Risk Measures (VAR)
What is Expected Shortfall? How is it Calculated?
Also known as Conditional VAR or CVAR. Average of all losses which are greater or Equal to VAR, average loss in the worse (1-p)% cases. NOT THE WORSE CASE SCENARIO, which would be 100% loss. ex: for a 95% VAR, CVAR will represent the average of the outcomes in the worst 5% of all cases. Expected Upside - will estimate that in the best 5% of all cases, opposite of Expected Shortfall
What is Marginal VAR?
Also known as incremental VAR. The additional amount of risk that a new investment position adds to the portfolio. Marginal VAR helps managers study the effects of adding or subtracting positions from an investment portfolio. VAR risk for one investment must be compared to the VAR risk of the whole portfolio. An investment may have a high VAR
What is the parametric method of calculating VAR? Advantages? Disadvantages?
Also known as the Variance/Co-variance VAR. Most commonly used in practice with hedge fund managers. Only variables you need is the mean and the standard deviation of the portfolio. Assume that the portfolio is normally distributed. Formula is: Mean - Sx(z-Score) Advantages - simple, data is easy to obtain Disadvantages - assumption of normality, exposing the portfolio to massive risk if the standard deviation moves away from historical mean. Also need to rely on the stability of the standard deviation through time and the variance/co-variance matrix. Without adjusting VAR for extreme events you expose your portfolio to additional risk.
What is the historical method of calculating VAR? Advantages? Disadvantages?
Better to use if you can't determine the distribution of your return. Much easier than parametric VAR, rank past historical returns in terms of lowest to highest and computing (with predetermined confidence rate) what your lowest return historically has been. Advantages - past data has been incorporated into the risk calculation without being forced into the assumption of a normal distribution. No var/co-var matrix is needed to calculate Sx, thus avoids the risk of a changing matrix over time. Disadvantages - assumes that the past will exactly replicate the future, which is very unlikely. Only as strong as the data used (quantity and quality)
Why is Expected Shortfall considered better than VAR? What are its disadvantages?
Expected shortfall will show you the average of the worse case scenario, while the VAR will only show the probability and amount of loss to expect with a certain amount of confidence. VAR = How bad can things get? CVAR = If things get bad, what is our loss? ex: if a $100 bond has a 2% probability of default (98% chance of repayment) with 95% confidence the VAR will capture 95% of the distribution and it will show a value of $0. ES will capture the worst 5% of the distribution 2 out of the 5 result in a loss of $100, thus if averaged the ES is $40 ($200/5) Disadvantages: estimates of measure may not be as accurate as estimates of VAR, may be less stable if the distribution is not normal
What's GVAR? How can you calculate it? Advantages? Disadvantages?
Global Vector AutoRegressive or GVAR is a practical modeling framework for the analysis of... Advantages - allows for interdependence at a variaty of levels, allows for long-run relationships in addition to short-run which are consistent with data
What are the challenges is using VAR as a measure of risk?
Looking at risk in terms of VAR can give people a false sense of security, VAR is only giving the probability of a certain loss it does not by any means guarantee the amount of that loss Does not measure worse case loss, 99% still leaves the 1% with an unknown amount of loss. As demonstrated by the Housing Crisis those 1% losses are sometimes big enough to take down a firm.
What is the Monte Carlo method of calculating VAR? Advantages? Disadvantage?
More complex analytical tool, try to map out possible return scenario for the portfolio on a computer generated model and determine the probability of loss using the model. Advantages - offers infinite number of possible scenarios, removes assumption of normality, most accurate measure of portfolios true VAR Disadvantages - exposed to huge model risks that could alter return paths, model complexity and scale is also an issue.
What are the challenges in calculating VAR for a mixed portfolio?
Need to measure not only return and volatility of individual assets, but also the correlations between them. When the number and diversity of positions grow, the difficulty and cost of measuring risk grows exponentially. The VAR of A&B, is NOT the sum of VAR A and VAR B. Need to factor in correlation, sometimes a higher individual VAR can result in a lower portfolio VAR.
What is non-Linear VAR? How would you calculate it?
Non-linear risk exposure arises in the VAR calculation of a portfolio of derivatives, such as options. Since they are dependent on a variety of characteristics (implied volatility, time to maturity, underlying asset price, current interest rate) it is difficult to group them under the same characteristics using the standard VAR approach. Calculation:
What do you know about extreme value theory?
Solution to the problem of VAR, describes a distribution that characterizes the losses/gains specifically in extreme events (on the tail of a distribution) and creates new distribution using extreme data Generalized Extreme Value (GEV): Take blocks of data based on time interval and taxes the max loss in each block and puts them into a distribution Generalized Pareto Distribution (GPD): modern approach which select bar and anything over that bar is extreme loss and should be characterized by its own distribution
What is Value at Risk (VAR)?
Statistical technique used to measure and quantify the level of financial risk within a firm or portfolio over a specific time frame. Measured by assessing the potential loss, probability of occurrence, and time frame.
What's wrong with VAR as a measurement of risk?
There is no standard protocol for the statistics used to determine the assets or firm wide risk. Statistics can be pulled from multiple places and risks could potentially be understated or overstated. The inputs make all the difference, invalid or skewed inputs could result in a majorly skewed and incorrect VAR, always be completely sure of inputs before validating VAR (Ex: stats pulled from a period of low volatility may understate the potential for risky events to occur and the magnitude or they might be understated using a normal distribution probability, which don't account for extreme or "Black Swan" events. This happened during the financial crisis as risk occurrence and risk magnitude were both grossly understated, resulting in collapses of financial institutions and portfolios.)
How do you calculate VAR?
VAR = [(Expected Weighted Return of the Portfolio - (z-score of the confidence interval x standard deviation of the portfolio)) x Portfolio Value]
