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) = ....

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.

What is the significance of Parts A, C, and E then, if the comparison should be between those of a similar beta and not of a similar return?

[NEAS: Use the principles:

If two portfolios have the same beta, the one with the higher expected return is preferred.

If two portfolios have the same expected return, the one with the lower beta is preferred.

We can do the comparison between portfolios with similar betas or portfolios with similar expected returns.]

Corpfin, Mod 7: Long and Short Portfolios

The comments in this thread are correct. Just as we borrow or lend at the risk-free rate, we buy and sell stock portfolios. Small investor rarely sell stocks short; hedge funds do this all the time. The hedge funds are the arbitragers who keep the market efficient.

The weights for each portfolio are derived algebraically, as done by Forum Guru.

Part G doessnt make sense!!!

Sure 1&2 is great if you are a risky investor. But lets say you are not as risk tolerant and are happy with the small gain from 2&3, given the very low Beta?
How can one be better than the other?

Does anyone have any thoughts?

[NEAS: Suppose Stock A has a beta of 0.5 and an expected return of 10% and Stock B has a beta of 1.5 and an expected return of 20%.  If risk free rate is 8% and the market risk premium is 8%, a risk averse investor would prefer a combination of the risk free asset and Stock B instead of Stock A.]

Assuming you have 2 stocks to pick, if you invest x% in Stock A, then you are investing 1-X% in stock B.

Now, back to -1.5(12%)+2.5(16%)

It should be -1.5(12%)+(1-(-1.5))(16%)

= -1.5(12%)+2.5(16%)

Given:

Portfolio     Expected return     beta

#1              12%                    0.5

#2              16%                     1.1

#3              20%                     2

 

in part B, it asked to combine #&2 to have same beta as #3

let x be the weight in #1, then (10x) is the weight in #2

=> x(0.5) + (1-x)(1.1) = 2

solve for x, we have x=-1.5.

Which means we short 1.5 share of #1 and buy 2 shares of #2

using the same weight to compute the combined expected return.

-1.5(12%)+2.5(16%)=22%

 

Similarly for #1&3 vs #2, and #2&3 vs #1. You should get to those returns.

After you worked out all comb.

                Return    Beta      Equivalent to        Return

#1&2           22%       2              #3                   20%

#1&3          15.2%     1.1            #2                   16%

#2&3          13.33%    .5             #1                   12%

 

The way I see it is, #1&2 abd 3 having same beta, the return is higher for #1&2 than #3, clearly comb. #1&2 is better than #3

Same argument applied to the other.

Summary

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, but which is worst? #1 or #3?

comb #1&2 gives you return of 22%, which is more 2% more than #3 alone. (with help of #2, it inc. by 2%)

comb #2&3 gives you 13.33% return, 1.2% more than #1 alone. (with help of #2, it only inc. by 1.5%)

Since #2 is the best, this tell us that #3 is the worst.

This is my logic

[NEAS: #2 is clearly the best. For the worst, reason as follows: If the other two stocks lie on the CAPM line, we can derive the risk free rate and the market risk premium.  If so, what is the expected return for the third stock?]

In Part a. I got that you buy -1 of portfolio #1, which means you buy (1-x)=2 of Portfolio #2.  So then I applied those weights to the betas of portfolios 1 and 2.

So, beta combined portfolio = -1*.5 + 2*1.1

and return of combined portfolio = 20%

Once you do that for all the various combinations of portfolios you have to interpret which is the best and worst portfolio.  That's where I get stuck, so if anyone has any ideas let me know.

[NEAS: Use the principles:

If two portfolios have the same beta, the one with the higher expected return is preferred.

If two portfolios have the same expected return, the one with the lower beta is preferred.]

I interpreted it a bit different.  I solved the equation that they gave in part a (x*.12 + (1-x)*.16 = .2).  I interpreted the "x" values as the amount of each portfolio to purchase in order to produce the desired return.  Then I used the "x" values as weights a to solve for the beta in part b.  I think that's why they had the remark that said the "x" being negative means that you sell the portfolio and a positive weight means you buy it.

[NEAS: Correct.  To get 20% as a weighted average of 12% and 16%, one of the weights must be negative.  In financial terms, we short sell that stock, meaning we borrow the stock from a broker and sell it in the market.]