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.

---

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

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.

---

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.

---

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.

---

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.

---

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.

---

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.

---

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.

---

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.

---

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.

---

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