A “Highly Improbable” Event?

A historical analysis of the natural gas spread merchandise that bought downwards Amaranth

Nick Maouis, the founder of Amaranth, claims that the 6-billion dollar loss that his fund suffers is due to a “highly improbable” trial inwards the natural gas market. Some analysts create got thrown doubts on this claim. To meet how improbable this loss is, let’s accept a quick await at the historical surgical operation of this merchandise since 2000. This is non alone of forensic (and perchance legal) interest: if Mr. Maouis’ claim were true, it would create got furnished us a glimpse of a potentially highly profitable trading strategy.

The bet that Amaranth together with its caput trader Brian Hunter made is that the March-over-April spread inwards natural gas futures volition increment inwards value throughout the twelvemonth prior to the contract expiration. Unfortunately for their investors, the spread decreases rather than increases inwards September, resulting inwards a $6 billion drib inwards value. We don’t know the exact fourth dimension when Amaranth bought this spread. However, it is in all probability that they create got started buying inwards Apr of this year. Apr is the fourth dimension when the nation’s natural gas storage inventory coming out of the wintertime is known together with therefore provides a foundation to bet on adjacent winter’s natural gas sufficiency. I plotted below the profit-or-loss of buying this spread (long 1 March contract of the next year, together with brusk 1 Apr contract) inwards Apr together with exiting the seat at the destination of September every twelvemonth since 2000. (Click on the graph twice to larn far bigger.)

To my surprise, this merchandise loses coin iii out of vi previous years. The 1 twelvemonth that this merchandise was rattling profitable is 2005: it made to a greater extent than than $16,000 profits per twosome of contracts. This is consistent amongst a Wall Street Journal study that Mr. Hunter made $1 billion for Amaranth inwards 2005. That was indeed due to an improbable trial terminal year: Hurricane Katrina.

Note equally good from the 2006 graph that, consistent amongst tidings reports, the merchandise was genuinely quite profitable upwards till the showtime of September. This newspaper profits may non travel easily realized past times Mr. Hunter though, since a lot of it may travel due to his aggressively increasing his seat together with driving upwards the market.

Now at that topographic point tin travel several objections to my analysis. You powerfulness intend that if nosotros concur on to this spread seat longer, tell till December, it would create got been to a greater extent than profitable historically. My question shows otherwise. Holding till Dec would create got resulted inwards losing iv out of the previous five years, losing fifty-fifty inwards 2005. You powerfulness equally good fighting that this is an extremely simplistic version of Mr. Hunter’s strategy. No uncertainty Mr. Hunter used diverse complex options strategies, continuously adjusted amongst diverse telephone substitution factors such equally conditions prediction together with natural gas inventory reports equally inputs. However, from a lead chances administration signal of view, the portfolio that Mr. Hunter owns seems highly correlated to a apparently vanilla spread seat that I described. The fact that this apparently vanilla seat loses coin one-half the fourth dimension historically would non create got been reassuring.

In a hereafter article, I volition push clitoris around calendar spread trades inwards liberate energy futures that create create got a much amend profits consistency.

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How Much Leverage Should You Lot Use?

Maximizing increase without risking bankruptcy

Many hedge fund disasters come upwardly non from making the incorrect bets – that tumble out to the best of us – but from making besides big a bet yesteryear overleveraging. On the other hand, without using leverage (i.e. borrowing on margin to purchase stocks), nosotros oft cannot realize the total increase potential of our investment strategy. So how much leverage should you lot use?

Surprisingly, the respond is well-known, but picayune practiced. It is called the Kelly criterion, named afterwards a mathematician at Bell Labs. The leverage f is defined equally the ratio of the size of your portfolio to your equity. Kelly measure says: f should equal the expected excess furnish of the strategy divided yesteryear the expected variance of the excess return, or

f = (m-r)/s²

(The excess furnish beingness the furnish m minus the risk-free charge per unit of measurement r.)

This quantity f looks similar the familiar Sharpe ratio, but it is not, since the denominator is s², non s equally inward the Sharpe ratio. However, if you lot tin approximate the Sharpe ratio, say, from or together with thus backtest results of a strategy, you lot tin also approximate f simply equally easily. Suppose I convey a strategy alongside expected furnish of 12% over a flow alongside risk-free charge per unit of measurement beingness 4%. Also, let’s tell the expected Sharpe ratio is 1. It is slow to calculate f, which comes out to hold upwardly 12.5.

This is a shocking number. This is telling you lot that for this strategy, you lot should hold upwardly leveraging your equity 12.5 times! If you lot convey $100,000 inward cash to invest, together with if you lot actually believe the expected values of your returns together with Sharpe ratio, you lot should borrow coin to merchandise a $1.2 1000000 portfolio!

Of course, estimates of expected returns together with Sharpe ratio are notoriously over-optimistic, what alongside the inevitable data-snooping bias together with other commons pitfalls inward backtesting strategies. The mutual recommendation is that you lot should halve your expected returns estimated from backtests when calculating f. This is oft called the half-Kelly criterion. Still, inward our example, the recommended leverage comes to 6.25 afterwards halving the expected returns.

Fixing the leverage of a portfolio is non equally slow or intuitive equally it sounds. Back to our $100,000 example. Say you lot followed the (half-) Kelly measure together with bought a portfolio worth $625,000 alongside or together with thus borrowed money. The side yesteryear side day, disaster struck, together with you lot lost 5%, or $31,250, of the value of your portfolio. So at nowadays your portfolio is worth solely $593,750, together with your equity is at nowadays solely $68,750. What should you lot do? Most people I know volition simply stick to their guns together with produce nothing, hoping that the strategy volition “recover”. But that’s non what the Kelly measure would prescribe. Kelly says, if you lot desire to avoid eventual bankruptcy (i.e. your equity going to null or negative), you lot should at nowadays farther cut back the size of your portfolio to $429,688. Why? Because the recommended leverage, 6.25, times your electrical current equity, $68,750, is close $429,688.

Thus Kelly measure requires you lot to sell into a loss (assuming you lot convey a long-only portfolio here), together with buys into a profits – something that requires steely champaign of report to achieve. It also runs counter to the commons mean-reversion expectation. But fifty-fifty if you lot strongly believe inward mean-reversion, equally no incertitude many of the ruined hedge funds did, you lot postulate to visit protecting you lot together with your investors from the possibility of bankruptcy earlier the marketplace position reverts.

Besides helping you lot to avoid bankruptcy, the Kelly measure has or together with thus other of import mathematically proven property: it is a “growth-optimal” strategy. I.e. if your destination is to maximize your wealth (which equals your initial equity times the maximum increase charge per unit of measurement possible using your strategy), Kelly measure is the way.

Notice this destination is non the same equally many hedge managers’ or their investors’ goal. They oft desire to maximize their Sharpe ratio, non increase rate, for the argue that their investors desire to hold upwardly able to redeem their shares at whatever fourth dimension together with hold upwardly reasonably for sure that they volition redeem at a profit. Kelly measure is non for such investors. If you lot adopt the Kelly criterion, at that topographic point may hold upwardly long periods of drawdown, highly volatile returns, depression Sharpe ratio, together with and thus forth. The solely affair that Kelly guarantees (to an exponentially high flat of certainty), is that you lot volition maximize the increase potential of your strategy inward the long run, together with you lot volition non hold upwardly bankrupt inward the interim because of the inevitable short-term marketplace position fluctuations.

For farther reading:

Poundstone, William. (2005). Fortune’s Formula. New York: Hill together with Wang.

Thorp, Edward O. (1997; revised 1998). The Kelly Criterion inward Blackjack, Sports Betting, together with the Stock Market. www.bjmath.com/bjmath/thorp/paper.htm

Maximizing Compounded Charge Per Unit Of Measurement Of Return

A elementary formula that few traders utilize

Here is a fiddling puzzle that may stymie many a professional person trader. Suppose a sure enough stock exhibits a truthful (geometric) random walk, yesteryear which I hateful at that topographic point is a 50-50 hazard that the stock is going upward 1% or downwardly 1% every minute. If you lot purchase this stock, are you lot nearly likely, inward the long run, to brand money, lose money, or endure flat?

Most traders volition blurt out the respond “Flat!”, in addition to that is wrong. The right respond is you lot volition lose money, at the charge per unit of measurement of 0.5% every minute! That is because for a geometric random walk, the average compounded charge per unit of measurement of furnish is non the short-term (or one-period) furnish m (1% here), only is m – s²/2, where s (also 1% here) is the measure departure of the short-term return. This is consistent alongside the fact that the geometric hateful of a laid of numbers is ever smaller than the arithmetics hateful (unless the numbers are identical, inward which illustration the 2 agency are the same). When nosotros assume, equally I did, that the arithmetics hateful of the returns is zero, the geometric mean, which gives the average compounded charge per unit of measurement of return, must endure negative.

This quantity m – s²/2 holds the cardinal to selecting a maximum increase strategy. In a previous article (“How much leverage should you lot use?”), I described a scheme to maximize the long-run increase charge per unit of measurement of a given investment strategy (i.e., a strategy alongside a fixed m in addition to s) yesteryear leveraging. However, frequently nosotros are faced alongside a alternative of dissimilar strategies alongside dissimilar expected returns in addition to risk. How produce nosotros direct betwixt them? Many traders retrieve that nosotros should pick the 1 alongside the highest Sharpe ratio. This is reasonable if a trader ready each of his or her bet to convey a constant size. But if you lot are a trader interested inward maximizing long-run wealth (like the Kelly investor I mentioned inward the previous article), the bet size should ever endure proportional to the compounded return. Maximizing Sharpe ratio does non guarantee maximal increase for multi-period returns. Maximizing m – s²/2 does.

For farther reading:

Miller, Stephen J. The Arithmetic in addition to Geometric Mean Inequality. ArithMeanGeoMean.pdf

Sharpe, William. Multi-period Returns. http://www.stanford.edu/ wfsharpe/mia/rr/mia_rr3.htm

Poundstone, William. (2005). Fortune’s Formula. New York: Hill in addition to Wang.

An Update On The Issue Energy Stocks Vs Futures Arbitrage Trade

I argued earlier inwards the outset of Oct ("An arbitrage merchandise betwixt issue energy stocks as well as futures") that issue energy stocks are overvalued relative to issue energy futures. At that time, a portfolio of long one forepart calendar month QM (crude oil Emini time to come contract) as well as curt 640 shares of XLE (energy stocks ETF) has a value of -$2,584. Where is it now? As of the closed of Oct 31, Dec QM is at $58.725, piece XLE is at $55.73 a share. The portfolio is straightaway at -$6,305 (the multiplier for QM is 500). The spread has clearly widened: it is straightaway at a 3-year low.

We are straightaway faced alongside the park arbitrage trader's quandary. Is this an unprecendented profits chance to double upwardly on this trade, or was this a colossal blunder on my part? I came across this New York Times article most the earnings reports from Exxon as well as Shell that gave me approximately comfort. While both issue energy companies posted huge profits, the article quoted Fadel Gheit, a senior issue energy analyst at Oppenheimer & Company, that for the 4th quarter, "“the enquiry is non if earnings volition decline, the enquiry is past times how much.” According to the article, analysts enjoin that for every dollar the toll of a barrel of unsmooth oil drops, Exxon forgoes $500 1000000 inwards profit.

So yes, alongside my fingers crossed, I am nevertheless waiting for the hateful solar daytime when this spread closes up.

Gold Vs. Gold-Miners: Roughly Other Arbitrage Opportunity?

Recently in that place is mounting involvement inwards buying golden (for example, encounter this before why I believe discover energy futures in addition to discover energy companies ETF are “cointegrated”, i.e. when their spread wanders far from a hateful value, in that place is a high probability that they volition revert to the mean. The same analysis tin last made well-nigh other pairs of commodity futures in addition to ETF’s. Therefore I apply this to gold.

Looking or in addition to then for ETF’s that agree golden miners, I constitute GDX. It started trading on May 23, 2006 in addition to thence has a relatively brusk history for us to analyze. We could own got paired it against the front-month golden futures contract GC, exactly this may last inconvenient because i has to rollover the contracts monthly. So instead, nosotros duad it against an ETF that holds golden every bit a commodity. GLD is i such example. (So is IAU, exactly GLD is far to a greater extent than liquid.) Using the same Matlab cointegration parcel that I mentioned inwards the previous article, I produce upward one's heed that fifty-fifty alongside the brusk history, GLD cointegrates alongside GDX alongside a 90% probability. Also, the parcel tells us the proper combination is sixty shares of GLD vs. 100 shares of GDX. So if nosotros bird a duad yesteryear buying sixty shares of GLD in addition to shorting 100 shares of GDX, nosotros tin plot the value over fourth dimension here:

There were indeed numerous instances of reversion to the mean. I was able to accept wages of the high or in addition to then mid-July in addition to shorted this spread profitably, in addition to I likewise bought the spread or in addition to then the depression inwards early on September in addition to exited my positions profitably or in addition to then mid-September. As of the 1st of November, the spread is in i trial once again inwards sufficiently negative territory to warrant attention.

There are some caveats alongside trading this spread. First, it is non ever slowly to borrow GDX or GLD to short. It depends on if your broker has a expert securities lending desk. Secondly, the history of GDX is short. So whatsoever analysis must last taken alongside a grain of salt. To overcome this brusk history, I could own got constructed my ain handbasket of golden mining stocks in addition to plot the toll of this handbasket against the golden futures GC. If you lot intend to invest heavily into this spread, I would definitely recommend doing this slice of difficult work.

Cointegration Is Non The Same Every Minute Correlation

A reader asked me latterly why I believe that liberate energy stock prices (e.g. XLE) are correlated amongst unsmooth crude futures front-month contract (QM). Actually I don’t believe they are necessarily correlated – I solely recollect they are “cointegrated”.

What is the departure betwixt correlation as well as cointegration? If XLE as well as QM were actually correlated, when XLE goes upwards i day, QM would probable acquire upwards too on the same day, as well as vice versa. Their daily (or weekly, or monthly) returns would accept risen or fallen inwards synchrony. But that’s non what my analysis was about. I claim that XLE as well as QM are cointegrated, pregnant that the 2 toll serial cannot wander off inwards reverse directions for real long without coming dorsum to a hateful distance eventually. But it doesn’t hateful that on a daily terra firma the 2 prices accept to motion inwards synchrony at all.

Two hypothetical graphs illustrate the differences. In the outset graph, stock Influenza A virus subtype H5N1 as well as stock B are correlated. You tin encounter that their prices motion inwards the same management almost everyday.

Now catch stock Influenza A virus subtype H5N1 as well as stock C.

Stock C clearly doesn’t motion inwards whatsoever correlated fashion amongst stock A: some days they motion inwards same direction, other days opposite. Most days stock C doesn’t motion at all! But respect that the spread inwards stock prices betwixt C as well as Influenza A virus subtype H5N1 e'er provide to nearly $1 later on a while. This is a manifestation of cointegration betwixt Influenza A virus subtype H5N1 as well as C. In this instance, a profitable merchandise would move to purchase Influenza A virus subtype H5N1 as well as brusk C at around twenty-four hours 10, as well as thence acquire out both positions at around twenty-four hours 19. Another profitable merchandise would move to purchase C as well as brusk Influenza A virus subtype H5N1 at around twenty-four hours 31, as well as thence closing out the positions around twenty-four hours 40.

Cointegration is the foundation upon which distich trading (“statistical arbitrage”) is built. If 2 stocks only motion inwards a correlated manner, in that place may never move whatsoever widening of the spread. Without a temporary widening of the spread inwards either direction, in that place is no chance to brusk (or buy) the spread, as well as no argue to await the spread to revert to the hateful either.

For farther reading:

Alexander, Carol (2001). Market Models: Influenza A virus subtype H5N1 Guide to Financial Data Analysis. John Wiley & Sons.

Are Political Futures Markets Actually Predictive?

Today I volition accept a brief pause from quantitative trading inward the fiscal markets. Instead, I volition accept a critical await at political futures markets. There has been a lot of enthusiasm lately for such markets (e.g. www.tradesports.com, based inward Ireland, is the most pop one.) Media pundits together with scholars alike produce got oft said that these markets offering a ameliorate prediction of election outcomes than thought polls, sometimes claiming that they trounce polls three-quarters of the time. I produce got been an avid player inward these markets, simply I would similar to offering a contrarian view: I believe that these markets oft follow, rather than predict, events. The so-called “predictability” of these markets is oft ill-defined. The prediction changes constantly over time, together with and so depending on when you lot accept a snapshot of the markets, you lot tin e'er detect an 2nd when, retrospectively, the prediction matches the actual election outcomes really closely.

As an example, I watched alongside entertainment the tradesports.com futures marketplace prediction of the Virginia Senate race betwixt Democrat Jim Webb together with Republican George Allen. This is ane of the 2 unopen races that volition decide the command of the Senate. For months, the marketplace predicts that the Democrat volition lose (the probability of winning, which is the same equally the cost divided yesteryear 100, is e'er below 50% until the laid about of November). Then inward November, the marketplace began to run into the light, together with started to predict a Democratic win. See the nautical chart below.

But await what happened on the black of the election:

As the vote counts started to live on released, the marketplace initiative of all idea the Republican was going to win, driving the prices downwards to the teens. That was due to the votes from the conservative southern Virginia, which were the initiative of all to come upwards in. Then, equally the vote counts from the to a greater extent than liberal northern Virginia were published at to a greater extent than or less 11:30 pm, the prices shot upwards to higher upwards $60, together with continued on to over $80. Clearly, the marketplace does non know to a greater extent than well-nigh the futurity than your average word anchor.

As soul interested inward the predictability of election outcomes based on futures markets, this raises a serious question. What is the proper fourth dimension to accept a snapshot of the market? Should it live on 1 calendar month earlier the election (in which instance this marketplace prediction failed, presuming a Democratic win later the recount)? Or should it live on 1 calendar week earlier the election, inward which instance this marketplace prediction succeeded? And without an respond to this question, how tin ane claim whether the prediction is accurate or inaccurate?

A Commodities Fund Manager's Comments On Aureate Vs Gold-Miners Arbitrage

John Netto, a main inwards a commodities fund that focuses heavily on gold, wrote me the next concerning my article on arbitrage betwixt aureate too gold-miners: "... at that topographic point is a paradox that exists inwards many instances amongst aureate companies too the underlying metal, which could potentially unwind most pairs traders. This is the dynamic of non-recourse loans that companies accept on when doing a project. This would never present upwards inwards a quantitative model simply tin set companies inwards a orbit that when aureate rises, they tin acquire wound to approximately degree. Banks that create non-recourse loans demand the companies to sell futures to guarantee payment for the projection inwards example the toll of aureate falls. This way, they volition non lose if the projection no longer becomes a feasible trouble concern endeavour. If aureate rises, these companies must present massive mark-to-market losses on their books based on novel accounting rules. So the theory that aureate companies tin merchandise correlated to the toll of the underlying is correct, even then a dynamic exists that has the potential on a per fellowship footing to materially touching on that."

I notice Mr. Netto's comments really insightful. I would brand i farther point: if the mark-to-market accounting losses are temporary too volition recover adjacent quarter, nosotros tin hold off their stock prices to revert. This is precisely the cointegration scenario that I talked virtually -- a toll reversion afterward approximately catamenia of time, simply non a day-to-day or week-to-week correlation.

An Updated Analysis Of The Arbitrage Betwixt Golden Together With Gold-Miners

In my article nearly the arbitrage chance betwixt golden together with gold-miners, I cautioned that nosotros should direct keep the analysis amongst a grain of common salt because of the brusque history of GDX (a gold-miners ETF). Adam Phillips of Van Eck Global, the occupation solid which created GDX, has kindly pointed out to me that GDX is designed to rail the Amex Gold Miners Index, GDM, which has a much longer history. Hence I repeated the analysis amongst golden location prices vs. GDM for the final three years. The results confirm my before analysis amongst much higher statistical significance: GDM cointegrates amongst golden prices amongst over 99% probability. Here I plot the departure betwixt the location prices of 6.1 troy ounce of golden together with the GDM index multiplied yesteryear 3.68 (to compare amongst my before plot, I normalize the golden prices together with the GDM index together with then that the Gold-GDM spread yields around the same dollar value equally the GLD-GDX spread at whatever time):

The mean-reversion of this spread is fifty-fifty to a greater extent than obvious than my plot inwards the before article. Also, amongst the longer history, nosotros acquire a much improve experience for the gain of fluctuations. While the value of the spread is nearly -$213 equally of the unopen of November 9, it tin give the axe for certain acquire much lower before reverting, based on the highs together with lows of the final three years.


FOOTNOTE

A reader of my before article made an interesting comment nearly shorting ETF’s such equally GDX together with GLD. He argued that since ETF shares tin give the axe hold upwards constantly created, it should non require existing shares to hold upwards borrowed for shorting. I asked Mr. Phillips of Van Eck Global nearly this, together with he confirmed to me that a newer ETF similar GDX tin give the axe inwards fact hold upwards difficult to borrow. He went on to nation that the borrowing of ETF’s has nix to practice amongst the issuer. The issuer tin give the axe indeed practice an unlimited furnish of the shares, precisely the trader however demand to borrow them from his or her broker for shorting. He besides told me he is currently working difficult to eliminate whatever borrowing problems inwards GDX that may direct keep existed.

Gld-Gdx Spread Reverted To 0 This Morning

Just a quick banknote on the GLD-GDX spread that I accept been talking about. This morn (Nov 17) the negative spread completely reverted as well as has gone into positive territory.

Correction: Maximizing Compounded Charge Per Unit Of Measurement Of Return

A few readers pointed out a typo in addition to an arithmetics mistake inwards my article "Maximizing Compounded Rate of Return". In the geometric random walk illustration where the stock tin plough over notice become upward or downwardly 1% at every step, the hateful charge per unit of measurement of provide m is 0%, (not 1%), in addition to the compounded charge per unit of measurement of provide is -0.005% (not -0.5%). My sincere thank yous to all my readers who mercilessly scrutinize my ideas in addition to banking concern fit my numbers!

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Extended Analysis Of Loose Energy Futures Together With Stocks Arbitrage

A reader of my article “An arbitrage merchandise betwixt liberate energy stocks in addition to futures” suggested that I should hold off at a longer history of unsmooth crude oil prices vs. XLE. So I performed the same cointegration analysis for the front-month unsmooth crude oil futures contract CL vs. XLE since Dec 1998. (I piece of occupation CL instead of QM, the mini unsmooth crude oil contract, due to its longer history.) Here is the plot of the dollar value of long ane contract of CL in addition to brusk 1,217 shares of XLE. (My previous analysis called for ane contract of QM vs. 640 shares of XLE. The divergence inwards shares is due to the half-size of QM relative to CL, in addition to likewise to the larger dataset here.)

An interesting characteristic emerged from this extended analysis. CL in addition to XLE are however flora to endure cointegrated over this long period, albeit alongside a slightly lower probability (90%). However, nosotros tin come across something of a government shift some mid-2002, when CL went from mostly under-valued to over-valued relative to XLE. (Even afterwards including this government alongside lower relative unsmooth crude oil prices inwards my calculations, I however uncovering the electrical current spread to endure undervalued past times virtually $10,521 every bit of the unopen of November 17, which is nigh its 6-year low.)

What was the argue for this apparent shift inwards mid-2002? And are nosotros inwards the middle of a similar government shift inwards the contrary direction? Maybe our readers who accept a ameliorate grasp of the economical fundamentals of the liberate energy markets tin shed calorie-free on this.

Cointegration Of Oih Amongst Location Crude Oil Price

Both my friend Yaser Anwar over at the Jim urged me to exam the crude services ETF OIH instead of XLE for cointegration alongside unsmooth crude price. Their reasoning is that OIH is composed of crude drilling companies such every bit Schlumberger together with Baker Huhges, every bit opposed to XLE, which is composed of oil-production companies similar Exxon. The oil-drillers are to a greater extent than cyclical together with react to a greater extent than to location crude cost rather than far futures contract prices. The promise is that OIH volition tend to cointegrate amend alongside location crude cost than XLE because of this. The fact that OIH has higher volatility every bit a upshot is non a describe of piece of occupation concern to the arbitrageur (as opposed to the hedger), who profits from high volatility. In whatever case, its volatility should “cancel out” that of the location crude cost together with upshot inwards a spread that may genuinely endure less volatile. I follow their advice together with bear out the analysis of CL vs. OIH.

The plot is of the dollar value of long 1 contract of Cl together with brusque 497 shares of OIH. They create cointegrate alongside over 90% probability. (I besides plotted the 1 criterion departure lines of the spread to facilitate those who desire to expect for gauge entry points.) The cointegration probability is non measurably amend than that betwixt CL together with XLE. However, the electrical flow spread (as of the unopen of November 20) is undervalued past times exclusively $9,617 (or 1.48 criterion deviation), every bit opposed to $10,508 (or 1.74 criterion deviation) for the CL-XLE spread. (I determined the criterion departure of the CL-XLE spread to endure close $6,040). So inwards recent months, ane tin indeed country that OIH is trading to a greater extent than inwards describe alongside location crude cost than XLE. But every bit an arbitrageur who thinks the larger the spread, the bigger the profits opportunity, this is non an endorsement for buying the CL-OIH spread instead. Rather, I would watch adding this spread every bit a agency of diversification.

Thanks, Yaser together with Jim, for this suggestion!

Trading A Platinum-Gold Seasonal Spread

Quantitative traders tin sometimes lose sight of the fact that many profitable trading strategies are extremely simple, requiring no math at all. Such is the representative amongst a seasonal spread merchandise betwixt platinum in addition to aureate that was profitable inwards all simply 1 of the concluding vii years. This is far to a greater extent than consistent than the seasonal spread merchandise that ruined Amaranth (see my before article).

The strategy is extremely simple: purchase two July contracts of PL in addition to brusk 1 June contract of GC around the terminate of February, in addition to locomote out the positions around mid-April. (The aureate futures contract specifies 100 ounces, spell platinum is solely 50, thus nosotros require to purchase two contracts of PL vs. 1 contract of GC.) I firstly read near this strategy inwards an article yesteryear Jerry Toepke inwards the SFO Magazine inwards the showtime of 2006 in addition to I decided non solely to backtest it, simply equally good newspaper merchandise this strategy inwards 2006 to come across if it industrial plant its magic again. Both the backtest in addition to the newspaper merchandise worked equally advertised, despite beingness widely publicized yesteryear the magazine. I plot the P/L inwards this chart:


This spread earned an average of $6,600 every yr since 1995. We earned $15,400 inwards the best year, spell inwards the worst yr nosotros lose solely $3,810. With a margin requirement of solely $743 for trading this spread at NYMEX, the provide per merchandise is non bad!

What is the substitution argue this seasonal spread works? Amusingly, it has to produce amongst the terminate of the Chinese New Year. According to Mr. Toepke, the need for aureate is driven yesteryear need for jewelry. Asian countries such equally Republic of Republic of India in addition to PRC are the largest consumers of gold. H5N1 serial of festivals in addition to celebrations inwards these countries around year-end lasted till the terminate of the Chinese New Year's Day inwards February, later which need for delivery of aureate is seasonally exhausted. Platinum, on the other hand, is primarily used inwards catalytic converters for automobiles, in addition to the seasonality is much weaker. It is thus handy equally a hedge for aureate prices.

Further reading: Jerry Toepke, “Give Seasonal Spreads Some Respect”, Stocks, Futures in addition to Options Magazine, Jan 2006 issue.

Does Canada Belong To The Emerging Markets?

Many of us Canadians similar to mean value of our economic scheme every bit a fellow member of the advanced, post-industrial world, amongst the landscape dotted amongst brand-name companies such every bit Nortel Networks, Research In Motion, in addition to Four Seasons Hotels. In the dorsum of our minds, of course, nosotros know nosotros are too a resource-rich country. But still, it may come upward every bit a flake of an embarrassment to detect out that, of all the sector index funds nosotros tin give notice compare the MSCI Canada Index fund EWC to, it cointegrates entirely amongst the natural resources index fund IGE. Even the fiscal sector indices create non come upward close, despite the presence of numerous fiscal services companies inwards the Canada Index. As usual, inwards the nautical chart below, I plotted the spread betwixt 100 shares of IGE in addition to 400 shares of EWC, in addition to nosotros tin give notice come across for ourselves how this spread stubbornly sticks only about zero.






One may banking concern complaint that IGE too cointegrates amongst the Emerging Markets index fund EEM. (The nautical chart below is the spread betwixt 100 shares of IGE in addition to 100 shares of EEM.)


This is non surprising. But does this imply the unsettling determination that the Canadian economic scheme cointegrates amongst the emerging markets? No. I volition non bore you lot amongst yet some other chart: only hold out assured that cointegration is non a transitive relation.

Artificial News Together With Stock Picking

There was an article inward the New York Times a brusk piece agone nearly a novel hedge fund launched past times Mr. Ray Kurzweil, a poineer inward the champaign of artificial intelligence. (Thanks to my swain blogger Yaser Anwar who pointed it out to me.) The stock picking decisions inward this fund are supposed to endure made past times machines that "... tin forcefulness out honor billions of marketplace transactions to come across patterns nosotros could never see". While I am sure enough a believer inward algorithmic trading, I accept popular off a skeptic when it comes to trading based on "aritificial intelligence".

At the jeopardy of over-simplification, nosotros tin forcefulness out characterize artificial news equally trying to jibe past times information points into a business office amongst many, many parameters. This is the instance for approximately of the favorite tools of AI: neural networks, determination trees, in addition to genetic algorithms. With many parameters, nosotros tin forcefulness out for sure capture small-scale patterns that no human tin forcefulness out see. But produce these patterns persist? Or are they random noises that volition never replay again? Experts inward AI assure us that they accept many safeguards against plumbing fixtures the business office to transient noise. And indeed, such tools accept been really effective inward consumer marketing in addition to credit carte fraud detection. Apparently, the patterns of consumers in addition to thefts are quite consistent over time, allowing such AI algorithms to piece of employment fifty-fifty amongst a large position out of parameters. However, from my experience, these safeguards piece of employment far less good inward fiscal markets prediction, in addition to over-fitting to the dissonance inward historical information remains a rampant problem. As a thing of fact, I accept built fiscal predictive models based on many of these AI algorithms inward the past. Every fourth dimension a carefully constructed model that seems to piece of employment marvels inward backtest came up, they inevitably performed miserably going forward. The principal argue for this seems to endure that the amount of statistically independent fiscal information is far to a greater extent than express compared to the billions of independent consumer in addition to credit transactions available. (You may intend that in that location is a lot of tick-by-tick fiscal information to mine, but such information is serially-correlated in addition to far from independent.)

This is non to state that quantitative models produce non piece of employment inward prediction. The ones that piece of employment for me are ordinarily characterized past times these properties:

• They are based on a audio econometric or rational basis, in addition to non on random regain of patterns;
• They accept few or fifty-fifty no parameters that involve to endure fitted to past times data;
• They involve linear regression only, in addition to non plumbing fixtures to approximately esoteric nonlinear functions;
• They are conceptually simple.

Only when a trading model is philosophically constrained inward such a trend produce I dare to permit testing on my small, precious amount of historical data. Apparently, Occam’s razor plant non exclusively inward science, but inward finance equally well.

Market-Cap Together With Growth-Value Arbitrage

Predicting whether small-cap or increment stocks volition outperform large-cap or value stocks inwards the side yesteryear side quarter is a favorite pastime of fiscal commentators. To many fiscal economists, however, the interrogation is long agone settled yesteryear the so-called Fama-French Three-Factor Model. This model postulates that the returns of a stock depend mainly on three factors: the full general marketplace position index returns, the market-cap of the stock, as well as the book-to-price ratio. Furthermore, every bit an empirical fact, over the long term (i.e. for whatever 20-year period), small-caps shell large-caps yesteryear an average compounded annual charge per unit of measurement of 3.12%, as well as value stocks shell increment stocks yesteryear 4.06% (the latter effect applies when nosotros restrain ourselves to the large-cap universe).

This model is really convenient to us arbitrageurs. Statistical arbitraguers to a greater extent than ofttimes than non don’t know how to predict marketplace position index returns, simply nosotros tin soundless brand a living inwards a ship marketplace position yesteryear buying a small-cap, value portfolio as well as shorting a large-cap, increment portfolio, as well as human face to earn 3-4% (on one-side of capital) a year. For example, despite the much anticipated imminent demise of small-caps over the final twelvemonth or so, I establish that if nosotros long the small-cap value ETF IJS, as well as brusk the large-cap increment ETF IVW from Nov 15, 2005 to Nov 15, 2006, nosotros would induce got earned nearly 10% return. The 3-4% average returns human face meager, simply greenback that since this is a market-neutral, self-funding portfolio, your prime number broker (if y'all merchandise for a hedge fund or a proprietary trading firm) volition let y'all to leverage this furnish several times.

Some traders volition honor twenty years a fighting likewise long. Is at that topographic point whatever aid from academic theory on whether small-cap value volition outperform large-cap increment side yesteryear side month, as well as non side yesteryear side twenty years? Influenza A virus subtype H5N1 latterly published column explaining this inwards the New York Times recently.) The substance of this article is that when marketplace position persuasion is positive, human face small-caps to underperform large-caps yesteryear 0.26% a month, as well as value stocks to outperform increment stocks yesteryear 1.24% a month. Conversely, when the marketplace position persuasion is negative, human face small-caps to outperform large-caps yesteryear 1.45% a month, as well as value stocks to underperform increment stocks yesteryear 1.04% a month. How 1 computes “sentiment” is complicated: it is a linear combination of half dozen variables: closed-end fund discount, NYSE portion turnover, number as well as first-day returns on IPOs, equity portion inwards novel issues, as well as the dividend premium. (The authors used information from 1963-2001 for this study.) Now, without genuinely computing all these variables, most would grip that the electrical flow persuasion (as of Dec 2006) is fairly positive. This implies, every bit Mr. Hulbert noted, that small-cap volition underperform large cap inwards the coming months, opposite to the long-term trend. However, the other long-term trend, that value volition shell growth, volition soundless grip inwards the close future. It is upward to the reader to honor a distich of ETF’s that volition accept maximum payoff of this prediction, simply I volition aid hither yesteryear tabulating unopen to of the available funds.

	Value	Blend	Growth
Large cap	IVE	IVV/SPY	IVW
Mid cap	IJJ	IJH	IJK/JKH
Small cap	IJS	IJR	IJT

Further reading:

Bernstein, William (2002), The Cross-Section of Expected Stock Returns: Influenza A virus subtype H5N1 Tenth Anniversary Reflection.
O’Shaughnessy, James P. (2006), Predicting the Markets of Tomorrow. Penguin Books.

Dna, Cryptology, Speech Communication Recognition, Together With Trading

There is an interesting New York Times article on a mathematician too cryptologist who used to operate for the wildly successful hedge fund Renaissance Technologies too is forthwith famous for decoding DNA's. This article caught my eyes because quite a few of my erstwhile colleagues from the speech communication recognition question grouping at IBM likewise went over to Renaissance equally researchers too portfolio managers. Renaissance is an extraordinary hedge fund inward Long Island that has an average annual provide of 35% since 1989, after charging 5% administration fee too 44% incentive fee. They profess to hire exclusively scientists, engineers too mathematicians amongst equally piddling background inward finance equally possible. They started off trading futures, simply has since too so diversified into equities models, too is artificial intelligence may intend that I am beingness inconsistent here, equally I was less than enthusiastic virtually the application of that bailiwick to trading. There is, however, quite a big departure betwixt data theory too artificial intelligence. The erstwhile is characterized past times sophisticated theory amongst really few parameters, the latter, unproblematic theory amongst a lot of parameters.)

There is i published trading model that is based squarely on question inward data theory. It is called Universal Portfolios, created past times Stanford data theorist Prof. Thomas Cover. It is an elegant too quite intuitive model, simply I don't know how good it performs nether realistic conditions. I promise to write virtually about of my question on this too a related degree of models inward a time to come article.

Further reading:

Cover, Thomas M. too Thomas, Joy A. (1991), Elements of Information Theory. John Wiley & Sons, Inc.

Another Limitation Of Artificial Tidings In Addition To Information Mining

Sometime agone I espoused my views that AI in addition to information mining techniques may non endure suited for predicting fiscal markets. Here nosotros convey an article from the Chief Scientist at IBM's Entity Analytic Solutions Group who believes these techniques are non check for counterterrorism either. Why? The same reasons I mentioned: non plenty historical data.

Do Element Models Live On Inwards The Curt Term?

Besides pair-trading, “factor model” is the close pop workhorse of the statistical arbitrageur. In a previous article, I discussed the close well-known ingredient model – the Fama-French Three-Factor model, alongside the full general marketplace index returns, the market-cap of the stock, too the book-to-price ratio equally the exclusively iii factors driving returns. However, equally I explained earlier, this ingredient model has a really long horizon. For the quantitative trader who needs to brand coin every month, the natural instinct is to expect for a to a greater extent than “sophisticated” ingredient that plant inwards the brusk term, or fifty-fifty to railroad train roughly variety of model that role dissimilar factors every calendar month inwards answer to “market condition”. Alas, other than hearsays too second-hand gossips, I accept never witnessed an actual success of this approach inwards a hedge fund or proprietary trading grouping – at to the lowest degree a success that lasts for to a greater extent than than a year.

I am of course of didactics non privy to the electrical flow surgical procedure numbers of ingredient models run past times roughly of the close successful hedge funds today. However, in that location is a shape of ETF (called “XTF”) marketed past times PowerShares Capital Management that uses a similar ingredient approach for its stock pick criteria. According to media reports, each stock inwards these XTF’s is scored past times 25 variables such equally cash flow, earnings growth, cost momentum, etc. This sounds similar a classic ingredient model to me. This model is reportedly designed past times the quantitative unit of measurement at American Stock Exchange. To abide by out if they accept indeed discovered the holy grail of ingredient models, I looked at the surgical procedure of these XTF compared to their benchmarks.

Here I tabulate the XTF’s for each marketplace cap too value category, their corresponding benchmark marketplace index ETF’s, too finally the YTD differential returns upwards to Dec 13, 2006. (PJG too PJM accept equally good brusk a history for this comparison.)

	Value	Blend	Growth
Large cap	PWV-IVE=4.8%	PWC-IVV=-3.6%	PWB-IVW=-5.0%
Mid cap	PWP-IJJ=0.1%	PJG-IJH=N/A	PWJ-IJK=3.1%
Small cap	PWY-IJS=-0.7%	PJM-IJR=N/A	PWT-IJT=-4.9%

The differential returns are all over the place: roughly positive, others negative. To me, this is symptomatic of a ingredient model that does non accept predictive power. (After all, if the differential returns are consistently negative, nosotros could accept long the ETF, brusk the XTF, too brand consistent profits!) At the really least, this ingredient model may accept a horizon much longer than what close traders would live interested inwards – inwards which case, why non but role the uncomplicated Fama-French model?

This is non to tell that exotic, proprietary ingredient models accept no use: they tend to live pretty useful for peril management, equally volatilities too correlations are ofttimes easier to predict than returns. But beware every fourth dimension your peril administration software vendor tries to sell yous an alpha generator!

Universal Portfolios

Let me depict a portfolio optimization scheme that, over the long run, is supposedly guaranteed to outperform the best stock inward the portfolio.

Before nosotros begin, let’s concord that nosotros volition rebalance our portfolio every hateful solar daytime so that each stock has a fixed pct resources allotment of capital, exactly equally your favorite fiscal consultant would receive got advised you. What this way is that if you lot ain IBM as well as MSFT, as well as IBM went upwardly later on 1 hateful solar daytime whereas MSFT went down, you lot should sell some IBM as well as role the working capital missive of the alphabet to purchase some to a greater extent than MSFT. There is a technical term for such portfolios: they are called “constant rebalanced portfolios”. Notice also the similarity amongst the Kelly criterion which I wrote about before: Kelly criterion asks you lot to hold a constant leverage, which is similar maintaining a fixed pct resources allotment betwixt cash (debt) as well as stock.

But what should the fixed pct resources allotment be? Here is where the scheme gets interesting. Suppose nosotros start amongst an equal working capital missive of the alphabet allocation, for lack of whatever amend choice. At the cease of the day, your portfolio has a sure enough internet worth. But as well as so you lot tin terminate calculate what the internet worth would receive got turned out if you lot had started amongst a unlike allocation. Indeed, nosotros tin terminate run this simulation: elbow grease all possible initial allocations, as well as calculate the hypothetical internet worth of the resulting portfolio. Use these hypothetical internet worth equally weights (after normalizing them yesteryear the core of all internet worth), as well as compute a weighted-average pct allocation. Finally, adopt this weighted average resources allotment equally the novel desired resources allotment as well as rebalance the portfolio accordingly. So genuinely the “fixed” pct resources allotment is non fixed after-all: it gets adjusted daily, but in all likelihood non yesteryear much. Repeat this procedure everyday, e'er calculating a novel weighted resources allotment yesteryear simulating diverse initial allocations since hateful solar daytime 1.

This scheme of portfolio optimization tin terminate hold upwardly proven to attain a internet worth greater than exactly belongings the best stock, given long plenty time. If this sounds similar a miracle, it is partly because this is inward fact an ingenious effect of data theory, as well as partly because at that topographic point are diverse caveats that genuinely throttle its practical application. The proof that it plant (at to the lowest degree inward theory) is rather technical as well as I volition allow the interested reader peruse the master copy articles): nosotros acquire by to lose coin fifty-fifty when a toll serial exhibits a geometric random walk. So it is non likewise surprising that nosotros tin terminate also brand coin using similar data theoretic juggling.

Now for the caveats. Every fourth dimension an data theorist start proverb “In the long run, …”, you lot volition hold upwardly well-advised to ask: How long? In my geometric random walk example where the volatility (standard deviation) of returns every menses is 1%, nosotros detect that the compounded charge per unit of measurement of furnish is an agonizingly pocket-size -0.005% per period. In the instance of the universal portfolio scheme, the out-performance over the best stock inward the portfolio is similarly subject on the volatilities of the stocks: the higher the volatility, the faster the out-performance. Let me run a simulation amongst a portfolio consisting of 2 ETF’s RTH as well as OIH. If nosotros were to run the Universal Portfolio scheme from 2001/5/17 – 2006/12/29, I detect that the cumulative furnish is 32% (without transaction cost). Contrast that amongst exactly buying-and-holding the best ETF (namely OIH here): the cumulative furnish is 54%. The Universal Portfolio loses. Does this hateful the theory is wrong? Not really: RTH as well as OIH may exactly receive got likewise depression volatility. Herein lies the foremost practical caveat amongst the Universal Portfolio scheme: it tin terminate receive got likewise long to realize its attain goodness if the volatility is low.

How attain nosotros detect ETF’s that receive got high plenty volatility to realize the out-performance of Universal Portfolio? Actually, nosotros tin terminate but boost the volatility of RTH as well as OIH artificially yesteryear increasing their leverage. So let’s tell nosotros leverage both of them 2x. This way their daily returns as well as volatilities are both doubled. Now the best ETF (which is nonetheless OIH here) has a furnish of 23% (why is it lower than the un-leveraged case? Remember the formula m-s2/2 inward my previous article.) , but the Universal Portfolio has a furnish of 45%. So at 1 time the Universal Portfolio wins. But this is a Pyrrhic victory: if you lot element inward a transaction cost of 10 footing points, the Universal Portfolio scheme genuinely returns alone 4%. This is the minute caveat of Universal Portfolios: because of the frequent rebalancing required, transaction costs tend to consume upwardly all the out-performance.

Now at that topographic point is a concluding caveat. The reader may inquire why I don’t exactly pick 2 stocks instead of 2 ETF’s to illustrate this scheme. Aren’t most stocks to a greater extent than volatile than ETF’s as well as thence much amend suited for this scheme? Indeed, most academic papers, including Prof. Cover’s master copy paper, role a yoke of stocks for illustration. But if nosotros attain that, nosotros run the guide a opportunity of introducing survivorship bias. Naturally, if you lot know ahead of fourth dimension that none of these 2 stocks volition become bankrupt, the Universal Portfolio scheme may expect great. But if you lot run a simulation where 1 of the stocks all of a abrupt went bankrupt 1 hateful solar daytime (which tend to hold upwardly a fairly mathematically discontinuous affair), the Universal Portfolio scheme volition most probable non trounce belongings exactly the non-bankrupt stock inward the beginning. Using ETF’s eliminated this problem. But as well as so ETF’s are far less volatile.

So given all these caveats, is Universal Portfolio genuinely practical? Prof. Cover seems to holler back so. That’s why he has started a hedge fund to essay it.

Quantitative Sports Betting

Here is an interesting WSJ Steve Halpern for the tip!)

Factor Models: The Ground Continues...

A reader JR only posted approximately real thoughtful comments on my article on element models. You tin rank the axe read his comments in addition to my reply here.

Sentiment Equally Contrarian Indicator

More insights from article on Market-cap as well as growth-value arbitrage.)

What Is Your Destination Loss Strategy?

A reader late asked me whether setting a halt loss for a trading strategy is a practiced idea. I am a big fan of setting halt loss, but in that location are sure as shooting myriad views on this.

One of my quondam bosses didn't believe inward halt loss: his declaration is that the marketplace seat does non help almost your personal entry price, in addition to hence your halt toll may move somebody else’s entry point. So halt loss, to him, is irrational. Since he is running a portfolio alongside hundreds of positions, he doesn’t regard preserving working capital missive of the alphabet inward exactly 1 or a few specific positions to move important. Of course, if you lot are an private trader alongside fewer than a hundred positions, preservation of working capital missive of the alphabet becomes a lot to a greater extent than important, in addition to and hence does halt loss.

Even if you lot are highly diversified in addition to preservation of working capital missive of the alphabet inward specific positions is non important, are in that location situations where halt loss is rational? I sure as shooting yell back that applies to trend-following strategies. Whenever you lot incur a big loss when you lot own got a trend-following position, it ususally way that the latest entry signal is contrary to your master entry signal. In this case, ameliorate acknowledge your mistake, closed your position, in addition to mayhap fifty-fifty move into into the contrary side. (Sometimes I wishing our politicians yell back this way.) On the other hand, if you lot employ a mean-reverting strategy, in addition to instead of reverting, the marketplace seat sticks to its master administration in addition to causes you lot to lose money, does it hateful you lot are wrong? Not necessarily: you lot could exactly move also early. Indeed, many traders inward this instance volition double upwards their position, since the latest entry signal inward this instance is inward the same administration every bit the master one. This raises a query though: if incurring a big loss is non a practiced plenty argue to give upwards to the market, how would you lot always determine if your mean-reverting model is wrong? Here I suggest a halt loss measure that looks at around other dimension: time.

The simplest model 1 tin apply to a mean-reverting procedure is the XLE-CL, GDX-GLD, EEM-IGE, in addition to EWC-IGE). It is a uncomplicated model that says the side past times side alter inward the spread is contrary inward sign to the divergence of the spread from its long-term mean, alongside a magnitude that is proportional to the deviation. In our case, this proportionality constant θ tin move estimated from a linear regression of the daily alter of the spread versus the spread itself. Most importantly for us, if nosotros solve this equation, nosotros volition uncovering that the divergence from the hateful exhibits an exponential decay towards zero, alongside the half-life of the decay equals ln(2)/θ. This half-life is an of import number: it gives us an guess of how long nosotros should human face the spread to stay far from zero. If nosotros move into into a mean-reverting position, in addition to iii or iv half-life’s afterwards the spread withal has non reverted to zero, nosotros own got argue to believe that mayhap the government has changed, in addition to our mean-reverting model may non move valid anymore (or at least, the spread may own got acquired a novel long-term mean.)

Let’s straight off apply this formula to our spreads in addition to encounter what their half-life’s are. Fitting the daily alter inward spreads to the spread itself gives us:



These numbers produce confirm my sense that the GDX-GLD spread is the best 1 for traders, every bit it reverts the fastest, spell the XLE-CL spread is the most trying. If nosotros arbitrarily determine that nosotros volition acquire out a spread in 1 lawsuit nosotros own got held it for iii times the half-life, nosotros own got to concur the XLE-CL spread almost a calendar twelvemonth earlier giving up. (Note that the half-life count solely trading days.) And indeed, spell I own got entered in addition to exited (profitably) the GDX-GLD spread several times since final summer, I am belongings the XLE - QM (substituting QM for CL) spread for the 104^th day!

(By the way, if you lot desire to banking company check the latest values of the iv spreads I mentioned, you lot tin subscribe to them at epchan.com/subscriptions.html for a nominal fee.)

Stop-Loss Strategy: Re-Post

Due to a technical glitch, many subscribers to this weblog were non notified of my latest article on stop-loss strategy together with a method to approximate optimal belongings menses for mean-reverting strategies.
So hither is the permanent link again.

Cointegration Betwixt Fossil Oil As Well As Bond Yield? Not!

An explained before, the fact that these two numbers are anti-correlated produce non forbid them from existence cointegrated. And inwards fact, the Economist article plotted the unsmooth crude prices together amongst bond yield over the terminal twelvemonth together, together with they look tantalizingly to a greater extent than or less existence cointegrated.

My curiosity piqued, I proceeded to become a longer history of these information to examine.

In the graph above, I plotted the (normalized) divergence betwixt the 10-year treasury yield together with crude price. One tin flame run into that over the terminal twelvemonth together with a half, they are indeed cointegrated to a adept degree. (To run into that, uncovering the spread is range-bound, or mean-reverting, from mid-2005 to the present.) But this human relationship breaks downwardly completely over the longer history.

Though I recall that the Economist periodical is doing a disservice to its readers for plotting this graph over merely i twelvemonth together with making innuendos of linkage, it is a squeamish representative of the danger of studying cointegration over a brusk window.

Index Tracking, Arbitrage, Together With Cointegration

Mr. Lange, a reader of mine from Germany, alerted me to the next subscribers only area. (Mr. Lange has graciously allowed me to portion this exposition amongst other readers of this blog.)

In Praise Of Day-Trading

A recent article past times Mark Hulbert inwards the NYTimes talked nearly the Value Line's rankings, together with how this organisation is under-performing the marketplace set index inwards recent years. Mr. Hulbert asked Professor David Aronson of Baruch College whether this drib inwards functioning agency that the organisation has stopped working. Prof. Aronson says no: he believes that it takes 10 or to a greater extent than years [my emphasis] of under-performance of this strategy earlier i tin say that it has stopped working! This statement, if taken out-of-context, is thence apparently untrue that it warrants unopen to elaboration.

To evaluate whether a strategy has failed bears a lot of resemblance to evaluating whether a item merchandise has failed. In my previous article on stop-loss, I outlined a method to create upward one's heed how long it takes earlier nosotros should croak a losing trade. This has to produce amongst the historical average belongings menstruation of similar trades. This sort of thinking tin besides endure applied to a strategy equally a whole. If your strategy, similar the Value Line system, holds a set for months or fifty-fifty years earlier replacing it amongst others, together with thence yes, it may accept many years to detect out if the organisation has in conclusion stopped working. On the other hand, if your organisation holds a set for simply hours, or perchance simply minutes, together with thence no, it takes entirely a few months to detect out! Why? Those who are well-versed inwards statistics know that the larger the sample size (in this case, the publish of trades), the smaller the pct departure from the hateful return.

Which brings me to day-trading. In the pop press, day-trading has been given a bad-name. Everyone seems to recall that those people who sit down inwards sordid offices buying together with selling stocks every infinitesimal together with never belongings over-night positions are no amend than gamblers. And nosotros all know how gamblers terminate up, right? Let me say yous a niggling secret: inwards my years working for hedge funds together with prop-trading groups inwards investment banks, I create got seen all kinds of trading strategies. In 100% of the cases, traders who create got achieved spectacularly high Sharpe ratio (like vi or higher), amongst minimal drawdown, are day-traders.

Use The Correct Discount Charge Per Unit Of Measurement To Avoid Jail Time

Here is a fascinating story nigh the one-time treasurer of Essex County, New Jersey, who was sentenced to vii in addition to a one-half years inward prison theatre because the prosecutor used the incorrect discount charge per unit of measurement to value for sure tax-exempt bonds.

Another Article On Political Futures Markets

A NYTimes article yesterday talked almost the political futures marketplace order intrade.com inward the context of the Nov election, especially the Virginia Senate race, which I blogged about before. I urged my readers to curb their enthusiasm for using such markets for prediction inward my article, piece the NYTimes article is surely much to a greater extent than enamored of them. However, I intend nosotros tin post away all handgrip that such markets are really efficient inward synthesizing all existing data in addition to sentiment inward making a prediction, precisely it cannot give away data that nobody tin post away mayhap know at this point, such every bit who is going to win the 2008 full general election.

Do Gilt In Addition To Fossil Oil Cointegrate?

I produce got written extensively hither nearly cointegration betwixt gold-miners in addition to aureate ETF's (GDX vs GLD), every bit good every bit betwixt unloose energy companies in addition to stone oil ETF's (XLE vs USO). (See, for e.g., this article, or this article.) On or hence other occasion, I besides commented on an Economist periodical article nearly the possible cointegration betwixt bond yield in addition to stone oil prices. However, my immature human blogger here) is over fourteen months. Therefore, it may postulate historical information dorsum to the 1970's to convince ourselves of their cointegration. (My ain information on unsmooth stone oil in addition to aureate prices solely acquire every bit far dorsum every bit the 1990's. If whatever reader knows of historical information beginning that goes dorsum further, delight allow me know.) If, however, i is willing to accept their cointegration past times religious belief despite the inadequate data, in addition to hence i may believe that aureate is currently (as of February 12, 2007) only slightly undervalued relative to stone oil (the spread is nearly $8). I sure don't recommend entering into a lay on either side at this point!

Index Arbitrage Amongst Xle

In looking for pairs of fiscal instruments to duad trade, nosotros produce non accept to restrict ourselves to pairs that tumble out inwards "nature". We tin oftentimes laid upward our ain baskets of stocks to merchandise against an index (or an ETF representing this index). In fact, such pairs unremarkably present improve cointegration properties than whatever stock or ETF pairs. I accept alluded to this index arbitrage consider inwards an before post, together with the details of the methodology are explained inwards my half-life for mean-reversion is nearly twenty days, which agency yous accept to concur a seat for at most a quarter. (My ain dominion is to decease when the spread hasn't reverted inwards iii times the half-life.) If yous acquire inwards into a seat when the z-score is nearly ±2, yous tin await a net of nearly $2,000 on an investment of nearly $58,000 on 1 side. This comes to a provide per merchandise of nearly 3%. You tin of degree boost this provide past times using options to implement the XLE seat instead.

As an aside, if yous role Interactive Brokers, yous tin easily merchandise an entire handbasket of stocks using their Basket Trader.

I accept created an online spreadsheet alongside (almost) real-time values of this spread inwards the subscription area. (The detailed composition of this handbasket of 10 stocks are too described there.) Note that inwards theory, every fourth dimension the XLE changes composition, nosotros volition accept to re-compute our handbasket composition equally well. But fortunately XLE composition does non alter rattling much or rattling often, together with then I volition alone update my handbasket at most in 1 lawsuit a month.

Platinum-Gold Spread Revisited

Now that Chinese New Year's Day is over, it is fourth dimension to revisit the Platinum-Gold spread that I talked nearly final November. The theory is that amongst the demand for gilt seasonally exhausted due to the destination of Asian festivities, gilt prices volition spend upwards relative to platinum. We straightaway convey the chance to exam this theory again.

Maximizing Chemical Compound Charge Per Unit Of Measurement Of Provide Vs Maximizing Sharpe Ratio

A reader, Mr. A. Goldstein, made a real useful observation close my article "Maximizing Compound Rate of Return". In that article I argued that if your destination is to maximize the chemical compound charge per unit of measurement of return, you lot should maximize the quantity m – s²/2, where m is the short-term (1-period) charge per unit of measurement of return, together with s is its measure deviation. In general, this is not the same equally maximizing the Sharpe ratio of a strategy. However, Mr. Goldstein pointed out that, if you lot too optimize the leverage of your strategy using Kelly's criterion, together with thence maximizing Sharpe ratio does inwards fact maximize the chemical compound charge per unit of measurement of supply also. This follows from a calculation inwards department seven of medico Edward Thorpe's newspaper www.bjmath.com/bjmath/thorp/paper.htm.

Mr. Goldstein too suggested a beta arbitrage strategy which he has allowed me to part amongst my readers inwards a futurity post.

Is Increasing Beta Or Increasing Leverage A Amend Fashion To Growth Returns?

In my previous post, I reported an sharp observation from my reader Mr. Goldstein that maximizing chemical compound charge per unit of measurement of return, maximizing leverage, as well as maximizing Sharpe ratio are all tightly connected. This makes intuitive feel because the higher the Sharpe ratio of a strategy, the smaller the drawdown, as well as so the higher the leverage yous tin apply to it inwards guild to maximize chemical compound return.

Mr. Goldstein also made closed to other rattling interesting observation. He noted that in that location are unremarkably ii ways to growth the returns of a portfolio of stocks: either yesteryear picking high-beta stocks, or yesteryear increasing the leverage of the portfolio. In both cases, nosotros are taking on to a greater extent than adventure inwards guild to generate to a greater extent than returns. But are these ii ways equal? Or is 1 improve than the other? It turns out that in that location is some research out in that location which suggests increasing leverage is the improve way, due to the fact that the marketplace seems to hold upwardly chronically under-pricing high-beta stocks. This gives ascent to a strategy called "Beta Arbitrage": purchase low-beta stocks, curt high-beta stocks, as well as earn a positive return.

I myself receive got non studied this shape of arbitrage inwards depth, as well as so tin neither endorse nor criticize it. However, if this question is correct, it does debate against including equally good many volatile stocks inwards your portfolio or trading strategy. If yous desire to accept on to a greater extent than adventure as well as generate higher return, but plough the knob as well as growth your leverage as well as so mass size.

Seven Factors That Capture Virtually Of Hedge Funds' Returns

The Economist magazine simply published an article on this topic previously.) The 7 factors are (are you lot ready?):

1) excess provide on the S&P 500 index;
2) a pocket-size minus large part constructed every bit the deviation of the Wilshire pocket-size too large
capitalization stock indices;
3) excess returns on portfolios of lookback straddle options on currencies;
4) excess returns on portfolios of lookback straddle options on commodities;
5) excess returns on portfolios of lookback straddle options on bonds;
6) the yield spread of the United States of America 10 twelvemonth treasury bond over the iii calendar month T-bill, adjusted for the duration of the 10 twelvemonth bond;
7) the modify inwards the credit spread of the Moody's BAA bond over the 10 twelvemonth treasury bond, too appropriately adjusted for duration.

According to the researchers, factors 3)-5) are constructed to replicate the maximum possible provide to trend-following strategies on their respective underlying assets.

See, it is non that hard to run a hedge fund later all!

Hedging Isn't E'er Better

Many of the strategies I wrote nigh inward this spider web log are market-neutral strategies: long i musical instrument as well as brusk exactly about other i every bit a hedge. In many hedge funds, these are the exclusively strategies that are allowed: investors imagine that exclusively market-neutral hedge funds tin deliver consistent returns inward bull as well as acquit markets alike, as well as the typically smaller drawdowns experienced past times such funds let them to obtain higher leverage from their prime number brokerages. However, over the years I receive got expire convinced that this bias inward favor of marketplace neutral strategies is misplaced inward several ways.

First off, it is a fleck dizzy to operate difficult to uncovering a market-neutral strategy as well as hence that nosotros tin receive got a smaller drawdown as well as hence that nosotros tin increase its leverage to boost its return. After all these leveraging, the drawdown is oftentimes dorsum to the same degree every bit a long-only strategy! Why non exactly run a long-only strategy at a lower leverage, but that is oftentimes simpler inward blueprint as well as that incurs lower transaction costs (since at that spot is exclusively one-side of the merchandise to execute)?

Secondly, at that spot is a misconception that long-only strategies volition certainly lose coin inward acquit markets. This is in all probability truthful when you lot are asset overnight -- but long-only day-trading strategies are oftentimes profitable inward both bull as well as acquit markets.

Thirdly, at that spot are strategies where exclusively the long trades work. Influenza A virus subtype H5N1 unproblematic instance is a strategy that buys an index at its 10-day low, as well as move out when... well, at that spot are multiple ways to move out as well as most of them work! If you lot effort the mirror icon of this strategy, i.e. brusk an index at its 10-day high, it industrial plant far less well. This exactly reflects the positive hateful render of the equity market, as well as why non receive got wages of that?

Finally, related to the 3rd point, sometimes the brusk hedge fails exactly because the brusk musical instrument is truly quite unlike inward nature than the long one, despite their superficial similarity. An example is provided past times Mr. Sandy Fielden at Logical Information Machines. There is a normally profitable merchandise where you lot long a May gasoline futures contract as well as simultaneously brusk a May heating petroleum contract inward the spring. The logic is that every bit the weather condition gets warmer, the driving flavor volition laid about which drives the toll of gasoline futures up, as well as the need for heating volition decrease which drives the toll of heating petroleum futures down. This hedged merchandise is supposed to eliminate full general liberate energy marketplace risk. However, the weather condition is sometimes unpredictable, as well as inward 2005, this merchandise went quite incorrect primarily because the wintertime lasted longer. On the other hand, if you lot exclusively move inward the long side of this trade, i.e. purchase gasoline futures inward the spring, it industrial plant similar a charm every twelvemonth inward the past times 10 years! (I receive got posted a detailed analysis of this long-only gasoline futures merchandise inward my Premium Content area.)

Therefore, if you lot merchandise for yourself as well as non for exactly about institutions alongside a mandate exclusively for market-neutral strategies, at that spot is no bespeak to live bounded past times the same rules that they receive got to play by.