Risk Assessment - Value at Risk

Question 1

Please give a general definition of the Value at Risk (VaR).

Answer 1

The Value at Risk is the worst loss that can be expected over a given holding period with a confidence level predefined by a decision maker.

Question 2

Why does it belong to the family of downside risk measures?

Answer 2

VaR is a downside risk because it focuses on the potential losses of an asset position,

Question 3

What are the main goals of Value at Risk?

Answer 3

The main goals of value at risk are to measure risk in monetary units and get a risk measure that can be used to compare different types of risk.

Question 4

What are the different approaches by estimating the VaR?

Answer 4

VaR can be estimated using a number of different types.

1. parametric approaches = variance covariance estimation
2. non-parametric approaches = historical simulation

Question 5

Please explain the components of the VaR-Calculation.

Answer 5

1. Risk Position (RP) =
   -Asset Position valued at current market price
2. Volatility =
   - Standard Deviation of daily returns
3. Holding period T=
   - Period of time (in working days/ trading days) it takes to sell the position.
   - It depends on asset type
4. Confidence Level =
   -Probability set by the decision maker
   - determines the quantile of the standard distribution

Question 6

What drives the length of the holding period?

Answer 6

Drivers of the length of the holding period are internal procedures or external regulations. For an example maybe in the company they need a meeting of the investment committee to make the decision

Question 7

What are advantages of VaR?

Answer 7

• Get a risk measure that can be used to compare different types of risk
• further advantage of VaR is that it just focusses on the downside risk, so it definitely does not include opportunities, because it focusses on the losses
• It includes the confidence level in the calculation, that means the personal characteristic of the decision maker is included in the risk measure, because the decision maker defines the confidence level.
• VaR concept can be applied to other risks as well, e.g.:
  -Default risk
  -cash flow at risk
  -business risk

Question 8

Interpretation of VaR

Answer 8

With a probability of (Confidence Level) losses from holding X stocks over the next (Holding Period) will not be higher than (VaR).

OR

With a probability of (1-Confidence Level) losses from holding X stocks over the next (Holding Period) will be higher than (VaR).

Question 9

How would VaRs change if the confidence level increases?

Answer 9

The higher the confidence level the higher the VaR because z increases.

Question 10

How would VaRs change if the hodling period reduces?

Answer 10

The shorter the holding period the lower the VaR, as falls.

Question 11

How would VaRs change if the volatilities increases?

Answer 11

The higher the volatility the higher the VaR.

Question 12

Does the VaR Calculation considers all relevant developments?

Answer 12

• The VaR just calculated is an absolute VaR
  -The absolut VaR does not consider all relevant developments.
  -The expected return has not been included in the Calculation, so the absolute VaR implicitly assumed that the expected return is 0.

Question 13

Briefly descirbe the relative VaR?

Answer 13

A relative VaR expresses (ausdrücken) the loss relative to the expected value.

Question 14

Briefly describe the properties of VaR

Question 15

What is a portfolio?

Answer 15

A portfolio is a collection or bundle of different asset positions which are owned by the same investor, group of investors or the same company.

Question 16

What is the reason for the difference between the portfolio´s volatility and the weighted average of individual volatilities? (Same with Portfolio VaR)

Answer 16

The reason for the difference is that the weighted average of individual volatilities do not consider diversification effects, the portfolio´s volatility do.

The sum is the hypothetical portfolio VaR in the absence of a diversification effect. It is higher than the actual portfolio VaR because of this diversification effect

Question 17

Please describe briefly what correlation -1, +1 and 0 mean?

Answer 17

-1 = Perfect, negative Correlation, Maximum Diversification effect

+1= Perfect, positive Correlation, no diversification effect

0= No correlation, Medium diversification effect

e.g. correlation is 0.25 -> weak positive correlation

If there is a perfect, positive correlation = The weighted average of individual volatilities can be used to calculate the volatility

Question 18

Why is the historical simulation often used in reality? What are problems of the historical simulation?

Answer 18

-The advantage of Historical Simulation is that there is no need to use any type of a distribution assumption.
- The advantage of historical simulation become more apparent if more complex portfolios with non-linear relationships are considered.
-The problem of the historical simulation is that it only uses a single value for the calculation of the VaR and all other values are not taken into account. Thus, the result will not change if the daily returns would look different

Question 19

What is the idea of a a hybrid approach?

Answer 19

A hybrid approach is a mix between a non-parametric approach and a parametric approach.
- The problem of historical simulation is that it only uses the information for a single day and neglects all other available information.
- The parametric approach is not focusing on a single day but focusing on the volatility of the returns, which means that information about all returns are also included in the calculation
-Both alternatives reintroduce the assumption of a normal distribution. Thus, they can be considered as hybrid approaches between a non-parametric and a parametric approach.

Question 20

What are advantages of parametric approaches?

Answer 20

The parametric approach is not focusing on a single day but focusing on the volatility of the returns, which means that information about all returns are also included in the calculation

Question 21

Please describe briefly the Lower Partial Moments

Answer 21

The Lower Partial Moment is an additional risk measure that can be used in order to receive additional information about losses which are larger than the VaR.

Question 22

Describe briefly the idea of LPM0,1,2

Answer 22

LPM0= gives the probability that positions value falls below the reference value

LPM1= represents the average shortfall
-(If losses are larger than the maximum acceptable loss, losses are larger than the maximum acceptable loss by X on average)

LPM2= usually the square root is uses, shows the dispersions of the shortfalls

Question 23

Briefly describe the expected shortfall.

Answer 23

The Expected Shortfall is the average of losses which are larger than the VaR at a given confidence level 1 − a

Question 23

A decision maker is measuring risk using VaR. Can the decision maker expect that the potential loss is definitely less than the VaR. Please explain briefly.

Answer 23

The decision maker can not expect that the potential loss is definitely less than the VaR, even if a high confidence level near 1 is used, there is still a small risk left that the loss will be bigger than the VaR.

Question 24

Describe briefly the Component VaR

Answer 24

The Component VaR allows to decompose the VaR of the portfolio while taking into account diversification effects