AT&TExampleConsidera positionof $5 million in AT&TThe daily volatility of AT&T is 1% (approx16% per year)The SD per 10 days is50.000/10 = $158,144TheVaR is158,114 x 2.33 = $368,4056RiskManagementandFinancialInstitutions3e,Chapter15,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 15, Copyright © John C. Hull 2012 AT&T Example ⚫ Consider a position of $5 million in AT&T ⚫ The daily volatility of AT&T is 1% (approx 16% per year) ⚫ The SD per 10 days is ⚫ The VaR is 50,000 10 = $158,144 158,114 2.33 = $368,405 6
Portfolio (page 325) Now consider a portfolio consisting of bothMicrosoft and AT&T Suppose that the correlation between thereturns is 0.37RiskManagementandFinancialInstitutions3e,Chapter15,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 15, Copyright © John C. Hull 2012 Portfolio (page 325) ⚫ Now consider a portfolio consisting of both Microsoft and AT&T ⚫ Suppose that the correlation between the returns is 0.3 7
S.D. of Portfolio A standard result in statistics states that0x+y=/o+o+2pox0yIn this case x = 200,000 and oy = 50,000and p = 0.3. The standard deviation of thechange in the portfolio value in one day istherefore 220.2278RiskManagementandFinancialInstitutions3e,Chapter15,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 15, Copyright © John C. Hull 2012 S.D. of Portfolio ⚫ A standard result in statistics states that ⚫ In this case sX = 200,000 and sY = 50,000 and r = 0.3. The standard deviation of the change in the portfolio value in one day is therefore 220,227 X Y X Y X Y s + = s + s + 2rs s 2 2 8
VaR for Portfolio The 10-day 99% VaR for the portfolio is220,227 × V10 ×2.33 = $1,622,657The benefits of diversification are(1,473,621+368,405)-1,622,657=$219,369 What is the incremental effect of the AT&Tholding on VaR?9RiskManagementandFinancialInstitutions3e,Chapter15,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 15, Copyright © John C. Hull 2012 VaR for Portfolio ⚫ The 10-day 99% VaR for the portfolio is ⚫ The benefits of diversification are (1,473,621+368,405)–1,622,657=$219,369 ⚫ What is the incremental effect of the AT&T holding on VaR? 220,227 10 2.33 = $1,622,657 9
The Linear ModelWe assume The daily change in the value of a portfoliois linearly related to the daily returns frommarket variablesThe returns from the market variables arenormally distributed10RiskManagementandFinancialInstitutions3e,Chapter15,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 15, Copyright © John C. Hull 2012 The Linear Model We assume ⚫ The daily change in the value of a portfolio is linearly related to the daily returns from market variables ⚫ The returns from the market variables are normally distributed 10