What does rho measure? Group of answer choices None of these The rate of change of delta with the asset price. The sensitivity of a portfolio value to interest rate changes. The rate of change of the portfolio value with the passage of time.
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Consider a portfolio of options on a single asset. Suppose that the delta of the portfolio (calculated with respect to actual changes) is 12, the value of the asset is $10, and the daily volatility of the asset is 2%. What is the delta with respect to proportional changes? Estimate the one-day 95% VaR for the portfolio from the delta.
Akash M.
The rate of return of an asset is the change in price divided by the initial price (denoted as $r$ ). Suppose that $\$ 10,000$ is used to purchase shares in three stocks with rates of returns $X_{1}, X_{2}, X_{3}$. Initially, $\$ 2500, \$ 3000,$ and $\$ 4500$ are allocated to each one, respectively. After one year, the distribution of the rate of return for each is normally distributed with the following parameters: $\mu_{1}=0.12, \sigma_{1}=0.14, \mu_{2}=0.04, \sigma_{2}=0.02, \mu_{3}=0.07, \sigma_{3}=0.08$ (a) Assume that these rates of return are independent. Determine the mean and variance of the rate of return after one year for the entire investment of $\$ 10,000$. (b) Assume that $X_{1}$ is independent of $X_{2}$ and $X_{3}$ but that the covariance between $X_{2}$ and $X_{3}$ is $-0.005 .$ Repeat part (a). (c) Compare the means and variances obtained in parts (a) and (b) and comment on any benefits from negative covariances between the assets.
Joint Probability Distributions
Linear Functions of Random Variables
The rate of return of an asset is the change in price divided by the initial price (denoted as $r$ ). Suppose that $\$ 10,000$ is used to purchase shares in three stocks with rates of returns $X_{1}, X_{2}$, $X_{3} .$ Initially, $\$ 2500, \$ 3000,$ and $\$ 4500$ are allocated to each one, respectively. After one year, the distribution of the rate of return for each is normally distributed with the following parameters: $$ \mu_{1}=0.12, \sigma_{1}=0.14, \mu_{2}=0.04, \sigma_{2}=0.02, \mu_{3}=0.07 $$ $\sigma_{3}=0.08$ a. Assume that these rates of return are independent. Determine the mean and variance of the rate of return after one year for the entire investment of $\$ 10,000$. b. Assume that $X_{1}$ is independent of $X_{2}$ and $X_{3}$ but that the covariance between $X_{2}$ and $X_{3}$ is $-0.005 .$ Repeat part (a). c. Compare the means and variances obtained in parts (a) and (b) and comment on any benefits from negative covariances between the assets.
Madhur L.
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