On February 5, 2018, XIV (a note that paid the inverse of short-term Cboe Volatility Index (VIX) futures) opened near $100 and finished the day with an indicated value of $4.22. Its own hedge rebalancing had swamped the volatility futures market, and the pattern recurs across this lesson: complexity combined with leverage, crowding, or weak diligence produces tail events.
Multifactor asset pricing. A factor is a distinct source of return that earns its own premium. Other factors cannot fully explain that return, so factors should not be highly correlated with each other. A legitimate factor also needs a sound economic foundation supported by rigorous research, and its premium must persist over long periods. A multi-factor model expresses systematic risk with several factors, either alongside the market portfolio or in place of it. When the factors are tradable, the ex ante (expected-return) form is:
The ex post (realized-return) form adds a residual:
Common mistakes
- Trusting VaR estimated from calm history. VaR depends on an estimated return distribution, and that estimate is only as good as the data behind it. Amaranth-style estimates from calm, mean-reverting periods understate the size of long, trending moves.
- Generalizing one pricing study to every product. Principle 2 says the payoff level relative to cost determines pricing, and each study covers specific products: ARBN fair value about 4.5% below issue price, a 15% to 20% wealth transfer on equity-linked annuities, and 2% to 3% fees at Bank of Scotland.
- Hedging an arbitragable asset reflexively. The law of one price means a German trader earns the same euro-denominated return on gold whether the transactions are conducted in euros or francs, with no hedge, and adding an FX forward can introduce currency risk.
Bottom line
- Factors are distinct, economically grounded, persistent premiums in three categories (macroeconomic, fundamental/style, statistical); a model's intercept signals alpha only when all systematic factors are included and tradable.
- Empirical factor models face expected false discoveries (tests times significance level, on average), correlation without causation, and CAPM insufficiency; factor investing rests on Ang's three observations and ten long/short premiums whose sizes vary over time, with momentum crashes and implementability...
- The AMH implies changing premiums, relative efficiency, adaptation, and decaying alpha; volatility is predictable, negatively correlated with equity returns, and modeled by Heston and Bates, while hedging can raise negative skewness.
- Complexity and opacity fuel complexity crashes and perverse incentives (STRIPS, CMOs, RMBS); tail cases teach four lessons: excessive leverage, overconfidence under liquidity pressure, fast-moving technology risk, and diligence against fraud.
Exam shortcut
For leverage, rearrange to solve for any missing variable. When comparing a structured note's price with its fair value, state the gap with a clear denominator (5.25% of issue price versus 5.54% of fair value in Example 1).
The full lesson (about 17,005 words, 113 min read) adds 2 worked examples, all 4 common mistakes, a self-check, free in the app.
Learning objectives
- measures volatility
- vega gamma theta
- vol as factor
- modeling vol processes
- implied vol structures
- option strategies vol
- delta neutral vol
- variance vol derivatives
- correlation dispersion
- vol correlation summary
- structured products wrappers
- exotic option features
- global structured cases
- structured product valuation
- currency hedging re
- currency risk perfect markets
- currency risk alts
- futures quanto
- intl re overview
- intl re challenges
- crypto investment styles
- crypto fund strategies
- crypto trading strategies
- crypto risk risk management
- market manipulation cryptocurrencies
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