1. EF5603
Implementation Of
Value-at-Risk
In Financial Institutions
Dr. LAM Yat-fai (林日辉博士)
Doctor of Business Administration (Finance)
CFA, CAIA, FRM, PRM, MCSE, MCNE
PRMIA Award of Merit 2005
E-mail: quanrisk@gmail.com
2:00 pm to 3:15 pm
Saturday
1 November 2008
Big question
How to implement a real Value-at-Risk
system in my bank?
Expected return vs risk
What is the expected return of my portfolio?
The single most important number for
investments
What is the risk of my portfolio?
Does the expected return justify the risk to be
taken?
Historical return vs expected return
Historical return
Value Value
turn Today
Re 100%
Expected return
Adjusted historical return
CAPM
Discounted future cash flows
P/E multiples
0
0 ×
−
=
Value

2. Risk measures
Equities – volatility, Beta
Debts – duration, convexity
Options – Delta, Gamma, Vega
Different financial instruments have different
risk measures
How many risk measures you can read in one
day?
Single universal risk measure
What is the risk of a bank’s entire trading
portfolio over the next 24 hours?
Want a single universal measure which can
incorporate the risks of all financial
instruments, taking into account netting,
correlation, margining and hedging
Worst scenario
Long position
lose all you have on hand
Short position
unlimited loss
Accumulator
half of a company
the life
Value-at-risk
1-day value-at-risk at 95% confidence level
The maximum loss that will occur tomorrow, if
the worst 5% situations are not considered
The minimum loss that will occur tomorrow, if
the only worst 5% situations are considered

3. Value-at-Risk
1-day
95% confidence level
5%
VaR
95%
VaR Average(S )-Percentile(S , %) % 5 95 1 1 =
Variance-covariance method
=Σ=
V m S
m S
= =
w
1 1
w
2 2
w
3 2


= ⋅ ⋅
Q Correl Q
σ
σ

σ ρ ρ ρ
...
12 13 1
2
1
ρ σ
2
21 2
. ... .
ρ σ
. ... .
: : : ... :
n
ρ σ
σ
σ
σ
σ
2
95% 0
2
1
2
31 3
2
0
1
1
0
1.65
. . ...
:
1,2,3,...
VaR V
Correl
w
Q
k n
V
w
T
n n
n
k
k
n
k
k k
≈

     

     

=
     

     

=
Historical simulation
k ,
j
=
= ⋅
Σ=
−
= ⋅ ⋅
,0
i ,
j
S
i j
, 1
For j to
S S
i j i
S

 
Portfolio Share S
i k k
S
S

 

−
( ) ( ,5%)
1 500
, ,0
95%

1 , 1
= −
i i
n
k k j
VaR Average Portfolio Percentile Portfolio
Monte Carlo simulation
Parameters 1,000 simulations
,
( )
( )
S
k i
S
=
μ μ
Average
=
k , day k ,
i
σ μ
k , day k ,
i
ρ ρ ρ
11 12 13
ρ ρ ρ
21 22 23
ρ ρ ρ
31 32 33

=
= −
k k day
k day
k k day
k i
k i
Mean
SD
Stdev
,
2
,
,
, 1
,
2
Correl
ln
σ
σ
μ
μ
=

  

  

=
−
=
For i 1 to 1000
=
x MultNormal(n,Mean,SD,CorrMatrix)
( )
( )
=
S S x
i j i j
Σ=
= ⋅
Portfolio Share S
i j i j
( ) ( ,5%)
exp
99%
1
,
, 0 ,
= −
i i
n
j
i,j
VaR Average Portfolio Percentile Portfolio

4. Components of industry VaR system
Market data provider
Pricing engine
VaR computation
Market data
Latest market quotes
Statistics and financial time series
Equity – volatility, beta, correlation
Interest rate – Hibor, Libor
Interpolation
Volatility surface
Interpolated interest rate
Pricing engine
To calculate tomorrow’s price of stocks, derivatives,
fixed income and credit instruments
Stock prices with CAPM and Beta
Derivative prices with Delta-Gamma-Vega
approximation
Fixed income prices with
cash flow mapping
duration and convexity approximation
Major industry VaR solutions
VaR system Market data Pricing
1. RiskMetrics Reuters RiskMetrics
2. Algorithmics Bloomberg NumeriX
3. Konto Reuters NumeriX

5. Use of VaR in banks
- internal risk management
Single VaR number provides little information
comparison – by day, trader, desk
Component VaR
who, what contribute the most/least VaR
Limit setting
a limit to be violated once a month on average
Risk adjusted return
return attributed to skill vs risk
Rouge trader detection
difficult to manipulate both return and risk
Regulatory requirement
10-day 99% VaR x 3
CA-G-3 “Use of internal models approach to
calculate market risk”
http://www.info.gov.hk/hkma/eng/bank/spma/
attach/CA-G-3.pdf
Capital reporting
General market risk
Interest rates – treasury yield curves
Equities – equity indices
FX – exchange rates
Commodities – commodity prices
Specific risk
Credit quality – bond prices
Profit and loss – equity prices
Incremental risk – being proposed by BIS
Limitations of VaR
VaR makes a lot of approximations
as good as its model assumptions
VaR gives an order of magnitude, not an accurate number
VaR does not tell anything beyond the confidence level
to be complemented with stress test
No single VaR system can cover all financial instruments
VaR system costs from HKD 0 to HKD million
http://www.riskgrades.com
VaR does not work well with credit derivatives
sub-additively
expected short fall – a even better risk measure

6. A low cost VaR solution
- Bloomberg portfolio manager
Bloomberg portfolio uploader
Bloomberg portfolio analytics
Equities, fixed income, warrants
Bloomberg VaR
Bloomberg stress test
Bloomberg scenario analysis
Bloomberg portfolio manager
Bloomberg portfolio analytics Bloomberg VaR

7. Black-Scholes formulas
= − −
c S N d K rT N d
( ) exp( ) ( )
0 1 2
= − − − −
p K rT N d S N d
∫−∞
2
r T
2
r T
S
S
1
= −
= −
+ −
=
+ +
=
x
dt
t
N x
d T
T
K
d
T
K
d
)
2
exp(
2
( )
)
2
ln( ) (
)
2
ln( ) (
where
exp( ) ( ) ( )
2
1
0
2
0
1
2 0 1
π
σ
σ
σ
σ
σ
Questions and Answers