# Puzzling Portfolio return?

I have been scratching my head and banging it on the desk over this particular question, verification greatly appreciated…cheers! An analyst determines that a portfolio with a 35% weight in Investment A and a 65% weight in investment B will have a standard deviation of returns equal to zero. Investment A has an expected return of 8% Investment B has a std deviation of returns of 7.1% and a covariance with the market of 0.0029 The risk free rate is 5% and the market risk premium is 7% If no arbitrage opportunities exist, the expected rate of return of the combined portfolio is closest to; A. 5% B. 6% C. 7% D. 8% The correct answer is A 5%, which is obviously not what I have calculated amidst my confusion over the sd & covariance on portfolio B… Thanks for any verification, much appreciated!

eesh, thats rough. well i tried it by figuring out beta for B. and then doing a weighted avg of the expected returns but that doesnt come out to 5. only thing i can think of is that if no arbitrage opportunity exists, portfolio with a SD of 0 must have a return equal to the risk free rate of 5.

Hhhmmm…That is a fair point with respect to SD of 0 and RFR…it makes some sense.

Yup, I think jut111 has it. Stndrd dev. measures the risk of the portfolio, with stnrd dev of 0 we have not only eliminated the all the unsystematic risk to get to M portfolio (think of the CML chart), but also eliminated all systematic risk (systematic risk will still carry some value of stnadrd dev with it), taking us down to only the risk free rate, again picture the CML chart.

0 portfolio std dev -> 0 variance -> 0 portfolio beta. In the capm equation, all you have left is the rfr.