## Nontechnical Background Information

We can observe the current prices of assets (commodities like gold or wheat, or financial assets like stocks) from transactions that are taking place every instant in markets all over the world. But the public and policymakers often need to make decisions that depend on what’s going to happen to asset prices in the future. For a large number of assets, we use prices from option markets to estimate the chance or probability of a future changes in that asset’s price. Thus, on this web page we provide estimates of the probability of a 20% increase in the S&P 500 over the coming year, or the probability of a 20% fall in the dollar value of the Euro over the next six months.

To be more precise, we provide estimates of what economists call risk-neutral probabilities. We do so because the Federal Reserve Bank of Minneapolis has concluded that the economic policymakers will typically find risk-neutral probabilities useful in their decision-making. Most importantly, the risk-neutral probability accounts for how valuable resources will be in the future relative to today. For example, suppose we find that the risk-neutral probability of a 20% fall in real estate prices is larger than the risk-neutral probability of a 20% increase in real estate prices. We can conclude that market participants’ current valuation of resources in the former “large decline” case is higher than their current valuation of resources in the latter “large increase” case. Policymakers can best compare current economic costs against future economic benefits (or vice versa) if they make use of this kind of information about the current valuation of future resources.

More Technical Information:

## Definitions of Statistics Used in RNPD Analysis

Mean = $\mu$ = $\int xf(x)dx$ = $E(x)$

Standard deviation = $\sigma$ = $\sqrt{x^2f(x)dx - \mu^2}$ = $E[(x-\mu)^2]$

Skew = $\frac{E[(x-\mu)^3]}{\sigma^3}$

Kurtosis = $\frac{E[(x-\mu)^4]}{\sigma^4}$

## Research/Analysis/Speeches

Optimal Outlooks - Executive Summary
Narayana Kocherlakota
Ann Arbor, Michigan, June 8, 2012

Optimal Outlooks - Executive Summary
Narayana Kocherlakota
Minneapolis, Minnesota, June 3, 2012

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