Question

In: Finance

.p2(2) VaR (Value at Risk) is defined as ///////////////////////////////////// In words: The maximum loss over a...

.p2(2)

VaR (Value at Risk) is defined as

/////////////////////////////////////

In words: The maximum loss over a predetermined period with a confidence interval.

formula : VaR=position * z * sigma

where position : the value of your portfolio

z : depends on the confidence interval

=norm.inv(0.01,0,1)=-2.326347874 # for 99%

=norm.inv(0.05,0,1)=-1.644853627 # for 95%

sigma : the period standard deviation

Assume that we have 100 shares of IBM stocks, 200 shares of

Wal-Mart and 300 shares of Citi Group (ticker is C). What is the

VaR of our portfolio within next 10 days with a confidence

interval of 99%?

Solutions

Expert Solution

Answer )

Data of Said shares IBM ,WAL-MArt and Citi group for return is takenfrom yahoo finance, fromlast ten days of trading till today (7th May 2018)

Price of the shares are given below used in VAR calculation

Citigroup Inc.(c) WTM IBM
7-May-18 68.54 85.77 143.67
4-May-18 67.94 87.53 143.91
3-May-18 67.94 86.23 141.99
2-May-18 67.99 86.34 142.45
1-May-18 68.25 87.41 145
30-Apr-18 68.27 88.46 144.96
27-Apr-18 68.99 87.29 146.48
26-Apr-18 69.18 87.94 146.72
25-Apr-18 69.36 87.17 145.94
24-Apr-18 69.12 86.53 145.56

Calculation :

Porfolio Detail at Start Data( as on 24 Apr-18)
$-value weights No of share Price OF share
IBM 14,556 0.276741 100 145.56
WALMart 17,306 0.329024 200 86.53
Citi group 20,736 0.394236 300 69.12
Level of Certainty 0.99
Number of observations 9
Date Prices Returns Portfolio Ascend. No of VaR VaR
(yyymmdd) Asset 1 Asset 2 Asset 3 Asset 1 Asset 2 Asset 3 change ordered obs. historic
24-Apr-18 145.56 86.53 69.12
25-Apr-18 145.94 87.17 69.36 0.002607206 0.00737 0.00347 0.004513 -0.21765 1 -11447.9
26-Apr-18 146.72 87.94 69.18 0.00533043 0.00879 -0.0026 0.003344 -0.08345 2 -4389.11
27-Apr-18 146.48 87.29 68.99 -0.001637108 -0.0074 -0.0028 -0.00398 -0.04223 3 -2221.3
30-Apr-18 144.96 88.46 68.27 -0.010431058 0.01331 -0.0105 -0.00264 -0.04213 4 -2216.17
1-May-18 145 87.41 68.25 0.0002759 -0.0119 -0.0003 -0.00397 -0.04075 5 -2143.51
2-May-18 142.45 86.34 67.99 -0.017742681 -0.0123 -0.0038 -0.01047 -0.04038 6 -2124.09
3-May-18 141.99 86.23 67.94 -0.003234428 -0.0013 -0.0007 -0.0016 -0.03986 7 -2096.36
4-May-18 143.91 87.53 67.94 0.013431472 0.01496 0 0.00864 -0.03757 8 -1975.97
7-May-18 143.67 85.77 68.54 -0.001669101 -0.0203 0.00879 -0.00368 -0.03497 9 -1839.29
Assets Value Std. Dev. VaR Abs. VaR
of asset
1 14,556 0.8918% 302 302
2 17,306 1.2687% 511 511
3 20,736 0.5256% 254 254

FInally Summary

Level of Certain. =   0.99
Normal dist. Value 2.326
Worse Case VaR = 1,066
Div. VaR = 697

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