When the market is thin, lean on your model

Question

Your private model estimates fair value at $108$ with a standard deviation of $3$ . The market is trading around $100$ , but it is thin and stale, so you judge its effective standard deviation to be $5$ .

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

Accepted Answer

The rule is always the same, weight each signal by its precision, but the answer flips when the market is imprecise. Precisions: private 1/9 \approx 0.1111, market 1/25 = 0.04. \hat\mu = \frac{108/9 + 100/25}{1/9 + 1/25} = \frac{12 + 4}{0.1111 + 0.04} = \frac{16}{0.1511} \approx 105.88. Your fair value is about 105.88, most of the way toward your model, not the screen. Because the market's variance is large (25 versus your model's 9), your private view now carries over 73\% of the weight. Compare this with a deep, fast market: there \sigma{	ext{mkt}} would be tiny, the price would dominate, …

When the market is thin, lean on your model

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