标题: Reading 37: Risk Management －LOS f [打印本页]
作者: cfaedu 时间: 2008-9-17 17:18 标题: [2008] Session 12－Reading 37: Risk Management －LOS f
CFA Institute Area 3-5, 7, 12, 14-18: Portfolio Management
Session 12: Risk Management
Reading 37: Risk Management
LOS f: Compare and contrast the analytical (variance-covariance), historical, and Monte Carlo methods for estimating VAR and discuss the advantages and disadvantages of each.
作者: cfaedu 时间: 2008-9-17 17:18
John Dumas is in charge of $100 million of equity portfolio. He expects a return of 10 percent with a standard deviation of 8 percent. What will be the minimum value of portfolio at 95 percent probability. Z scores from standard normal distribution are:
- 10% = 1.28
- 5% = 1.65
- 2.5% = 1.96
- 1% = 2.33
Answer and Explanation
Maximum possible loss at 95% probability = 10 - 1.65*8 = -3.2 million.
Minimum value of portfolio at 95% probability = 100 - 3.2 = 96.80 million.
作者: cfaedu 时间: 2008-9-17 17:19
Robert Meznar is currently employed as a senior software architect in a large established software company. He is 38 years old, and his current salary is $80,000 after tax. Meznar recently sold his stock (acquired through stock options) in an Internet start up company. The entire proceeds of $2 million is held in treasury securities.John Snow, CFA, of Capital Associates has been forwarded the file of Meznar to suggest an appropriate portfolio. Snow relies heavily on the following forecasts, furnished by the firm, for long term returns for different asset classes. He has already developed three possible portfolios for Meznar.
John Snow, CFA, of Capital Associates has been forwarded the file of Meznar to suggest an appropriate portfolio. Snow relies heavily on the following forecasts, furnished by the firm, for long term returns for different asset classes. He has already developed three possible portfolios for Meznar.
| Asset Class | Return | Standard Deviation | X | Y | Z |
| U.S. Stock | 12.0% | 16% | 40% | 30% | 25% |
| Non U.S. Stocks | 14.0 | 24% | 0 | 15 | 25% |
| U.S. Corporate bonds | 7.0 | 10% | 60 | 15 | 0 |
| Municipal Bonds | 5.0 | 8% | 0 | 20 | 25 |
| REIT | 14 | 14% | 0 | 20 | 25 |
What may be the lowest value of portfolio Z within the next one year according to value at risk, at 95 percent probability given the standard deviation of portfolio Z is 22%?
Answer and Explanation
VAR = Vp[Expected return-(z)(standard deviation)]Expected return = (.25)(12) + (.25)(14) + (.25)(5) + (.25)(14) = 11.25%
VAR = 2,000,000[.1125-(1.65)(.22)] = -501,000
2,000,000 - 501,000 = 1,499,000
Expected return = (.25)(12) + (.25)(14) + (.25)(5) + (.25)(14) = 11.25%
VAR = 2,000,000[.1125-(1.65)(.22)] = -501,000
2,000,000 - 501,000 = 1,499,000
作者: cfaedu 时间: 2008-9-17 17:19
Gregory Chambers is interested in estimating the daily VAR (with 99% probability) of bank's fixed income portfolio, currently valued at $30 million. The portfolio has the following returns over the past 200 days (ranked from high to low).
1.9%, 1.87%, 1.85%, 1.79%......-1.78%, -1.81%, -1.84%, -1.87%, -1.91%
What will be the VAR estimate using the historical method?
Answer and Explanation
VAR = (-0.0187)(30,000,000) = -$561,000 therefore the 1% daily value at risk is $561,000.
作者: cfaedu 时间: 2008-9-17 17:21
Which of the methods for calculating Value At Risk (VAR) do asset managers most commonly use?
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| B) | Monte Carlo simulation. |
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Answer and Explanation
The variance/covariance (or parametric) method is most commonly used by asset managers.
作者: cfaedu 时间: 2008-9-17 17:22
A portfolio manager determines that his portfolio has an expected return of $20,000 and a standard deviation of $45,000. Given a 95 percent confidence level, what is the portfolio's VAR?
Answer and Explanation
The expected outcome is $20,000. Given the standard deviation of $45,000 and a z-score of 1.65 (95% confidence level for a one-tailed test), the VAR is 54,250 [=20,000 1.65 (45,000)].
作者: cfaedu 时间: 2008-9-17 17:22
Consider a portfolio that has the following characteristics:
- An expected return of 12 percent
- $1,000,000 portfolio value
- Annual standard deviation equal to 6 percent
What is the value at risk (VAR) for the portfolio at the 99 percent probability level?
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| D) | 99% confident the maximum loss for any one year is $1,800. |
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Answer and Explanation
VAR = (portfolio value)[expected Rp + Z(σ)]
($1,000,000)[.12 + (-2.33)(.06)]
= -$19,800
VAR = (portfolio value)[expected Rp + Z(σ)]
($1,000,000)[.12 + (-2.33)(.06)]
= -$19,800
作者: cfaedu 时间: 2008-9-17 17:22
Which methodology for computing value at risk (VAR) relies on the assumption of normally distributed returns?
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C) | Variance/Covariance VAR. |
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Answer and Explanation
The variance/covariance VAR methodology relies on the assumption that returns are normally distributed.
The variance/covariance VAR methodology relies on the assumption that returns are normally distributed.
作者: cfaedu 时间: 2008-9-17 17:23
Which of the following statements exhibits a weakness of historical value at risk (VAR)?
| A) | The manager of the Quality Value Fund has a normal distribution of returns and calculates a historical daily VAR of $300. The manager of the Pinnacle Fund has a negatively skewed return distribution and calculates a daily VAR of $360. |
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B) | The manager of the Matrix Small Cap Index Fund calculates a historical daily VAR at the 95% confidence level of $4,080 using Russell 2000 Index returns from 1987-2001. The manager of the Smith Small Cap Index Fund, which is the same size as the Matrix Small Cap Index Fund, calculates a historical daily VAR at the 95% confidence level of $4,210 using Russell 2000 Index returns from 1990-2001.
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| C) | In order to account for instability in the standard deviation of fund returns, the manager of the Spencer Fund uses a decay factor in her VAR calculation. |
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| D) | The manager of the Williams Balanced Fund has an allocation of 50 percent equity and 50 percent fixed income and calculates a historical daily VAR of $2,100. The manager of the Paulson Balanced Fund has an allocation of 60 percent equity and 40 percent fixed income and calculates a historical daily VAR of $2,800. |
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Answer and Explanation
The manager of the Matrix Small Cap Fund uses index data from 1987-2001, while the manager of the Smith Small Cap Index Fund uses index data from 1990-2001, and each comes up with a different VAR calculation. This discrepancy illustrates that historical VAR is sample driven in that different samples of the same data, in this case Russell 2000 Index returns, may lead to different VARs. The other answer choices describe situations where VAR may differ, but none are the result of a weakness in historical VAR.
作者: cfaedu 时间: 2008-9-17 17:24
Which of the common methods of computing value at risk relies on the assumption of normality?
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| B) | Monte Carlo simulation. |
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Answer and Explanation
The variance/covariance method relies on the assumption of normality.
作者: cfaedu 时间: 2008-9-17 17:24
Which value at risk methodology is most subject to model risk?
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C) | Monte Carlo simulation. |
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Answer and Explanation
Monte Carlo simulation is subject to model risk.
作者: cfaedu 时间: 2008-9-17 17:25
Which of the following factors is the common weakness in historical and Monte Carlo Simulation approach to VAR estimation?
| A) | Both assume that historical variance-covariance matrix is stable. |
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| B) | A lot of data is needed for time period of interest. |
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C) | For some assets you may face model risk. |
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| D) | Both assume normal distribution. |
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Answer and Explanation
The historical method uses actual returns for the position in question. An advantage of the historical method is not having to assume any particular distribution. A disadvantage is that it assumes past performance is representative of what can occur in the future, which may not be the case. The Monte Carlo simulation method for calculating VAR usually involves generating random numbers with a computer. The generated numbers represent possible returns of the asset or portfolio. An advantage is that Monte Carlo simulation does not require the normality assumption and can accommodate the required assumptions for complex relationships. A disadvantage is the requirement for many managerial assumptions and a great deal of computer time and calculations. The historical method and Monte Carlo Simulation both suffer from modeling risk.
The historical method uses actual returns for the position in question. An advantage of the historical method is not having to assume any particular distribution. A disadvantage is that it assumes past performance is representative of what can occur in the future, which may not be the case. The Monte Carlo simulation method for calculating VAR usually involves generating random numbers with a computer. The generated numbers represent possible returns of the asset or portfolio. An advantage is that Monte Carlo simulation does not require the normality assumption and can accommodate the required assumptions for complex relationships. A disadvantage is the requirement for many managerial assumptions and a great deal of computer time and calculations. The historical method and Monte Carlo Simulation both suffer from modeling risk.
作者: cfaedu 时间: 2008-9-17 17:25
All of the following are advantages in Monte Carlo simulation approach to VAR estimation EXCEPT:
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| B) | no assumption needed regarding normality. |
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| C) | no assumption needed regarding linearity. |
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| D) | more flexible than other VAR estimation methodologies. |
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Answer and Explanation
作者: cfaedu 时间: 2008-9-17 17:28
The method for calculating value at risk that is the simplest and rests heavily on means and variances is the:
Answer and Explanation
The delta-normal method uses means and variances and makes calculations under the assumption that the distribution of returns is normal.
作者: cfaedu 时间: 2008-9-17 17:36
The method for calculating value at risk that uses the fewest assumed inputs is the:
Answer and Explanation
The historical method uses past values and makes no explicit assumptions about inputs. It assumes that past patterns are indicative of future patterns.
作者: cfaedu 时间: 2008-9-17 17:36
A disadvantage of the Monte Carlo method for calculating value at risk is that:
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| B) | it requires the normality assumption. |
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| C) | all of these choices are correct. |
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D) | it is computationally intensive. |
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Answer and Explanation
For the Monte Carlo method, the advantages are that it does not require the normality assumption, and it is flexible insofar as it can accommodate a variety of assumptions regarding complex relationships. The main disadvantage is that it is often computationally intensive.
作者: cfaedu 时间: 2008-9-17 17:38
In response to Coopers statement regarding VARs incomparability across managers, Myers is most likely to: | A) | agree and add that it is because of the complexity of the calculations involved. |
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| B) | disagree and add that the characteristics of a competitor's portfolio can be estimated through VAR modeling techniques. |
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| C) | disagree because calculations do not rely on normal return distributions. |
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D) | agree and add that this is due to its inherent model risk. |
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Answer and Explanation
VAR is relatively incomparable across managers due to its inherent model risk. For example, two people can be given an assignment to compute the VAR for the same underlying asset and the results will likely be different due to the use of different methodologies and model assumptions. Neither answer is necessarily wrong. The bottom line here is that peer group evaluation using VAR is not very useful unless one can be sure that the same VAR techniques and assumptions are used to evaluate all portfolios.
With respect to the use of stress testing in VAR analysis, Burns and Smith are, respectively:
Answer and Explanation
Burns is incorrect and Smith is incorrect. A particular VAR estimate is based on a given model and its parameters. In stress testing (or scenario analysis), the analyst varies the inputs to the VAR estimation process sometimes to the extreme and analyzes the impact of this movement on the computed VAR. Stress testing is "what if" analysis, and its main contribution is that it shows how reliable a particular VAR estimate is.
In response to Myers question about the most fundamental problem associated with estimating VAR, Bishop is most likely to reply that the main problem is: | A) | the lack of available data to compute VAR. |
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| B) | that VAR is difficult to calculate. |
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C) | the inability to accurately derive the "true" probability distribution for the asset or portfolio under evaluation. |
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| D) | that VAR calculations depend on symmetrical payout profiles. |
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Answer and Explanation
The fundamental problem with VAR analysis is that the analyst must estimate the "true" probability distribution for the asset or portfolio under evaluation. This means that in order to give the analyst reliable results, the quantitative model must accurately describe the price process of the asset.
Regarding credit risk and VAR, Banks and Myers are, respectively:
Answer and Explanation
Banks is correct but Myers conclusion is incorrect. Since credit risk increases when the value of the position held increases, we should focus on the upper not lower tail of the distributions of gains on positions held.
McAdams, Blatt and Berry are, respectively: A) | correct; incorrect; incorrect. |
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| B) | correct; correct; incorrect. |
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| C) | incorrect; correct; incorrect. |
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| D) | incorrect; incorrect; incorrect. |
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Answer and Explanation
A key advantage of Monte Carlo simulation is the ability to deal with the assumptions required to handle complex relationships. McAdams statement is correct. The key advantage of the historical method is that you do not have to assume a particular distribution. Therefore, Blatt is incorrect. A major disadvantage of the historical method is that we have to assume that past performance is representative of future performance; it is not a disadvantage of the variance-covariance method. Therefore, Berry is also incorrect.
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