Lecture 5: Value at Risk and Expected Shortfall Flashcards
“We are X percent certain that we will not lose more than V dollars in time T”.
Here, the “V” denotes what?
V ≥ 0 denotes the dollar amount at risk - the value at risk (VaR)
What is the main drawback of VaR as a risk measure?
Hint: this limitation is attempted mitigated by the expected shortfall measure
VaR tends to ignore big losses that occur with a sufficiently small probability - i.e., losses beyond the set confidence level are ignored.
This is a cause for concern for financial regulators, when loss distributions are not normally distributed (i.e., in reality)
The expected shortfall measure is unimportant if losses are normally distributed.
TRUE/ FALSE
TRUE
Define expected shortfall
Expected shortfall (ES) is the expected loss during time T conditional on the loss being greater than VaR –> i.e., when you are out in the tail of the distribution
Which of the following is NOT a formal rule for a coherent risk measure?
A) Monotonicity
B) Translation invariance
C) Homogeneity
D) Heterogeneity
E) Subadditivity
D) Heterogeneity
One of the formal rules for a coherent risk measure states that if one portfolio/asset consistently performer better than another, the overperforming portfolio/asset should have a lower risk than the worse-performing.
This rule is termed _______
A) Monotonicity
B) Translation invariance
C) Homogeneity
D) Subadditivity
A) Monotonicity
One of the formal rules for a coherent risk measure states that if K extra cash is added to your portfolio, the risk should be reduced by K due to the cash functioning as a buffer.
This rule is termed _______
A) Homogeneity
B) Subadditivity
C) Translation invariance
D) Monotonicity
C) Translation invariance
One of the formal rules for a coherent risk measure states that if you double the size of all assets in your portfolio (i.e., maintaining the portfolio weights), you double the risk of your portfolio.
This rule is termed _______
A) Homogeneity
B) Subadditivity
C) Translation invariance
D) Monotonicity
A) Homogeneity
One of the formal rules for a coherent risk measure states that risk cannot increase if you merge two portfolios (diversification)
This rule is termed _______
A) Homogeneity
B) Subadditivity
C) Translation invariance
D) Monotonicity
B) Subadditivity
VaR is always a coherent risk measure - but ES is not.
TRUE/FALSE
FALSE: ES is always coherent, while VaR is not
VaR is not always a coherent risk measure. Which of the formal rules MAY it not satisfy? Select 1-4
A) Homogeneity
B) Subadditivity
C) Translation invariance
D) Monotonicity
The (B) sub-additivity condition only holds for some distributions (e.g. the normal distribution).
VaR will always satisfy this condition if we are working with a normally distributed function. However, if this is not the case, it should not be surprising if VaR increases as two portfolios are merged!
____ ____ measures the contribution of each security to the portfolio VaR.
Fill in the blank.
Marginal VaR (mVaR)
Low beta assets tend to have high mVaRs in a well-diversified portfolio and vice versa.
TRUE/ FALSE
FALSE:
HIGH beta assets tend to have high mVaRs in a well-diversified portfolio and vice versa
Increasing the weight in assets/sub-portfolios with negative mVaR can ____ (increase/ decrease) the risk of the total portfolio.
Fill in the blank
Increasing the weight in assets/sub-portfolios with negative mVaR can decrease the risk of the total portfolio
The accuracy of expected shortfall can be difficult to test in practice. Why?
ES is not easy to test in practice: it requires a high number of observations with losses higher than VaR, which are scarce, since these are tail-events
