### Is minimizing the var the same as minimizing the variances

Assignment Help Operation Management
##### Reference no: EM13918885

This problem requires a basic understanding of the normal probability distribution. In- vestors are often interested in knowing the probabilities of poor returns. For example, for what cutoff return will the probability of the actual return falling below this cutoff value be at most 1%?
Consider the solution to the Markowitz portfolio problem given in Figure 8.9. The mean return of the portfolio is 10% and the standard deviation (calculated by taking the square root of the variance, which is the objective function value) is

s = 227.13615 = 5.209237

Assume that the portfolio scenario returns are normally distributed about the mean return. From the normal probability table, we see that less than 1% of the returns fall more than 2.33 standard deviations below the mean. This result implies a probability of 1% or less that a portfolio return will fall below

10 - (2.33)(5.209237) = -2.1375

Stated another way, if the initial value of the portfolio is \$1, then the investor faces a probability of 1% of incurring a loss of 2.1375 cents or more. The value at risk is 2.1375 cents at 1%. This measure of risk is called the value at risk, or VaR. It was popularized by JPMorgan Chase & Co. in the early 1990s (then, just JP Morgan).

A table of normal probabilities appears in Appendix B, but they are also easily calcu- lated in LINGO and Excel. In LINGO the function @PSN(Z) and the equivalent function NORMDIST in Excel provide the probability that a standard normal random variables is less than Z.

a. Consider the Markowitz portfolio problem given in equations (8.10) through (8.19). Delete the required return constraint (8.18), and reformulate this problem to minimize the VaR at 1%.

b. Is minimizing the VaR the same as minimizing the variances of the portfolio? Answer Yes or No, and justify.

c. For a fixed return, is minimizing the VaR the same as minimizing the variances of the portfolio? Answer Yes or No, and justify.

Text Book: An Introduction to Management Science: Quantitative Approaches to Decision. By David Anderson, Dennis Sweeney, Thomas Williams, Jeffrey Camm, James Cochran.

#### What was the percentage change in productivity

A parcel delivery company delivered 103,000 packages in 2001 wh r n it's average employment was 84 drivers. In 2002 the firm handled 112,000 delivered with 96 drivers. What wa

#### What is the value internal assesement tools

Consider your strategic plan. Describe a few key sources of information used for locating vital internal information. What is the value internal assesement tools have on formu

#### Employ techniques of strategic workforce planning

Explain how the dean of a college would employ techniques of strategic workforce planning to decide how many faculty and staff to employ in the coming academic year and which

#### The reasons for the use of job order cost system method

A job order cost system is a system that accumulates costs for each job. Consider the aspects of job order costing and respond to the following: Discuss the types of industrie

#### About balanced scorecard and competing forces

what have you learned about balanced scorecard/competing forces? Are measures missing? What measures are superior? What is your root cause analysis of what makes an organizati

#### What is the firms expected profit

Q in the above table is the optimal newsvendor quantity and "Expected Profit" is the news-vendor expected profit if Q is ordered. The firm will produce some parkas well in a

#### The realities of the contemporary business world include

The realities of the contemporary business world include all of the following trends EXCEPT: A coal extracting company is worried about the depleting coal reserves in various

#### Traditional line planning and contemporary line planning

What is the key difference between traditional line planning and contemporary line planning? What is the relationship between organizational structure and merchandise planning