Homework Answers
Expected shortfall as in the question, is a risk measure which is also known as conditional VaR. VaR is a tool where it is used to measure a the risk of a portfolio by evaluating the coherence.
To prove that the expected shortfall is a coherent risk measure, we'll take an example to discuss. If we consider two assets and calculate over it's closing stock prices to decide which investment is risky, we calculate the VaR to find out the confidence interval and evaluate the expected shortfall with the help of daily returns' distributions. Hence, it is proven that an expected shortfall aligns with the properties of coherent risk such as monotonicity, sub-additivity and homogenity.
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coherent risk measure
Prove that expected shortfall is a coherent risk measure.
Prove that expected shortfall...
2. What is the difference between expected shortfall and value at risk? What is the theoretical...
2. What is the difference between expected shortfall and value at risk? What is the theoretical advantage of expected shortfall over value at risk?
What is the one-day 95% VaR (value at risk) and the ES (expected shortfall)? p =...
What is the one-day 95% VaR (value at risk) and the ES (expected shortfall)? p = 1/24 for −12 ≤ π ≤ 0 p = 1 /20 for 0 ≤ π ≤ +10
What difference does volatility scaling make on estimating the VaR and expected shortfall when we use historical simulation?
What difference does volatility scaling make on estimating the VaR and expected shortfall when we use historical simulation?
Beta is a measure of systematic risk. It is a relative risk measure to show you...
Beta is a measure of systematic risk. It is a relative risk measure to show you how sensitive the stock price is related to market movement, i.e., the S&P 500 index. When calculating beta, you need to regress y (stock return) against x (S&P 500 index return) and the coefficient of the x is the beta, please refer to the excel posted on module 6. I would like you to comment on the betas of the following ETFs: UGAZ, TVIX...
Prove that convex combination of probability measure is also a probability measure
Prove that convex combination of probability measure is also a probability measure
5. Coherent States (Answer only question 5 for part a, b, and c) A coherent state is an Eigenstat...
5. Coherent States (Answer only question 5 for part a, b, and
c)
A coherent state is an Eigenstate of annihilation / lowering
operator
c) Baker- Campbell- Hausdorff Formula [Hint: Define the functions fa-eaA+8), ģ(A)-eä eABe-12 č. Note that these functions are equal at -0, and show that they satisfy the same differential equation: df/di (A+ B)f and dg/da (A+B)g Therefore, the functions are themselves equal for all λ.] A useful application of BCH formula is given in problem 5...
Beta is a measure of ______? - Firm specific risk - Unique risk - Diversifiable risk...
Beta is a measure of ______? - Firm specific risk - Unique risk - Diversifiable risk - Market risk
Which statement is TRUE? a) All of these statements are false b) The measure of risk...
Which statement is TRUE? a) All of these statements are false b) The measure of risk for a security held in a diversified portfolio is standard deviation c) As more stocks are added to a portfolio, total risk is expected to fall but at an increasing rate. So if one were to invest in enough stocks, total risk could be eliminated. d) Diversification reduces the portfolio’s expected return because it reduces the portfolio’s total risk e) Proper diversification can reduce...
measure of total risk
A measure of total risk is the ______________
Risk Measures: What is the best measure of risk for an asset held in isolation (i.e.,...
Risk Measures: What is the best measure of risk for an asset held in isolation (i.e., comparing risk of one asset to one other asset)? What is the best measure of risk for an asset held in a portfolio?
2. What is the difference between expected shortfall and value at risk? What is the theoretical advantage of expected shortfall over value at risk?
5. Coherent States (Answer only question 5 for part a, b, and
c)
A coherent state is an Eigenstate of annihilation / lowering
operator
c) Baker- Campbell- Hausdorff Formula [Hint: Define the functions fa-eaA+8), ģ(A)-eä eABe-12 č. Note that these functions are equal at -0, and show that they satisfy the same differential equation: df/di (A+ B)f and dg/da (A+B)g Therefore, the functions are themselves equal for all λ.] A useful application of BCH formula is given in problem 5...
Risk Measures: What is the best measure of risk for an asset held in isolation (i.e., comparing risk of one asset to one other asset)? What is the best measure of risk for an asset held in a portfolio?
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