Calculating Risk Measure with VaR
The choice of adequate VAR is mainly essential as it mainly helpful in making sufficient investment decisions by calculating the overall risk from investment. The following choice needs to be conducted for identifying the adequate VAR (i) normal distribution based on a 252-day rolling window, (ii) the normal distribution with a variance estimated by the EWMA, and(iii) historical simulation based on a window of 252 days.
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2.1 Calculating VAR with normal distribution based on 252 rolling window:
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Particulars
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Qantas
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Fairfax Media
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Sample mean
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-0.08%
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-0.01%
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Sample’s standard deviation
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0.0198
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0.0196
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Confidence level
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5%
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99%
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Normal quartile
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2.3263
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2.3263
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VAR 1(day)
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-4.69%
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-4.56%
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2.2 Calculating normal distribution with EWMA:
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Items
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Value
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Value
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Sample’s mean
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0.01%
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-0.03%
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Sample variance
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0.05%
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0.05%
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Standard deviation
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2.24%
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2.30%
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Confidence level
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99%
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99%
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Normal quantile
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2.3263
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2.3263
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VaR (1 day)
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-0.10%
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-0.15%
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2.3 Calculating historical simulation based on 252 days:
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Particulars
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Qantas
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Fairfax Media
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Historical VAR
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-5.001%
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-4.520%
|
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Method
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Normal Distribution
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Normal Distribution
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Historical Simulation
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Volatility
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Rolling Window
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EWMA
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|
–
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|
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Number of observation
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252
|
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1260
|
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252
|
|
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VaR(1, 99%)
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-4.69%
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-0.10%
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-5.00%
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|
|
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Normal Var Qantas
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Normal Var Fairfax
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EWMA Qantas
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EWMA Fairx
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Historical Var Qantas
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Historical Var Fairfax
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Green: Exceedances ≤ 4
|
210
|
213
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0
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0
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195
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213
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Yellow: 5 ≤ Exceedances ≤ 9
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42
|
39
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0
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0
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56
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39
|
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Red: 10 ≥ Exceedances
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1
|
1
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253
|
253
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2
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1
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The above table mainly depicts the relevant Basel traffic lights, which could help in identifying the most adequate technique that could be used in discovering adequate VAR. From the overall evaluation, historical simulation is mainly depicted as the most viable approach, which could be used in detecting the overall VAR calculation.
From the overall VAR calculation the VAR(10,99%) mainly indicates that the VAR(.99%) * 10^(1/2) = -30.11%.
In addition, total portfolio value is 42,200 * -30.11% = -12,705.67. Therefore, there is a chance that the total value of the portfolio will mainly lose the 30.11% or 12,705.67 in investment.
4. Calculating the hedging strategy:
4.1 Beta calculation:
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Covariance of NAB and S&P200 = Standard deviation of S&P200 * Correlation between NAB and S&P200 * Standard deviation of NAB
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Particulars
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Qantas
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Fairfax Media
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|
correlation Qantas and S&P200
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0.399162361
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0.399162361
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Standard deviation
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0.022429941
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0.023046568
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Standard deviation S&P200
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0.009261863
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|
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covariance
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0.00829%
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0.00842%
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covariance
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0.00829%
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0.00852%
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Beta
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0.9667
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0.9932
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4.2 Number of future contract:
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|
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Qantas
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Fairfax Media
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Particulars
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Value
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Value
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Value of shares
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3.33
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0.89
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Number of shares
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10,000
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10,000
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Value of shares
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33,300
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8,900
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Beta
|
0.9667
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0.9932
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S&P
|
5665.79981
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|
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Points per $
|
25
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|
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Notion value of index
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141,645
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|
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Number of Future contracts
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0.23
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0.06
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Total number of futures needs to be sold
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0.29
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|
There for seeing the overall table 0.29 or 1 futures need to be hedged, as futures are mainly conducted on certain lots. Therefore, the S&P 200 futures will mainly sold in January 3, 2017 and then bought in January 16, 2017. This time horizon will mainly help in depicting the relevant profits and reduction in risk that might be conducted with the hedge.
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Particulars
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Value
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Value
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Shorting
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0.29
|
|
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Selling 1 contract at January 3, 2017
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5736.3999
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143,410.00
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Buying 1 contract at January 16, 2017
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5699.3999
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142,485.00
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Cost of holding
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42,200
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Profit on futures
|
925.00
|
|
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Net cost of NAB shares with futures contracts
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41,275.00
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|
Therefore, after using short hedge the overall profits attained from investment is mainly at 925. In addition, the overall use of hedge has mainly helped in reducing the systematic risk that might affect the overall value of portfolio.
4.3 VAR of the portfolio:
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Particulars
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Value
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Expected return of the portfolio
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0.0103%
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Expected return of Qantas
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0.0148%
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Expected return of Fairfax
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-0.0297%
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Expected return of the index
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0.0117%
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Covariance of Oantas and Fairfax
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0.0065%
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Covariance of Oantas and S&P 500
|
0.0002%
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Covariance of Fairfax and S&P 500
|
0.0002%
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Normal quantile at 99% confidence level
|
2.3263
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Var Qantas
|
-0.05001
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Var Fairfax
|
-0.04520
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Var S&P 200
|
0.0086%
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VaR (1, 99%)
|
-1.1073%
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VaR (10, 99%)
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-3.5015%
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The evaluation of the hedge mainly helps in reducing the cost of holding both Qantas and Fairfax Media. Thus, the overall opportunity for losing the investment is mainly calculated at -3.50515%. Where -3.50515% * 41,275.00 = -1445.25, will mainly be lost from the investment opportunity.
4.4 Valuation of Put option:
The overall 100 put options is mainly identified as the most viable investment instrument, which needs to be bought to hedge for the overall shares in both Qantas and Fairfax Media. This bout a 100 put needs to be both doe Qantas and Fairfax Media for hedging the overall portfolio. This option is mainly used in reducing the overall damage potential losses, which might be incurred from an investment.
4.5 Valuation of six step put option:
The annual volatility of both the stock are mainly depicted as follows.
The overall valuation of the put options is mainly identified, as the most viable method, which could help in reducing the overall loses from investment. From the overall evaluation share price of Qantas and Fairfax Media are depicted as follows.
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Particulars
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Qantas
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Fairfax Media
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Share price
|
3.33
|
0.89
|
|
Put
|
0.3751
|
0.1033
|
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Price rise
|
3.9789
|
1.0686
|
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Number of shares
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10,000
|
10,000
|
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Value from put
|
2,737.82
|
753.83
|
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Value from portfolio
|
39788.96196
|
10686.46232
|
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Portfolio value
|
46,983.78
|
|
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Actual portfolio value
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42,200.00
|
|
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Increment in Value
|
4,783.78
|
|
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Particulars
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Qantas
|
Fairfax Media
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|
Share price
|
3.33
|
0.89
|
|
Put
|
0.3751
|
0.1033
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|
Price decline
|
2.7869
|
0.7412
|
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Number of shares
|
10,000
|
10,000
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Value from put
|
(9,181.85)
|
(2,520.46)
|
|
Value from portfolio
|
27869.287
|
7412.181658
|
|
Portfolio value
|
46,983.78
|
|
|
Actual portfolio value
|
42,200.00
|
|
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Decline in value
|
4,783.78
|
|
From the above two table the entire relevant decline in value and increment in value due to the price action of both Qantas and Fairfax Media could effectively be evaluated. The use of option stock could eventually help the company in making adequate investment decisions. Thus, it could be evaluated that decline and increment in share value mainly increased the overall portfolio be 4783.78.
4.5 Profit diagram:
The above figure mainly depicts the relevant payoff, which could be conducted by an investment option. The overall portfolio value mainly use adequate investment options, which could help in generating higher revenue from investment. In addition, the overall profits of the portfolio mainly increased after being stagnant for some time and attaining breakeven point. Therefore, the loss in premium is could be generated from the overall income that is generated from investment.
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