Exam 20: Value at Risk

A portfolio has a current value of $1000. The annual profit $X$ is distributed normally with mean 100 and standard deviation 100. How much capital is adequate for the portfolio at a 95%-VaR?

Identifying the risk contribution of an asset to a portfolio is more difficult than identifying its return contribution because

"Subadditivity" is the requirement of a coherent risk measure that

"Monotonicity" is the requirement of a risk-measure that if Portfolio A dominates Portfolio B (in the sense of always doing at least as well as B in every state of the world and strictly better in some states), then the risk of Portfolio A should be less than the risk of Portfolio B. Which of the following statements is correct?

VaR as a risk measure has the following deficiency:

Consider a two-asset portfolio invested with $10 in each asset. The mean returns of the two assets are $10 \%$ and $15 \%$ . The correlation of returns is 50%. The standard deviation of returns is 20% and 30%, respectively. What are the risk-contribution proportions of each asset to the 99%-VaR of this portfolio?

If a portfolio is doubled in size, keeping its portfolio structure (holdings proportions) the same as before, the VaR will

The expected shortfall (ES) measure does not satisfy the following coherence property of risk measures:

Worst-case scenario analysis develops a measure that computes, say, for one year's returns

A portfolio has a current value of $1000. The annual profit $X$ is distributed normally with mean 100 and standard deviation 100. What is the probability that the portfolio will be worth less than 800 after one year?

The delta-normal method for computing VaR has many advantages. Which of the following is not a characteristic of the delta-normal approach?

The value-at-risk of a portfolio is

Which of the following is not a valid statement about VaR?

You invest $100 in a corporate bond. You estimate that with probability 0.94, the corporation will pay back the promised amount of $110 at the end of one year; with probability 0.04, the corporation will default and the recovered amount will be $70; and with probability 0.02, the corporation will default and you will recover nothing. The 95%-VaR in this scenario is

VaR fails the following requirement of a "coherent" risk measure:

You invest $100 each in two bonds. Each bond will pay you $110 at the end of the year with probability 0.98 and nothing with probability 0.02. The correlation between the bonds is zero. In this scenario, the 99%-VaR of your portfolio is

VaR-bases risk decomposition is the calculation that allocates the total VaR of a portfolio to each of its assets or subportfolios. Which of the following statements is most valid?

Historical simulation as a method of computing VaR has the following major benefit in comparison to the delta-normal method:

Consider a $900 portfolio with three assets, each held in equal value. The VaR of the portfolio is such that an increase in $1 of any of the asset holdings results in a $0.05 increase in VaR. The VaR of this portfolio is approximately equal to:

You invest $100 in a corporate bond. You estimate that with probability 0.95, the corporation will pay back the promised amount of $110 at the end of one year; with probability 0.04, the corporation will default and the recovered amount will be $70; and with probability 0.01, the corporation will default and you will recover nothing. The 95%-VaR in this scenario is