Kingpin804

Value at risk (VAR) is a benchmark associated with a given probability. The actual loss:

A) may be much greater.

B) cannot exceed this amount.

C) is expected to be the average of the expected return of the portfolio and VAR.

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VAR is a benchmark that gives an estimate of what magnitude of loss would not be unusual. The actual loss for any given time period can be much greater.

Kingpin804

All of the following are considered to be strengths of the historical value at risk (VAR) methodology EXCEPT:

A) no assumption regarding a normal returns distribution is required.

B) minimal data is needed.

C) no variance/covariance matrix is required.

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Historical VAR requires a lot of returns data, which may not be available for some asset classes.

Kingpin804

All of the following are considered to be weaknesses of the variance/covariance value at risk (VAR) methodology EXCEPT:

A) the variance/covariance matrix may not be stable over time.

B) market data necessary to compute VAR is often not available.

C) the VAR computation becomes complex as portfolio complexity increases.

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One of the strengths of the variance/covariance VAR is that the required market data is readily available in most cases.

Kingpin804

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.

B) A lot of data is needed for the time period of interest.

C) For some assets you may face model risk.

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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.

Kingpin804

The method for calculating value at risk that is the simplest and rests heavily on means and variances is the:

A) historical method.

B) Monte Carlo method.

C) delta-normal method.

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The delta-normal method uses means and variances and makes calculations under the assumption that the distribution of returns is normal.

Kingpin804

The method for calculating value at risk that uses the fewest assumed inputs is the:

A) Monte Carlo method.

B) delta-normal method.

C) historical method.

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The historical method uses past values and makes no explicit assumptions about inputs. It assumes that past patterns are indicative of future patterns.

Kingpin804

Which of the following statements exhibits a weakness of historical value at risk (VAR)?

A) 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.

B) 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.

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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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 VAR’s. Both remaining answer choices describe situations where VAR may differ, but none are the result of a weakness in historical VAR.

Kingpin804

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.

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% probability given the standard deviation of portfolio Z is 22%?

A) $1,900,000.

B) $1,760,000.

C) $1,499,000.

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VAR = Vp[Expected return-(z)(standard deviation)]
Expected return = (0.25)(12) + (0.25)(14) + (0.25)(5) + (0.25)(14) = 11.25%
VAR = 2,000,000[0.1125 − (1.65)(0.22)] = −501,000
2,000,000 − 501,000 = 1,499,000

Kingpin804

John Dumas is in charge of $100 million of equity portfolio.  He expects a return of 10% with a standard deviation of 8%.  What will be the minimum value of portfolio at 95% probability.  Z scores from standard normal distribution are:

• 10% = 1.28
• 5% = 1.65
• 2.5% = 1.96
• 1% = 2.33

A) 92.8 million.

B) 96.80 million.

C) 98.4 million.

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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.

Kingpin804

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?

A) $570,000.

B) $978,000.

C) $561,000.

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VAR = (-0.0187)(30,000,000) = -$561,000 therefore the 1% daily value at risk is $561,000.