QuoteOriginally posted by: daveangelthe most you can lose in one period is 100%, so seeing -110% is a bit farcical.I do not know of any trading account or broking arrangement that allows you to run a deficit. You capital cannot be less than or equal to zero unless your risk is zero as well.I'm not saying you won't get a margin call from your broker if the liability side of a position goes over some threshold. And if things go sufficiently pear shaped, then the position will get liquidated if that's possible. But if the liquidity isn't there, then one can be stuck with a position that creates an unlimited liability. Perhaps this does not happen often, but I'm just trying to create a logical measure of returns that handles corner cases.A margin call only complicates the estimation of returns. How do I compare two portfolios that start with the same capital and then one requires a margin call? Whatever measure of returns should create a proper ordering of the portfolios. For example, let's compare a single-stock portfolio in which the share price of long position goes from $100/sh to $0/sh (-100% return) versus a single-stock portfolio in which a short position goes from $100/sh to $300/sh (presumably worse than a -100% return on the original capital, regardless of subsequent injections of capital to cover the liability).And I would not call the situation farcical because -110% returns can occur. If you watch the sad fates of novice futures & options traders, I'm sure you will find a non-negligible percentage of people whose losses exceeded 100% of their original investment. One can hope that such things don't happen in the institutional world, although I wonder it LTCM and some of the more recent imploded hedge funds aren't examples of this. Again we have the problem of creating a measure of returns that handles both the case in which one loses 100% of one's original capital and the case when one loses more the 100% of one's original capital.

QuoteAnd I would not call the situation farcical because -110% returns can occur. If you watch the sad fates of novice futures & options traders, I'm sure you will find a non-negligible percentage of people whose losses exceeded 100% of their original investment. One can hope that such things don't happen in the institutional world, although I wonder it LTCM and some of the more recent imploded hedge funds aren't examples of this. Again we have the problem of creating a measure of returns that handles both the case in which one loses 100% of one's original capital and the case when one loses more the 100% of one's original capital.LTCM did not lose more than 100% of investor equity - there is no way you can. There is no recourse back to the investor. So the most they can lose is 100%. QuoteA margin call only complicates the estimation of returns. How do I compare two portfolios that start with the same capital and then one requires a margin call? Whatever measure of returns should create a proper ordering of the portfolios. For example, let's compare a single-stock portfolio in which the share price of long position goes from $100/sh to $0/sh (-100% return) versus a single-stock portfolio in which a short position goes from $100/sh to $300/sh (presumably worse than a -100% return on the original capital, regardless of subsequent injections of capital to cover the liability).It happens all the time. One portfolio has leverage the other doesnt - the one with leverage has greater volatility thanks to leverage - its no more complicated than that. Your example of short position going against you is not very meaningful. So long as you are able to post the variation margin and hold the losses then you as the short are not bankrupt. The return on your investment must include your net wealth (and if its a fund then its the net assets in the fund.) this is not a very difficult game.

QuoteOriginally posted by: daveangelLTCM did not lose more than 100% of investor equity - there is no way you can. There is no recourse back to the investor. So the most they can lose is 100%.That may be true for the LTCM-investor contract (limited liability is a relatively recent innovation in the financial world, by the way), but its not true for retail futures broker-investor contracts. An individual investor can be liable to a futures broker for more than 100% of their account's initial capital. If an individual investor puts all their money in some leveraged illiquid position and the position moves severely against them, then the investor will be liable to make up the difference. Moreover, for the purposes of analysis we need some notion of returns that go below -100% -- how do we distinguish between a fund that losses 100% of its investor's equity and a fund that loses 100% of investor's equity and loses some fraction of its ability to meet the obligations of its positions to other stakeholders (e.g., counterparties in a derivatives contract). If LTCM had only lost 100% of investors' money, it would have made news but not been a crisis to the global financial system. What made LTCM so dangerous was that it was going to default on the contractual obligations attendant to its positions. So, again, we're left needing a mathematical measure of return that includes the "worse-than-losing-100%-of-investors-original-investment" case.

QuoteThat may be true for the LTCM-investor contract (limited liability is a relatively recent innovation in the financial world, by the way)That is not true - it has always been the case that equity investors have their liability limited to their investments. The ability to walk away from an investment and leave it with the bondhodlers (lenders) has always been a central tenet of capitalism.QuoteAn individual investor can be liable to a futures broker for more than 100% of their account's initial capital. If an individual investor puts all their money in some leveraged illiquid position and the position moves severely against them, then the investor will be liable to make up the difference. Moreover, for the purposes of analysis we need some notion of returns that go below -100%This is all about recourse/non-recourse lending which I have discussed with Alan prior. If my net worth were $100,000 and I opened a futures account and posted $10,000 and started trading and should I then lose 110,000 then my broker has recourse to the rest of net worth of $90,000 which leaves him in the hole for 10,000 and me bankrupt. But that is capitalism and thats how it works. But my return on equity is still -100% and not -900% ! If there is recourse then it not just what you ponied up that is at risk but your entire wealth.QuoteIf LTCM had only lost 100% of investors' money, it would have made news but not been a crisis to the global financial system. What made LTCM so dangerous was that it was going to default on the contractual obligations attendant to its positions. So, again, we're left needing a mathematical measure of return that includes the "worse-than-losing-100%-of-investors-original-investment" case. Indeed the fact that counterparties were on hook for the losses beyond the equity in the fund is what made them so nervous. BTW LTCM did not lose 100% of their investors equity. I believe there was some recovery of between 10 and 20%. One of the (many) problems that LTCM faced, and its entirely of their own making, was the fact that they kept their counterparties in the dark so as to keep their strategy as opaque as possible. The net risks was known to them (LTCM) but the individual counterparties only had a partial view of the trade.

QuoteOriginally posted by: daveangelQuoteThat may be true for the LTCM-investor contract (limited liability is a relatively recent innovation in the financial world, by the way)That is not true - it has always been the case that equity investors have their liability limited to their investments. The ability to walk away from an investment and leave it with the bondhodlers (lenders) has always been a central tenet of capitalism.The concept of limited liability wasn't formalized until the 19th century (e.g., the UK had unlimited liability until the Limited Liability Act of 1855). The move to limited liability was quite controversial and the first forms of it used partially paid shares in which the shareholder could buy a share for a fraction of the share price, but be liable to the company for the full share price if the company fell into debt. Even after true limited liability became common, some hold-outs remained. For example, American Express' publicly traded shares carried unlimited liability until 1965.QuoteOriginally posted by: daveangelQuoteAn individual investor can be liable to a futures broker for more than 100% of their account's initial capital. If an individual investor puts all their money in some leveraged illiquid position and the position moves severely against them, then the investor will be liable to make up the difference. Moreover, for the purposes of analysis we need some notion of returns that go below -100%This is all about recourse/non-recourse lending which I have discussed with Alan prior. If my net worth were $100,000 and I opened a futures account and posted $10,000 and started trading and should I then lose 110,000 then my broker has recourse to the rest of net worth of $90,000 which leaves him in the hole for 10,000 and me bankrupt. But that is capitalism and thats how it works. But my return on equity is still -100% and not -900% ! If there is recourse then it not just what you ponied up that is at risk but your entire wealth.OK, let's say that my net worth is $100,000 of which I put $10,000 into a future's position with 20:1 leverage. If the underlying moves by 1%, my leveraged position moves by 20% -- that's caused by the volatility amplification factor. If the underlying moves by 4%, my leveraged position moves by 80%. But what if the underlying moves by -6%? I lose 100% of my initial $10,000 plus incur an additional $2,000 liability to the broker. So what's the return? If it's -12% because I'm tapping into other reserves, then shouldn't I compute all returns on a de-leveraged basis? And what if the underlying moves by 51% up or down? The mathematical calculation of the return becomes complicated by the margin calls and the recourse-nature of the contract with the broker. If I compute returns based on total networth, then I'm removing some or all of the leverage factor (i.e, the 20:1 leverage is a phantom and the volatility is not multiplied by the full leverage ratio of the instrument). If I compute returns based only on the initial allocation of capital, then I can easily get values worse that -100%.Again, my goal is a measure of return that creates a logical ordering of various return events in the context of alternative trading strategies or alternative subportfolios. A 20:1 leveraged position in which the underlying drops 6% and incurs a heavy additional input of new capital just to clear the liability with the broker seems "worse" than a long position that goes bankrupt and loses 100% of the initial capital.Perhaps this problem is due to a misalignment of the scope of the analysis of returns with respect to the legal boundaries of the investing entities. Perhaps one can never define the return of a subsegment of a portfolio if the positions in that segment have recourse beyond the boundaries of the subsegment. If I took my $100,000 and divided it into 10 limited liability entities with $10,000 in capital each and invested each entity in leveraged instruments, then each entity would experience the full leverage of the contracts being traded (e.g., a $10,000 net worth entity with a $10,000 position in a 20:1 leveraged contract experiences a 100% loss if the underlying moves by -5%). But if I create notional segments that lack legal barriers, then the returns are always referenced to the total value of the combined net worth which might dilute the leverage of the contracts (e.g., a $100,000 net worth entity with a $10,000 position in a 20:1 leveraged contract experiences only a 10% loss if the underlying moves by -5%). Does that sound right?