2. Risk and Financial Crises

Finance-focused summary (probability, risk, and crisis assumptions)

Core framing: crisis since 2007, modeled via probability

• The lecturer contrasts a historical narrative of the 2007–2009 financial crisis with a probability / shock-accumulation view:
  • A crisis can be the accumulation of many small events (“shocks”) that produce large outcomes through probability laws.
  • Narrative elements mentioned include:
    • stock, housing, and commodities bubbles
    • collapse phases
    • institutional failures
    • bank runs
    • government bailouts
    • rebound

Macro/market context & timeline highlights

• Stock market bubble/collapse cycle
  • collapse around 2000–2002/2003
  • rebound post-2003
  • another major decline 2007–2009
• Extreme historical daily moves used to challenge probability assumptions:
  • Oct 28, 1929: about -12% in a day
  • Oct 30, 1929: about +12.53% (largest one-day increase ever cited)
  • Oct 19, 1987: about -20.47% in one day
• Specific modern references:
  • Northern Rock bank run (UK) in 2007
  • Lehman Brothers bankruptcy (U.S.) around Sept 15, 2008

Key finance concepts introduced (returns, expectations, risk measures)

Return definition and bounds

• Return over a time interval: capital gain plus dividends (noted in the sidebar).
• Constraints:
  • Simple return is bounded below by -100% due to limited liability (you can’t lose more than you invested).
  • Gross return is always > 0.

Central tendency / “success” metrics

• Expected value: the probability-weighted average of a random variable.
• Sample mean: arithmetic average of observed returns over n periods.
• Geometric mean (for performance with compounding):
  • Uses gross returns multiplied over time.
  • Explicit caution: geometric mean “makes sense only when all values are non-negative.”
    • A year with -100% return implies gross return = 0, so geometric mean becomes 0, forcing recognition of wipeout risk.

Risk metrics and relationships

• Variance: expectation of squared deviation from the mean.
• Standard deviation: square root of variance.
• Covariance: co-movement of two return series:
  • positive when both series move above/below their means together
  • negative when they move in opposite directions
  • ~0 when unrelated
• Correlation: covariance scaled by standard deviations (range -1 to +1).

• Portfolio variance identity (key framework):

  • [ \mathrm{Var}(x+y)=\mathrm{Var}(x)+\mathrm{Var}(y)+2\cdot \mathrm{Cov}(x,y) ]

  • If independence holds (covariance ≈ 0), variance adds.

Crisis risk interpretation: two major assumption breakdowns

1. Failure of independence

   • Independence is treated as foundational to:
     • the law of large numbers (averaging independent shocks reduces uncertainty)
     • risk models like Value at Risk (VaR) that assume stable relationships and/or relative independence
   • Lecturer’s claim: VaR calculations were too optimistic during the crisis because dependence increased under stress (correlations and tail co-movement rose).
   • VaR framework mentioned (post-1987 crash):
     • Example interpretation: “5% probability of losing $10 million in a year.”
   • Proposed alternative after the crisis:
     • CoVaR (conditional dependence / co-risk), attributed to Brunnermeier (Princeton) and collaborators:
       • motivation: portfolios may co-vary more than expected when markets break (covariance spikes in crisis episodes)

2. Fat tails / outliers (non-normality)

   • Traditional assumption: returns are normally distributed.
   • Counterpoint: empirical evidence shows fat tails—rare but repeatable extreme moves:
     • 1929 +12.53% one day after a large down day (challenges independence and normality)
     • 1987 -20.47% one day (lecturer cites implied probability under normality as ~10^-71, i.e., effectively zero)
   • Educational point: with enough data, extremes appear—contradicting the belief that such moves “can’t happen.”

Methodology / step-by-step frameworks explicitly described

• Computation logic for evaluating investment returns

  • Define return as: (price change + dividends) over a period.
  • Use:
    • arithmetic mean of returns as an estimate of expected return
    • geometric mean of gross returns for long-run compounded performance
  • Apply a discipline: a -100% year forces geometric mean to 0 (wipeout dominates).

• Variance/covariance-based portfolio risk construction

  • Compute variance using squared deviations from the mean.
  • For combining assets:
    • include the covariance term
    • if independent, covariance is 0, otherwise it matters

• Assumption-testing logic via probability distributions

  • Compare observed extremes against:
    • the normal (bell-shaped) distribution
    • fat-tailed alternatives (e.g., Cauchy as an illustrative example)

Company/sector instruments & tickers mentioned

• S&P 500 (market proxy)
• Apple (AAPL, discussed as “Apple computer,” with split adjustments)
• IBM and General Motors (GM) (used as return examples for covariance)
• Historical/market index proxy:
  • S&P Composite Index (noted it wasn’t exactly the S&P 500 in early years like 1928)
• Stocks/sectors in a narrative example (Yale endowment story):
  • Home Depot
  • Walmart
  • “internet stocks” (general)
• Other institutions:
  • Northern Rock (bank; not a ticker given)
  • Lehman Brothers (bank/investment bank; not a ticker given)

Key numbers and explicit examples

• Crisis magnitude references
  • Stock market peak-to-trough:
    • 2000–2002 decline: cited around -40%
    • 2007–2009 decline: cited as “almost half,” phrased around -50%
• Apple performance example (2000–~2010 decade)
  • Apple price growth described as ~25×
  • discussion includes a 2-for-1 split in 2005 and why split-adjusted returns matter
  • monthly returns emphasized as highly variable (randomness and volatility)
• Single-period extremes
  • Oct 28, 1929: about -12%
  • Oct 30, 1929: +12.53% (largest one-day increase cited)
  • Oct 19, 1987: about -20.47% (S&P measure)
  • probability under normality for the 1987 move claimed as ~10^-71
• Apple vs market beta example
  • regression slope (beta) cited as 1.45
    • Apple returns respond about 1.5× the S&P move
    • idiosyncratic risk dominates the scatter

Explicit recommendations / cautions

• Use geometric mean rather than arithmetic mean for evaluating long-run investment outcomes, because arithmetic mean can look good despite rare catastrophic loss.
• Do not rely on independence and normality in crisis modeling:
  • VaR may underestimate risk when dependence and fat tails emerge
  • consider CoVaR / conditional dependence approaches

Disclosures / disclaimers

• No explicit “not financial advice” (or similar) disclaimer appears in the provided subtitles.

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Presenters / sources mentioned (end)

• Professor Robert Shiller (speaker)
• Elan Fuld (teaching assistant; mentioned for review/coverage)
• Professor Brunnermeier (Princeton; associated with the CoVaR concept)