Just married young couple facing a decision problem for：
housing
rent a house:
2000 per month, 2% annual incremental rate, deposit can be included approximately into
the fixed cost, which is 5000 per year.
buy a house:
You can choose whatever you can afford
mortgage rate 6%, the lowest down-payment is 30%
annual incremental rate for houses. N~(0.08,0.05)
since real estate is illiquid, you cannot pay your costs from the house before you sell it.
You cannot leverage it for external loans.
You can only collect the payment form. the sell at the beginning of the next year.
You must have an accommodation at all time
children education
suppose you only have one child in three years from now, he/she will require your support
until he/she gets a master degree, in details, the cash flows are bellows:
preliminary school: 6 X 8000 (when your child is 6-year old)
middle school: 6 X 10000
college: 4 X 20000
master: 3 x 25000
annual incremental rate for tuition fees are 5% since your child enters primary school
investment
US stock, log-return from the ticker SPY
World stock, log-return from the ticker EFA
Bond, log-return from the ticker AGG
Gold, log-return from the ticker GLD
Real estate, log-return from the ticker VNQ
for all risky assets, the subsequent returns will be draw from an normal distribution, namely,
N~(mu, sigma) from the period 2007-2017
your cash will grow at the risk-free rate: 3%
all returns are annually rebalanced, all your investments are liquid
Income and living cost assumptions
200,000 initial saving, family income 150,000 after tax, fixed annual incremental rate 3%
progress annual incremental rate, 6%, happens in every 5 years.
living cost at 10000 per month, fixed annual incremental rate 5%
Unexpected opportunity/expense
for simplicity, we assume there is a 10% chance in every year, you encounter an unexpected
chance that doubles your cash on hand.
for simplicity, we assume there is a 3% chance in every year, you encounter an unexpected
expense with a known probability, respectively:
[1000 (0.15), 5000 (0.3), 10000 (0.25), 15000 (0.1), 20000 (0.1), 50000 (0.05), 100000 (0.05)].
At any time, you have changes to borrow, at 8.5%, annual rate.
Question:
suppose the planning horizon is 40 years, your goal is maximizing your expected final wealth
(including cash, value of your house and investment portfolio) at the end of year 40.
How will you make your asset allocations?