1. VALUE AT RISK

2. VALUE AT RISK VALUE AT RISK Definition :
The expected maximum loss ( or worst loss ) over a target horizon within a given confidence interval
Evolved through the requirements of SEC to provide a minimum capital requirement in provision for risks taken by financial institutions

3. Models to estimate VaR Historical Market Data
assumption is that historical market data is our best estimator for future changes and that
asset returns in the future will have the same distribution as they had in the past
Variance – Covariance (VCV)
assuming that risk factor returns are always (jointly) normally distributed and that the change in portfolio value is linearly dependent on all risk factor returns
Monte Carlo Simulation
future asset returns are more or less randomly simulated

4. Historical Market Data
involves running the current portfolio across a set of historical price changes to yield a distribution of changes in portfolio value, and computing a percentile (the VaR).
Benefits
Simple to implement
does not assume a normal distribution of asset returns
Drawbacks
requires a large market database
computationally intensive calculation.

5. VALUE AT RISK (VAR) Market Value x Risk Variability Confidence Level =
Worst Loss

6. DEFINITION : Market Value : Risk variability :
Current market value of the respective transaction to be managed
Mark to market at the end of time horizon
Risk variability :
Usually the standard deviation of the risk to be managed
The higher the variability the higher is VAR

7. DEFINITION : Time Horizon : Confidence Level :
Time period to be considered correspond to time required for corrective actions as losses starts to develop
Annualized
The longer the time horizon the higher is VAR
Confidence Level :
Confidence level of loss occurring
The higher the confidence level the higher is VAR

8. Example :
Current market value of transaction USD 100,000 paid by 3 months usance L/C
Standard deviation of Rp/USD is 10%
Time horizon is 3 months
Confidence level is 95%
VAR = 100,000 X 0.10 X X 0.95
= USD 4,  Maximum expected loss

9. WEAKNESSES OF HISTORICAL SIMULATION
Past is not prologue, history does not always repeat it selves
Trends in the data, since all data are treated equal, despite the fact that some periods might experience higher volatility
For new assets or market risks no historical data available

10. MODIFICATIONS OF HISTORICAL SIMULATION
Weighting the recent past more, assuming that the recent past is a better predictor of the immediate future than the distant past ( can be using indexes to adjust each return based on its timeline)
Combining historical simulation with time series models, by fitting a time series models through the historical data
Volatility updating, by comparing past volatility with recent volatility and then adjusting the past return accordingly e.g. past volatility = 0.5, recent volatility 0.75, past return 10%, recent predicted return is 0.75/0.5* 10%=15%

11. Variance – Covariance (VCV)
Basic assumption is that the risk factors are normally distributed
Hence are the returns also normally distributed

12. Variance – Covariance (VCV)
VAR formula for VCV :
σ = standard deviation of the risk
Sigma for 95% confidence level is 1.645
Sigma for 99% confidence level is 2.33

13. Exchange rate (USD/Rp)
EXAMPLE :
Exchange rate (USD/Rp)
Loss / Gain (p)
Probability (r)
d2 = r * p2
9.600
-400
0.025
4.000
9.700
-300
2.250
9.800
-200
0.050
2.000
9.900
-100
0.200
10.000
0.400
10.100
100
10.200
200
10.300
300
10.400
400
Average =
S =
d2 =
d =
With 95% confidence interval the VAR = * Rp = Rp
 The maximum potential loss for exchange rate risk is Rp

14. ASSESMENT OF V-CV METHOD
Strength :
simple to compute after making assumptions about the distribution of returns and inputted the means, variances and covariances or returns
Weaknesses :
Wrong distributional assumptions, if it turns out that the returns a re not normally distributed and the outliers are higher, computed VaR can be lower that actual VaR
Input error, if data used to calculate are for example based on historical data, which is not reflecting the current situation
Nonstationary variables, happens if the underlying assumed correlation does not hold anymore, e.g. interest rate is adjusted by FED

15. Monte Carlo Simulation
Decide on N, the number of iterations to perform.
For each iteration:
Generate a random scenario of market moves using some market model.
Revalue the portfolio under the simulated market scenario.
Compute the portfolio profit or loss (PnL) under the simulated scenario. (i.e., subtract the current market value of the portfolio from the market value of the portfolio computed in the previous step).
Sort the resulting PnLs to give us the simulated PnL distribution for the portfolio.
VaR at a particular confidence level is calculated using the percentile function.
For example, if we computed 5000 simulations, our estimate of the 95% percentile would correspond to the 250th largest loss; i.e., ( ) * 5000.

16. STRENGTH OF MONTE CARLO SIMULATION
Does not need to rely on historical data, those historical data can still be used as benchmark and then adjust accordingly
Does not need to assume normal distribution for the returns
Can be used for any type of portfolio including options or option like securities

17. WEAKNESSES OF MONTE CARLO SIMULATION
Needs to estimate the probability distribution for all the market risk variables that we want to consider
Number of simulations that need to be run on the model will be substantially large

18. MODIFICATION ON MONTE CARLO SIMULATION
Scenario simulation, only likely combination are run through the model
Monte Carlo simulation with Variance-Covariance method modification, assuming normal distribution for the returns

19. Indications on method to use
For Value at Risk for portfolios, that do not include options, over very short time periods (a day or a week) and normality can be assumed, the variance-covariance approach does a reasonably good job.
If the risk source is stable and there is substantial historical data (commodity prices, for instance), historical simulations provide good estimates.
In the most general case of computing VaR for nonlinear portfolios (which include options) over longer time periods, where the historical data is volatile and non-stationary and the normality assumption is questionable, Monte Carlo simulations do best.

20. LIMITATIONS OF VaR :
Return distributions cannot always be correctly predicted
History may not be a good predictor
Nonstationary correlations
Only looking at the downside risk (negative side of risk)
Best for calculating short term risk
Difficult to use for comparing different investments

21. VaR can lead to suboptimal decision
Overexposure to risk, managers will tend to be more bold in making risky investments while actually the rest of 5-10% probability of incurring risk might be huge
Agency problem, because VaR usually uses past data, managers who knows about irregularity in the volatility can misuse them for his own advantage.

22. VAR is best used for financial institutions, since they are dealing with short term assets which are related to the common market risks
VAR for nonfinancial institutions should be used as a secondary measure, unless it is for short term assets.