price sensitivities = #1 valuable output of risk-run

[[complete guide]] P433, P437 …

After reading these pages, I can see that per-deal PnL and markt-to-market numbers are essential, but to the risk manager, the most valuable output of the deal-by-deal “risk run” is the family of sensitivities such as delta, gamma, vega, dv01, duration, convexity, correlation to a stock index (which is different from beta) , ..

Factor-shocks (stress test?) would probably use the sensitivity numbers too.

In Baml, the sensitivity numbers are known as “risk numbers”. A position has high risk if it has high sensitivity to its main factor (whatever that is.)

VaR can overstate/understate diversification benefits

understate the curse of concentration overpraise diversified portfolio
mathematically definitely possible probably not
correlated crisis yes possible, since VaR treats the tail as a black box. yes. portfolio becomes highly correlated. Not really diversified
chain reaction possible. Actually, Chain reaction is still better than all-eggs]1-basket yes. diversification breaks down

Well-proven in academic — VaR is, mathematically, not a coherent risk measure as it violates sub-additivity. Best illustration — Two uncorrelated credit bonds can each have $0 VaR but as a combined portfolio the VaR is non-zero. The portfolio is actually well diversified, but VaR would show risk is higher in the diversified portfolio — illogical, because the individual VaR values are simplistic. Flaw of the mathematical construction of VaR.

Even in a correlated crisis, the same could happen — based on probability distribution, individual bond’s 5% VaR is zero but portfolio VaR is non-zero.

A $0 VaR value is completely misleading. It can leave a big risk (a real possibility) completely unreported.

[[Complete guide]] P 434 says the contrary — VaR will always (“frequently”, IMHO) say the risk of a large portfolio is smaller than the sum of the risks of its components so VaR overstates the benefit of diversification. This is mathematically imprecise, but it does bring my attention to the meltdown scenario — two individual VaR amounts could be some x% of the $X original investment, and y% of $Y etc, but if all my investments get hit in GFC and I am leveraged, then I could lose 100% of my total investment. VaR would not capture this scenario as it assumes the components are lightly correlated based on history. In this case, the mathematician would cry “unfair”. The (idealized) math model assumes the correlation numbers to be reliable and unchanging. The GFC is a “regime change”, and can’t be modeled in VaR, so VaR is the wrong methodology.

[12] VaR: stress^historical based

I think my OC colleague Rajesh hinted once — there are two common methodologies to compute "minimum loss in the worst 5% scenarios"

1. stress test
2. historical

In Historical, you record the actual (unrealized + realized) losses for the past x (like 252) trading days and plot a histogram, and directly pin point "minimum loss in the worst 5% of those trading days".

I think the way you record the losses (or gains) is like "for IBM, daily price relative is 95%, +10%, 102%, 92% …."

In stress test, I think you simulate a drop in vol and/or a drop in underlier etc

CVA==marketValue of option-to-default

Monte Carlo is the only way to estimate it…

Classic PresentValue discounts each cash flow , but ignores the possibility of non-payment.

CVA simulates more than 1000 “paths” into the future over 50 to 75 years. Each path probably has a series of (future) valuation dates. On each valuation date, there’s a prediction of the market. A prediction includes many market factors. I believe my FRM book lists 9 standard market factors in the “stress test” chapter.

Each path can be described as a predicted evolution of the entire “universe”.

On each path, a specific shock or stress can be applied.

I guess that on each valuation day, the net amount Alan owes me is predicted (and the net amount Bob owes me is predicted) , known as my exposure to Alan. Multiply this exposure by the probability of Alan’s default and also the recovery rate, we get a kind of predicted loss. I think this is the basis of the CVA.

Most of the contracts are derivative contracts. Max Expiry is 75 years.

Even exchanged-traded assets’ valuation need to be predicted on a given valuation date on a simulation path. That’s because the exchange-traded product could be a collateral. A falling collateral value impacts the recovery amount, so this valuation affects the exposure indirectly.

risk-factor-based scenario analysis [[Return to RiskMetrics]]

Look at [[return to risk riskMetrics]]. Some risk management theorists have a (fairly sophisticated) framework about scenarios. I feel it’s worth studying.

Given a portfolio of diverse instruments, we first identify the individual risk factors, then describe specific scenarios. Each scenario is uniquely defined by a tuple of 3 numbers for the 3 factors (if 3 factors). Under each scenario, each instrument in the portfolio can be priced.

I think one of the simplest set-up I have seen in practice is the Barcap 2D grid with stock +/- percentage changes on one axis and implied vol figures on the other axis. This grid can create many scenario for an equity derivative portfolio.

I feel it’s important to point out two factors can have non-trivial interdependence and influence each other. (Independence would be nice. In a (small) sample, you may actually observe statistical independence but in another sample of the same population you may not.) Between the risk factors, the correlation is monitored and measured.

risk mgmt gotcha – monitor current market

[[FRM1]] P127 gave an example of this common failure by risk mgmt department — historical data (even very recent ones) could be misleading and under-report the VaR during a crisis.

I guess it takes unusual insight and courage to say “Historical data exhibits a variance that’s too low for the current situation. We must focus on the last few days/hours of market data.”

risk mgmt gotcha – correlation spike

[[FRM1]] P126 gave an example to illustrate a common failure of risk mgmt in finance firms. They fail to anticipate that correlation of everything, even correlation between credit risk and mkt risk, will increase during a crisis.

I remember the Goldman Sachs annual report highlighting the correlations between asset classes.

Increased correlation moves the distribution of potential loss, presumably leftward. Therefore a realistic VaR analysis need to factor it in during a crisis.

maturity bucketing for VaR

[[complete guide]] P 457 pointed out VaR systems often need to aggregate cashflow amounts across different deals/positions, based on the “due date” or “maturity date”.

Example — On 12/31 if there are 33 payable amounts and 88 receivable amounts, then they get aggregated into the same bucket.

I think bucketing is more important in these cases:

  • a bond has maturity date and coupon dates
  • a swap has multiple reset dates
  • most fixed income products
  • derivative products — always has expiry dates

In StirtRisk, I think we also break down that 12/31 one day bucket by currency — 12/31 USD bucket, 12/31 JPY bucket, 12/31 AUD bucket etc.

Q: why is this so important to VaR and other market risk systems? (I do understand it hits “credit risk”.)
%%A: For floating rate products, the cashflow amount on a future date subject to market movements
%%A: FX rate on a future date 12/31 is subject to market movements
%%A: contingent claim cashflow depends heavily on market prices.
%%A: if 12/31 falls within 10D, then 10D VaR would be impacted by the 12/31 market factors

2 key risks in U.S. treasury ^ IRS trading

The LTCM case very briefly outlined that for a stand-alone 20Y T bond position, there’s

1) interest rate risk [1], and
2) liquidity risk of that particular instrument. I guess this means the bid/ask spread could become quite bad when you need to sell the bond to get much-needed cash.

LTCM case analysed a swap spread trade, whereby the IRS position provides a perfect hedge for the interest rate risk. I think we can also consider duration hedge.

As to liquidity risk. I feel T bond is more liquid than IRS.

generalized tail risk n selling puts, intuitively

There are many scenarios falling into this basic pattern — earn a stream of small incomes periodically, and try to avoid or hedge the tail risk of a sudden swing against you. (Some people call these disasters “black swans” but I think this term has a more precise definition.)
eg: AIA selling CDS insurance…

eg. market maker trading against an “informed trader”, suffering adverse selection.

eg: Currently, I’m holding a bit of US stocks in an overvalued market…
eg: merger arbitrage …
eg: peso problem and most carry trades.

back testing a VaR process, a few points

–Based on

Let me first define my terminology. If your VaR “window” is 1 week, that means you run it on Day 1 to forecast the potential loss from Day1 to Day7. You can run such a test once a day, or once in 2 days etc — up to you.

The VaR as a big, complicated process is supposed to be a watchdog over the traders and their portfolios, but how reliable is this watchdog? VaR is a big system and big Process involving multiple departments, hundreds of software modules, virtually the entire universe of derivatives and other securities + pricing models for each asset class. Most of these have inherent inaccuracies and unreliability. The most visible inaccuracy is in the models (including realized volatilities).

VaR is a “policeman”, but who will police the policeman? Regular Back test is needed to keep the policeman honest — keep VaR realistic and consistent with market data. Otherwise VaR can become a white elephant and an emporer’s new dress.

go short on tail-risk — my take

Many sell-side [1] traders are described as being short tail-risk. In other words, they go short on tail-risk.

[1] some hedge funds too

*** If you are long tail-risk (insurance buyers), you are LONGING for it to increase. You stand to profit if tail risk increases, such as underlier moving beyond 3sigma. Eg — buy deep OTM options, buy CDS insurance.

*** If you are short tail-risk (insurance sellers), you hope tail risk drops; you mentally downplay the extreme possibilities; you stand to Lose if tail risk actually escalates. Eg — sell OTM options, sell CDS insurance agressively (below the market).

As a result, you would earn premiums quarter after quarter, but when an extreme tail risk does materialize, your loss might not be fully compensated by the premiums, because the insurance was (statistically) underpriced, because you underestimated the probability and magnitude of tail risk.

Maybe you (the trader) is already paid the bonus, so the consequence is borne by the insurance seller firm. In this sense, the compensation system encourages traders to go short on tail risk.

mkt-risk system is nice-to-have@@ (2nd post)

Is market-risk system nice-to-have, as described in ?

Q1: which app budget to cut when a firm must cut IT budget by half? Bang for the buck! I feel risk app stacks up well against a lot of systems like reporting, Massive and expensive market data engines, HR, mobile, algo trading, high-frequency, DMA, fancy pricers, real-time curve-builders.

Anything real time, anything high volume (to the cutting edge) tends to be expensive — developer, hardware/software/hosting. Do they give better benefit/cost ratio?

Now a slightly less important question —
Q1b: which app budget to increase when times are good?

Q: who makes the budget decisions? How powerful is the risk app’s sponsor in a budget war?

Risk apps do look like white elephants — expensive, sophisticated but unreliable analysis. See Bottom line — you can criticize 99% of trading platform components as non-essential, questionable numbers, poor data quality, expensive and poor value for money. 30 years ago, successful traders flourished without custom applications. Some still do.

Recently, There is a lot of regulatory pressure on firms to be more “serious” about risk management but I always felt big banks (and big buy-sides) tend to pay lip service. True? An eq der risk system veteran gave me a few pointers. (I will add the least amount of annotation…)

* Risk, compared to other systems, has larger data volume.
* Risk uses more computation and more computer power. If you have a server farm, what are the top 2 use cases?
* Compared to cash products, Derivatives requires more risk analysis

I feel risk engine uses more math, more complicated business logic, more database, more business insight, more quant know-how than other components.

Another (management-level) veteran told me most investment banks lack the real time risk capabilities of GS and JPM.

1+2 big users of pricing/valuation engine

See also post on secDB usages (

—–A) pre-trade. For any large/small trader, order origination is all about timing, sizing and …YES, pricing.

A1) quote pricing – on both sell-side and buy-side
** limit order pricing (also stop/stop-limit orders)
** RFQ pricing
** market-maker’s pricing engine. Note MM can be a sell-side or buy-side

A1b) pricing other orders — not all out-going orders are quotes, but I feel quote pricing is the dominant system. If you send out a non-limit order, you can often leverage the same quote pricer. Examples —
A1b1 market orders — trader must decide at what price level to generate a mkt order
A1b2 cancellations — someone must decide at what price level to cancel an order.

A2) hedging — a composite pricing task, though it’s included in the pre-trade section. You already have positions so you must mark them and analyze their sensitivities, then price your hedging orders

A3) pre-trade valuation analysis. Very important in structured/exotic trading desk.

A4) pricing control — compliance, both internal and external (regulatory)
—–B) post-trade
B1) marking — mark to market, either real time or periodic. Basis of VaR and pre-trade pricing
** General Ledger — I worked with KPMG auditors. They have a big responsibility to scrutinize these valuations
** regulatory reporting

B2) market-risk — most complex usage
** sensitivity — affects hedging pricing
** correlation and hedging
** VaR

B3) margin calc
B4) collateral re-valuation. Most long-term contracts are backed by collateral and need to be re-valued.
B5) market-value based fee calculation — the oxygen of portfolio managers
B6) bonus
If I must name Big 3 users, I’d single out 1) quote pricer (including market-making), 2) marking and 3) VaR. 

In one major derivative desk (market leader), the same pricing model is used in 2 primary pricers — RFQ and risk. These are 2 distinct software applications, though based on the same pricing model.

book-value risk ^ mkt-value risk – 2 views on interest rate risk points out that interest rate sensitivity is measured in 2 (completely) different ways
– a book value perspective, which perceives risk in terms of its effect on accounting earnings,
– a market value perspective – sometimes called an economic perspective – which perceives risk in terms of its effect on the market value of a portfolio.

I believe Book-value perspective is the layman’s perspective. It ignores time value of money or NPV and treats future cash flows same as current cash flow, assuming a single universal discount factor of

VaR≠a maximum loss: illustrating Condition VaR

Update — At 95% confidence level, VaR is a dollar amount like $9M. $9M is the worst (maximum) loss within the 95% part of the bell curve. $9M is the most optimistic (minimum) loss within the tail.

Q: Everyone should know the theoretical maximum loss is 100% [1]. That’s theoretical max. How about realistically? Can we say Value-at-risk is a realistic estimate of “maximum loss” in your portfolio, from a large number of extensive simulations and analysis? The original creators of VaR seems to say No. See

Compared to ExpectedShortfall aka ConditionalVaR,  the original VaR measures the most optimistic level of loss i.e. the smallest loss within the fat tail.  Therefore, the magnitude of those big losses are not considered.

“Expected” is used in the statistical sense, like “average”, or average-width [2] of normal bell curve.

Q: Does ES consider the magnitude of the loss in the worst, worst cases?
A: yes. Superior to VaR. Measures severity of fat tail losses.

For a given portfolio and a given period, the 5% expected shortfall is always worse (larger) than 5% VaR. This is Obvious on any probability density distribution curve, not just the Normal distribution bell curve. If PDF is hard to comprehend, try histogram.

— Example —
“My 10-day 5% Expected Shortfall = $5m” means in the worst 5% caseSSS, my AVERAGE-loss is that amount.
In contrast, “My 10-day 5% VaR == $4m” means in the worst 5% caseSSS, my MINIMUM-loss is that amount. Most optimistic estimate.

VaR makes you feel confident “95% of the time, our loss is below $4m” but remember, this level of loss is the SMALLEST-loss in the fat tail. How badly you lose if you are 5% unlucky and one of those 5% cases happen, you can’t tell from VaR.

[1] In leveraged trading, you could lose more than 100% of the fund you bring in to the trading account, because the dealer/broker actually lends you money. If you lose all of the $10,000 you brought in and lose $2000 more, they could go to your house and ask you to compensate them for that loss.

[2] actually “average distance from the vertical-axis”. Vertical-axis being the mean PnL = 0.

risk system can be front office (KK


One of my systems was a real time risk monitor. Traders use this same system to book trades, price potential trades, make market, monitor market data, conduct scenario analysis. If this is not front office app, then I don’t know what is.

If I don’t say this app also handles real time risk, then no one will question it is front office. In fact, trading floor guys told me traders use this app more than any other app.

However, at the heart of this application is real time risk engine. All those “front office” features are built on top of the pricing module in this risk engine.

In another bank I worked, I know a Fixed Income derivative trading app that’s responsible for position management, deal pricing, live market data, quote pricing, contract life-cycle event processing — all front office functionality, but at the heart, this is a risk system. The team is known as “Risk team”. In fact, there was no other front office app for these derivatives. This was the only thing traders had. If you call it middle office, then there’s nothing front office.

In many derivative systems (including fx options and fx swaps presumably), pricing engine takes center stage in both front and middle office. Derivative traders’ first and last job is (i believe) monitoring her open positions/deals and trade according to existing exposures and sensitivities. That’s the defining feature of derivative trading.

Experts often say derivatives were created as risk management tools. They reduce risk and introduce risk, too. They are creatures of risk.

finance presents distinct risks to different people

Investors talk about returns, growth, opportunities, aggressive/conservative, hedging, tail risk, risk profile..—-> market risk. Not credit risk, not liquidity risk, not counter-party risk.

Regulators talk about systemic risk, controls, reserves, transparency, protecting (those to be protected). They mean —-> liquidity risk.

Exchanges talk about integrity, stability … —> c-risk

Traders are accused of taking the profit but not the risk since it’s other people’s money. We are talking about —–> market risk, not liquidity risk. Credit analysis and approval is, i guess, not the trader’s job.

In an economy, investment banks are dwarfed by commercial banks. For their credit card, car loan, student loan, mortgage departments, risk means —–> credit risk, not liquidity risk, not market risk.

Hedge funds and mutual funds traders? market risk

Hedge funds owners during a crisis? liquidity risk

secDB – designed for mkt-making and prop trading

GS 2010 annual report said “A particular technological competitive advantage for GS is that GS has only one central risk system.” Presumably, this is a market risk system. Not much credit risk, or  liquidity risk, or counter-party risk.

It’s instructive to compare several major business models
+ prop-trading and principal-investment — maintain positions ==> need secDB
+ dealing and market-making — need to maintain (and hedge) positions ==> probably needs SecDB esp. option/swap market making
+ security lending — holds client’s positions under bank’s name ==> Needs secDB
– brokerage and agency-trading — don’t need to maintain positions by strict definition. In practice I guess they often lend assets to clients and hold client’s positions as collateral. That would need secDB
– asset management — managing client’s money only, so maintain positions on behalf of clients. If you care about the fund manager’s positions, then you need secDB. In addition, I guess managers often co-invest — need secDB
– high-volume, low-margin electronic trading is usually(??) agency trading
+ if there’s a high volume system that needs secDB, I’d guess it’s prop trading similar to hedge funds

Looking into the design of SecDB (dependency graph + OODB), I feel it’s designed for prop desk.

In citigroup, the research department supports prop desk as its #1 user. I guess the market maker desk would be #2.

When GS say “aggregate positions across desks”, I feel it means prop desk + sell-side “house” desks. I think they mean house money i.e. positions under GS own name, not client names. Risk means risk to the bank’s positions, not client’s positions. (No bank will spend so much money to assess risk to clients’ positions.)

risk system can be front office #quartz

most market-risk (and MOST credit-risk) IT systems are considered middle office, but Kirat Singh’s presentations suggest a specialized developer role in risk/research space is more “front office” because these developers interact with quants and traders.

How do we identify such a developer position among millions of risk developer positions?
+ real time (at least intraday) risk numbers
+ job responsibility often mentions risk and pricing in one breath
+ pre-trade analysis
+ a key part of the trading strategy
+ a key part of models
+ business users are prop traders or fund managers, not agency traders
+ derivatives needs more risk management than cash products

In contrast, middle office risk systems
– are heavily batch-driven
– i feel some traders treat those risk numbers as unreliable, unlike the real time risk numbers they look at before every trade.

3 major risk-calculators in an investment bank

Background — Imagine a typical investment bank. The risk engines below are owned by distinct branches of the IT organization. Not integrated (A major shortcoming in risk systems today is such data silos.)  For the bank CRO (Chief Risk Officer), how are these systems related? How do we interpret their risk numbers in a consolidated big picture?

– c-risk (credit risk) systems calculate bank’s potential loss due to defaults OR counter party credit rating drops
– Sophisticated m-risk (market risk) engines calculate expected Market Value drops due to price swings
– L-risk (liquidity risk)? Among other things, it covers capital reserve (Basel). L-risk is Less computerized. Perhaps no daily valuation of assets/liabilities, long and short positions.

— some comparisons among the domains —
There is significant overlap between credit-risk vs market-risk processes. In the bigger picture, unrealized loss due to counter party credit is covered by both c-risk and m-risk. Real cash loss (i.e. realized) is the subject of both by L-risk and c-risk.  Credit risk engine is more about calculating unrealized loss (i.e. MV drop) due to credit quality change. In contrast, realized loss due to default is the subject of liquidity risk.
Unrealized MV loss due to credit quality hurts valuation of loan portfolios and incoming collateral, and hurts our consolidated assets and our own credit rating. Therefore it is a liquidity risk.
At the heart of credit risk analysis (unlike market risk or liquidity risk) is the credit review on individual borrowers/issuers including countries.
M-risk is more quantitative than c-risk and L-risk. Therefore most IT jobs are in m-risk. VaR is the most quantitative domain in finance. The star player in the “team”. Useful for short term m-risk.

For long-term m-risk, Stress-test (aka scenario-test) is the primary risk engine. Stress test is also one of the engines for c-risk estimation.

I feel liquidity risk is more critical to a bank than credit risk or market risk, as liquidity means solvency.
How about collateral valuation engines? I think this straddles c-risk and L-risk systems. Outgoing collateral reduces a bank’s liquidity. Collateral we hold in the form of bonds are valued daily in our c-risk calculator.

How about margin risk calculator (for prime brokerage or listed derivatives)? I assume these margin accounts only hold liquid assets, credit-risk free. In such a case, it’s basically a stress test m-risk engine. Not so much VaR. Not much c-risk. It does hit bank’s capital reserve since collateral adds or reduces a bank’s liquidity.

Now, if a margin risk calculator must support risky bonds in the margin account, then this system might affect m-risk, c-risk and L-risk.

collateral risk, repo, margin call

Repo are sometimes open-ended, but overnight repo is most common. Overnight repo requires automatic (not semi-manual like in BofA) processing.

Margin call is usually daily, but can be intra-day. I don’t think there’s monthly margin call.A typical Collateral IT system supports mostly 3 main collateral assets – futures, options and repo

–Funding efficiency?
Q: If I have a combined 50b portfolio and I want to repo it with various lenders to borrow cash, then how much cash can I get?
A: depends on my asset “distribution”. Diversification — good; A few highly concentrated positions — bad. Why? If we pledge a gigantic 10% of IBM Corp’s entire outstanding shares as a single collateral, then lender worries about worst case i.e. borrower default. Lender must liquidate, but selling so many IBM shares means huge market impact.

–repo — Both cash-lender and cash-borrower need to worry about counter-party credit .
If borrower’s (pledged) collateral appreciates while on loan, then borrower is at risk of loss due to lender bankruptcy while holding the security. The asset we have lost is worth more than the cash we borrowed — we pledged too much

If collateral depreciates, obviously lender is worried.

limitations of risk models – Haitao discussion

See also post about FRM critique on risk metrics.

[haitao] Your view on risk management matches with one of our professor’s, he also believes that using risk models such as VaR does not suffice the purpose of risk management, it is really a very broad field that needs to be explored further. This is actually at frontier of academic research, in particular, Professor mentioned 3 flaws associated with VaR: 1. Not considering the magnitude of loss beyond VaR. 2. VaR penalizes firm diversification. 3. Fattail issues related assuming distribution of critical events failed to reflect market situations. I have also attached his research paper drafted in 2010, he is very well known in Fix Income field.

[Bin] I feel VaR is the best concept I know today (except Expected Shortfall) but very, very imperfect. As I said earlier,

I feel any attempt to predict how market reacts to extreme events is futile as such extreme events are rare and we have limited experience with them. — Black Swan theory

How do you predict the impact of a comet hitting the earth, if you have not analyzed 100 similar collisions?

When liquidity dried up in 2008, I was told every bank held on to whatever cash it had and refused to lend. All our models fail. US government had to create about 1000 billion new dollars. No one can predict this either.

Similarly, some governments (Germany after WWI??) prints so much money that a cows price shot up not 100% but 100,000,000% in a year. No risk system can handle such inflation. I remember photos of German children playing with bundles of bank notes as toy bricks.

More recently, Iceland, Greek and Irish governments went bankcrupt. I doubt any VaR system accounts for such extreme possibilities.

What kind of risk system predicted the impact of Freddie and Fannie failures (or Lehman, Bears and AIG)? I doubt. I feel even the strongest (like Goldman Sachs) would not survive if AIG goes bankrupt without government bailout, since AIG is insurance for GS.

You can have lots of smart hedges to protect big risky positions but what if the instrument used in the hedge itself becomes illiquid and worthless, or the counterparty is unable to fulfill its obligation? Can risk models predict that half of all market participants go bankrupt together?

Many derivative markets are subject to tighter regulation. Perhaps liquidity and spread will worsen?? VaR systems must adjust for such policy changes and predict the implications? Hopeless in my opinion.

Sometimes I feel the risk analysts are ostriches burying their heads. They know a lot of extreme market events are not accounted for in their system but they just wish them away (just to keep their jobs and keep their research projects alive). They see the emperors new dress is naked but dont dare to say.

[haitao] I recall some of the interview questions from BB in Hong Kong and Singapore:

a. All sort of behavioral questions: Tell me a time…Why us…Why this position…Leadership…

Problem solving…Resolve Conflicts…etc
b. What do you think tax cuts extension impact on yield curve?
c. What is your view on Asian markets particularly Chinese stock market in 2011?
d. Why do you think Commodity price should surge even higher? What are the factors cause such dynamics?
e. For historical US and Japanese interest rates, one of them is normally distributed and the other is log-normally distributed, which is which? Justify your answers?
f. Explain Fix Income to a layman.
g. Discussion on recent market events.


real time risk – option mkt-maker

Core component is the valuation engine. Each vol surface gets rebuilt every 10 minutes. Positions are re-valued every minute on average.

I believe option position valuations change more often because spot moves more often than implied volatility.

(Similarly, in Sprite of Baml Stirt, the FX spot moves more often than fwd points. It also moves more often than interest rate market data, including IR futures prices.)

I was told it’s hard for any eq vol market maker to survive without a real time pricer. When client calls for a quote, it’s problematic to rely on a 2-hour stale vol surface.

Re-pricing in 2 areas —
1) position mark-to-market (most important)
2) outgoing quote/RFQ pricing

I feel these 2 areas are related. If you are a market maker in an index (stoxx for eg), then your own position will influence your outgoing quotes. I guess the Reason is — position means market-risk, and position means hedging. Everyone needs to hedge, esp. a market maker.

For volatility instruments, delta-hedging must be adjusted constantly.

VaR for cash bonds

I believe Reo doesn’t calculates VaR. However, the cash bond positions might be analyzed by some other system. Result is probably posted to the Risk website, but what data?


Most basic is Perhaps dv01 at position level and rolled up to account level. If you have a price-yield convertor, and you know the current price (perhaps chosen by a trader), you can calculate the price at 1 bps above the present yield and the price 1 bps below the present yield. You can get your own dv01.

credit risk in trading vs commercial banking

Hi Rob,

I feel there are 2 major users of credit risk data.

* traders use it as part of market risk data
* lenders use it to decide on interest rate and perhaps collateral

Everyday thousands of individuals and organizations borrow money from banks, from corporate/muni bond markets, from repo market, from swap market … The interest rate they pay is calculated based on their credit score or credit rating. Essentially it boils down to default risk. For example, Treasuries have the lowest interest because these issuers have the maximum credit rating, even though the Greece government can default just as any issuer.

It's impossible to “guess” how much interest to charge a borrower. It has to be calculated. Therefore, Credit risk is an indispensable system for lending institutions. Not for traders. I feel traders generally look at market risk numbers after executing a trade. That's the all-important concept of VaR.

Credit risk (and market risk) data help traders get a better idea of their risk exposure, and may prompt them to set up hedges or trade less/more aggressively going forward. However, a trader could choose to trust her intuition more than the risk numbers.

Please correct my understanding. You can simply put “no” after any incorrect observation. If you can explain it's even better. Thanks.

guarantor and risk margin in FI trading – Citi context

Recently, FICC trading partners started using 3rd party guarantors. Think of guarantors as private clearing houses who provide integrity, reassurance against counterparty defaults.

Both buyer and seller could open margin accounts with the guarantor, and gain leverage. With leverage/margin comes default risk. As with futures exchange margin accounts, assets are marked to market nightly.

Guarantor takes, ideally, no risk and earns a fee. However, to maintain their zero-risk, they must carefully compute marks and issue margin calls.

At the core, the all-important marking process is basically asset valuation as-if-liquidating, and implemented using VaR. This is what (I guess) how it works — If VaR says “over next 10 days, in the 1% worst cases our smallest[1] loss is 3%”. For margin valuation purpose, we simply say equity is 3% lower than current value??

[1] Contrast conditional VAR. Largest loss is 100% loss

Q: What FICC products use guarantors?
A: Mostly fixed income, not much “CC”. Futures contracts usually need a guarantor (i guess the exchange itself — Futures always trade on exchanges). A lot of derivatives too.

Bond buyers can also benefit from a guarantor. Investor deposits an initial margin amount with the guarantor, buys the bond using the margin account, receives margin calls when valuation drops. If for 2 years she always meets the margin requirement, then she enjoys the leverage advantage — doesn’t need to put up the full capital. Guarantor basically lends money to her to finance her investment.

credit risk analysis in Singapore

(a blog post. Your comments are appreciated.)

To me, credit risk is all about default risk. There's a whole industry around the rating, measurement/analysis, monitoring, hedging and control of default risk. As such, Credit risk is relevant to both investment banking (buy/sell, underwriting, M&A etc) and commercial banking (ie lending), but how relevant? I feel credit risk is one of many components of market risk in investment-banking, but credit risk is absolutely central to commercial banking.

For the Singapore financial industry, commercial banking generates (much) larger revenue than i-banking, and is a far more important industry to the national economy. Most S'pore businesses need to borrow from banks.

I guess credit risk analysis is more important than market risk analysis in S'pore.

mkt-risk systems — front office or back office@@

Some say the risk manager's job begins when the trader's job is done. Robert said no. Better trading firms maintain real time risk system so risk can be assessed before execution. Most pre-trade calculations (pricing and quantity) are risk-bound. How much can you lend to anyone and at what rate and repayment frequency? What price do you buy/sell/bid/offer anything? But these are not the most well-known risk systems — consider the opening remark.

I believe the meanings of “market risk system” are wide ranging. Looks like the #1 core component is valuation, and other fundamental components include

* VaR
* scenario/stress testing — GSS risk

credit risk analytics important to trading desks@@

Now I realize the entire credit business (all those credit desks) in any trading firm operates around credit risk or “default risk” of individual issuing companies. I guess credit risk is at the center of all the securitization, CDS trading and straight buying ans selling of corporate bonds.

Am still unsure how precise a mathematician can be about calculating, predicting, measuring default probability. They probably take in tons of reported company financial data and feed them into some complex model.

Muni bonds have non-zero credit risk. In fact many muni bonds are below AAA rating. However, I don’t hear about credit risk analytics in the muni business. In fact, one high yield muni trader I know always prices his offers by hand, without any automatic calculation.

High yield means low rating, right? So credit risk is higher and should be factored into the pricing logic. The trader seems to go by gut feelings?

Q: I know credit risk modeling is used in consumer and corporate loan pricing, but is it also used in fixed income trading? In such areas as interest rate swap, credit default swap, corporate bond trading?
A (from a practitioner): yes

Q: people tell me market risk and credit risk are 2 main focus areas for any bank, but if a bank holds lots of credit instruments (high yield bonds, IRS, CDS securities…) then i feel market risk measurement must depend on credit risk measurement. Right?
A (from a practitioner): yes

VaR — estimating portfolio value if there’s a downtown


Let me rephrase my last question at Newark. Say our IBM position has current market value of $1m. We want to know the likelihood of losing more than 100k in the next 2 weeks. We can use IBM stock volatility stats to compute the likelihood to be… say 5.5%. Meaning we have a 5.5% chance of losing $100k or more in 2 weeks.

Now the portfolio holds SUN stocks too. Current MV = 1m of IBM + 2m of SUN = 3m. What's the likelihood of losing $300k+?

First assume SUN and IBM are unrelated. The volatility of the portfolio can be computed based on the 2 volatility stats. We can then derive the likelihood of losing $300k+ as … say, 6%. We have a 6% chance of losing 300k ore more in the next 10 days.

In reality IBM and SUN stocks are correlated. I guess portfolio volatility can be adjusted based on the covariance.

Option valuation volatility is very similar to stocks, i guess? Reason — Probability distribution curve is very similar?

Makes sense?

PnL attribution — first lesson

For any derivative risk engine, one of the most essential information
business wants to see everyday is PnL attribution. illustrates that a typical
report has
Column 1: PnL — This is the PnL as calculated outside of the PnL
Explained report
Column 2: PnL Explained — This is the sum of the explanatory columns
Column 3: PnL Unexplained — This is calculated as PnL – PnL
Explained (i.e., Column 1 – Column 2)
Column 4: Impact of Time (theta) — This is the PnL due to the change in time.
Column 5: Impact of Prices (delta) — This is the change in the value
of a portfolio due to changes in underlier price
Column 7: Impact of Volatility (vega) — This is the PnL due to
changes in (implied) volatility
Column xxxx: new trades, cancels, shows that usually
the attribution numbers (theta att, delta att, vega att…) add up to
be close to total unrealized PnL (Column 1). The mismatch is known as
PnL unexplained (Column 3)
A market maker should be delta-hedged (regulatory pressure) so delta
attribution is kept low — MM should stay unaffected by stormy
markets. See
Let’s take volatility attribution for example. has a nice hierarchical diagram showing
the breakdown of vol attribution.

risk and P/L importance in a trading desk

Outside margin/collateral management (Reg T etc), risk is fundamentally a nice-to-have to most trading system.

i feel the VaR measurement is rather subjective — a elastic yardstick. Many traders can distort mark to market.

I don’t think it’s a real time thing. When a trader executes trades, she has no time to evaluate risk. Trade execution system can automatically check compliance but not risk.

Now I feel a sell-side (and big buy-sides) is more serious about risk management.

business risks of a credit trading desk

See also CFA Reading 63

* credit default risk
* credit rating risk — credit rating of the issuer may drop, leading to a lower valuation
** if you short a bond but its credit rating improves, you short position devalues and you suffer an unrealized loss
* interest rate risk — rising IR hurting long positions; falling IR hurting short positions.
* volatility risk. I think if volatility decreases, option (call/put) valuation drops on your book.
* currency risk
* other market factors that lead to a deterioration in valuation. I feel interest rate and credit are the 2 root causes. Any other factors?

risk engine – eg of valuable finance IT domain knowledge

Some friends said that financial domain knowledge gained in financial IT projects over many years can often be learned in a few months by a new entrant.

However, Miao gave an interesting example to the contrary — risk-management. RM is knowledge-based, model-based, expert-system, with Artificial Intelligence. An experienced risk-management “analyst” builds and improves a mathematical model to produce a risk score/assessment based on a large number of inputs. Continuous improvement on the model takes years. The model must be implemented by developers. I think the developer can, if he so chooses, learn to understand the model and the rationales.

For a developer, this domain knowledge takes years. In my “dnlg framework”, this dnlg requires 1) jargons 2) math.

However, I think 90%-99% of the developers don’t have this exposure.

More importantly, this dnlg is not portable.


(except options@@) risk is nice-to-have to traders (锦上添花)

Credit risk, credit rating and credit analysis is essential in calculating interest rate, loan amount etc. I think this is a very old trade.

Here I limit myself to market risk or “trading risk”, not credit risk nor operational risk. Trading firms largely pay lip service to computerized risk data. In fact, the “risk management” concept is increasingly vague and all-encompassing .

Risk systems (mark to market, PnL, VaR…) is not in the “critical path” like pricing, market data, execution, trade booking, position management. People can often wait to read risk numbers after market close. I was told GS and some sophisticated trading houses have more real time risk data. However, GS could be lucky. Or GS could be profitable for other reasons but nevertheless want to publicize their risk system for political reasons.

In the extreme case, a trader can execute trades over the phone with a counter party, bypassing all computer systems.

Compared to traders, higher management cares more about risk. Some traders often don’t care about risk, even though real time risk numbers could be available. If that is the case, then it means risk numbers are less relevant to traders than other data such as position data or market data. However, in eq options, i was told the real time “sensitivities” of open positions are truly important to traders. Greeks and vol are the focus.

VaR is the single most important risk output to higher management.