Measuring change to our trading book
and VaR topics
• On a trading desk we are interested in how
buying/selling affects our book
• Change to:
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Total position
Position of each bond
Risk profile of each bond or group of bonds
Risk profile of the book (Risk, LGD)
Trading activity
VaR
How is VaR applied/validated?
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Used to set “Limits”
Industry standard component to regulatory capital calculation
Multipliers - stress testing or just multiply VaR.
Validated by comparing to “clean” PnL (PnL due to market moves vs. fee based pnl)
We “backtest” by comparing to actual “clean” PnL
PnL can be attributed to 2 variables:
1. Spread (credit spread)
2. Yield (treasury rate)
Good VaR quote:
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“One to three times VaR are normal occurrences. You expect periodic VaR breaks. The loss distribution typically has fat
tails, and you might get more than one break in a short period of time. … So an institution that can't deal with three times
VaR losses as routine events probably won't survive long enough to put a VaR system in place. Three to ten times VaR is
the range for stress testing. Institutions should be confident they have examined all the foreseeable events that will cause
losses in this range, and are prepared to survive them. …Foreseeable events should not cause losses beyond ten times
VaR. If they do they should be hedged or insured, or the business plan should be changed to avoid them, or VaR should
be increased. It's hard to run a business if foreseeable losses are orders of magnitude larger than very large everyday
losses. It's hard to plan for these events, because they are out of scale with daily experience. Of course there will be
unforeseeable losses more than ten times VaR, but it's pointless to anticipate them, you can't know much about them and
it results in needless worrying. Better to hope that the discipline of preparing for all foreseeable three-to-ten times VaR
losses will improve chances for surviving the unforeseen and larger losses that inevitably occur. A risk manager has two
jobs: make people take more risk the 99% of the time it is safe to do so, and survive the other 1% of the time. VaR is the
border."
How is VaR applied? Cont…
In April 1995, the Basle Committee came forth with another set of proposals, which was
nothing short of a regulatory innovation: the Internal Model approach. For the first
time banks would be allowed to use their own risk management models to determine
their VaR and with it their capital requirement. This capital requirement follows simply
by multiplying the VaR by an add-on factor. This add-on factor, sometimes called the
“hysteria factor”, may vary between three and four, depending on the accuracy of the
bank model in the past. The hysteria factor is intended to provide additional protection
against environments that are much less stable than historical data would lead to
believe.
As a result of above banks set about justifying their risk models to regulators
And of course they were motivated to reduce their regulatory capital 
Problems with VaR
David Einhorn and Aaron Brown debated VaR in theGlobal Association
of Risk Professionals Review[14][23]
Einhorn compared VaR to an:
“Airbag that works all the time, except when you have a car
accident”
He further charged that VaR:
1. Led to excessive risk-taking and leverage at financial institutions
2. Focused on the manageable risks near the center of the distribution
and ignored the tails
3. Created an incentive to take excessive but remote risks.
4. Was potentially catastrophic when its use creates a false sense of
security among senior executives and watchdogs.
Credit Risk Component
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Our credit risk measure is LGD “Loss Given Default”
For detailed coverage of LGD refer to online paper:
– Basel Committee on Banking Supervision “An explanatory Note on the Basel
II IRB Risk Weight Functions July 2005
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Expected Loss = Probability of Default * Loss Given Default
Probability of Default - per rating grade, which gives the average
percentage of obligors that default in this rating grade in the course of
one year
Loss Given Default - per rating grade, which gives the percentage of
exposure the bank might lose in case the borrower defaults
– EL = PD * LGD
– LGD = EL / PD
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We will measure LGD’s before and after ratings downgrades/upgrades!
Regulatory Capital
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Capital is needed to cover the risks of peak losses, and therefore it has a loss
absorbing function. (Black Jack analogy)
Good quote:
“The worst case one could imagine would be that banks lose their entire credit portfolio in a
given year. This event, though, is highly unlikely, and holding capital against it would be
economically inefficient. Banks have an incentive to minimize the capital they hold,
because reducing capital frees up economic resources that can be directed to profitable
investments. On the other hand, the less capital a bank holds, the greater is the
likelihood that it will not be able to meet its own debt obligations, i.e., that losses in a
given year will not be covered by profit plus available capital, and that the bank will
become insolvent. Thus banks and their supervisors must carefully balance the risks
and rewards of holding capital.”
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How to manage it?
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Pricing of Credit Exposures (add a “vig”)
“Provisioning” (putting reserves from revenues aside)
Hedging with “protection” (insurance) - e.g., Credit Default Swaps
Deliverables for next week
• Measure change of position intra-day
– This will allow us to capture “new business” or trading
• Two trading book files:
– Opening position
– Closing position
• Calculate total position change – one integer number
• Our “position” in the bond is the Amount of the bond
• Calculate total LGD change - one integer number
• Results for next week:
– 2 numbers using two new trading book files on site
– Single client call to your server
– Performance measured on total round trip time of successive
calls to the server – “real time” as measured by the client:
– $time run.sh
• Once we have the ability to measure daily change we
will add the VaR measure (due in two weeks)
VaR Implementation Notes
• Load historical data file – one per security in the
trading book
• You can hack at SBB_io .h/.cc
• Build a separate “PnL Vector” for each bond
• Assume all historical files will live in a sub dir “./var”.
• For each SecID in our book(s), look up a file named
“SecID.txt” in that sub dir
• For ex., ./var/SBB_001.txt
• Once you have a vector for each bond:
• Add yield change to current yield to get new_price
• The base_price is the price in the end-of-day file
• daily_price_change = new_price - base_price
• pnl_change = daily_price_change * Amount
VaR Implementation Notes...
• Now that we have vectors for each bond how do we get book
measure?
• Add up individual bond vectors to get a total book vector
• This method captures correlation between financial instruments
• Ascending sort gives you largest negative PnL
• Largest negative is the worst case loss
• Our confidence interval and sample size will determine our VaR
• The final step once you have a book PnL vector is which element
to point to ...
• There will be at least 100 daily changes
• 99% confidence interval means your worst daily change is your
VaR if 100 PnLs
• Amount to multiply is either long or short (+ or -)
• This means that a short position is a gain on a negative PnL day
• Refer to : var_example.xls