Exam 20: Value at Risk

Given two portfolios $P _ { 1 }$ and $P _ { 2 }$ ,which risk measure $R ( )$ does not always satisfy the "sub-addivity" property (i.e. ,that $R \left( P _ { 1 } + P _ { 2 } \right) \leq R \left( P _ { 1 } \right) + R \left( P _ { 2 } \right)$ where $R (. )$ is the measure of portfolio risk)?

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 98%-VaR of your portfolio is

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

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

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:

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

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 99%-VaR in this scenario is

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

Which of the following best characterizes the mathematical properties of the risk measure VaR?

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 95%-VaR of your portfolio is

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

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

Which of the following measures of risk does not have the linear homogeneity property?