End of Horizon VaR Intra-Horizon VaR

Source: http://www.slideshare.net/amithetfield/maxvar-slides-v0

General Spreadsheet for Calculation of VaR and MaxVaR with Drift5%

Calculation of VaR Calculation of MaxVaR

Mu 12.30% Mu 12.30%Sigma 19.48% Sigma 19.48%T 1 T 1 Probloss = VaR-IProb 5.00% Prob 5.00% #VALUE!m 0.1040 m 0.1040 Probloss = VaRm*T 0.1040 m*T 0.1040 #VALUE!Sigma*sqrt(T) 0.1948 Sigma*sqrt(T) 0.1948VaR -21.63% phi1 0.0193 #VALUE!VaR -21.63% exp(2mz/Sigma^2) 0.1940Via VBA #VALUE! phi2 0.1584

MaxVaR -29.90%Via VBA #VALUE!

Prob< VaR 5.00% Prob< MaxVaR #VALUE! #VALUE!ES or CVaR -29.77% ES-I or CVaR-I #VALUE!

General Spreadsheet for Calculation of VaR and MaxVaR without Drift5%

Calculation of VaR Calculation of MaxVaR

Mu 12.30% Mu 12.30%Sigma 19.48% Sigma 19.48%T 1 T 1 Probloss = VaR-IProb 5.00% Prob 5.00% #VALUE!m 0.1230 m 0.1230 Probloss = VaRm*T 0.1230 m*T 0.1230 #VALUE!Sigma*sqrt(T) 0.1948 Sigma*sqrt(T) 0.1948VaR -19.73% phi1 0.0181 #VALUE!VaR -19.73% exp(2mz/Sigma^2) 0.1575Via VBA #VALUE! phi2 0.2027

MaxVaR -28.50%Via VBA #VALUE!

Prob< VaR 5.00% Prob< MaxVaR #VALUE! #VALUE!ES or CVaR -27.87% ES-I or CVaR-I #VALUE!

cumulative standard distribution

Intra-Horizon Value at Risk versus End of Horizon Value at Risk (Normal)

GivenMu ( Mean ) 12.30% Loss Threshold -10%Sigma ( Vol Ann. ) 19.48%CL 95.00%

Time in Years 1 2 3 4 5 6 7 8 9 10End of Horizon VaR #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!End of Horizon Expected Shortfall (CVaR) without Drift -27.87% -32.21% -32.68% -31.15% -28.33% -24.60% -20.19% -15.23% -9.82% -4.04%Intra-Horizon VaR-I #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!Intra-Horizon Expected Shortfall (CVaR-I) without Drift #VALUE! -44.46% -49.70% -53.07% -55.36% -56.97% -58.12% -58.96% -59.58% -60.04%End of Horizon Loss Probability #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!Intra-Horizon Loss Probability #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!Joint Probability #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!Intra-Horizon Prob Loss > VaR #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!Intra-Horizon Prob Loss > -10.0% #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

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Intra-Horizon Value at Risk versus End of Horizon Value at Risk (GBM )

GivenMu ( Mean ) 12.30% Loss Threshold -10%Sigma ( Vol Ann. ) 19.48%CL 95.00%

Time in Years 1 2 3 4 5 6 7 8 9 10End of Horizon VaR #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!End of Horizon Expected Shortfall (CVaR) with Drift -29.77% -36.01% -38.37% -38.73% -37.81% -35.98% -33.46% -30.40% -26.89% -23.00%Intra-Horizon VaR-I #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!Intra-Horizon Expected Shortfall (CVaR-I) with Drift #VALUE! -47.28% -53.67% -58.06% -61.25% -63.64% -65.47% -66.89% -68.00% -68.89%End of Horizon Loss Probability #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!Intra-Horizon Loss Probability #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!Joint Probability #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!Intra-Horizon Prob Loss > VaR #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!Intra-Horizon Prob Loss > -10% #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

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Google Search Number of references"Intra Horizon VaR" 10 Intra-Horizon Risk"intra horizon value at risk" 1 VaR-I"within horizon VaR" 3"within horizon Value at Risk" 4 Within Horizon VaR"MaxVaR" "value at risk" 433 MaxVaR"Continuous Value at Risk" 54 Continuous VaR

Boudoukh, Jacob (Kobi), Stanton, Richard H., Richardson, Matthew P. and Whitelaw, Robert F., MaxVaR: Long Horizon Value at Risk in a Mark-to-Market Environment (March 2004). Available at SSRN: http://ssrn.com/abstract=520805 or http://dx.doi.org/10.2139/ssrn.520805Bhattacharyya, Malay, Misra, Nityanand and Kodase, Bharat (December 2009). MaxVaR for non-normal and heteroskedastic returns, Quantitative Finance, Vol. 9, No. 8, 925 — 935.Damiano Rossello, MaxVaR with non-Gaussian distributed returns, European Journal of Operational Research, 2008, vol. 189, issue 1, pages 159-171Kritzman, Mark and Rich, Don R., The Mismeasurement of Risk. Financial Analysts Journal, Vol. 58, No. 3, May/June 2002. Available at SSRN: http://ssrn.com/abstract=316584Yen, Simon H., Lin, Shao-chieh, Re-examining the Contributions of Intra-Horizon Risk Measures

Within this area, RiskLab-Madrid has developed a software product to measure the VaR (Value at Risk) and MaxVaR which uses extreme value theory (EVT). This product is already being used in Santander Financial Securities.The Windham Portfolio AdvisorState StreetNorthfield

http://www.youtube.com/watch?v=HjylDBgJgl4http://www.northinfo.com/documents/393.pdfhttp://www.finance.nsysu.edu.tw/SFM/program/FullPaper/103-268144970.pdfhttp://www.towerswatson.com/assets/pdf/6534/TW-EU-2012-26014_The_wrong_type_of_snow_update.pdfhttp://www.slideshare.net/amithetfield/maxvar-slides-v0

Boudoukh, Jacob (Kobi), Stanton, Richard H., Richardson, Matthew P. and Whitelaw, Robert F., MaxVaR: Long Horizon Value at Risk in a Mark-to-Market Environment (March 2004). Available at SSRN: http://ssrn.com/abstract=520805 or http://dx.doi.org/10.2139/ssrn.520805Bhattacharyya, Malay, Misra, Nityanand and Kodase, Bharat (December 2009). MaxVaR for non-normal and heteroskedastic returns, Quantitative Finance, Vol. 9, No. 8, 925 — 935.Damiano Rossello, MaxVaR with non-Gaussian distributed returns, European Journal of Operational Research, 2008, vol. 189, issue 1, pages 159-171Kritzman, Mark and Rich, Don R., The Mismeasurement of Risk. Financial Analysts Journal, Vol. 58, No. 3, May/June 2002. Available at SSRN: http://ssrn.com/abstract=316584Yen, Simon H., Lin, Shao-chieh, Re-examining the Contributions of Intra-Horizon Risk Measures

Within this area, RiskLab-Madrid has developed a software product to measure the VaR (Value at Risk) and MaxVaR which uses extreme value theory (EVT). This product is already being used in Santander Financial Securities.

http://www.towerswatson.com/assets/pdf/6534/TW-EU-2012-26014_The_wrong_type_of_snow_update.pdf

http://www.finance.nsysu.edu.tw/SFM/program/FullPaper/103-268144970.pdf

Boudoukh, Jacob (Kobi), Stanton, Richard H., Richardson, Matthew P. and Whitelaw, Robert F., MaxVaR: Long Horizon Value at Risk in a Mark-to-Market Environment (March 2004). Available at SSRN: http://ssrn.com/abstract=520805 or http://dx.doi.org/10.2139/ssrn.520805Bhattacharyya, Malay, Misra, Nityanand and Kodase, Bharat (December 2009). MaxVaR for non-normal and heteroskedastic returns, Quantitative Finance, Vol. 9, No. 8, 925 — 935.

Within this area, RiskLab-Madrid has developed a software product to measure the VaR (Value at Risk) and MaxVaR which uses extreme value theory (EVT). This product is already being used in Santander Financial Securities.