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Finance

Keeping heads out of textbooks

November 2, 2009 in Finance

Wall Street & Technology briefly discusses some survey results and concludes: “Wall Street’s Quants Feel Misunderstood.” There’s the obligatory quote from Dr. Wilmott:

“These numbers are alarming,” said Dr. Wilmott. “They indicate that even with the events of the past year, financial institutions are still not taking the importance of financial education seriously, especially as it pertains to improving relationships and understanding between quants and their managers.”

There’s some “alarming” statistics: since last year, quants feel that 86% of their managers have the same or less understanding of their quantitative roles.

But looking at the actual survey results, it’s not quite so bad. In fact, there’s a good deal of exaggeration, depending on how you frame the data. Only 4.5% feel that their managers have less understanding since last year – meaning a full 82% felt that the level of understanding is roughly unchanged. So this largely becomes a question of whether or not the present level of understanding is satisfactory. Most people’s knee-jerk reaction (and that of the original article) will unequivocably be, “Of course it’s not!” However, is that because managers haven’t kept up with quantitative advances, or because quants have run far ahead of their supervisors (and of where they need to be)?

I think it’s a little of both. Certainly, when Things Were OK, supervisors were less incentivized to follow the activities of the mathematicians under them. As long as the numbers danced (higher and higher), it didn’t really matter what they were. Meanwhile, each quant is incentively to pursue ever-more obscure models to squeak out minute bits of alpha. In the end, we wind up with quants doing overly-complex work for managers with too-relaxed supervisory roles. The question isn’t “Does your manager understand what you do?” as much as it is “Do YOU understand why you do what you do?”

The problem here is not that quants ran amuck and screwed up the system (see the replies to question #2), it’s that no one even knew what they were doing in the first place. The article is putting a normative spin on the survey results, but it’s silly to believe that if supervisors understood what quants were doing, everything would be fine. Just the same, if quants only worked within the limits of their supervisors’ knowledge, disaster would result as well (what’s the point of roles, anyway?). What is missing – and what surveys like this fail to address – is the need for proper communication of goals, objectives, methods and ideas. Yes, it might be hard for a mathematician to boil his ideas down to simple English or a supervisor to pick up some mathematical tenets, but the resulting clarity will be well worth the effort in either case.

So in the end, is it bad that quants feel like most of their managers only somewhat understand what they do? It’s hard to say. If the quants are doing their job “properly”, then yes. If supervisors are slacking off, then yes. But if quants are running ahead with inappropriate methods, then although the answer is still yes, the solution isn’t necessarily to educate the supervisors – it’s to teach them how to reign in the quants. Alternatively, it’s to teach the quants a little about their real business objectives.

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Fuzzy AIG math

October 28, 2009 in Finance

A bit of out-of-context math from a recent Bloomberg article on AIG:

The Federal Reserve Bank of New York, the regional Fed office with special responsibility for Wall Street, opened an $85 billion credit line for New York-based AIG. That bought it 77.9 percent of AIG and effective control of the insurer.

The government’s commitment to AIG through credit facilities and investments would eventually add up to $182.3 billion.

So, to review: $85B was a 77.9% stake, so $182.3B works out to… 167.1%?

(Obviously, it doesn’t work like that.)

But wait, there’s more.

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More Zero Hedge nonsense

October 26, 2009 in Finance

Via Naked Capitalism:

I just came across a post on Zero Hedge called “An Overview Of The Fed’s Intervention In Equity Markets Via The Primary Dealer Credit Facility.” Now, that’s a mouthful. As far as I can discern, the post’s purpose is to expose alleged equities market manipulation by the Federal Reserve. However, I found the argument rather conspiratorial. And despite claims of an alleged smoking gun, there is no evidence in the post that that Federal Reserve is manipulating anything except interest rates. And the Fed made clear that that was what it intended to do.

The full post is here.

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First rule of trading is you don’t talk about trading

October 16, 2009 in Finance

In a post that caught my eye because it was titled “Smart Risk, Stupid Risk” – but then failed to elaborate in any way – CNBC chimes in with a few caveats about investing during earnings season:

You snooze, you lose If you’re waiting to find out the earnings before you make an investment in a company, you’re already too late the party.

Listen to what the market is saying by watching what it’s DO-ing Successful trading is about watching the price action and reacting to it. It’s far less about trying to outsmart the markets.

TMI (Too Much Information) Earnings season is exciting to watch and fun to talk about, but so what? It just creates more confusion than clarity. My Advice: Pick a few companies in play and focus on them rather than spreading yourself too thin.

Mix it up a bit Here’s a news flash: Just because you have always traded US equities does not mean you should only trade them. In reality, there are lots of different ways to make lots of money, like metals, oil and currencies.

In other words (which is to say, my words):

You need to trade before anything happens.
You need to wait for something to happen before you trade.
Focus on what you know.
Focus on what you don’t know.

Then again, the post does come with a healthy disclaimer: “[Author] Doug Hirschhorn’s expertise is in the psychology of achieving peak performance. He is not a financial advisor and does not make trading or investment recommendations or provide trading or investment advice. He is an expert on the mental game. Although Doug Hirschhorn has a Ph.D. in Psychology with a specialization in sport psychology, he is not a licensed psychologist and does not provide therapeutic, clinical or counseling services.”

Buyer beware.

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Because a little marketing goes a long way

October 16, 2009 in Finance

From the WSJ’s back page:

Why bother? Despite posting a strong third quarter, Goldman Sachs Group went to extra lengths to put gloss on the results. The first bullet point in its earnings release says the firm ranked No. 1 in global mergers and acquisitions announced in the year through Sept. 25. That’s according to numbers from Dealogic, which ranked rival Morgan Stanley a close No. 2.

For at least three years, Goldman has used Thomson Reuters as a league-table source in its earnings releases. Why the switch? Well, Thomson Reuters ranked Morgan Stanley as No. 1 for the same period. The difference between the tables is partly because Dealogic gives Morgan Stanley fewer dollars of credit for advising General Motors.

But things change quickly in the deal world. Also Thursday, Xstrata dropped its bid for Anglo American. As a result, Goldman, which had been advising Anglo, was dropped to No. 2 on Dealogic’s table. But who’s counting?

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Haven’t we seen this movie before?

October 14, 2009 in Finance,Risk

In a recent profile of KKR, Breakingviews.com (via the NYTimes) attempted to value the company by taking a look at Blackstone’s operations. I don’t have any comment on the analysis itself, but two excerpts stood out in my mind:

[Blackstone] didn’t do as well collecting performance fees and investment gains because its holdings have been falling in value. But if history is any guide, its investments should rebound.

…

So, although it sounds generous given the last year’s market conditions, it’s not unreasonable to assume those [illiquid assets] might gain 20 percent annually from their current valuations for the next five years.

Does anyone else shudder a little when reading sentences like these?

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Felix takes on Tyler Durden

October 2, 2009 in Finance

I’m very happy to see someone of Felix Salmon’s stature calling out the Zero Hedge crowd for what they are: a bunch of delusional conspiracy theorists. I’ve held that site at more than an arm’s length since I discovered that their posts are actually zero-intelligence back in April and again in June. Felix has it absolutely right when he says, “The Zero Hedgies, in other words, are the 4chan of the financial blogsphere, which is maybe one of the more depressing aspects of the degree to which the financial blogosphere has matured.”

Most of Zero Hedge’s counterarguments will revolve around the fact that there audience is not solely comprised of “day traders” – and what’s so bad about day trading, anyway? – but it doesn’t matter. The audience is the symptom, not the cause. It’s not as if ZH has brilliant, insightful articles that just happen to draw hundreds of thousands of idiots to their page – ZH is a financial tabloid, pure and simple. The only difference between them and, say, Dealbreaker is that they post incomprehensible stories accompanied by cryptic Bloomberg screens and obscure market jargon. And it works amazingly well – their most egotistical and vocal readers can’t admit that they aren’t in on the secret, so they don’t dare suggest that the emperor has no clothes.

And the rest of us tune in because, well, who can ignore a crowd? I admit I rubberneck on the highway – and the whole time incensed that everyone else was slowing down. Every now and then, yes, there’s a nugget of truth amidst the ZH mire. But months ago, I got tired of wading through muck to find it. Felix’s suggestion of a disaggregated ZH (with disaggregated RSS feeds) would go some way toward roping me back. But to be honest, at this point it probably wouldn’t make a different; I have so little trust in anything ZH posts.

Here’s a more complete excerpt from Felix’s post:

Who are these people who flock to zerohedge.com and lap up everything they’re served? They clearly love the chart-filled posts about intraday movements in the stock market, which is one clue. I think what we’re dealing with here is, essentially, retail day-traders, as profiled by Hagan back in February. (Hagan told me that even back then, before ZH really took off, the day-traders he was writing about were constantly reading the site.)

You need to be a little bit delusional to be an individual day-trader, paying substantial sums for information, technology, and trading spreads every day and yet somehow reckoning that by zooming in and out of highly-levered ETFs you can not so much beat as utterly obliterate broader market returns. All day-traders think they’re above-average; they have to, otherwise they wouldn’t have the hubris necessary to do it in the first place….

At that point it becomes quite easy to see how they would be attracted to a conspiracy theorist like ZH, who writes dense and often hard-to-decipher posts about the arcana of how the market works. The masses read Dan Brown for fun; the day-traders read Zero Hedge for profit.

And in case that’s not enough, here’s an excerpt from Felix’s followup:

That’s what the wisdom-of-crowds hypothesis says: that if you take a million idiots, all trading with and against each other, yes you’ll get occasional mass delusions, and bubbles and busts, and ad-hoc groupings of vaguely like-minded individuals, like ZH. But somehow, in aggregate, those million idiots will be more right, more often, than any regulatory panjandrum or media pooh-bah. And anybody who’s spent any time with bankers and buy-siders will tell you that there’s precious little correlation between intelligence, on the one hand, and success in the markets, on the other….

So ZH is probably a pretty accurate representation of many people who pay close attention to what the markets are doing on a minute-to-minute or even day-to-day basis. Which is as good a reason as any not to do that.

To Felix: Bravo!

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The rise of VaR

October 1, 2009 in Finance,Quotes,Risk

Simon Johnson and James Kwak take a look at how VaR got to be so popular in the first place. They make the insightful observation that a bad (or at least an incomplete) model can gain acceptance not only because of its simplicity but, oddly, because of its output as well.

Indeed, VaR succeeded not just because it seemed to capture risk accurately (“losses exceeded only 5% of the time” and so on), but because it provided the answer that financial agents were looking for. Most cynically, its greatest disadvantage – failing to look at what actually happens in crisis times, rather than just defining the crisis itself – turned into its biggest sell point when it came to market adoption. In a bizarre twist, the model was chosen because it gave the right answer; not because it answered the right question.

It reminds me of a passage from the ever-insightful Hitchhiker’s Guide to the Galaxy:

“I checked it very thoroughly,” said the computer, “and that quite definitely is the answer. I think the problem, to be quite honest with you, is that you’ve never actually known what the question is.”

“But it was the Great Question! The Ultimate Question of Life, the Universe and Everything!” howled Loonquawl.

“Yes,” said Deep Thought with the air of one who suffers fools gladly, “but what actually is it?”

But you don’t come here for HHG2G quotes (or do you?). Here’s the key excerpt from Johnson and Kwak’s analysis:

David Colander made this point about economic models: The sociology of the economics profession gave preference to elegant mathematical models that could describe the world using the smallest number of parameters. “Common sense does not advance one very far within the economics profession,” he says.

A similar point can be made about VAR models. Sure, maybe all the financial professionals who design and work with VAR know about its shortcomings, both mathematical and practical. But nevertheless, using VAR brought concrete benefits to specific actors in the banking world by helping them rationalize bad bets. If common sense would lead a risk manager to crack down on a trader taking large, risky bets, then the trader is better off if the risk manager uses VAR instead.

Not only that, but imagine the situation of the chief risk manager of a bank in, say, 2004. As Andrew Lo has argued, if he tried to reduce his bank’s exposure to structured securities such as collateralized debt obligations, he would be out of a job; VAR gave him a handy tool to rationalize a situation that defied common sense but that made his bosses only too happy. And at the top levels, chief executives and directors who probably did not understand the shortcomings of VAR were biased in its favor because it told them a story they wanted to hear.

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An interview with Mandelbrot

October 1, 2009 in Finance,Math

The FT has posted a lengthy video interview with the brilliant mathematician Benoit Mandelbrot, whose book The (Mis)behavior of Markets first inspired me to enter finance and risk management in particular.

I do find that some of John Auther’s questions mar an otherwise interesting (but extremely high-level) overview of Mandelbrot’s thoughts on finance. Right from the beginning, he introduces Mandelbrot by discussing his early critique of “the theory of efficient markets, which led to the very complicated investment product that crashed disastrously in the last two years, causing the crisis” – a claim I disagree with – and later questions demonstrate some level of discomfort with the subject material. But these are relatively minor quibbles – on the whole it’s a great interview.

The second part of the interview looks into how the efficient markets hypothesis was able to capture the attention of financial economists, and Mandelbrot concludes that it is because it makes the world appear simpler than it actually is – a direct analogue to the manner in which VaR rose to popularity.

In any case, though there’s little in the interview you haven’t heard before, Mandelbrot is always fascinating and the video is well worth your time.

(via Charles Davi)

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Measuring aggregate risk in CDS markets

September 25, 2009 in Finance,Risk

The ECB recently published this lengthy report (PDF link) on the state of the CDS market, with particular focus on counterparty risk. It is well worth a read for either a cursory overview or more in-depth look at the mechanics and concerns of that market.

Section 3.4 regarding counterparty risk measures was especially interesting to me. Consider the passage on the use of gross outstanding notional as an indicator of risk (emphasis mine):

The notional amount of a credit default swap refers to the nominal amount of protection bought or sold on the underlying bond or loan. Notional amounts are the basis on which cash flow payments are calculated.

The gross notional amount reported by the BIS is the total of the notional amounts of all transactions that have not yet matured, prior to taking into account all offsetting transactions between pairs of counterparties. As outlined above, gross notional amounts thus represent a cumulative total of past transactions. Using gross notional amounts as an indicator of counterparty risk may be misleading, as many trades are concluded with a single counterparty.

Once negotiated, CDSs bind both counterparties until the agreed maturity. Market participants basically have three choices when increasing or reducing their CDS exposures.

First, they can terminate the contract, provided the counterparty agrees to the early termination. Second, they can fi nd a third party to replace them in the contract, provided the counterparty consents to the transfer of obligations (“novation”). As a third option, dealers that want to unwind or hedge their positions can also enter into offsetting transactions, sometimes (though not necessarily) negotiated with the same counterparty as the hedged deal. The third solution is used extensively, and so the number of trades has surged, resulting in an increase in total gross notional amounts. Indeed, this technique, by contrast with the other two, does not eliminate previous deals and instead adds them together. The end result is that external market commentators tend to pay too much attention to the gross market values in relation to other measures of the real economy such as GDP, whereas net notional amounts, where accounted for, may be downplayed or perceived as being very low or moderate in relative terms given the huge gross notional amounts outstanding.

The gross notional amount reported by the BIS is the total of the notional amounts of all transactions that have not yet matured, prior to taking into account all offsetting transactions between pairs of counterparties. As outlined above, gross notional amounts thus represent a cumulative total of past transactions. Using gross notional amounts as an indicator of counterparty risk may be misleading, as many trades are concluded with a single counterparty.

Once negotiated, CDSs bind both counterparties until the agreed maturity. Market participants basically have three choices when increasing or reducing their CDS exposures.

First, they can terminate the contract, provided the counterparty agrees to the early termination. Second, they can fi nd a third party to replace them in the contract, provided the counterparty consents to the transfer of obligations (“novation”). As a third option, dealers that want to unwind or hedge their positions can also enter into offsetting transactions, sometimes (though not necessarily) negotiated with the same counterparty as the hedged deal. The third solution is used extensively, and so the number of trades has surged, resulting in an increase in total gross notional amounts. Indeed, this technique, by contrast with the other two, does not eliminate previous deals and instead adds them together. The end result is that external market commentators tend to pay too much attention to the gross market values in relation to other measures of the real economy such as GDP, whereas net notional amounts, where accounted for, may be downplayed or perceived as being very low or moderate in relative terms given the huge gross notional amounts outstandingNotional amounts are the basis on which cash flow payments are calculated.

The gross notional amount reported by the BIS is the total of the notional amounts of all transactions that have not yet matured, prior to taking into account all offsetting transactions between pairs of counterparties. As outlined above, gross notional amounts thus represent a cumulative total of past transactions. Using gross notional amounts as an indicator of counterparty risk may be misleading, as many trades are concluded with a single counterparty.

Once negotiated, CDSs bind both counterparties until the agreed maturity. Market participants basically have three choices when increasing or reducing their CDS exposures.

First, they can terminate the contract, provided the counterparty agrees to the early termination. Second, they can fi nd a third party to replace them in the contract, provided the counterparty consents to the transfer of obligations (“novation”). As a third option, dealers that want to unwind or hedge their positions can also enter into offsetting transactions, sometimes (though not necessarily) negotiated with the same counterparty as the hedged deal. The third solution is used extensively, and so the number of trades has surged, resulting in an increase in total gross notional amounts. Indeed, this technique, by contrast with the other two, does not eliminate previous deals and instead adds them together. The end result is that external market commentators tend to pay too much attention to the gross market values in relation to other measures of the real economy such as GDP, whereas net notional amounts, where accounted for, may be downplayed or perceived as being very low or moderate in relative terms given the huge gross notional amounts outstanding.

It’s easy to come up with an example which illustrates the problems with gross notionals (the ECB’s “third solution”):

Dealer A sells $1mm of protection to Fund X. The gross notional at this time is $1mm, and the maximum that could be lost (in an extreme case with 0% recovery and the original contract transacted at a zero spread) is also $1mm. Now Dealer B sells $1mm of protection on the same name to Fund Y. The gross notional is $2mm, and so is the maximum loss in the market. But what if Dealer B had sold CDS to Dealer A instead? Then the gross notional would still be $2mm, but only $1mm could be lost, as Dealer A has hedged its position completely. Thus, gross notional has overstated the risk present in the marketplace.

Net notional is a much better measure, but, in line with my parenthetical aside, does not quite capture the risk at hand; it only does so under extreme circumstances. (It also isn’t nearly as dramatic a number, so the media is more loathe to deal with it.)

In my experience, jump to default (JTD) and jump-or-bleed to safety (JTS) measures are instructive methods for evaluating risk. Most commonly, these measures are evaluated with respect to the reference issuer, but they are easily applied to the counterparty as well. However, calculating them in aggregate – at the market level – requires knowledge of the various contracts’ market values, data which is not presently made public (gross and net notional values are available from the DTCC).

Finally, the ECB makes the salient point that any market-wide counterparty risk measure must account for collateralization. There is some ambiguity there, however, because a contract which is fully collateralized on a mark-to-market basis still has considerable counterparty risk in a jump event. Frequently, protection buyers may find that to be wrong-way risk, meaning that the exposure to a counterparty is inversely related to that counterparty’s credit rating. For example, a counterparty defaults, driving credit spreads wider (a profitable event for the protection buyer) but also making other counterparties more likely to default (a very bad thing for the protection buyer).

In failing to find a clear, universal or simple risk metric for this market – which I don’t think is necessarily preferable given the over-reliance and under-comprehension placed on VaR after its wide dissemination – we may find that the best outcome is to strive for transparency in understanding. A strong education in the mechanics and risks of complex markets is an important step forward and a necessary prerequisite for market participants in both direct and regulatory roles.

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Because no one knows commodities like we do

September 22, 2009

Why did a post up titled “How To Play Natural Gas With Small Cap Stocks” pop up in Silicon Alley Insider’s RSS feed? A little investigating (elementary, my dear Watson) shows that it’s actually from The Money Game – another blog under the Business Insider umbrella. The blogs themselves and current RSS feeds show no [...]

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You can keep the note

September 14, 2009

I re-watched the classic Marx Brothers movie Duck Soup last night and three (barely) finance-related bits stuck out. Yes, this as a thinly veiled attempt to get the Marx Brothers on TGR. First, a timely discussion of the politics of debt, in Groucho’s extended introduction: Groucho: “Now, how about lending this country 20 million dollars [...]

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Yet more risky testimony

September 11, 2009

Nassim Taleb and Chris Whalen also participated in Wednesday’s House hearing on risk management. The full text of their remarks are available here (Taleb) and here (Whalen). Taleb’s thoughts are familiar, consisting largely of his well-known opinions on VaR and financial regulation. Whalen, however, provides an excellent quote: The problem is not with models themselves. [...]

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Bookstaber’s testimony on risk

September 11, 2009

Rick Bookstaber testified to the House on Wednesday regarding risk management; the text of his remarks is available here. It is a must-read. The bulk of his testimony focuses on VaR: it’s use, misuse and role in the recent crisis. I find his greatest insight in this paragraph: I remember a cartoon that showed a [...]

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Only in America

September 3, 2009

The law firms of Pearson, Simon, Warshaw & Penny, LLP and Tydings & Rosenberg, LLP have just announced a class-action lawsuit against ProShares Trust on behalf of everyone who has ever owned shares of SKF, the double-short financials leveraged ETF. Key quote from the press release: For example, in a six week period from September [...]

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Greater fool theory

August 21, 2009

Today’s Dilbert: I think the last panel could stand alone.

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An unhelpful VIX

August 19, 2009

A post at Vix and More includes the following graph of the VIX and the forward-looking 21-day realized volatility: The post discusses the fact that realized vol has remained well below implied vol, but I think there’s a much more interesting facet to this chart. First, consider what is being plotted: the VIX, marked in [...]

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Deconstructing the Gaussian copula, part III

August 11, 2009

The intuition behind copula models: dependence, correlation, single factors and more.

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Deconstructing the Gaussian copula, part II and a half

August 11, 2009

An aside on static recovery assumptions in CDO pricing.

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VaR at risk

July 31, 2009

In a piece called “The Risk Mirage,” BusinessWeek assails its peers for falling for VaR-based evaluations of Goldman’s risk levels: [A] VaR-based analysis of any firm’s riskiness is useless. VaR lies. Big time. As a predictor of risk, it’s an impostor. It should be consigned to the dustbin. Firms should stop reporting it. Analysts and [...]

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Recovering from false news

July 17, 2009

Via Alea, a very interesting econometric study on the impact of false news on stock prices. In September 2008, an article on United Airlines’ 2002 bankruptcy resurfaced and was distributed as if it were new information. The company’s stock plummeted immediately, but bounced back and by the end of the day was off only 11% [...]

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Dilution in action

July 17, 2009

A lot of sites are reporting Bank of America’s year-over-year income comparison without batting an eye: Bank of America posted income of $3.22 billion, or 33 cents a share, down from $3.41 billion, or 72 cents a share, a year earlier. The number wasn’t particularly surprising (EPS slightly beat, revenue slightly missed) but couldn’t anyone [...]

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Stocks are a zero-sum game

July 15, 2009

I firmly hold that all financial contracts are zero-sum games. Recently, however, I have heard many arguments premised on the idea that the stock market is positive sum because economic growth creates wealth, which is reflected in universally rising stock prices. But in this scenario, you purchase $1 of stock on Day 1. On Day [...]

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CDS Markets, briefly (or not so briefly)

July 15, 2009

In response to Daniel Indiviglio’s call for “someone who understands the derivatives market,” I posted the following comment on the Atlantic Business blog – and I reprint it here not just because it turned out a surprisingly complete thought, but because I’m a glutton for blogging laziness: The CDS market works similarly to any other [...]

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Deconstructing the Gaussian copula, part II

July 9, 2009

A math-free introduction to CDO pricing.

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Trading Twitter

June 24, 2009

Bubble 2.0 datapoint of the day: StreamBase has announced that their CEP (complex event processing) software for algorithmic trading now supports Twitter. One CIO admits in an otherwise Hallelujah-esque article that “traders he has spoken to haven’t yet jumped onto the Twitter bandwagon.” But here’s the clincher (emphasis mine): A key benefit of Twitter is [...]

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Things that keep me up at night: the FDIC

June 19, 2009

Is the FDIC too big to fail?

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Yet more reverse convertibles: positive sum games?

June 19, 2009

Did Felix Salmon really just write this in defense of his reverse convertibles stance?? For one thing, stocks generally go up over time: they’re a positive-sum game. … Retail investors, as a rule, have no business buying instruments with limited upside but 100% downside — I’d even include individual bonds in that, despite the fact that [...]

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More reverse convertibles: cutting the nose to spite the face?

June 18, 2009

Felix is back at the forefront of the “ban reverse convertibles” charge. He makes some salient points, but continues to encourage a slippery slope form of regulation that would ultimately handicap an industry to protect the naive daytrader. Referring to embedded short options in general, he notes: But retail-facing financial instruments should never embed such [...]

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Wilmott’s stages of derivatives

June 18, 2009

Wilmott adapts the Kubler-Ross stages of grief to describe derivatives. An excellent read. Confused disbelief: I’m a great believer in education playing a bigger role in derivatives in future. But not the sort of education that we’ve got at the moment. I understand Warren Buffett when he says “The more symbols they could work into their writing [...]

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