23.01.30 · economics / personal-finance

Personal finance: credit, debt, investing

draft3 tiersLean: none

Anchor (Master): Mas-Colell, Whinston & Green, Microeconomic Theory; relevant academic sources

Intuition [Beginner]

Debt is borrowing from your future self. You get money now; you repay it later, with interest. This can be sensible (borrowing to buy a home that builds equity, or to fund education that increases your earning power) or destructive (borrowing for consumption at high interest rates that outpace your ability to repay).

The key distinction is good debt versus bad debt:

Good debt: Lower interest rate, funds an asset that appreciates or generates income (mortgage, student loans for high-value degrees, business loans). The return on the investment exceeds the cost of borrowing.
Bad debt: High interest rate, funds consumption that provides no lasting value (credit card debt for discretionary spending, payday loans). The cost of borrowing far exceeds any return.

Credit is your ability to borrow. A credit score is a number (typically 300-850 in the US) summarising your creditworthiness based on payment history, amounts owed, length of credit history, and other factors. A higher score means cheaper borrowing; a lower score means higher interest rates or denial of credit. Credit scores determine not just whether you get a loan but how much you pay for it -- over decades, the difference between a good and bad credit score can cost tens of thousands of dollars.

Investing is using money to buy assets expected to generate returns over time. The basic principle is the risk-return trade-off: higher expected returns come with higher risk (possibility of loss). Diversification -- spreading investments across different assets -- reduces risk without proportionally reducing expected return.

Visual [Beginner]

The Risk-Return Spectrum

  Risk & Return
  High |                                 Stocks
       |                        Corporate bonds
       |               Real estate
       |        Municipal bonds
       |   Index funds
  Low  | Savings accounts, Treasury bills
       +-----------------------------------------------
       Low                                    High
                  Liquidity / Safety


Diversification

  Portfolio A: All money in one stock
    -- If the company fails, you lose everything.

  Portfolio B: Money spread across 500 stocks (index fund)
    -- If one company fails, the impact is small.
    -- You capture the average return of the market.

  "Don't put all your eggs in one basket."
  Diversification reduces risk without sacrificing
  expected return (to a point).


Credit Score Ranges (FICO)

  300-579: Poor        -- Difficult to get credit; highest rates
  580-669: Fair        -- Subprime rates; limited options
  670-739: Good        -- Most lenders accept; moderate rates
  740-799: Very good   -- Competitive rates; broad access
  800-850: Excellent   -- Best rates; preferred borrower

Worked Example [Beginner]

You have a credit card with a $2,000 balance and a 24% APR. The minimum payment is 2% of the balance or $25, whichever is greater.

Minimum payment only: If you pay only the minimum each month, the first payment is $40 (2% of $2,000). The interest charge that month is $$2, 000 \times 0.24/12 = $40$ . Your payment barely covers the interest. It would take approximately 30 years to pay off the $2,000 balance, and you would pay over $5,000 in interest -- more than twice the original debt.

Fixed payment of $100/month: The balance declines steadily. Payoff takes about 25 months, and total interest paid is approximately $480. You save over $4,500 in interest by paying $60 more per month.

This example illustrates why high-interest debt is so dangerous. The APR of 24% means you pay 2% of the balance per month in interest alone. If you earn 1% on savings, the gap between your borrowing cost and your savings return is 23 percentage points. Every dollar of credit card debt you carry is a guaranteed 24% annual loss.

Investing example: A broad stock market index fund has historically returned about 7% per year after inflation. If you invest $300/month for 30 years:

$F V = 300 \times \frac{( 1 + 0.07/12 ) ^{360} - 1}{0.07/12} = 300 \times 1219.97 = $365, 991$

Your total contributions: $108,000. Market returns: $257,991. Compound growth did most of the work.

Check Your Understanding [Beginner]

Formal Definition [Intermediate+]

Credit and interest

The annual percentage rate (APR) is the annualised cost of borrowing, including fees:

$A P R = (1 + \frac{r _{p er i o d i c}}{n})^{n} - 1$

where $r_{p er i o d i c}$ is the periodic interest rate and $n$ is the number of compounding periods per year. For credit cards with daily compounding, the effective APR exceeds the stated APR.

Amortisation: A fixed-payment loan (e.g., a mortgage) is amortised so that each payment covers interest on the remaining balance plus a portion of principal:

$P M T = P \times \frac{r ( 1 + r ) ^{t}}{( 1 + r ) ^{t} - 1}$

where $P$ is the principal, $r$ is the periodic interest rate, and $t$ is the number of payments.

Credit scoring

Credit scoring models (FICO, VantageScore) use weighted factors:

Factor	Approximate Weight
Payment history	35%
Amounts owed (utilisation)	30%
Length of credit history	15%
Credit mix	10%
New credit inquiries	10%

Credit utilisation (outstanding balance divided by credit limit) should ideally be below 30%. High utilisation signals financial stress and reduces the score.

Risk and return

The expected return on an asset:

$E [R] = i = 1 \sum n p_{i} R_{i}$

Variance (risk measure):

$σ^{2} = i = 1 \sum n p_{i} (R_{i} - E [R])^{2}$

For a portfolio of two assets with weights $w_{1}$ and $w_{2} = 1 - w_{1}$ :

$σ_{p}^{2} = w_{1}^{2} σ_{1}^{2} + w_{2}^{2} σ_{2}^{2} + 2 w_{1} w_{2} σ_{1} σ_{2} ρ_{12}$

where $ρ_{12}$ is the correlation between returns. When $ρ_{12} < 1$ , diversification reduces portfolio risk below the weighted average of individual risks.

The Capital Asset Pricing Model (CAPM)

$E [R_{i}] = R_{f} + β_{i} (E [R_{m}] - R_{f})$

where $R_{f}$ is the risk-free rate, $β_{i} = \frac{C o v ( R _{i} , R _{m} )}{V a r ( R _{m} )}$ measures systematic risk, and $E [R_{m}] - R_{f}$ is the market risk premium. Only systematic risk (correlated with the market) is compensated; diversifiable risk is not priced.

Key Concepts [Intermediate+]

Credit: The ability to borrow money with a promise to repay, typically with interest.
APR (Annual Percentage Rate): The annualised cost of borrowing, including interest and fees.
Credit score: A numerical rating of creditworthiness. Higher scores mean cheaper access to credit.
Good debt: Borrowing that finances appreciating assets or income-generating investments (mortgage, education, business).
Bad debt: Borrowing for consumption at high interest rates (credit cards, payday loans) where the cost exceeds the benefit.
Amortisation: The gradual repayment of a loan through fixed payments covering both interest and principal.
Stock: Partial ownership of a company. Returns from dividends and price appreciation.
Bond: A loan to a company or government, paying regular interest and returning principal at maturity.
Index fund: A fund that tracks a market index, providing diversification at low cost.
Diversification: Spreading investments across different assets to reduce risk.
Risk-return trade-off: Higher expected returns require accepting higher risk.
Retirement accounts: Tax-advantaged accounts for long-term savings (401(k), IRA, RRSP, pension schemes). Tax deferral or tax-free growth significantly increases long-term returns.
Predatory lending: Loans with deceptive terms, excessive fees, or interest rates designed to trap borrowers in cycles of debt (payday loans, subprime mortgages, rent-to-own).

Exercise 1. A borrower takes a 30-year mortgage for $300,000 at 6% fixed rate. Calculate the monthly payment. How much total interest is paid over the life of the loan? Compare with a 15-year mortgage at 5.5%.

Exercise 2. You have a portfolio with 60% in stocks ( $E [R] = 10%$ , $σ = 20%$ ) and 40% in bonds ( $E [R] = 5%$ , $σ = 8%$ ). The correlation is 0.2. Calculate the portfolio's expected return and standard deviation. How does diversification affect the risk-return profile?

Academic Perspectives [Master]

Modern portfolio theory

Markowitz (1952) introduced the mean-variance framework: investors should hold portfolios on the efficient frontier -- the set of portfolios offering the maximum expected return for each level of risk. Diversification is not merely prudent but mathematically optimal: by combining assets with correlations less than 1, investors achieve lower risk for any given expected return.

The Capital Asset Pricing Model (Sharpe, 1964; Lintner, 1965) extended Markowitz by showing that, under equilibrium assumptions, all investors hold a combination of the risk-free asset and the "market portfolio" (all risky assets in value weights). The model predicts that only systematic risk ( $β$ ) is compensated; diversifiable risk is not priced because rational investors eliminate it through diversification.

Critiques of CAPM include: the single-factor model is too simplistic (Fama and French, 1993, proposed a three-factor model; subsequent work adds more factors); $β$ is estimated with error; and behavioural biases cause investors to hold under-diversified portfolios.

Efficient market hypothesis

Fama (1970) proposed the Efficient Market Hypothesis (EMH): asset prices reflect all available information. Under the strong form, even insider information is reflected in prices. Under the semi-strong form, all public information is reflected. Under the weak form, past price data cannot predict future returns.

EMH implies that active management (stock-picking) cannot consistently beat the market net of fees, which is the theoretical basis for index fund investing. Grossman and Stiglitz (1980) showed that markets cannot be perfectly efficient: if prices perfectly reflected all information, there would be no incentive to gather information, so some degree of inefficiency must persist to reward informed trading.

Behavioural finance

Behavioural finance challenges the assumptions of rational investors and efficient markets:

Overconfidence: Investors overestimate their ability to pick stocks, leading to excessive trading (Barber and Odean, 2000 showed that frequent traders underperform the market).
Herding: Investors follow the crowd, amplifying price movements and creating bubbles and crashes.
Loss aversion: Investors hold losing stocks too long (to avoid realising a loss) and sell winning stocks too early (disposition effect).
Mental accounting: People treat money differently depending on its source or intended use, violating the principle of fungibility.

Behavioural finance explains market anomalies (momentum, value premium, size premium) that the efficient market hypothesis cannot easily accommodate. However, it does not provide a unified alternative theory; it is primarily a collection of empirically documented deviations.

Institutional and structural perspectives

Critics note that personal finance advice often assumes a stable income, access to employer-sponsored retirement plans, and the ability to absorb short-term losses in investment portfolios. Many households do not meet these conditions. The shift from defined-benefit to defined-contribution pensions has transferred financial risk from employers (and the financial system) to individuals, many of whom lack the financial literacy to manage this risk effectively.

From a structural perspective, predatory lending practices (payday loans with APRs exceeding 300%, subprime mortgages with teaser rates that reset to unaffordable levels, rent-to-own schemes) exploit information asymmetry and financial desperation. Regulation (interest rate caps, disclosure requirements, the Consumer Financial Protection Bureau) addresses these market failures, though the appropriate level of regulation is contested.

Austrian school

Austrian economists emphasise that interest rates should reflect genuine time preference -- the trade-off between present and future consumption. Central bank manipulation of interest rates distorts this signal, encouraging excessive borrowing and malinvestment. The Austrian prescription for personal finance is straightforward: save, avoid debt, and invest in real productive assets rather than financial speculation driven by artificially low rates.

Historical Context [Master]

Markowitz (1952): "Portfolio Selection" founded modern portfolio theory, formalising the mathematics of diversification. Nobel Prize, 1990.
Modigliani and Miller (1958): The capital structure irrelevance proposition -- under perfect markets, a firm's value is independent of how it is financed. Extended to personal finance: the cost of debt matters, not its mere existence.
Sharpe (1964): The Capital Asset Pricing Model provided the first tractable model of asset pricing. Nobel Prize, 1990 (shared with Markowitz).
Fama (1970): The Efficient Market Hypothesis formalised the idea that market prices reflect available information, providing the theoretical basis for passive investing.
Bogle (1976): John Bogle founded the first index fund for retail investors (Vanguard 500 Index Fund). His argument: low fees and broad diversification beat active management for most investors. Index funds now hold a majority of US equity fund assets.
Subprime mortgage crisis (2007-2008): Predatory lending, securitisation of risky mortgages, and regulatory failure led to a global financial crisis. Millions of homeowners faced foreclosure. The crisis demonstrated the consequences of financial illiteracy, predatory practices, and systemic risk. Regulatory responses included the Dodd-Frank Act and the Consumer Financial Protection Bureau.
Rise of passive investing (2010s-present): Index funds and ETFs have grown to dominate equity fund flows, driven by evidence that active management consistently underperforms net of fees. The trend has raised concerns about market concentration (three firms -- BlackRock, Vanguard, State Street -- manage a large share of US equities) and reduced price discovery.

Bibliography [Master]

Barber, B. M., & Odean, T. (2000). Trading is hazardous to your wealth. Journal of Finance, 55(2), 773-806.
Bogle, J. C. (1999). Common Sense on Mutual Funds. Wiley.
Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. Journal of Finance, 25(2), 383-417.
Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.
Grossman, S. J., & Stiglitz, J. E. (1980). On the impossibility of informationally efficient markets. American Economic Review, 70(3), 393-408.
Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77-91.
Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19(3), 425-442.