# Expected rate of return for a portfolio

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 standard deviation ofreturns 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 are available, the expected rate ofreturn on the combined portfolio is closest to: A. 5.0%. B. 6.0%. C. 7.0%. D. 8.0%. How does investment B has two standard deviations? Is it a type? The answer for this question is A.

your misreading it. the top part says that the total portfolio will have a SD of zero. in that case, if no arbitrage opportunity exists, the E® of the portfolio must be equal to the risk free rate of 5%

i thought the E® is based on the weights of each A and B with respect to their own expected returns. No?

Anybody with a more detail explanation? Thanks.

how would one calculate the beta here? they give you covariance but nothing about market variance… anyone know how to figure that out?

its simply the rf…since there is NO arbitrage, you must rely on the prices of Treasuries!

I think if this portfolio did exist, there would be an arbitrage opportunity - I’d borrow 5% any day and buy this… But as the question says, there is no arbitrage opportunity and the risk is zero so it must equal the risk free rate i.e. 5%.

OK, I understand that but why is the answer A and not B then?

are you joking now?

Thanks all for their inputs!