Capital Market Line Question contain, capital, another, question, efficient

manchester88

Here is another question from Schweser QBank.
All portfolios on the capital market line are:
A) unrelated except that they all contain the riskfree asset.
B) perfectly positively correlated.
C) distinct from each other.
Answer and Explanation
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The introduction of a riskfree asset changes the Markowitz efficient frontier into a straight line. This straight efficient frontier line is called the capital market line (CML). Since the line is straight, the math implies that any two assets falling on this line will be perfectly, positively correlated with each other. Note: When ra,b = 1, then the equation for risk changes to sport = WAsA + WBsB, which is a straight line.
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I failed to understand why the assets on CML will be positively correlated. I thought the idea is to achieve diversification by adding all types of risky assets (along with RFR) to eliminate the unsystematic risk. Perfectly Positive correlation won’t add to the diversification.

Mechanic

The CML has only one asset – the entire market. As you move along the line, you are either adding cash or borrowing cash at the RFR. Doing so changes the standard deviation of the combined portfolio but the various points along the line move in perfect sync with one another.
For example, compare three investment accounts, one that holds only $100k of Apple stock, another that holds Apple plus $10k of cash, and another that holds Apple less $10k of margin borrowings. The standard deviation of cash is always zero. The returns of three portfolios will rise and fall at the same time, but only as Apple stock moves. Hence, they are perfectly correlated, even though the returns may be different.

cyber21

very well explained.
Thank You and have a nice weekend.