Two assets with identical expected returns and STD's

map1 Wrote: ------------------------------------------------------- > gdiddy Wrote: > -------------------------------------------------- > ---- > > > > We know in this case that r = 1, so let’s leave > > out r > > > > > > How would you know it? Just because they both have > the same STDV and expected values? That post was referring outside the question. I wasn’t in any way saying that we knew the correlation in the problem.

map1 Wrote: ------------------------------------------------------- > If the portfolio is only of the 2 assets, do you > really need the weight of each? The weight of one > only is enough. Not true. What if you’re purchasing one of the assets on margin?

Why would how you finance the portfolio affect the volatility?

Why does that matter, gdiddy? Assets A and B are available to you. You put 100% of your money in A (lets say $100), and borrow $30 to purchase B. The weight of your porfolio is $100/$130= 0.77 in A, and 0.23 in B. We can say, the portfolio’s weight is 100% split into Wa and (1-Wa).

Maybe I’m interpreting this wrong, but I’m basing this on the information in reading 51 of book 4, pages 258 and 259. Expected return would increase due to leverage, but so would overall risk. Am I right?

cpk123 wrote: > similarly when r=-1 > w1s1 - w2s2 would be your answer. Which I agree with, but should we require that w1 >= w2 to avoid a negative sigma, assuming s1=s2? Also, if s1 is not equal to s2, then I am not sure that we can ensure that the portfolio’s sigma is going to be positive. The formulas do not indicate that we should use absolute value.

No there is no way that you can get a negative sigma. When r = -1, we have Var(w1*A +w2*B) = w1^2*Var(A) + w2^2*Var(B) +2*w2*w1*Cov(A,B) = w1^2*Var(A) + w2^2*Var(B) - 2*w2*w1*Sqrt(Var(A)*Var(B)) = (w1*sigmaA - w2*sigmaB)^2 and the ^2 keeps it positive for any w1, w2…

JDV, you calculated Var, but what is sigma? Is it (w1*sigmaA - w2*sigmaB)?

It will be the +ve square root. So those factorings have already happened when you squared, subtracted, etc. etc.

Is sigmaP = (w1*sigmaA - w2*sigmaB)?

sigmaP = |w1*sigmaA - w2*sigmaB| for r = -1 where |x| = absolute value of x

It would be nice if we could have an equation editor in AnalystForum. :slight_smile:


Is it still this question?

“If the two assets have the same risk wouldn’t the protfolio have the same risk, regardless of the weight of each?”

This is false. For instance, lets say that correlation is -1. So, if asset A goes up 10%, asset B goes down 10%.

If weights are 50/50, then risk is zero.

If weights are 99/1, then risk is not zero.

Is this sufficiently clear?