Buy vs. Rent: An Expected Value Analysis

The Myth of "Throwing Money Away"

The most common argument for buying: "Rent is throwing money away." This is wrong. Rent pays for shelter. A mortgage payment includes interest (also "thrown away"), property tax, insurance, maintenance, and opportunity cost of your down payment.

The Real Math

Costs of Buying (monthly, on a $400K home with 20% down)

• Mortgage payment (P&I at 7%): $2,130
• Property tax: $500
• Insurance: $150
• Maintenance (1% annually): $333
• HOA (if applicable): $200
• Total: $3,313/month
• Of which equity building: ~$530/month (year 1)
• Of which "thrown away": ~$2,783/month

  Costs of Renting (equivalent home)

• Rent: $2,200/month
• Renter's insurance: $30/month
• Total: $2,230/month
• Difference invested at 8%: $1,083/month

  The Expected Value Calculation

  The key variable is home appreciation rate:

  - Scenario A (3% appreciation, 60% probability): After 10 years, home worth $537K. Equity: $257K. Net gain after selling costs: ~$220K.

• Scenario B (0% flat, 25% probability): After 10 years, home worth $400K. Equity: $120K. Net after costs: ~$85K.
• Scenario C (-10% crash, 15% probability): Home worth $360K. Equity: $80K. Net after costs: ~$40K.

  Meanwhile, renting and investing the difference at 8% for 10 years: ~$200K.

  EV of buying: (0.60 x $220K) + (0.25 x $85K) + (0.15 x $40K) = $159K

In many markets, renting and investing the difference actually wins on pure expected value.

When Buying Wins

Buying has advantages that don't show up in EV:

• Forced savings (you build equity even if you wouldn't invest)
• Stable housing costs (fixed mortgage vs rising rents)
• Tax benefits (mortgage interest deduction)
• Emotional value of ownership

  The Framework

  Use our decision wizard to plug in your specific numbers: your rent, the home price you're considering, your down payment, local appreciation rates, and your investment return assumptions. The math will tell you which option has the higher expected value for your situation.