Formula Sheet Risk

2 asset case standard deviation

[pic 1]

14.1

Change in $ value of portfolio in 1 day

[pic 2]

14.2

Standard deviation of portfolio n-asset case

[pic 3][pic 4]

14.3

Same as above but with:[pic 5]

[pic 6]

Parallel shifts of yield curve (y) effect on portfolio change.

[pic 7]

14.4

Rate of change of the value of portfolio

[pic 8][pic 9] 

Return on stock in 1 day

[pic 10]

[pic 11]

14.5

Same as 14.1 but with[pic 12]

[pic 13]

Taylor approximation

[pic 14]

Greeks

[pic 15][pic 16][pic 17][pic 18][pic 19]

Prob of default between t and t+Δt conditional on no default between time 0 and t

[pic 20]

19.1

Altman’s Z

[pic 21]

19.2

Probability of default when λ varies over time

[pic 22]

Average hazard rate between time 0 and t

[pic 23]

Probability of default when λ is constant

[pic 24]

19.3

Average default intensity

[pic 25]

Loss Given Default (LGD)

1 – recovery rate

24.1

Cost of liquidation – normal market

[pic 26]

24.2

Cost of liquidation – stressed market

[pic 27]

24.3

Liquidity-adjusted VaR

[pic 28][pic 29]