Hi,
I was going through Portfolio Risk and Return Chapter 2 and was reading the construction of optimal portfolio for investors with heterogeneous beliefs. The investor has selected his portfolio as the market portfolio and now wants to add securities outside the index( say S&P 500). It was given that if the Alpha of this stock is positive, we include it, with its weight being = (Alpha/Non-systemic variance of stock).
Can you please explain me the derivation of the weight formula.
I’ve never seen that weight formula at Level I.
I don’t understand it neither.
CFA level 1 curriculum, reading 44 (p 382) states, that alpha divided by nonsystematic risk, measures the abnormal return per unit of risk added by the security to a well-diversified portfolio. It’s somehow contradictory to earlier reading, which emphasizes that investor should be compensated only for systematic risk, and security’s contribution to portfolio’s risk is measured by beta (systematic risk).
That’s kind of the sharpe ratio of the stock using excess return over required return instead of stock return - rf if you think about it.
yes alpha can be considered as excess return over required rate, but why is it devided by nonsystematic risk, when from portfolio viewpoint you should only consider systematic risk?
I believe it’s writen in one of the sentences on page 382 - “because we are concerned with maximizing risk-adjusted return, securities … with greater nonsystematic risk should be given less weight in the portfolio”.
Market participants will be conpensated only for systematic risk => you want to add new security only if it has higher excess return on systematic risk compared to the unsystematic risk you will bear.