funds throughout the world, correlations between stocks, bonds and commodities have become much higher than the days of Markowitz (founder of modern portfolio theory). Most of the cause points to speed of information between newly developed funds making similar price impacting transactions concurrently. The markets have changed.

While the investment fund industry grows, fund managers of similar sentiment tend to take action concurrently. This leads to unprecedented high levels of correlation between individual stocks, hence resulting in more volatile markets. In present industry conditions, and evident from recent turmoil, the volatility added risk has become effective regardless of diversification.

ING as an Example

ING, a fund management business based in Australia, likes their investment advisors boast “safety” of their holdings due to diversification. Look up ING fund unit prices, every single one has declined since the sell off of last July; some have taken draw downs up to 70%. So much for the magic of “diversification” huh?

Last Words

Does it even matter why or how this phenomenon has occurred? It simply happens, and knowing it alone could help you become a more informed investor or trader. The world changes, so does industries, and it takes work to adapt and stay profitable.

The market exists for the purpose of asset accumulation or reduction. With every transaction you make, the goal should remain to enlarge account size; anything else serves no purpose but noise. Read a few books and learn what risk management actually entails; it will make everything easier.