Much like financial markets, prediction markets (PM) have existed in
some informal capacity for hundreds of years; the earliest known
records, dating back to 1503, describe the practice of betting upon
papal succession. Much like traditional financial markets, the process
of centralization took many hundreds of years, as the value of
centralized exchanges slowly began to impress itself upon the
participants. The start of the contemporary era of PM and political
betting, perhaps the foremost type of PM, was heralded by the *Iowa
Electronic Markets*, established during the 1988 presidential election
by the University of Iowa. Since then, many sites and markets have come
and gone in the relatively unregulated and nascent field. Currently,
PredictIt, run by the *Victoria University of
Wellington*, dominates the space in both trade volume and number of
independent markets. Other markets include *Betfair* and *Augur*.

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In today's post, we will dig into the nature and value of analyst
recommendations in order to try to answer an old but controversial
question: do sell-side analyst recommendations hold any predictive
power; and if so, when and why? The data we will use for this analysis
is the *FactSet Estimates - Broker Recommendations* dataset, available
free of charge on Quantopian.

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In this post, we will look into the relationship between
diversification, risk, and leverage: first covering the history of
diversification and risk and then expounding upon the mathematical link
between leverage and diversification. Much of the material in this post
is related to another post of mine which you can view here: ETFs, Volatility and Leverage: Towards a New Leveraged ETF Part 1.

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In part one of this three part series, we will explore the concept of
levered ETFs, common misconceptions, the effect of volatility on the
returns of a portfolio, and the compounded returns of the S&P 500
utilizing different leverage ratios. We will also touch on the basic
mathematical underpinnings of volatility drag and ideal leverage ratio.

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