FIN415 Risk Management: Quantitative Analysis of VaR, and BASEL II

This assignment provides a comprehensive analysis of risk management principles, focusing on Value at Risk (VaR), expected shortfall, and the Basel I and II accords. It includes calculations of VaR and expected shortfall for individual investments and portfolios, demonstrating the subadditivity condition. The assignment also explores the use of EWMA and GARCH models for estimating daily volatility, and calculates one-month 99% VaR with and without power law application. Furthermore, it assesses capital requirements under Basel I for various financial instruments and determines risk-weighted assets for credit risk under the Basel II advanced IRB approach. The net stable funding ratio and the calculation of extra deposits needed are also addressed, along with the bid-offer spread for a trader. Desklib offers a wealth of similar solved assignments and study resources for students.

Running head: RISK MANAGEMENT
Risk Management
Name of the Student:
Name of the University:
Authors Note:

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Table of Contents
9.1:..............................................................................................................................................3
a) VaR for one of the investments when confidence level is 95%:...........................................3
b) Expected shortfall when confidence level of 95%:...............................................................3
c) VaR for the portfolio consisting of two investments with confidence level of 95%:............3
d) Expected shortfall for a portfolio consisting of the two investments when the confidence
level is 95%:...............................................................................................................................4
e) Indicating whether VaR does not satisfy the subadditivity condition whereas expected
shortfall does:.............................................................................................................................4
9.2: Indicating the better estimate of VaR that takes account of the autocorrelation:...............4
10.1: Estimating daily volatility using both approaches............................................................5
10.2:............................................................................................................................................5
a) The EWMA Model:...............................................................................................................5
b) The GARCH (1,1) Model:.....................................................................................................6
10.3:............................................................................................................................................6
a) Indicating the one-month 99% VaR of the portfolio:............................................................6
b) Indicating the one-month 99% VaR if power law applies:....................................................6
12.1:............................................................................................................................................7
a) Capital required under BASEL 1, two-year forward contract:..............................................7
b) Capital required under BASEL 1, long position:...................................................................7
c) Capital required under BASEL 1, two-year swap involving oil and depicting the impact if
netting amendment implies:.......................................................................................................7
12.2:............................................................................................................................................8
a) Transaction with two-year interest rate swap:.......................................................................8
b) Transaction with nine-month foreign exchange forward contract:........................................8

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c) Transaction with long position in a six-month option:..........................................................9
12.3: Indicating total risk-weighted assets for credit risk under the Basel II advanced IRB
approach:..................................................................................................................................10
13.1:..........................................................................................................................................10
a) Depicting about net stable funding ratio:.............................................................................10
b) Indicating what extra deposits needs to be raised:...............................................................11
21.1: Indicating the bid-offer spread for the trader..................................................................11
Bibliography:............................................................................................................................12

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9.1:
a) VaR for one of the investments when confidence level is 95%:
From the evaluation it could be understood that a loss of $1 million is extends from
94% to 96%, which indicates the 95% VaR is at the levels of $1 million.
b) Expected shortfall when confidence level of 95%:
Particulars Value
Loss percentage 20% of 1 million
Loss percentage 80% of 10 million
Expected loss (0.20×$1 million) + 0.80×$10 million)
Expected loss $8.2 million
c) VaR for the portfolio consisting of two investments with confidence level of 95%:
Particulars Value
Chance of loss for 20 million 0.04 × 0.04 = 0.0016
Chance of loss for 11 million 2×0.04 × 0.02 = 0.0016
Chance of loss for 9 million 2×0.04 × 0.94 = 0.0752
Chance of loss for 2 million 0.02 × 0.02 = 0.0004
Chance of loss 2×0.2 × 0.94 = 0.0376
Loss is at the level 0.94 ×0.94 = 0.8836
Therefore 95% VaR $9 million

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d) Expected shortfall for a portfolio consisting of the two investments when the
confidence level is 95%:
Particulars Value
Chance of loss for 20 million 0.0016/0.05 = 0.032
Chance of loss for 11 million 0.0016/0.05 = 0.032
Chance of loss for 9 million 0.0468/0.05 = 0.936
The expected loss $9.416 million
e) Indicating whether VaR does not satisfy the subadditivity condition whereas expected
shortfall does:
The overall VaR does not satisfy the subadditivity condition, as 9 > 1 + 1, while the
shortfall is at 9.416 < 8.2 + 8.2.
9.2: Indicating the better estimate of VaR that takes account of the autocorrelation:
There is relevant correct multiplier for the variance, which comprises of the following
equation.
10 + (2×9×0.12) + (2×8×0.122) + (2×7×0.123) +
(2×6×0.124) + (2×5×0.125) + (2×4×0.126) + (2×3×0.127)
+ (2×2×0.128) + (2×1×0.129) = 12.417
Estimating the increment in VaR with the following equation:
2× √12.417/10 = 2.229

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10.1: Estimating daily volatility using both approaches
Week Closing stock price Price relative Daliy relative U2
1 30.20000
2 32.00000 5.96% 0.05789 0.00335
3 31.10000 -2.81% (0.02853) 0.00081
4 30.10000 -3.22% (0.03268) 0.00107
5 30.20000 0.33% 0.00332 0.00001
6 30.30000 0.33% 0.00331 0.00001
7 30.60000 0.99% 0.00985 0.00010
8 30.90000 0.98% 0.00976 0.00010
9 30.50000 -1.29% (0.01303) 0.00017
10 31.10000 1.97% 0.01948 0.00038
11 31.30000 0.64% 0.00641 0.00004
12 30.80000 -1.60% (0.01610) 0.00026
13 30.30000 -1.62% (0.01637) 0.00027
14 29.90000 -1.32% (0.01329) 0.00018
15 29.80000 -0.33% (0.00335) 0.00001
Standard deviation 1 2.20% (0.01333) 0.00675
Standard deviation 2 2.30%
10.2:
a) The EWMA Model:
The percentage change in price is mainly calculated at the level of -0.00667 (-2/300 =
-0.00667).
With the use of EWMA Model the variance can be calculated from the below
equation
0.94 × 0.0132 + 0.06 × 0.006672 = 0.00016153
√0.00016153 = 0.1271 or 1.271%

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b) The GARCH (1,1) Model:
The percentage change in price is mainly calculated at the level of -0.00667 (-2/300 =
-0.00667).
With the use of GARCH Model the variance can be calculated from the below
equation
0.000002 + 0.94 × 0.0132 + 0.04 × 0.006672 = 0.00016264
√0.00016264 = 0.1275 or 1.275%
10.3:
a) Indicating the one-month 99% VaR of the portfolio:
The calculation is based on 99% VaR for the portfolio, which is at depicted from the
overall equation.
10 × N−1 (0.99)
N−1 (0.95) =14.14∨$ 14.14 million
b) Indicating the one-month 99% VaR if power law applies:
The probability of loss being greater is depicted in the following equation.
α = 3, K×10-3 = 0.05. where K = 50
50x3 = 0.01 or x = (5000)1/3 = $17.10 million

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12.1:
a) Capital required under BASEL 1, two-year forward contract:
Particulars Value
Current worth 2,000,000
Currency worth 50,000,000
Capital required 4,500,000
b) Capital required under BASEL 1, long position:
Particulars Value
Current worth 4,000,000
Currency worth 20,000,000
Capital required 5,200,000
c) Capital required under BASEL 1, two-year swap involving oil and depicting the
impact if netting amendment implies:
Particulars Value
Current worth -
Currency worth 30,000,000
Capital required 3,600,000
Particulars Value

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Total credit amount 13,300,000
Risk weight 266,000.00
Capital required 21,280.00
Hence, the use of netting applies the current exposure within millions of dollars 2+4-5
= 1. Therefore, with the NRR is mainly at levels of 1/6 = 0.1667, where the credit equivalent
amount is in million of dollars.
1+ (0.4+0.6×0.1667) × (0.05×50+0.06×20+0.12×30) = 4.65
The risk weighted amount is at the levels of 0.2×4.65 = 0.93
The capital required 0.08×0.93 = 0.0744, which is reduces the capital by 65%.
12.2:
a) Transaction with two-year interest rate swap:
Particulars Value
Current worth 3,000,000
Currency worth 100,000,000
Capital required 3,500,000
b) Transaction with nine-month foreign exchange forward contract:
Particulars Value
Current worth -
Currency worth 150,000,000

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Capital required 1,500,000
c) Transaction with long position in a six-month option:
Particulars Value
Current worth 7,000,000
Currency worth 50,000,000
Capital required 7,500,000
The total credit amount is mainly at the levels of 3.5+1.5+7.5 = 12,500,000. The risk
assessment is mainly at the level of 50%, which makes the risk weighted amount to
6,250,000, while the capital required is calculated at the level of 0.08 * 6,250,000 = 500,000.
However, if netting applies then the values can be changed aggressively, where total
credit amount is at the levels of 3-5+7 = 5,000,000.
Therefore, with the NRR is mainly at levels of 5/10 = 0.5, where the credit equivalent
amount is in millions of dollars.
5+ (0.4+0.6×0.5) × (0.005×100+0.01×150+0.01×50) = 6.75
The risk weight is 50%, which makes the value at the levels of 3.375, while the equation
stands at the level of 0.08×3.375 = 270,000
Hence, the capital is reduced by 46%.

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12.3: Indicating total risk-weighted assets for credit risk under the Basel II advanced
IRB approach:
Basel II advance IRB approach equation is as follows.
= 0.12[1 + e−50×0.003 ] = 0.2233
b = [0.11852 − 0.05478 × ln(0.003)]2 = 0.1907
1+(3.0−2.5)× 0.1907
1−1.5 ×0.1907 =1.5 3
WCDR=N × N−1 ¿ ¿
Hence, the RWA is at the levels of
500 × 0.6 × (0.0720 − 0.003) × 1.53 × 12.5 = 397.13
Therefore, under the Basel I equation the overall capital required is at the levels of $
40 million.
13.1:
a) Depicting about net stable funding ratio:
Particulars Value
Stable Funding 25 0.9 15 0.8  44 0.5 161.0
Stable Funding 72.5
Required Stable Funding 3 0  5 0.05  4 0.5 18 0.65  60 0.85
101.0
Required Stable Funding 74.95
Net Stable Funding ratio 72.5 / 74.95 = 0.967 or 96.7%

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b) Indicating what extra deposits needs to be raised:
Particulars Value
Funds for retail deposit 72.5+0.9X = 74.95+0.05X
Funds for retail deposit 0.85X=2.45
Funds for retail deposit 2.88
21.1: Indicating the bid-offer spread for the trader
The overall proportional bid is mainly at the levels of 10/55 = 0.1818 and 10/30 =
0.333. The position values are mainly at the levels of $5,500 and $6,000 with the bid offers of
the portfolio. The portfolio calculation is mainly depicted as follows.
0.5×0.1818×5,500+0.5×0.3333×6,000 =1,500 or $1,500
The worst-case scenario indicates the unwinding value calculations.
0.5× (0.1818+2.326×0.054545) ×5,500+0.5× (0.3333+2.326×0.1) ×6,000 =2547 or $2,547