Forecasting Market Kurtosis with the Volatility Smile (Poorly)

Note: I want to thank Algoseek for providing historical SPY option-chain data at a very reasonable price. Algoseek provides all the market data you could possibly need, including equity, future, option, forex, crypto data, and more! If you're interested in high quality market data at low quality prices, check them out here!

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St. Petersburg Paradox, the Martingale, and Risk Management

Many financial practitioners have long been interested in gambling and games of chance, from Ed Thorpe's, a former hedge fund manager, seminal work on blackjack card counting Beat the Dealer, to the famous hedge fund titan poker tournament (Take 'Em to School Poker Tournament). The similarity is more than skin deep, with gambling methods such as the Kelly Criterion even making their way downtown to investment strategy and risk management. In this post, we're going to discuss the mathematics and implications for finance of two different gambling related topics: the St. Petersburg Paradox and the Martingale Strategy.

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Implied Volatility of At-The-Money Options

Note: I want to thank Algoseek for providing historical SPY option-chain data at a very reasonable price. Algoseek provides all the market data you could possibly need, including equity, future, option, forex, crypto data, and more! If you're interested in high quality market data at low quality prices, check them out here!

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Portfolio Construction with Risk Parity

Just like how there's more than one way to skin a cat, there's more than one way to construct a portfolio. The first systematic method of construction was Modern Portfolio Theory, put forth by Harry Markowitz. MPT's approach is simple: choose weights for each asset that maximize the amount of return received for the amount of risk or volatility taken. However, trying to maximize the risk-adjusted return of a portfolio leads to very unstable allocations, as ex-ante estimates of return are notoriously difficult and previous return isn't a good predictor of future performance.

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Risk Imparity: A Simple Strategy for Alpha Generation

Risk parity is a popular method of investing that aims to outperform the traditional 60/40 equity/bond portfolio by equalizing the risk of the bond portion with that of the equity part of the portfolio and then leveraging up the portfolio to hit the desired risk target. Using the covariance, and volatility of the components, we can generate a portfolio and leverage ratio for a given level of desired risk. This works for two reasons: bonds have a low or inverse correlation to equities and they generally have superior risk-adjusted returns as well, and combining low correlation assets allows us to lower the volatility of the portfolio. Bridgewater and Ray Dalio pioneered this approach in the 90s with the introduction of his now famous All Weather fund.

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