Kingpin804

Assuming that adequate daily data is available, a criticism of the Monte Carlo value at risk (VAR) methodology, but not the other VAR methodologies is that it:

A) requires a normal distribution of returns.

B) is relatively inflexible.

C) is exposed to model risk.

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The Monte Carlo VAR methodology uses a returns generation model to develop a set of returns scenarios or paths. If the model is incorrect, the validity of the VAR estimates is questionable. The historical VAR methodology will suffer model risk only if insufficient daily data is available, and a model is employed to derive estimates.

Kingpin804

A disadvantage of the Monte Carlo method for calculating value at risk is that:

A) it requires the normality assumption.

B) all of these choices are correct.

C) it is computationally intensive.

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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.

Kingpin804

All of the following are advantages in Monte Carlo simulation approach to VAR estimation EXCEPT:

A) no model risk.

B) no assumption needed regarding linearity.

C) no assumption needed regarding normality.

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The historical method of VAR relies on past patterns continuing into the future thus you are extrapolating in a linear fashion into the future. The analytical method assumes a normal distribution. The Monte Carlo method relies on neither assumption and any distribution or correlation between assets can be used. This leads to modeling risk in the Monte Carlo simulation because if your inputs are inaccurate your output will also be inaccurate.

Kingpin804

Which value at risk methodology is most subject to model risk?

A) Monte Carlo simulation.

B) Parametric.

C) Variance/covariance.

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Monte Carlo simulation is subject to model risk.

Kingpin804

Which of the methods for calculating Value At Risk (VAR) do asset managers most commonly use?

A) Variance/covariance.

B) Historical.

C) Monte Carlo simulation.

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The variance/covariance (or parametric) method is most commonly used by asset managers.

Kingpin804

Which of the common methods of computing value at risk relies on the assumption of normality?

A) Variance/covariance.

B) Monte Carlo simulation.

C) Historical.

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The variance/covariance method relies on the assumption of normality.

Kingpin804

A portfolio manager determines that his portfolio has an expected return of $20,000 and a standard deviation of $45,000. Given a 95% confidence level, what is the portfolio's VAR?

A) $74,250.

B) $54,250.

C) $43,500.

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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)].

Kingpin804

Which methodology for computing value at risk (VAR) relies on the assumption of normally distributed returns?

A) Variance/Covariance VAR.

B) Binomial VAR.

C) Historical VAR.

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The variance/covariance VAR methodology relies on the assumption that returns are normally distributed.

Kingpin804

Consider a portfolio that has the following characteristics:

• An expected return of 12%.
• $1,000,000 portfolio value.
• Annual standard deviation equal to 6%.

What is the value at risk (VAR) for the portfolio at the 99% probability level?

A) -$19,800.

B) $980,200.

C) 99% confident the maximum loss for any one year is $1,800.

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VAR = (portfolio value)[expected Rp + Z(σ)]
($1,000,000)[0.12 + (-2.33)(0.06)]
= -$19,800

mouse123

Mark Stober, William Robertson, and James McGuire are consultants for a regional pension consultancy. One of their clients, Richard Smitherspoon, chief investment officer of Quality Car Part Manufacturing, recently attended a conference on risk management topics for pension plans. Smitherspoon is a conservative manager who prefers to follow a long-term investment strategy with little portfolio turnover. Smitherspoon has substantial experience in managing a defined benefit plan but has little experience with risk management issues. Smitherspoon decides to discuss how Quality can begin implementing risk management techniques with Stober, Robertson, and McGuire. Quality's risk exposure is evaluated on a quarterly basis.
Before implementing risk management techniques, Smitherspoon expresses confusion regarding some measures of risk management. "I know beta and standard deviation, but what is all this stuff about convexity, delta, gamma, and vega?" Stober informs Smitherspoon that delta is the first derivative of the call-stock price curve, and Robertson adds that gamma is the relationship between how bond prices change with changing time to maturity.
Smitherspoon is still curious about risk management techniques, and in particular the concept of VAR. He asks, "What does a daily 5% VAR of $5 million mean? I just get so confused with whether VAR is a measure of maximum or minimum loss. Just last month, the consultant from MinRisk, a competing consulting firm, told me it was 'a measure of maximum loss, which in your case means we are 95% confident that the maximum 1-day loss is $5.0 million.'" McGuire states that his definition of VAR is that "VAR is a measure that combines probabilities over a certain time horizon with dollar amounts, which in your case means that one expects to lose a minimum $5 million five trading days out of every 100."
Smitherspoon expresses bewilderment at the different methods for determining VAR. "Can't you risk management types formulate a method that works like calculating a beta? It would be so easy if there were a method that allowed one to just use mean and standard deviation. I need a VAR that I can get my arms around."
The next week, Stober visits the headquarters of TopTech, a communications firm. Their CFO is Ralph Long, who prefers to manage the firm's pension himself because he believes he can time the market and spot upcoming trends before analysts can. Long also believes that risk measurement for TopTech can be evaluated annually because of his close attention to the portfolio. Stober calculates TopTech's 95% surplus at risk to be $500 million for an annual horizon. The expected return on TopTech's asset base (currently at $2 billion) is 5%. The plan has a surplus of $100 million. Stober uses a 5% probability level to calculate the minimum amount by which the plan will be underfunded next year.
Regarding the statements on delta and gamma, are Stober and Robertson correct or incorrect?

A) Only Robertson is correct.

B) Only Stober is correct.

C) Both are correct OR both are incorrect.

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Stober is correct, and Robertson is incorrect.
Gamma is the second derivative of the change in the underlying asset price movements. Stober correctly defines delta. (Study Session 14, LOS 34.b)

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Regarding the definitions of VAR, are MinRisk and McGuire correct or incorrect?

A) Neither is correct.

B) One is correct.

C) Both are correct.

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Both MinRisk and McGuire are correct.
VAR can be considered a minimum loss expected over a time horizon at a given probability. In this particular case, one would expect to exceed the VAR 5% of the time. MinRisk interpretation is also correct. Watch the wording in VAR questions.
VAR is a measure that combines probabilities over a certain time horizon with dollar amounts, which in the statement means that one expects to lose at least $5 million in five trading days out of 100. (Study Session 14, LOS 34.e)

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Of the following VAR calculation methods, the measure that would most likely suit Smitherspoon is the:

A) historical simulation method.

B) Monte Carlo simulation method.

C) variance-covariance method.

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Variance-covariance method.
The variance-covariance method, also known as the delta-normal method, only requires estimates of mean and standard deviation of returns to estimate VAR. This is the closest method to which Smitherspoon refers. (Study Session 14, LOS 34.f)

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Smitherspoon asks Stober if it would be possible to calculate the VAR for each individual portfolio manager as well as the overall Quality fund. Determine which of Stober's three responses is most incorrect.

• 
  "VAR is a universally accepted risk measure because it can be applied to practically any investment and is interpreted effectively the same way in each case; it is either the minimum or maximum loss at a given level of significance or confidence. For me to calculate the delta-normal VAR, you will need to provide me with each manager's historical returns distribution and expected return, the time frame you wish to use, and the desired level of significance. I can then calculate VAR for each manager using historical standard deviations and expected returns."
• 
  "We can calculate VAR using: the delta-normal method (also known as the mean variance approach), the historical method, or the Monte Carlo method. To calculate each manager's 95% VAR, all we would have to do is use standard deviations and expected returns to calculate 90% confidence intervals."
• 
  "Because of the way it is calculated, individual mean-variance VARs can probably be calculated for each of our portfolio managers, regardless of their style or assets under management. The overall fund VAR is then the sum of the individual VARs. To calculate the fund VAR directly, we would have to measure the fund's overall expected return and standard deviation. The problem with calculating it directly like this, however, is that to calculate the fund standard deviation we must consider the correlations of the managers' returns."

A) Response 2.

B) Response 3.

C) Response 1.

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Response 1 is almost a definition of VAR. Response 2 might appear incorrect at first, because of the reference to the 90% confidence interval. Remember, however, that VAR considers only the lower tail of the distribution. To calculate the 95% VAR we use the Z-value corresponding to a 90% confidence interval (1.65), because that isolates the lower 5% of the distribution. Response 3 has an incorrect component. The last statement about calculating the overall VAR directly is correct; you must incorporate the correlations of the managers' returns to calculate the overall fund standard deviation. That is the problem with using individual VARs to calculate a fund VAR; VAR is not additive. Adding individual VARs overstates the fund VAR, because adding them ignores the correlations of individual manager's returns. (Study Session 14, LOS 34.d)

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Using Stober's 5% probability level, the minimum amount by which TopTech's plan will be underfunded next year is closest to:

A) $5 million.

B) $300 million.

C) $25 million.

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$300 million
The current surplus is $100 million, and the asset base is also expected to generate $100 million ($2,000 million × 0.05). The 5% SAR of $500 million indicates that the underfunding of the plan at year end will be $300 (= 200 − 500) or more, 5% of the time. (Study Session 14, LOS 34.f)

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VAR is a more relevant measure of firm risk for:

A) Quality, because of its industry type.

B) Quality, because of its measurement process.

C) TopTech, because of its industry type.

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VAR will be a more relevant risk measure for Quality because its portfolio experiences less turnover and because VAR is evaluated more frequently.
Coupling a high turnover with a long time horizon decreases VAR's usefulness. VAR is calculated for a specific portfolio at a point in time. High turnover will change a portfolio's composition, which will also change the underlying statistical characteristics of the portfolio. These changes in statistical characteristics then decrease the usefulness of VAR calculations, especially in situations with long time horizons. (Study Session 14, LOS 34.e)