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. 50% in stocks via ETF SPY;

ii. 30% in bonds via ETF TLT.

iii. 20% in cash

Over the past few weeks, SPY went down from $340 to $255, and AGG went up from $140 per share to $178 per share. Cash has an interest rate of zero.

a. What is your 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 50-30-20 for SPY AGG and cash respectively? What to buy and what to sell in dollar amount? How many SHARES of SPY and AGG to buy or sell (5 points)?

Q2. Write your calculations please. (15 points)

VXX is the 1x vix futures ETF. ETF SVXY manages leverage of -0.5x of vix futures ETF (a short fund, shorting 50% of AUM).

a. Below is the price path for VXX, the 1x long etf. Fill in the blanks, including the calculation (3 points)

Day	0	1	2	3
Price	100	250	500	450
Daily Return	NA

b. what is the price path for SVXY? (4 points)

Day	0	1	2	3
Price	100

c. What is the daily position in the un-levered ETF and cash post rebalancing? (4 points)

Day	0	1	2	3
Position in unlevered ETF VXX	-50
Position in cash	150

c. What is the rebalancing trade in dollar terms? (4 points)

Day	0	1	2	3
Rebal Trade in ETF VXX	-50
Change in Cash	150

Q3. Portfolio Returns

i. stock has mean of 10% and stdev of 20%;

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 (3 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 stdev risk (3 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? (3 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? (3 points)

e. if you want to target 10% 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? (3 point)