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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?

A) $43,500.

B) $54,250.

C) $74,250.

D) $94,250.

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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)].

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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?

A) $980,200.

B) 8.0%.

C) -$19,800.

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

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

A) Binomial VAR.

B) Historical VAR.

C) Variance/Covariance VAR.

D) Monte Carlo 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.

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

A) Historical.

B) Monte Carlo simulation.

C) Variance/covariance.

D) Price matrix.

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Answer and Explanation

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

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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%?

A) $1,900,000.

B) $1,760,000.

C) $1,980,000.

D) $1,499,000.

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Answer and Explanation

VAR = V_p[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

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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) $561,000.

B) $978,000.

C) $1,123,000.

D) $570,000.

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Answer and Explanation

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

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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

A) 98.4 million.

B) 92.8 million.

C) 96.80 million.

D) 90.32 million.

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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.