Q1. Portfolio Returns

i. stock has mean of 8% and stdev of 20%;

ii bond has mean of 4% and stdev of 10%;

iii correlation b/w stock and bond of -0.2;

iv. cash return is 1% for lending and borrowing.

a. What is the mean and stdev of a portfolio of that is 2/3rd stock and 1/3rd in bond?

b. What is the mean and stdev of a fully invested yet unleveraged portfolio that assign weights based on the inverse of risk (risk parity fund, aka adjust allocation weights so the dollar standard deviation in each component is the same)?

c. how do you combine portfolio in Q1b with cash to match mean return in Q1a portfolio? What is the risk of this portfolio? (assume borrowing and lending cost of 1%)

d. If you want to mix portfolio in Q1b with cash, in order to match the risk of portfolio in Q1a, how much cash do you need and what is the resulting mean of the portfolio? (assuming cash return is 1%)

e. if you want to target 10% stdev risk per year, how would you combine Q1b risk parity portfolio with cash in this case?

f. if you want to target 10% stdev risk per year, yet you believe correlation has changed to +0.5. How would you combine Q1b risk parity portfolio with cash in this case?