# Consensus expected excess return from Active Portfolio Management

In the book Active Portfolio Management, when discussing components of expected return (page 92 in edition 2), the authors mention that the consensus expected excess return $$\beta_n\mu_B$$ is the expected excess return obtained if one accepts the benchmark as an ex ante efficient portfolio with expected excess return $$\mu_B$$. Is the benchmark portfolio $$B$$ the market cap weighted fully invested portfolio?

• $B$ is a bogey portfolio. My interpretation: Prior to chapter 4 the author seems to consider S&P 500 to be the market portfolio. In cases, where you're trading other financial products (eg. bonds and/or real estate) or equities on other markets, then S&P 500 would not be a representable benchmark for your portfolio (it doesn't define your universe). Thus, in chapter 4 he generalises the market portfolio to consider alternative benchmark portfolios. Eg. if you were to make a fund tracking the Nikkei 225 index, then the Nikkei 225 index itself, will be the bogey portfolio. See p. 88 - 90. – Pleb Jun 11 at 10:35
• Thanks for the answer! Quick follow-up: if $B$ is not the market cap weighted fully invested portfolio, then why would the fact that $B$ is an efficient portfolio with expected excess return $\mu_B$ imply that the consensus expected excess returns are $\beta_n \mu_B$? I assume by "consensus expected excess returns," the authors mean the expected excess returns under the CAPM framework. Doesn't that require the benchmark to be the "market" portfolio and consequently the same as portfolio $Q$ in the derivation? – Xiaohuolong Jun 11 at 14:10
• I understand that if $M$ is the market cap weighted fully invested portfolio, then under CAPM, the expected excess return on asset $n$ will be $\beta^M_n \mu_M$, where $\beta^M_n$ is asset $n$'s beta with respect to $M$. Here if $B$ is not $M$, how is it that under CAPM we can obtain that the expected excess return on asset $n$ is $\beta^B_n \mu_B$? – Xiaohuolong Jun 11 at 14:13
• Since I haven't read the book, but only found small snippets that might help answer your question, the only thing I can do is guess. Thus, I believe it is the authors intention to do a change of notation, such that he is setting the bogey portfolio $B$ to be the market portfolio $M$. The new benchmark might be a market-cap weighted fully invested portfolio. Sorry for not being of much help. – Pleb Jun 12 at 8:59