# “We are X percent sure that we will not lose more than V dollars in the next N days” X:Confidence Level(%) V:Value at Risk (\$) N:Time Horizon(Days) Nth-day.

## Presentation on theme: "“We are X percent sure that we will not lose more than V dollars in the next N days” X:Confidence Level(%) V:Value at Risk (\$) N:Time Horizon(Days) Nth-day."— Presentation transcript:

“We are X percent sure that we will not lose more than V dollars in the next N days” X:Confidence Level(%) V:Value at Risk (\$) N:Time Horizon(Days) Nth-day VaR = 1-day VaR * √ N

Single Asset Case Value at Risk : \$466,000 2.33 σ X = 99% N = 10 days 1% Consider Microsoft \$ 10 m VaR = \$1,473,621 Consider AT&T \$ 5 m VaR = \$ 368,405

 Multiple Asset Case  Portfolio : Microsoft (α m =\$10m) & AT&T (α a =\$5m)  N = 10 days;X = 99%;σ m = 2%; σ a = 1%  Correlation : ρ ma = 0.3 n n n σ 2 p = Σ α i 2 σ i 2 + 2 Σ Σ ρ i,j α i α j σ i σ j i=1i=1 j { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/9/2477374/slides/slide_6.jpg", "name": " Multiple Asset Case  Portfolio : Microsoft (α m =\$10m) & AT&T (α a =\$5m)  N = 10 days;X = 99%;σ m = 2%; σ a = 1%  Correlation : ρ ma = 0.3 n n n σ 2 p = Σ α i 2 σ i 2 + 2 Σ Σ ρ i,j α i α j σ i σ j i=1i=1 j

 10-day 99% VaR for Microsoft = \$ 1,473,621  10-day 99% VaR for AT&T= \$ 368,405  10-day 99% VaR for Portfolio= \$ 1,622,657 Benefits of Diversification = (1,473,621 + 368,405) – 1,622,657 = \$ 219,369  For perfectly correlated assets, benefits of diversification are nil.  Less than perfect correlation leads to some of the risks being “diversified away”.

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