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Published byKiya Longacre Modified over 3 years ago

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“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

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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

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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*
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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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