Value at Risk (week 6) Flashcards
Describe VaR
is the loss level V during time period of length T that we are X% certain will not be exceeded → with probability X, we will not lose more than V dollars on the portfolio over the next T
days.
What determines VaR
Portfolio composition (exposure to risk)
Investment horizon (size of risk)
confidence level (type of risk)
Can actual los frequency exceed VaR?
Yes, due to chance.
Advantages and disadvantages of VaR
Pros:
-Single number that summarizes total risk of FI → Aggregates all Greek letter for all risk factors underlying portfolio into 1 number
-Intuitive: easy to understand for top management
Cons:
-VaR does not tell how large loss can be if VaR is exceeded
-VaR is not an adequate measure of tail risk
-VaR is inherently backward-looking → Sensitive to data input → Perform stress test
-VaR is not a coherent risk measure for non-normal distributions, VaR of portfolio can exceed sum of VaRs of individual positions because it does not take into account that diversification lowers risk.
-The main weakness of VaR is tail risk, because VaR does not take into account the shape of the tail
Advantages and disadvantages of historical simulation method
Pros:
-Conceptually simple and historical data usually available
-Historical correlation between risk factors automatically -incorporated
-VaR can be computed for portfolio with non-linear assets
-Non-parametric: no distribution assumptions needed for risk factors
Cons:
-Depends fully on one historical price path → historical sample may not include any extreme events would produce a too low VaR
-Accuracy of VaR depends on number of observations on risk factors → trade-off between timelines (recent observations) and precision (more observations)
-Computationally intensive (slow) → portfolio revalued many times
Advantages and disadvantages of delta normal method
Pros:
-Easy to implement and computationally fast (for simple portfolio)
Theoretically appealing (based on Markowitz portfolio theory)
-Variance-Covariance matrix can be updated using DCC-GARCH models → Can allow for time-varying volatilities and correlations
-In theory, VaR estimate more precise than with historical simulations
Cons:
–If key assumptions fail, VaR estimate can be severely biased (we would prefer less precision over high bias, such as with the historical simulations)
-Cannot handle assets that are non-linear in risk factors (options).
-Linear models fail to capture skewness in probability distribution of option portfolio, even if stock distribution is normal. When assuming normal distribution, VaR underestimated for negative gamma portfolio and overestimated for positive gamma portfolio.
-Cannot handle risk factors that have a non-normal distribution
-Estimating variance-covariance matrix of a large portfolio is hard
Monte carlo simulation approach advantages and disadvantages
Pros:
-Flexible: can assume various distributions to account for non-normality
-Can handle non-linear products, such as options
-Does not require a lot of historical data (only for choosing parameters)
-Large number of simulations can be generated → Increases precision
-VaR can be computed for high confidence levels
Cons:
-If the assumed return distribution (model risk) is wrong, VaR can be severely biased
-Computationally inefficient (slow) because the complete portfolio has to be revalued many times
-> may use delta/gamma approximation to speed up the
calculation of change in value of some portfolio components
Describe expected shortfall
ES is the expected loss during time T conditional on the loss exceeding the Xt percentile of the loss distribution. Meaning it is conditional on exceeding VaR and ES measures expected tail loss, so it takes tail-risk into account.
Advantages and disadvantages of ES
Pros:
-In theory ES is a better risk measure than VaR
-Captures risk tail and recognizes diversification benefits
-Harder to game by traders than VaR: e.g., selling OTM put options
Cons:
-More difficult to understand and compute than VaR
-ES estimate determined by only a few tail observations → Imprecise
-Back-testing of ES calculation more difficult than back-testing VaR
-Accuracy of ES directly depends on accuracy of VaR
What are the key issues with volatility as a risk measure?
- Fat tails, heavier tails and more peaked than expected, very small and very large changes are more likely than the distribution suggests
- skewness (left skew (positive, large gains are more likely, risk is overestimated) or right skew (negative, lareg losses are more likely, risk is underestimated(
