Value at Risk Flashcards
What is VaR?
VaR is a statistical measure of the risk of loss. it gives the quantile of a forecast distribution of gains and losses measured in monetary units. It synthesis the maximum expected loss over a given horizon, such that there exists a small pre-specified probability that the actual loss will be greater.
qual é o numero quando 95%?
1.645
qual é o numero quando 99%?
2.326
como converter um confidence interval de 99% para um de 95%?
Var(95%) = var(99%) x 1.645/2.326
como converter um var de 1 dia para 10 dias?
var(95%,10days) = var(95%,1day) x raiz de 10
how to do a historical simulation
- collect historical data on risk variables
- calculate the gains and losses for your portfolio and draw the histogram
- select the confidence level (95%) and find the corresponding loss such that only 5% of historical cases represent losses that are larger
how to do the delta-normal method
supposing the risk variable’s returns have a normal distribution:
1. estimate the expected average return and the standard deviation for the distribution function
2. determine the quantile like 5%
3. use a linear approximation to calculate the variation of the portfolio’s value in dollars for the relevant model (e.g. duration for bonds)
how to calculate the VaR(95%) for a bond portfolio?
risk factor = interest rates
1. suppose interest rate variations have a normal distribution
2. suppose we can approximate bond price variations by using modified duration, which is a linear approximation
3. find the 5% quantile for interest rate variations and calculate the dollar loss for this rate of variation
in bonds, what is the worst thing that can happen?
the interest rates being higher
what are 5 risk factors that are quite stable, since we have multiple risk sources that we want to bring down into a small number of risk factors?
market (stock market indices)
rates (yield curves)
currencies (spot effects)
forwards and futures (forward curves)
volatility (VIX index)
in what consists the risk mapping process?
replacing each instrument by its exposure to the selected risk factor
what are the 2 types of risk measurement?
local valuation and full valuation
what are the 2 types of local valuation?
linear (full cov matrix, factor models and diagonal model) and nonlinear (gamma and convexity)
what are the 2 types of full valuation?
historical simulation and monte carlo
is duration an example of local valuation?
yes
what is the difference between delta-normal and historical simulation in terms of evaluation?
delta is linear historical is complete
what is the difference between delta-normal and historical simulation in terms of distribution shape?
delta is normal historial is the actual one
what is monte-carlo?
using an equation to produce artificial data, we need a stochastic process (with a random error term)
what is the riskmetrics approach?
very similar to delta-normal with 2 differences:
risk factor returns are measured as logarithms of price rations, rather than rates of return
variance forecasts are completed with a weighted average of previous forecasts
what is an alternative to VaR?
ES (expected shortfall) measure:
averaging all values to the left of the “cutoff”, it is the expected loss beyond the VaR value
does VaR assume that risk profile remains constant?
yes
what are the drawbacks of VaR?
it doesn’t describe the greatest losses
it doesn’t describe the loss in the left tail
it’s computed with a certain margin of error with several assumptions
on what depends the selection of the vaR method?
the instrument to be assessed
in the orange county case, what did he use the most ?
mostly reverse repurchase agreements and structured notes
what is a reverse repurchase agreement?
the buyer trades money for securities agreeing to resell them later
what are structured notes?
notes whose conditions are customised to some buyer’s specification, payments are not fixed but indexed to some financial variable
