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Continuous‐time filtering is explained, including the Kalman filter and filtering for a Markov chain with hidden states. Filtering theory is applied to analyze portfolio choice and equilibrium asset prices. When the expected return of an asset is unknown and is estimated from past returns, the myopic demand is a momentum strategy. When investors learn expected consumption growth from realized consumption growth, equilibrium prices are more sensitive to consumption shocks and the equity premium is higher. When the consumption growth rate follows a Markov chain with hidden states, return volatility tends to be higher when investors are less certain about which state the economy is in.
Title: Learning
Description:
Continuous‐time filtering is explained, including the Kalman filter and filtering for a Markov chain with hidden states.
Filtering theory is applied to analyze portfolio choice and equilibrium asset prices.
When the expected return of an asset is unknown and is estimated from past returns, the myopic demand is a momentum strategy.
When investors learn expected consumption growth from realized consumption growth, equilibrium prices are more sensitive to consumption shocks and the equity premium is higher.
When the consumption growth rate follows a Markov chain with hidden states, return volatility tends to be higher when investors are less certain about which state the economy is in.
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