Value at Risk

Question 1

What is VaR?

Answer 1

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.

Question 2

qual é o numero quando 95%?

Answer 2

1.645

Question 3

qual é o numero quando 99%?

Answer 3

2.326

Question 4

como converter um confidence interval de 99% para um de 95%?

Answer 4

Var(95%) = var(99%) x 1.645/2.326

Question 5

como converter um var de 1 dia para 10 dias?

Answer 5

var(95%,10days) = var(95%,1day) x raiz de 10

Question 6

how to do a historical simulation

Answer 6

1. collect historical data on risk variables
2. calculate the gains and losses for your portfolio and draw the histogram
3. select the confidence level (95%) and find the corresponding loss such that only 5% of historical cases represent losses that are larger

Question 7

how to do the delta-normal method

Answer 7

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)

Question 8

how to calculate the VaR(95%) for a bond portfolio?

Answer 8

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

Question 9

in bonds, what is the worst thing that can happen?

Answer 9

the interest rates being higher

Question 10

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?

Answer 10

market (stock market indices)
rates (yield curves)
currencies (spot effects)
forwards and futures (forward curves)
volatility (VIX index)

Question 11

in what consists the risk mapping process?

Answer 11

replacing each instrument by its exposure to the selected risk factor

Question 12

what are the 2 types of risk measurement?

Answer 12

local valuation and full valuation

Question 13

what are the 2 types of local valuation?

Answer 13

linear (full cov matrix, factor models and diagonal model) and nonlinear (gamma and convexity)

Question 14

what are the 2 types of full valuation?

Answer 14

historical simulation and monte carlo

Question 15

is duration an example of local valuation?

Answer 15

yes

Question 16

what is the difference between delta-normal and historical simulation in terms of evaluation?

Answer 16

delta is linear historical is complete

Question 17

what is the difference between delta-normal and historical simulation in terms of distribution shape?

Answer 17

delta is normal historial is the actual one

Question 18

what is monte-carlo?

Answer 18

using an equation to produce artificial data, we need a stochastic process (with a random error term)

Question 19

what is the riskmetrics approach?

Answer 19

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

Question 20

what is an alternative to VaR?

Answer 20

ES (expected shortfall) measure:
averaging all values to the left of the “cutoff”, it is the expected loss beyond the VaR value

Question 21

does VaR assume that risk profile remains constant?

Answer 21

yes

Question 22

what are the drawbacks of VaR?

Answer 22

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

Question 23

on what depends the selection of the vaR method?

Answer 23

the instrument to be assessed

Question 24

in the orange county case, what did he use the most ?

Answer 24

mostly reverse repurchase agreements and structured notes

Question 25

what is a reverse repurchase agreement?

Answer 25

the buyer trades money for securities agreeing to resell them later

Question 26

what are structured notes?

Answer 26

notes whose conditions are customised to some buyer’s specification, payments are not fixed but indexed to some financial variable