Angličtina pro matematiky IV
COURSE MATERIALS AND HOMEWORK WEEK VI.
Value at Risk
From Wikipedia, the free encyclopedia
1) Find the words in the text for these definitions.
a) a collection of investments held by an institution or an individual.
b) refers to accounting for the value of an asset or liability based on the current market price of the asset or liability, or for similar assets and liabilities.
c) is a bank regulation, which sets a framework on how banks and depository institutions must handle their capital.
d) is the process of evaluating a strategy, theory, or model by applying it to historical data.
In financial mathematics and financial risk management, Value at Risk (VaR) is a widely used risk measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, probability and time horizon, VaR is defined as a threshold value such that the probability that the mark-to-market loss on the portfolio over the given time horizon exceeds this value (assuming normal markets and no trading in the portfolio) in the given probability level.
For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one day period, assuming markets are normal and there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day in 20. A loss which exceeds the VaR threshold is termed a “VaR break.”
The 5% Value at Risk of a hypothetical profit-and-loss probability density function
VaR has five main uses in finance: risk management, risk measurement, financial control, financial reporting and computing regulatory capital. VaR is sometimes used in non-financial applications as well. Important related ideas are economic capital, backtesting, stress testing and expected shortfall.
Details
2) Read this part of the text and decide whether the statements are T or F.
a) For common parameters, only 1% and 5% and one day and two weeks are used.
b) The loss is observable only when there is no trading.
c) Consequences of disasters will be evident after a longer period of time.
d) A one-day 95% VaR is different from one-day 5% VaR.
e) If VaR is negative, the portfolio is making a profit.
f) The original definition of VaR was the maximum loss at any point during the period.
Common parameters for VaR are 1% and 5% probabilities and one day and two week horizons, although other combinations are in use.
The reason for assuming normal markets and no trading, and to restricting loss to things measured in daily accounts, is to make the loss observable. In some extreme financial events it can be impossible to determine losses, either because market prices are unavailable or because the loss-bearing institution breaks up. Some longer-term consequences of disasters, such as lawsuits, loss of market confidence and employee morale and impairment of brand names can take a long time to play out, and may be hard to allocate among specific prior decisions. VaR marks the boundary between normal days and extreme events. Institutions can lose far more than the VaR amount; all that can be said is that they will not do so very often.
The probability level is about equally often specified as one minus the probability of a VaR break, so that the VaR in the example above would be called a one-day 95% VaR instead of one-day 5% VaR. This generally does not lead to confusion because the probability of VaR breaks is almost always small, certainly less than 0.5.
Although it virtually always represents a loss, VaR is conventionally reported as a positive number. A negative VaR would imply the portfolio has a high probability of making a profit, for example a one-day 5% VaR of negative $1 million implies the portfolio has a 95% chance of making more than $1 million over the next day.
Another inconsistency is VaR is sometimes taken to refer to profit-and-loss at the end of the period, and sometimes as the maximum loss at any point during the period. The original definition was the latter, but in the early 1990s when VaR was aggregated across trading desks and time zones, end-of-day valuation was the only reliable number so the former became the de facto definition. As people began using multiday VaRs in the second half of the 1990s they almost always estimated the distribution at the end of the period only. It is also easier theoretically to deal with a point-in-time estimate versus a maximum over an interval. Therefore the end-of-period definition is the most common both in theory and practice today.
VaR risk management
3) Read this part of the text and try to replace the underlined words with synonyms.
a) exacerbate ………………….. b) routine events …………………………..
c) impairment ………………… d) it pointless to anticipate ………………..
e) foreseeable ………………….. f) to be hedged …………………………..
One specific system uses three regimes.
- One to three times VaR are normal occurrences. You expect periodic VaR breaks. The loss distribution typically has fat tails, and you might get more than one break in a short period of time. Moreover, markets may be abnormal and trading may exacerbate losses, and you may take losses not measured in daily marks such as lawsuits, loss of employee morale and market confidence and impairment of brand names. So an institution that can't deal with three times VaR losses as routine events probably won't survive long enough to put a VaR system in place.
- Three to ten times VaR is the range for stress testing. Institutions should be confident they have examined all the foreseeable events that will cause losses in this range, and are prepared to survive them. These events are too rare to estimate probabilities reliably, so risk/return calculations are useless.
- Foreseeable events should not cause losses beyond ten times VaR. If they do they should be hedged or insured, or the business plan should be changed to avoid them, or VaR should be increased. It's hard to run a business if foreseeable losses are orders of magnitude larger than very large everyday losses. It's hard to plan for these events, because they are out of scale with daily experience. Of course there will be unforeseeable losses more than ten times VaR, but it's pointless to anticipate them, you can't know much about them and it results in needless worrying. Better to hope that the discipline of preparing for all foreseeable three-to-ten times VaR losses will improve chances for surviving the unforeseen and larger losses that inevitably occur.
"A risk manager has two jobs: make people take more risk the 99% of the time it is safe to do so, and survive the other 1% of the time. VaR is the border."
Mathematics
4) Read the text and try to fill in the missing words.
fraction definition well-defined entity assumes fat tails probability
"Given some confidence level the VaR of the portfolio at the confidence level α is given by the smallest number l such that the a)…………. that the loss L exceeds l is not larger than (1 − α)"
l)\leq 1-\alpha\}=\inf\{l\in \real:F_L(l)\geq\alpha\}" type="#_x0000_t75">
The left equality is a b)……….. of VaR. The right equality c)………….. an underlying probability distribution, which makes it true only for parametric VaR. Risk managers typically assume that some d)……………of the bad events will have undefined losses, either because markets are closed or illiquid, or because the e)…………. bearing the loss breaks apart or loses the ability to compute accounts. Therefore, they do not accept results based on the assumption of a f)………… probability distribution. Nassim Taleb has labeled this assumption, "charlatanism." On the other hand, many academics prefer to assume a well-defined distribution, albeit usually one with g)………... This point has probably caused more contention among VaR theorists than any other.
Value at Risk
From Wikipedia, the free encyclopedia
5) Find the words in the text for these definitions.
e) a collection of investments held by an institution or an individual. portfolio
f) refers to accounting for the value of an asset or liability based on the current market price of the asset or liability, or for similar assets and liabilities. mark-to market
g) is a bank regulation, which sets a framework on how banks and depository institutions must handle their capital. regulatory capital
h) is the process of evaluating a strategy, theory, or model by applying it to historical data. back
In financial mathematics and financial risk management, Value at Risk (VaR) is a widely used risk measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, probability and time horizon, VaR is defined as a threshold value such that the probability that the mark-to-market loss on the portfolio over the given time horizon exceeds this value (assuming normal markets and no trading in the portfolio) in the given probability level.
For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one day period, assuming markets are normal and there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day in 20. A loss which exceeds the VaR threshold is termed a “VaR break.”
The 5% Value at Risk of a hypothetical profit-and-loss probability density function
VaR has five main uses in finance: risk management, risk measurement, financial control, financial reporting and computing regulatory capital. VaR is sometimes used in non-financial applications as well. Important related ideas are economic capital, backtesting, stress testing and expected shortfall.
Details
6) Read this part of the text and decide whether the statements are T or F.
a) For common parameters, only 1% and 5% and one day and two weeks are used. F
b) The loss is observable only when there is no trading. T
c) Consequences of disasters will be evident after a longer period of time. T
d) A one-day 95% VaR is different from one-day 5% VaR. F
e) If VaR is negative, the portfolio is making a profit. F
f) The original definition of VaR was the maximum loss at any point during the period.
Common parameters for VaR are 1% and 5% probabilities and one day and two week horizons, although other combinations are in use.
The reason for assuming normal markets and no trading, and to restricting loss to things measured in daily accounts, is to make the loss observable. In some extreme financial events it can be impossible to determine losses, either because market prices are unavailable or because the loss-bearing institution breaks up. Some longer-term consequences of disasters, such as lawsuits, loss of market confidence and employee morale and impairment of brand names can take a long time to play out, and may be hard to allocate among specific prior decisions. VaR marks the boundary between normal days and extreme events. Institutions can lose far more than the VaR amount; all that can be said is that they will not do so very often.
The probability level is about equally often specified as one minus the probability of a VaR break, so that the VaR in the example above would be called a one-day 95% VaR instead of one-day 5% VaR. This generally does not lead to confusion because the probability of VaR breaks is almost always small, certainly less than 0.5.
Although it virtually always represents a loss, VaR is conventionally reported as a positive number. A negative VaR would imply the portfolio has a high probability of making a profit, for example a one-day 5% VaR of negative $1 million implies the portfolio has a 95% chance of making more than $1 million over the next day.
Another inconsistency is VaR is sometimes taken to refer to profit-and-loss at the end of the period, and sometimes as the maximum loss at any point during the period. The original definition was the latter, but in the early 1990s when VaR was aggregated across trading desks and time zones, end-of-day valuation was the only reliable number so the former became the de facto definition. As people began using multiday VaRs in the second half of the 1990s they almost always estimated the distribution at the end of the period only. It is also easier theoretically to deal with a point-in-time estimate versus a maximum over an interval. Therefore the end-of-period definition is the most common both in theory and practice today.
VaR risk management
7) Read this part of the text and try to replace the underlined words with synonyms.
a) exacerbate ………………….. b) routine events …………………………..
c) impairment ………………… d) it pointless to anticipate ………………..
e) foreseeable ………………….. f) to be hedged …………………………..
One specific system uses three regimes.
- One to three times VaR are normal occurrences. You expect periodic VaR breaks. The loss distribution typically has fat tails, and you might get more than one break in a short period of time. Moreover, markets may be abnormal and trading may exacerbate losses, and you may take losses not measured in daily marks such as lawsuits, loss of employee morale and market confidence and impairment of brand names. So an institution that can't deal with three times VaR losses as routine events probably won't survive long enough to put a VaR system in place.
- Three to ten times VaR is the range for stress testing. Institutions should be confident they have examined all the foreseeable events that will cause losses in this range, and are prepared to survive them. These events are too rare to estimate probabilities reliably, so risk/return calculations are useless.
- Foreseeable events should not cause losses beyond ten times VaR. If they do they should be hedged or insured, or the business plan should be changed to avoid them, or VaR should be increased. It's hard to run a business if foreseeable losses are orders of magnitude larger than very large everyday losses. It's hard to plan for these events, because they are out of scale with daily experience. Of course there will be unforeseeable losses more than ten times VaR, but it's pointless to anticipate them, you can't know much about them and it results in needless worrying. Better to hope that the discipline of preparing for all foreseeable three-to-ten times VaR losses will improve chances for surviving the unforeseen and larger losses that inevitably occur.
"A risk manager has two jobs: make people take more risk the 99% of the time it is safe to do so, and survive the other 1% of the time. VaR is the border."
Mathematics
8) Read the text and try to fill in the missing words.
fraction definition well-defined entity assumes fat tails probability
"Given some confidence level the VaR of the portfolio at the confidence level α is given by the smallest number l such that the probability that the loss L exceeds l is not larger than (1 − α)"
l)\leq 1-\alpha\}=\inf\{l\in \real:F_L(l)\geq\alpha\}" type="#_x0000_t75">
The left equality is a definition of VaR. The right equality assumes an underlying probability distribution, which makes it true only for parametric VaR. Risk managers typically assume that some fraction of the bad events will have undefined losses, either because markets are closed or illiquid, or because the entity bearing the loss breaks apart or loses the ability to compute accounts. Therefore, they do not accept results based on the assumption of a well-defined probability distribution. Nassim Taleb has labeled this assumption, "charlatanism." On the other hand, many academics prefer to assume a well-defined distribution, albeit usually one with fat tails. This point has probably caused more contention among VaR theorists than any other.
Intro to Quant Finance: Value at Risk (VaR)
Answer these questions.
1) What is VaR? ……………………………………………………………………….
2) What is Monte Carlo? ………………………………………………………………
3) What are shortcomings? ……………………………………………………………
Listen to and watch the video and answer these questions.
1) How many approaches are there to VaR? ……………………………….
2) What does ROR stand for? ………………………………………………
3) What kind of data is the lecturer using? …………………………………
4) What is Volatility? ………………………………………………………
5) What is wrong with the given sample? ………………………………….
6) What is the name of a shape of the graph? ………………………………
7) What do we need for normal distribution? ……………………………….
8) Why is this distribution not normal? ……………………………………..
Fill in the missing expressions.
9) VaR is the worst expected ……….over some ……………. time period with some
selected …………………
10) The confidence depends on …………………….
11) 95% VaR of the area is to …………, …………… to the left.
12) The graph does not say anything about the magnitude of ………………………
13) You multiply the volatility by ……………………………….
14) VaR is nothing but a standard …………………………………..
Intro to Quant Finance: Value at Risk (VaR)
Answer these questions.
4) What is VaR? ……………………………………………………………………….
5) What is Monte Carlo? ………………………………………………………………
6) What are shortcomings? ……………………………………………………………
Listen to and watch the video and answer these questions.
15) How many approaches are there to VaR? …………………3…….
16) What does ROR stand for? ……………………rate of return…………
17) What kind of data is the lecturer using? …………Google stock data……
18) What is Volatility? …………………………standard deviation……
19) What is wrong with the given sample? ………………too short…….
20) What is the name of a shape of the graph? ………Bell curve, normal distribution…
21) What do we need for normal distribution? ………mean, volatility…….
22) Why is this distribution not normal? ……………………………………..
Fill in the missing expressions.
23) VaR is the worst expected …loss…….over some ……selected………. Time in period with some selected ……confidence……………
24) The confidence depends on ……user……………….
25) 95% VaR of the are is to …the right………, ……5%……… to the left.
26) The graph does not say anything about the magnitude of ………extreme losses………
27) You multiply the volatility by ……………critical value 95% confidence….
28) VaR is nothing but a standard ………………deviation scale…………………..