In: Finance
.p2(2)
VaR (Value at Risk) is defined as
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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%?
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 |