Hello, hoping someone can confirm my thinking or correct me. There is a graph that shows the risk and return for different values of the correlation coefficient. My question involves two risky assets that are perfectly negatively correlated. The graph shows that a portfolio of two assets( -1 correlation) with a specific weight in each would completely eliminate portfolio risk measured by portfolio variance. I understand that part but it also shows that such a portfolio would still have a positive expected return? Which is where I am confused.
Is this a % of the risk free rate? For example a portfolio of 50% in stock A while shorting stock A with 50%. Then just investing the $ from shorting A in the risk free rate?
Thanks for any help. This has been bothering me.
I’d have chosen B myself, but I’ve always been something of a contrarian.
Sorry never posted before and jumped the gun! S2000magician am I thinking correctly?
I’m not following your investment in A and shorting of A. Where’s the other risky asset?
Nevertheless, if you could, indeed, find two assets (a and B, say) whose correlation of returns is -1.0, then there would be a mix of A and B that would give you zero volatility of returns. Its expected return would lie between the expected returns of A and B. The easiest way to visualize that would be to plot A’s and B’s return vs. σ of returns, but with A’s σ of returns negative. If you then draw a straight line between the points for A and B, where that straight line crosses the Y-axes (expected return) would be the expected return of the zero-volatility portfolio.
In theory, that value should be the risk-free rate. If it were higher than the risk-free rate, investors would buy up that portfolio, causing its price to rise until its return dropped to the risk-free rate. If it were lower than the risk-free rate, investors would sell that portfolio, causing its price to fall until its return rose to the risk-free rate.
Okay, that makes sense! Thank you for the clarification. With my example I was thinking that risky asset 1=longing A and risky asset 2= shorting A.