Q1. Portfolio Rebalancing You have 100 million dollars in your investment account and choose to keep your money allocated in the following proportion and rebalance each quarter: i. 60% in stocks via ETF SPY; ii. 35% in bonds via ETF TLT. iii. 5% in cash Over the month of Sep, SPY went from $452 to $429, and TLT went from $149 per share to $144 per share. Cash has an interest rate of 0.1% annually.

a. What is your overall account $ balance before rebalancing? What proportion of that is in SPY, TLT, and CASH respectively? (5 points)

b. How do you rebalance your account to keep the allocation at 60-35-5 for SPY TLT and cash respectively? What to buy and what to sell in dollar amount? (5 points)?

Q2. Portfolio Returns (20 points)

i. stock has mean of 8% and stdev of 18%;

ii bond has mean of 6% and stdev of 12%;

iii correlation b/w stock and bond of -0.4;

iv. Risk free rate for cash lending and borrowing is at 2%.

a. What is the mean and stdev of a portfolio of that is 60% in stock and 40% in bond (4 points)?

b. What is the mean and stdev of a fully invested yet unleveraged portfolio in stock and bond, that assign weights based on inverse of VARIANCE risk (4 points)?

c. How do you combine portfolio in Q3b with cash to match mean return in Q3a portfolio? What is your cash position? What is the stdev risk of this portfolio? (4 points)

d. You want to mix portfolio in Q3b with cash, in order to match the stdev risk of portfolio in Q3a. What is your cash position? What is the resulting mean return of the portfolio? (4 points)

e. if you want to target 12% stdev risk per year, how would you combine Q3b risk parity portfolio with cash? What are the portfolio weights in cash, stock, and bond respectively? What are the mean returns for portfolio? (4 point)