Reading 37: Risk Management －LOS f advantages, methods, discuss, contrast

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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.

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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.

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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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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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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 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.

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.

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.

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.

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

A) Historical.

B) Monte Carlo simulation.

C) Variance/covariance.

D) Rounding estimation.

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Answer and Explanation

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