Arbitrage pricing theory

Solution

Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 23 / 2 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 23 / 2 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 23 / 2 / d / Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 32 / 1 / c / iii / Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 32 / 1 / c / i / Solution

{title2=$\mathbb E r_i-R=\sum_j b_{ij}\lambda_j$}
{wiki}

= APT
{c}
{synonym}

<Arbitrage pricing theory> relates <expected returns> to systematic <factor loadings> and their <risk premiums>. With idiosyncratic noise, a diversification or asymptotic argument needs additional assumptions. With no idiosyncratic noise and spanned factors, the formula is an exact consequence of <law of one price>: <portfolios> matching factor exposures can differ only by a constant payoff, which absence of <arbitrage> forces to be zero.

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