Please help me with these questions and answer them very thoroughly. Thank you in advance!

Q1:

In a risk model with a crisis dummy, for a given hedge fund: beta0(S&P 500)=0.5 and beta0(S&P 500) dummy = -0.5.

a)It is normal time (not crisis), the market (S&P 500) goes up by 10%, by how much is the hedge fund expected to move?

b)It is crisis, and market (S&P 500) goes down by 10%, by how much is the hedge fund expected to move?Show calculations.

Q2:

Assume a continuously compounded annual interest rate of 6%, 2.5% continuously paid dividend rate, storage cost is 2% and a spot price for a 6-month commodity contract of $100, what is the forward price?

Q3:

Provide an example of a non-linear factor model.Under which situations will you use such model?When will a non-linear factor model be used and when will a linear factor model will suffice?

Q4:

A hedge fund has a 2 and 20 fee structure.The fund has $200 million of AUM in the beginning of the year.At the end of that year, an additional $20 million was invested.Including this inflow of the capital, at the end of that year, the total AUM was $260 million.What is the annual management fee collected by the fund manager?What was the total profit and the incentive fee on the profit collected by the fund manager?Show your work.

Q5:

Describe systematic and systemic risks.

a)What is the difference between systematic and systemic risk?

b)How would you measure systematic risk?

c)How would you measure systemic risk?