Exam 20: Value at Risk

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:

VaR as a risk measure has the following deficiency:

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

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?

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

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

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

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?

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)?

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?

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?

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

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

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

The value-at-risk of a portfolio is

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

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

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?

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