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.

hazard rate – online resources

is decent —

Average failure rate is the fraction of the number of units that fail during an interval, divided by the number of units alive at the beginning of the interval. In the limit of smaller time intervals, the average failure rate measures the rate of failure in the next instant for those units surviving to time t, known as instantaneous failure rate.

is more mathematical.

http://www.omdec.com/articles/reliability/TimeToFailure.html has short list of jargon

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 http://www.jpmorgan.com/tss/General/Back_Testing_Value-at-Risk/1159398587967

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.