Trading on a private signal against an efficient price

Question

Your private model estimates an asset's fair value at $102$ , with a standard deviation of $4$ on that estimate. The market is trading around $100$ , and you judge the market price to be efficient with an effective standard deviation of $2$ (it already aggregates many participants' information).

What is your best estimate of fair value, and how aggressively should you lean on your private view?

Accepted Answer

Your private model is one signal; the market price is a second, independent-ish signal that already aggregates everyone else's information. Combine them by inverse-variance (precision) weighting: \hat\mu = \frac{X{	ext{priv}}/\sigma{	ext{priv}}^2 + X{	ext{mkt}}/\sigma{	ext{mkt}}^2}{1/\sigma{	ext{priv}}^2 + 1/\sigma{	ext{mkt}}^2}. With X{	ext{priv}} = 102,\ \sigma{	ext{priv}} = 4 (variance 16) and X{	ext{mkt}} = 100,\ \sigma{	ext{mkt}} = 2 (variance 4): \hat\mu = \frac{102/16 + 100/4}{1/16 + 1/4} = \frac{6.375 + 25}{0.0625 + 0.25} = \frac{31.375}{0.3125} = 100.4. Your fair value is 1…

Trading on a private signal against an efficient price

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