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Diversification
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Diversification

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Diversification

Thought this be better there then in my journal.

I would like to start a discussion on diversification across multiple instruments, and their correlation. I'm interested to hear if anyone has done any work on it, if not I'll start looking into it from scratch.

Attached is a chart showing the cumulative return of an automated strategy I run. These returns are in terms of risk. Obviously the "both" line is if I were running both at half size. (hope that makes sense).

The standard deviation (STDEVP) of the daily returns (in terms of R) are:

EurUsd: 1.025701
Oil: 1.129661
Both: 0.83984

Uncompounded returns (in terms of risk) are:

EurUsd: 13
Oil: 11
Both: 12

Will return to this later, or you can tell me what I should do, as I'm probably gonna get it wrong!

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Hotch View Post
Attached is a chart showing the cumulative return of an automated strategy I run.

I did not find the chart...

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Oops! My bad! Will continue tomorrow hopefully.

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Any thoughts yet?



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My thoughts: According to the modern portfolio theory by Harry M. Markovitz, diversication should increase risk-adjusted returns. Or otherwise put, positive and negative deviations from average returns should cancel out for multiple instruments which are not 100% positively correlated.

Thus your chart is really no surprise. The standard deviation of the portfolio is smaller than the standard deviation of the single instrument, which would allow you

-> to increase leverage
-> and therefore get a higher risk adjusted return

The only problem of this idea is that there is a significant tail risk. In case of a major financial crisis the negative or weak correlation may turn into a strong positive correlation, which effectively invalidates the concept when it is needed most.

The demise of Long Term Capital Management and the collapse of AIG both happened at a moment, when assets that had been previously uncorrelated all of a sudden showed a strong positive correlation. The leverage used by those two institutions turned against them forcing them into bankruptcy.

The same would happen with your example of crude oil and the Euro. In a flight to safety scenario both would go down synchronously with a near 100% correlation. Modern portfolio theory seems to have weak foundations as those instutions who tried to use it at their advantage failed.


Last edited by Fat Tails; April 1st, 2012 at 07:44 PM.
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As usual, Fat Tails has articulated the point far better than I ever could.


Apologies Mike, I did plan on posting a few bits of the maths, but it's pretty simple. In the end, it's the same old story: make your curve as smooth as you can.

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I just wanted to say I was interested to participate in a discussion on diversified portfolios in CME futures and found this thread. I don't know where to start - if you guys get the ball rolling, I'll try my best to contribute.


Fat Tails View Post
The demise of Long Term Capital Management and the collapse of AIG both happened at a moment, when assets that had been previously uncorrelated all of a sudden showed a strong positive correlation. The leverage used by those two institutions turned against them forcing them into bankruptcy.

The same would happen with your example of crude oil and the Euro. In a flight to safety scenario both would go down synchronously with a near 100% correlation. Modern portfolio theory seems to have weak foundations as those instutions who tried to use it at their advantage failed.

@Fat Tails

Those are the popular accounts of the story. What's really unfortunate is that these inaccurate explanations were written either by journalists (Lowenstein) or stupid analysts (Zerohedge) who didn't comprehend what went on, and somehow became the most widely-known accounts of the story that went around, and ended up demonizing Hank Paulson and the Fed when actual story would make it clear on hindsight that they were true heroes.

One of the real reasons why LTCM went under was because Goldman knew their entire portfolio holdings down to the last cent through rather controversial means - that most would consider illegal - and began hammering their distressed positions even as the Fed was trying to organize a bailout.

AIG's problem had very little to do with correlation. They had to post a collateral of only around $20 billion while they had $2.6 trillion in their balance sheet. To put this in perspective, imagine if you have $130,000 in cash spread across a few bank accounts, and you were forced into bankruptcy because you had a margin call of $1,000 on your retail brokerage account...

The real problem with AIG was that it was structured as 100 over different subsidiaries that were regulated under completely different regimes. They couldn't get AIA to write a cheque to AIG variable annuity or vice versa to meet that "margin call". Well, they could - it would take 6 months for regulatory approval, and it could only be delivered in the form of special dividends. The Fed assistance package could only be structured as a variably-timed series of debt and purchases of preferred equity (whose aggregate payoff resembles a fixed income product, which are notoriously difficult to valuate as compared to other derivatives). On the other hand, they needed to inject private funding, but no one was going to buy the common stock when the Fed was going to dilute their share. I think it was miraculous that the Fed managed to reorganize the entire capital structure and eventually get that liquidity upstream. In fact when the Fed finally liquidated their stake, the public profited $23b from the deal over the initial loss projections of $40b.

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artemiso View Post
@Fat Tails

Those are the popular accounts of the story. What's really unfortunate is that these inaccurate explanations were written either by journalists (Lowenstein) or stupid analysts (Zerohedge) who didn't comprehend what went on, and somehow became the most widely-known accounts of the story that went around, and ended up demonizing Hank Paulson and the Fed when actual story would make it clear on hindsight that they were true heroes.

One of the real reasons why LTCM went under was because Goldman knew their entire portfolio holdings down to the last cent through rather controversial means - that most would consider illegal - and began hammering their distressed positions even as the Fed was trying to organize a bailout.

@artemiso: Good you take a different view on the demise of Long Term Capital Management. I think we agree that LTCM had made a number of bets, which made sense under normal market conditions. The main problem was a flight-to-safety scenario, which was triggered by the default of Russia. Under this scenario all their "diversified" positions came under pressure at the same time. The negative correlation became positive. The problem was amplified by

-> the sheer size of the fund, which made it impossible to exit the markets that they had chosen without attracting predators like Goldman Sachs
-> the fact that the fund was highly leveraged, which made it extremely vulnerable
-> the stubbornness of its traders which made it increase exposure after the Russian meltdown had started

I think they were basicly doing arbitrage/mean reversion strategies, which are reasonable bets, if you can survive the drawdown imposed by other participants in the market. They would probably have survived with less leverage and a lower visibility of their positions in the markets. The main problem was leverage due to underestimating the risk of correlation of the positions they had in their books.



artemiso View Post
AIG's problem had very little to do with correlation. They had to post a collateral of only around $20 billion while they had $2.6 trillion in their balance sheet. To put this in perspective, imagine if you have $130,000 in cash spread across a few bank accounts, and you were forced into bankruptcy because you had a margin call of $1,000 on your retail brokerage account...

The real problem with AIG was that it was structured as 100 over different subsidiaries that were regulated under completely different regimes. They couldn't get AIA to write a cheque to AIG variable annuity or vice versa to meet that "margin call". Well, they could - it would take 6 months for regulatory approval, and it could only be delivered in the form of special dividends. The Fed assistance package could only be structured as a variably-timed series of debt and purchases of preferred equity (whose aggregate payoff resembles a fixed income product, which are notoriously difficult to valuate as compared to other derivatives). On the other hand, they needed to inject private funding, but no one was going to buy the common stock when the Fed was going to dilute their share. I think it was miraculous that the Fed managed to reorganize the entire capital structure and eventually get that liquidity upstream. In fact when the Fed finally liquidated their stake, the public profited $23b from the deal over the initial loss projections of $40b.

AIG is a completely different case. The London AIG Financial Products subsidiary under Joseph Cassano had entered into credit default swaps to insure AAA-rated securities for about $ 460 billion, out of which about 60 billion were collateralized debt obligations with little or an unknown value. Also AIG had other operations which were affected by the global financial crisis, such as their securities lending operations.

The problem here is again correlation of risks. Many of the AAA-rated securities lost value at the same time, triggering "margin calls" from counterparties. The securities lending business was equally affected by the financial crisis, thus further contributing to AIG's financial problems. In the end they could not meet their financial obligations.

The main difference between AIG and LTCM is that AIG had insured products - CDOs - which they did not understand. This points to irrecoverable losses, while most of the mark-to-market losses of LTCM could have probably been recovered, if the fund had survived its liquidity problems.

I am sure that you know more about this than I do.

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I don't really disagree with some of the things you said, but:


Fat Tails View Post
-> the stubbornness of its traders which made it increase exposure after the Russian meltdown had started

There's a very sound reason for doing this that I won't go into detail about.


Fat Tails View Post
The main problem was leverage due to underestimating the risk of correlation of the positions they had in their books.

The risk management put in place at LTCM was many years ahead of its time, and arguably, even the best quantitative risk management book that I know of in print today is still behind. It's been more than a decade and what they are trying to introduce in Basel III still falls short of the checks that they had in place. At the end of the day, whatever your sensitivities to the liquidity or convexity of your liabilities, it's not every day that a country defaults payment and the whole industry deleverages with it.



Fat Tails View Post
AIG is a completely different case. The London AIG Financial Products subsidiary under Joseph Cassano had entered into credit default swaps to insure AAA-rated securities for about $ 460 billion, out of which about 60 billion were collateralized debt obligations with little or an unknown value. Also AIG had other operations which were affected by the global financial crisis, such as their securities lending operations.

The problem here is again correlation of risks. Many of the AAA-rated securities lost value at the same time, triggering "margin calls" from counterparties. The securities lending business was equally affected by the financial crisis, thus further contributing to AIG's financial problems. In the end they could not meet their financial obligations.

My point was that this view entirely misses the mark as to the main culprit. Their exposures were trivial and the correlations were well within anticipation ($20b collateral obligations vs $2.6 trillion balance sheet). The liquidity lockup was what they hadn't anticipated.


Fat Tails View Post
The main difference between AIG and LTCM is that AIG had insured products - CDOs - which they did not understand. This points to irrecoverable losses...

I wouldn't fault you for taking this view. Even the former CEO had the view that the losses were irrecoverable and wanted to liquidate everything by the end of the month (Sep 08), and the liquidation costs would have absolutely taken them out. But his replacement had the courage and foresight to keep those positions, and they've done a massive job of de-risking their CDS protections and now in fact their property-casualty business has been extremely profitable for the last two years (again, good news like this doesn't seem to be mentioned in the media).

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