I found this post very helpful
Posted 6/11/2007 11:37 AM
Supreme Being
Group: Forum Members
Active: 7/6/2009
Posts: 68
Smiley,
I think you're on the right track here. If you make a CAPM line with #1 and #2 and use the given beta from #3, the expected return for #3 (given its beta of 2.0) should be 22.00%. Instead, we're told that #3 has only a 20.00% return. So, #3 has an expected return that is 2.00 percentage points worse than what is indicated. Another way to say this is that its expected return is 90.91% of what we would have expected (because 20.0% / 22.0% = 90.91%).
Now, for comparison's sake, if you make a CAPM line with #2 and #3 and use the given beta from #1, the expected return for #1 (given its beta of 0.5) should be 13.33%. Instead, we're told that #1 has only a 12.00% return. So, #3 has an expected return that is 1.33 percentage points worse than what is indicated. Another way to say this is that its expected return is 90.00% of what we would have expected (because 12.00% / 13.33% = 90.00%).
So, it looks to me like it's still unclear which portfolio is worse. Would you rather have a 20% expected return when you took the risk commensurate with a 22% expected return, or have a 12% expected return when you took the risk commensurate with a 13.33% return? If you don't like the two percentage point difference in portfolio #3, then you would say that #3 is the worst. If you don't like the fact that portfolio #1 only returns 90.00% of what we would have expected, then you would say that #1 is the worst.
The answer to "which portfolio seems worst" depends on by what measure you are defining "worst."
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