In this problem, if cash were 0.1% annually INSTEAD of zero interest rate would you then do $20,000,000 * 0.10%= $20000, and that would be the input for Account $ balance before rebalancing?

so like Account $ balance before rebalancing =$33,088,234.5 + $38,142,856.38 + $20000 = $71251090.88

The problem:

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