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YOUR TASK: CALCULATING PORTFOLIO VaR FOR VANE MALLORY

As noted previously, your boss tasked you with reporting VaR for several of the firm's portfolios. The CRO wants all portfolio VaRs reported at both the 90 percent and 99 percent confidence levels to gather as much information as possible about potential losses.

Christian Cross, the CRO of Vane Mallory, asked you to report on two portfolios. Each portfolio is equally weighted and contains five assets. One portfolio is comprised of energy commodities. The second portfolio you are responsible for monitoring contains equities. Information about the portfolios is provided next.

Potential Percentage VaR Losses (Gains) Based on the Various Confidence Levels or Probabilities

Exhibit 24.2 Potential Percentage VaR Losses (Gains) Based on the Various Confidence Levels or Probabilities

Portfolio 1: Energy Commodities

The firm holds a portfolio comprised of five different energy commodities: West Texas Intermediate (WTI) crude oil, Brent crude oil, natural gas, propane, and jet fuel. The firm invests equally in each asset. The current value of the portfolio is $50 million. Five years of monthly spot prices are used to determine the VaR inputs. All data were obtained from the U.S. Energy Information Administration, a division of the U.S. Department of Energy, for the period of 2008 to 2012.

The use of matrix applications in Microsoft Excel is convenient when analyzing portfolios. The expected return of the portfolio is 0.1484 percent, and the volatility (standard deviation) is 7.6366 percent. The covariance matrix and other important information are included in Exhibit 24.3. At the 90 percent and 99 percent confidence levels, the VaRs are approximately $4,696,515 and $8,896,649, respectively. The calculations are as follows:

Portfolio 2: Equities

This portfolio is comprised of the following equities (ticker): Alcoa, Inc. (AA), Citigroup, Inc. (C), Cisco Systems, Inc. (CSCO), Pfizer, Inc. (PFE), and Anadarko Petroleum Corporation (APC). The current value of the portfolio is $50 million, with $10 million invested in each company. One year (252 days) of asset returns are used in construction of VaR components. All asset prices were obtained from Yahoo! Finance for the period of May 22, 2012, through May 24, 2013.

Exhibit 24.3 The Covariance Matrix as Well as the Expected Return and Standard Deviation for Each Portfolio

Panel A: Energy Commodities

Covariance Matrix

WTI

Brent Crude

NatGas

Propane

Jet Fuel

WTI

0.0094

0.0081

0.0011

0.0066

0.0074

Brent Crude

0.0081

0.0083

0.0012

0.0070

0.0074

Nat Gas

0.0011

0.0012

0.0123

0.0019

0.0016

Propane

0.0066

0.0070

0.0019

0.0099

0.0067

Jet Fuel

0.0074

0.0074

0.0016

0.0067

0.0080

Expected Return (Portfolio):

0.0015

Standard Deviation (Portfolio):

0.0764

Panel B: Equities

Covariance Matrix

AA

c

CSCO

PFE

APC

AA

0.0002

0.0002

0.0001

0.0000

0.0002

C

0.0002

0.0004

0.0001

0.0001

0.0002

CSCO

0.0001

0.0001

0.0003

0.0000

0.0001

PFE

0.0000

0.0001

0.0000

0.0001

0.0000

APC

0.0002

0.0002

0.0001

0.0000

0.0003

Expected Return (Portfolio):

0.0014

Standard Deviation (Portfolio):

0.0119

Using matrix applications in Microsoft Excel, the expected return of the portfolio is 0.1440 percent, and the standard deviation is 1.1893 percent. The covariance matrix and associated calculations are provided in Exhibit 24.3, as a point of reference.

At the 90 percent confidence level, the VaR of the equity portfolio is approximately $731,409, while at the 99 percent confidence level the VaR is approximately $1,385,514. The calculations are:

The table presented in Exhibit 24.4 includes data for Apple (AAPL) and Hypercom (HYC). Question 7 will use the information in Exhibit 24.4 to have the reader conduct similar VaR calculations, using Apple Computer and Hypercom as the equities analyzed.

Exhibit 24.4 Data for Apple (AAPL) and Hypercom (HYC)

Date

AAPL Adj. Close

AAPL

Periodic ROR

Date

HYC

Adj. Close

HYC

Periodic ROR

31-Dec

$322.56

30-Sep

$3.10

3-Jan

$329.57

2.15%

1-Oct

$2.97

-4.28%

4-Jan

$331.29

0.52%

2-Oct

$2.90

-2.39%

5-Jan

$334.00

0.81%

5-Oct

$2.98

2.72%

6-Jan

$333.73

-0.08%

6-Oct

$3.07

2.98%

7-Jan

$336.12

0.71%

7-Oct

$3.11

1.29%

10-Jan

$342.45

1.87%

8-Oct

$3.04

-2.28%

11-Jan

$341.64

-0.24%

9-Oct

$3.04

0.00%

12-Jan

$344.42

0.81%

12-Oct

$3.07

0.98%

13-Jan

$345.68

0.37%

13-Oct

$3.13

1.94%

14-Jan

$348.48

0.81%

14-Oct

$3.14

0.32%

Average

0.7729%

15-Oct

$3.09

-1.61%

Variance

0.0051%

16-Oct

$3.04

-1.63%

Volatility

0.7125%

19-Oct

$3.02

-0.66%

20-Oct

$2.94

-2.68%

21-Oct

$2.99

1.69%

22-Oct

$3.01

0.67%

23-Oct

$3.27

8.28%

26-Oct

$3.11

-5.02%

27-Oct

$3.02

-2.94%

28-Oct

$3.00

-0.66%

29-Oct

$3.00

0.00%

30-Oct

$2.85

-5.13%

Average

-0.3822%

Variance

0.0882%

Volatility

2.9704%

 
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