14.11 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 STD per 10 days is 500010=$158144 · The var is 158114×233=$368405 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 14.11 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 STD per 10 days is • The VaR is 50,000 10 = $158,144 158,114 2.33 = $368,405
14.12 Portfolio (p. 344) Now consider a portfolio consisting of both IBM and at&t Suppose that the correlation between the eturns is 0.7 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 14.12 Portfolio (p. 344) • Now consider a portfolio consisting of both IBM and AT&T • Suppose that the correlation between the returns is 0.7
14.13 STD of portfolio a standard result in statistics states that x+y=√ox+a2+2px In this case ox=632, 456 and oy=158, 114 and p 0.7. The standard deviation of the change in the portfolio value is therefore 751, 665 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 14.13 STD of Portfolio • A standard result in statistics states that • In this case x = 632,456 and Y=158,114 and r = 0.7. The standard deviation of the change in the portfolio value is therefore 751,665 X Y X Y r X Y + = + + 2 2 2
14,14 Var for portfolio The VaR for the portfolio is 751,665×2.33=$1,751,379 The benefits of diversification are (1,473,621+368405)-1,751,379=$90,647 What is the incremental effect of the at&t holding on VaR? Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 14.14 VaR for Portfolio • The VaR for the portfolio is • The benefits of diversification are (1,473,621+368,405)-1,751,379=$90,647 • What is the incremental effect of the AT&T holding on VaR? 751,665 2.33 = $1,751,379