VaR - Historical Simulation - Example (250 Days at 98%)
ANSWER
(1 - 98%) × 250 = 5
1) Rank losses from worst to best
2) Take the X worst loss, where X is 250 days multiplied by 2% (5th worst loss).
VaR - Historical Simulation - Assumptions
ANSWER
Future returns follow historical return process
Does not require distribution assumption
Unable to account for shifts in parameter value
Advantages of Non-Parametric Methods
ANSWER
Intuitive and computationally simple
No distribution assumptions
Avoids complex variance-covariance matrices and
dimension problems
Data often readily available
Can accommodate more complex analysis
1
, Disadvantages of Non-Parametric Methods
ANSWER
Dependent on historical data
Volatile (quiet) periods lead to high (low) estimates
Structural shifts difficult to detect
Cannot account for events not in sample period
Difficult to estimate losses greater than maximum loss
within sample
Need sufficient data—not possible for new instruments or markets
VaR - Parametric Formula
ANSWER
VaR = -μ + (σ x zα)
VaR - Parametric Formula - Given Periodic Return
ANSWER
VaR = Pt x [-μ + (σ x zα)]
Where Pt is the beginning of period profit/loss
VaR - Parametric Formula - Given Total Asset Value
ANSWER
VaR = Portfolio Value x [E(R)-(σ x zα)]
2
ANSWER
(1 - 98%) × 250 = 5
1) Rank losses from worst to best
2) Take the X worst loss, where X is 250 days multiplied by 2% (5th worst loss).
VaR - Historical Simulation - Assumptions
ANSWER
Future returns follow historical return process
Does not require distribution assumption
Unable to account for shifts in parameter value
Advantages of Non-Parametric Methods
ANSWER
Intuitive and computationally simple
No distribution assumptions
Avoids complex variance-covariance matrices and
dimension problems
Data often readily available
Can accommodate more complex analysis
1
, Disadvantages of Non-Parametric Methods
ANSWER
Dependent on historical data
Volatile (quiet) periods lead to high (low) estimates
Structural shifts difficult to detect
Cannot account for events not in sample period
Difficult to estimate losses greater than maximum loss
within sample
Need sufficient data—not possible for new instruments or markets
VaR - Parametric Formula
ANSWER
VaR = -μ + (σ x zα)
VaR - Parametric Formula - Given Periodic Return
ANSWER
VaR = Pt x [-μ + (σ x zα)]
Where Pt is the beginning of period profit/loss
VaR - Parametric Formula - Given Total Asset Value
ANSWER
VaR = Portfolio Value x [E(R)-(σ x zα)]
2
