I am having problems getting the Betas to come to 2, 1.1, and .5 Are they supposed to comeout to that, or what am I doing wrong.

No, that is not what the combined betas come out to be, that is what each portfolio's individual betas are.  For example to get the combined beta of #1 and #2, solve (-1)(.5) + (2)(1.1) = ....

Rules for combining betas:

~ The beta of a portfolio is the value weighted average of the betas of the individual securities.

~ If a stock is sold short, its value is negative for the value weighted average.

~ Even if stocks A and B both have high betas, stock A – stock B may have a low beta and little systematic risk.

I am wondering what the point of A, C, E is too - I ended up with six possible scenarios, but now I'm only supposed to compare three of them to decide which is best?

For the record can anyone confirm these, because I'm not totally sure I've done it correctly!

A:  beta = 1.7, er = 20%

B: beta = 2, er = 22%

C: beta = 1.25, er = 16%

D: beta = 1.1, er = 15.2%

E: beta = .2, er = 12%

F: beta = .5, er = 6%

So to do part G, I look at B - D - F (combinations of AB, AC, BC) and compare them to stocks C, B and A on their own - and see which ER is higher, given the beta?

I am approaching 7.3 part G as follows:
1. #1&2 is better than #3

2. #1&3 is worse than #2

3. #2&3 is better than #1

This tells us, #2 is best and #1 and #3 are BOTH the worst. End of story. Perhaps this is sufficient and we need not dig into this problem deeper.

[NEAS: The homework problem says: "Seems the worst.  See the NEAS comment above on judging the worst stock.]

For part G, I understand that all portfolios lie on the same CAPM line.  But then I'm not sure what to do next.  I tried using the respective betas and expected returns to find the risk-free rate and market risk premium, which is what NEAS said to do.  But after that, how can you find the expected return of the 3rd stock?  What beta do you use for that one?  And after you find it, what does that tell you?

[NEAS: Any two of the three stocks gives a CAPM line, which gives the required return for the third stocks (based on its beta).  See if that return is higher or lower than its actual return.]

Thanks for getting back to me so quickly.

But I'm sorry...I still don't completely get it.  Which two stocks should we find the CAPM line for?  All three of the different combinations give you different values for the risk-free rate and the market risk premium.

And then it sounds like we should use the given beta from the third one to find the expected return and compare that to the given expected return for that stock, right?  But when I do that, I just get the same answers that I got in parts A-F.

If you make a CAPM line with #1 and #2 and use the given beta from #3, the expected return is greater than the given expected return.  So does that mean that #3 seems to be the worst portfolio?  (And it's 2 points greater compared with #1 where the line is 1.33 points greater, so #3 is worse than #1.)

Is this reasoning anywhere close to what it is or am I totally confused?

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."

I'm having trouble with 7.3. I have used two methods:

Method 1
Find the mixing weight of the portfolio.
Begin with r(combined) = a*r(1) + (1-a)*r(2). Substitute each r(i) with r(f) + ß(i)*MRP.
Set equal to r(f) + ß(combined)*MRP and solve for ß(combined).

This seems to work.

Method 2
Begin with CAPM of the combined portfolios:
r(combined) = r(f) + ß(combined)*MRP.
Since r(combined) is equal to r(3) by design, set equal to r(f) + ß(3)*MRP.

This implies that ß(combined) = ß(3).

Why does this not work? Does CAPM only work when applied to singular securities individually and not mixtures of different securities?

[NEAS: The CAPM works for both individual securities and portfolios. Write out your solution and post it on the discussion thread; this will help you see how to solve the problem.]

Okay.

Method 1:
a * .12 + (1-A)*.16 = .20
A = -1
r(combined) = -1*r(1) + 2*r2 = .2
= -1 * (rf + ß1*MRP) + 2 * (rf + ß2*MRP)
= rf + MRP*( -ß1 + 2ß2)
(rcombined – rf)/MRP = ßcombined = 2 ß2 – ß1 = 1.7

This results in a beta that is lower than Portfolio 3, and is correct.

Method 2, however, results in the two betas being the same which is wrong:

r(combined) = r(3) (as it says in the problem)
[r(combined) - r(f)]/MRP = [r(3) - r(f)] / MRP
which means
ß(combined) = ß(3) which is not the case.

This in fact would suggest that any two portfolios with the same expected rate of return have the same ß which is not the case. I hope you can tell me why this method is wrong so that I can correct any misunderstanding.