For this problem how would it be different if cash had an interest rate of 0.1% annually, instead of zero interest rate?

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)

Total investment amount = $100 million

Weight of ETF SPY = 50% Amount invested in ETF SPY = 50% of 100 million = 0.5 * 100,000,000 = $50,000,000 Old price of ETF SPY = $340 Number of shares of ETF SPY = 50,000,000/340 = 147,058.82

Weight of ETF TLT = 30% Amount invested in ETF TLT = 30% of 100 million = 0.3 * 100,000,000 = $30,000,000 Old price of ETF TLT = $140 Number of shares of ETF TLT = 30,000,000/140 = 214,285.71

Weight of Cash = 20% Amount invested in Cash = 20% of 100 million = 0.2 * 100,000,000 = $20,000,000

Current price of ETF SPY = $255 Current price of ETF TLT = $178 Current Amount invested in ETF SPY = Number of shares of ETF SPY * Current price of ETF SPY = 147,058.82 * $255 = $33,088,234.5

Current Amount invested in ETF TLT = Number of shares of ETF TLT * Current price of ETF TLT = 214,285.71 * $178 = $38,142,856.38

Current Amount invested in Cash = $20,000,000

Account $ balance before rebalancing = Current Amount invested in ETF SPY + Current Amount invested in ETF TLT + Current Amount invested in Cash = $33,088,234.5 + $38,142,856.38 + $20,000,000 = $91,231,090.88