Exam 20: Value at Risk

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 is the 99%-VaR of this portfolio?

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 98%-VaR in this scenario is

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)?

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

Monte Carlo is widely-used approach for computing VaR. Relative to other methods which of the following is a benefit of using this approach?

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

Value-at-Risk (VaR) is most closely defined as

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 99%-VaR?

If every position in a portfolio is doubled in size, the risk contribution of the original portion of the portfolio, as measured by VaR, will

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

Which of the following risk measures is not translation invariant (i.e., does not satisfy the property that if we add a risk-free asset to a portfolio with a return of $r$ , the risk of the portfolio should come down by the extent of this addition)?

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 90%-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 98%-VaR of your portfolio is