Personal Finance

1. Time Value of Money

1.1 Time Value of Money

• Future value (FV) vs. present value (PV): $FV=PV(1+r{)}^t$ , where
  • $t$ = # of periods over which the interest rate is earned
  • $r$ = interest rate
• Compound interest = earning interest on interest
• Simple interest = not accounting for compound interest

Example 1.1 Present Value of a Lottery Prize

You win a $1,000,000lottery!However,insteadofreceivingthefullamountupfront,thelotterypaysyou$50,000 per year for the next 20 years. Assuming a discount rate of 5% per year, what is the present value (PV) of this lottery prize?

Solution Since the payments are spread over time, we must discount each future payment to its present value using the formula for the present value of an annuity: $PV={\sum }_{t=1}^{20}\frac{50,000}{(1.05{)}^t}$

This formula accounts for the fact that money received in the future is worth less than money received today due to the time value of money.

We calculate the present value of each payment individually: $PV=\frac{50,000}{1.05}+\frac{50,000}{(1.05{)}^2}+\frac{50,000}{(1.05{)}^3}+\cdots +\frac{50,000}{(1.05{)}^{20}}$

Alternatively, we can use the present value formula for an annuity: $PV=\frac{C}{r}\times \left(1-\frac{1}{(1+r{)}^t}\right)$ where:

• $C=50,000$ (cash flow/payment for each period)
• $r=0.05$ (interest rate)
• $T=20$ (number of years / # of periods over which cash flow is paid)

Final Answer: the present value of the lottery winnings is approximately: \623,111$

2. Stocks and Bonds

Example 2.1: Investment Scenarios in a Business

Initial Setup

• John needs $200,000 to start the business.
• Possible first-year outcomes: $120,000profit,$30,000 profit, or bankruptcy.

Outcome 1: Winning Big

• Stock investment (50% ownership)
  • $50,000 dividend
  • $100,000 capital appreciation
  • Total return: 150% ($150,000returnon$100,000 investment)
• Bond investment (20% interest)
  • $20,000 interest payment
  • $3,000 capital appreciation
  • Total return: 23%
• John’s earnings: $50,000
• Company valuation increased by $200,000

Outcome 2: Scraping By (Profit of $34,000)

• Stock investment
  • $7,000 return
  • Total return: 7%
• Bond investment
  • $20,000 interest
  • Total return: 20%
• John’s earnings: $7,000

Outcome 3: Going Broke

• Stock investment
  • Capital loss of $100,000
  • Total return: -100%
• Bond investment
  • Invested $100,000,received$90,000 back
  • Total return: -10%

Comparing Investors

• Bond-like investor
  • Provided a long-term loan to the company
  • Average return: 11%
  • Safer: only 1/3 chance he will lose 1/10th of his investment
• Stock-like investor
  • Bought ownership in the company
  • Average return: 19%
  • Higher risk (1/3 chance will lose all of his investment), more frequent large losses

2. Budgeting, Compounding, and Inflation

2.1 Estimating Spending

Simple budgeting approach from All Your Worth, by Elizabeth Warren and Amelia Warren Tyagi

1. Must-haves: needs. bills you’d have to pay even if you lost your job.
2. Savings: reductions to debt, contributions your employer makes to your 401(k) account
3. Wants: everything else

Estimate

1. Monthly after tax income: take-home pay + contributions to retirement savings, health insurance
2. Monthly must have expenses: transport, basic groceries, rent, utilities, etc. Include expenses that do not come up every month.
3. Monthly savings: include contributions your employer makes to retirement, credit card balances

Personal finance rules of thumb

• keep must-have ⇐ 50% of after-tax income
  • tough if living in HCoL area
• save 20% of after-tax income
  • goal (not a minimum) for most
• spend 30% of after-tax income on wants
• Have an emergency fund

2.2 Prioritizing Savings

• if your employer makes matching contributions to your 401(k) retirement plan, always contribute enough to the plan to get the entire match
  • this counts as part of the 20% you’re saving of after tax income
• put half of the 20% you’re saving of after tax income (10% of after-tax income) into an IRA, 401k, or other retirement account
  • if your company makes matching contributions, that matching contribution counts toward the 10%
• 5%
  • first for a security fund - purpose: cope w/ the unexpected w/o going into debt
    • ~6 months of must-have expenses in this fund
    • don’t keep it in these places: checking account, certificate of deposit (not liquid enough), or stock market
    • keep it in: standard savings or money market account
  • once you have a security fund, can go to a downpayment on a home or payoff principal on the mortgage on the home you own instead
• 5%: save for something important to you

First save for your retirement, then for your children’s education

2.3 Save Early, Save Now

• Compound interest! Over a long enough time horizon makes a big difference
• Don’t buy on credit
• Save 20% of after-tax income
  • Automate savings
  • Sign up for 401k and get max matching contribution from employer
    • If company doesn’t offer this, set up IRA or Roth IRA (set up automatic contributions)
  • Pay yourself first
• Save more tomorrow
  • Put federal tax refund directly into savings
  • Commit to increasing savings rate when you get your next raise (some 401k plans will allow for this to be done automatically)
• Savings is not an all or nothing game! save what you can. k

2.4 Save More

1. Automate savings
2. Focus on the big stuff: see if you can spend less on insurance, mortgage. refinance (shop carefully - costs and fees from banks. get multiple quotes). car (usually cheaper to maintain an old car than to get a new car). find a place you can afford or get a roommate.
3. Save first, then buy. Don’t buy on credit.
4. Increase your income. could you get a degree to do so?
5. Comparison shop: crucial for big ticket items (e.g. computers). try to save money on regular, repeated purchases
6. Don’t neglect the small stuff. small, regular savings do add up.

2.5 Creating a Spending Plan

3 parts to a spending plan

1. Set goals
   1. Short term (3 months)
   2. Medium (3mos - 1 year)
      1. e.g. Emergency fund
   3. Long-term
2. Identify income and expenses (fixed and flexible)
3. Track and adjust spending
   1. Look at expenses and see where you can reduce

3. Credit Scores, Credit Cards, and Debit Cards

3.1 Credit Scores

Credit Scores Overview

• A credit score is a number used to predict whether a consumer will repay a loan
  • Different credit reporting agencies use different formulas to calculate scores
• FICO scores are the most widely used credit scores
• Three largest credit reporting agencies:
  • Equifax
  • Experian
  • TransUnion
• Each agency calculates its own FICO score and proprietary credit scores
• FICO score range: 300 (lowest) – 850 (highest)
• Median FICO score: 712

Credit Score Categories

• 300–619: Bad credit (25% of people)
• 620–660: Fair credit
• 661–720: Good credit
• 721+: Excellent credit
• 760+: Best terms on loans/mortgages

Why Credit Scores Matter

• Loan Approval: Affects ability to borrow money for mortgages, car loans, credit cards.
• Loan Terms: Higher scores = lower interest rates (saving thousands on a mortgage).
• Other Impacts:
  • Landlords check credit before renting
  • Insurance companies charge higher rates for bad credit
  • Utility & cell phone companies may require deposits for low scores
  • Employers check credit scores for hiring, especially in retail

How Credit Scores Are Calculated

1. Payment History (35%) – Most important factor
   • Late payments (30+ days) hurt your score
   • More accounts, larger balances, longer delays = bigger negative impact
   • Late payments stay for 7 years, bankruptcies for 10 years
   • Paying on time consistently improves score
2. Credit Utilization (30%) – How much you owe vs. total credit limit, aka debt burden
   • High balances close to credit limits lower the score
   • Example
     • $10,000limit,$9,900 owed = bad
     • $10,000limit,$1,000 owed = better
3. Credit History Length (15%) – Longer history improves score
   • Can still have a good score with a short history if well-managed
4. New Credit Inquiries (10%) – Applying for new credit lowers score
   • Too many inquiries signal financial distress
   • Tip: When shopping for mortgages or auto loans, get quotes within 1–2 weeks to count as a single inquiry
5. Credit Mix (10%) – Having a variety of credit types (credit cards, auto loans, mortgages) is slightly beneficial

What Doesn’t Affect Credit Score

• Race, color, religion, national origin, sex, marital status, public assistance status.
• Income is NOT a factor (low-income individuals can still have high credit scores).

Checking Your Credit Score

• FICO score available for $14.95 at myfico.com.
• Free credit scores available at CreditKarma.com (not exact FICO but close).
• More important than exact FICO score: Regularly checking credit reports for errors.
• 3 free credit reports per year (one from each major agency).

Signs of a Bad Credit Score

• Currently late on a credit card, loan, or medical bill
• 60+ days late on a payment in the past six months
• Maxed out or nearly maxed out credit cards
• Bankruptcy in the last three years

How to Improve Your Credit Score

• Pay bills on time (most important)
• Keep credit card balances low
• Pay off debt rather than shifting between cards
• Apply for new credit only when necessary
• Catch up on missed payments and maintain on-time payments
• Regularly check credit report for errors and dispute inaccuracies

Other Factors in Loan Approval

• Lenders also consider:
  • Income
  • Job stability
  • Residential stability (longer stays in one place preferred).
  • Debt-to-income ratio (ensures ability to repay loans).
• Spousal credit:
  • Joint accounts affect both spouses’ credit
  • If a loan is solely in your spouse’s name (and you didn’t co-sign), it doesn’t affect your credit score

3.2 Credit Reports

A credit report is used by credit agencies to calculate your credit score

The Consumer Financial Protection Bureau states that a credit report includes:

• Your credit history and status of credit accounts
• Payment history, available credit, and credit utilization
• Whether a debt collector is collecting on any outstanding debts
• Public records such as liens, judgments, and bankruptcies

Who Uses Credit Reports?

• Lenders: Determine loan approval, interest rates, and loan status
• Businesses: Inform decisions on insurance pricing, apartment rentals, and employment (if permission is granted)

What is NOT in a Credit Report?

• Checking or savings account details
• Bankruptcies older than 10 years
• Late payments or collections older than 7 years
• Criminal records, motor vehicle records
• Purchases made on credit cards
• Gender, ethnicity, religion, or political affiliation
• Medical history (although late medical bill payments may be included)

By law, you’re entitled to one free credit report per year from each of the three major credit reporting agencies (Equifax, Experian, Transunion)

• You can request all three at once or stagger them throughout the year
• Free reports do not include credit scores but contain the data used to calculate them

How to Request a Free Credit Report

• Website: annualcreditreport.com
• Phone: 1-877-322-8228
• Other websites may claim to offer free reports but often require purchases or subscriptions

When requesting a credit report, you’ll be asked for

• Social Security number
• Verification questions about past loans (lender name, monthly payment, etc.)

Reviewing Your Credit Report

• Contains details on all credit accounts from the past 7 years
• Lists whether payments were on time or delinquent
• Includes bankruptcies, liens, lawsuits, and debts turned over to collections
• If you find negative but accurate information (e.g., late payments, collections under 7 years old), you cannot remove it—only improve credit over time
• If you find errors, report them to the credit reporting agency
  • Common errors include incorrect names, incorrect payment statuses, or debts that were paid but still appear unpaid.
• If the lender or collection agency made an error, contact them to correct it
• If errors are not corrected, report them directly to the credit reporting agency

How Often Should You Check Your Credit Report?

• At least once a year (a good practice is to check at tax time)
• Request additional reports throughout the year from different agencies

Special Situations to Check Your Credit Report (from Making the Most of Your Money Now by Jane Bryant Quinn) 6. Before applying for an important loan (e.g., mortgage) 7. After separating from a spouse – Close joint accounts and ensure credit report reflects “closed by consumer” status 8. After paying off a court judgment – Ensure the report shows it as paid. 9. If you had a dispute with a store and refused to pay – You can add a 100-word explanation, but this won’t help with computer-based evaluations 10. If you were turned down for a job, rental, insurance, or credit due to a credit report issue – The company must disclose which credit bureau was used, and you are entitled to a free credit report within 60 days 11. If a dispute with a lender is resolved – Check that the resolved issue is no longer on your report

Why Credit Reports Matter

• Banks and credit card companies use them to decide on loans and interest rates.
• Insurance companies, employers, and landlords may also check them.
• It’s important to periodically review your report to ensure accuracy and correct errors.

3.3.1 Asset Allocation, Part 1

Investing in Index Funds

• Investing in index funds is smart and easy
• No need to pick stocks or fund managers
• Choose well-diversified indices with low fees

Asset Allocation: the decision of how much to invest in stocks vs. bonds and international stocks

• Often illustrated with pie charts
• The three main asset classes:
  • Equities (stocks)
  • Fixed income (government, municipal, and corporate bonds)
  • Cash (bank accounts, CDs, and money market funds)

Cash in Finance

• Not just physical money but includes savings accounts, certificates of deposit (CDs), and money market funds
• Less volatile than stocks and bonds but also lower returns
• Emergency funds should be held in bank accounts, not in investment accounts

Retirement Asset Allocation

• Choosing how much of retirement savings is invested in different asset classes
• Three main asset classes for most people:
  • US equities
  • International equities
  • Bonds
• Asset allocation should be reviewed every five years (since appropriate mix of stocks and bonds changes as you get older)

Target Date Funds (aka life cycle funds or age-based funds)

• These automatically adjust asset allocation as you get older
• The target date represents the planned retirement year
• Available in most 401(k) plans and major mutual fund companies
• Different funds may have similar allocations but vary in fees - pay attention to this

Sources of Retirement Income

• Typically a mix of:
  • Social Security (usually most important)
  • A pension (if applicable)
  • Personal retirement savings
  • Investment in home equity
• Social Security functions similarly to an investment in government bonds, providing guaranteed, inflation-indexed income

Risk and Age in Investing

• Younger investors can take more risk since they have time to recover from market downturns
• Older investors should reduce risk to protect their savings
• Example:
  • A 25-year-old with $20,000 in savings who loses half will still have time to rebuild wealth
  • A 65-year-old with $500,000 losing half could significantly impact their retirement plans

Stock Market Risks

• Stocks generally offer higher returns than bonds but are riskier
• Large market crashes
  • 2000-2002: S&P 500 lost nearly 50%
  • 2007-2009: S&P 500 lost slightly more than 50%
• Market recoveries are not guaranteed and can take years

Safe Investments

• Some investors prefer low-risk, inflation-protected US bonds
  • Example: Zvi Bodie, a finance professor, invests solely in these bonds
• Risk of being too conservative: Low-growth investments may not be enough for a comfortable retirement

Expert Recommendations for Stocks vs. Bonds

• Benjamin Graham: No more than 75% and no less than 25% in either stocks or bonds (stocks allocation should be between 25% and 75% of your total portfolio, and bonds allocation should also be between 25% and 75% of your total portfolio)
• Jack Bogle (Vanguard founder):
  • Bonds = Your age, Stocks = 100 - Your age.
  • Example: A 40-year-old should hold 60% stocks, 40% bonds.
• Jane Bryant Quinn (Personal finance writer):
  • Bonds = 110 - Your age, Stocks = the rest
  • Example: A 40-year-old should hold 70% stocks, 30% bonds

Other Asset Classes

• Commodities & Gold: Not recommended for most retirement portfolios
• Real Estate:
  • Homeownership is already a significant real estate investment
  • Equity index funds provide indirect exposure to real estate markets
• Cash:
  • Emergency cash should be in savings accounts or money market funds
  • Should not be held in retirement accounts like IRAs or 401(k)s

3.3.2 Asset Allocation, Part 2

Effect of Asset Allocation on Portfolio Volatility

• Holding different mixes of stocks and bonds affects portfolio ups and downs
• Stocks have larger fluctuations compared to bonds
  • Example: The Vanguard Total Stock Market Index Fund (stocks) vs. Vanguard Intermediate Term Bond Index Fund (bonds)
• A balanced portfolio (e.g., 50% stocks, 50% bonds) smooths out volatility

Graph Manipulation Considerations

• Changing the time period can make stocks or bonds appear more or less risky
• Adjusting the horizontal or vertical axis can distort perceived volatility

Target Date Funds and Asset Allocation

• Example: Vanguard 2045 Fund
  • 90% stocks, 10% bonds
  • Breakdown:
    • 63% US stocks
    • 27% International stocks
    • 8% US bonds
    • 2% International bonds
• International holdings reduce volatility:
  • Allocating ⅓ to ½ of stocks to international markets lowers risk
  • Holding international bonds also reduces risk but to a lesser extent
• Other firms (Fidelity, T. Rowe Price, TIAA-CREF, Schwab) have similar allocations

Cost Considerations in Target Date Funds

• Fees vary significantly across different companies
• Example: Fees on a $10,000investmentcanrangefrom$19 to $82 per year
• Fees are higher than S&P 500 Index Funds because of additional costs (e.g., international equities)
• Small fee differences matter over time—compare fees before investing

High Equity Allocation in Target Date Funds

• Most 2045 funds allocate ~90% to stocks, including ~30% international equities
• Experts typically recommend lower equity allocations
• One reason for higher stock allocation: Implicit US bond investment through Social Security
  • Experts account for Social Security and pensions as part of the bond allocation

Choosing Your Asset Allocation

• Consider portfolio performance relative to goals
  • If returns are strong near retirement, consider reducing risk
• Account for other investments:
  • Traditional pensions behave like bonds → Can justify more stock holdings
  • Home equity → Can afford more risk in financial investments
  • Rental properties → Additional assets reduce portfolio risk
• If a market crash would force selling stock funds, consider reducing risk preemptively
• Things to think about when choosing your allocations
  1. How is your portfolio doing relative to your goals?
  2. Your other investments
  3. Your comfort level w/ risk

Deferred Income Annuities (Longevity Insurance)

• Useful as an additional investment closer to retirement
• Lump sum payment to an insurance company in exchange for guaranteed lifetime payments

Key Takeaways

• Allocate between US stocks, international stocks, and US bonds
• International bonds have minimal impact but can provide slight risk reduction
• Reduce stock allocation with age (e.g., rule of thumb: allocate percentage equal to age in bonds)
• Social Security and pensions act like bond investments
• Target date funds adjust allocation automatically but may not fit individual needs
• Consider homeownership, other substantial investments, and risk tolerance when setting your allocation