Welcome to the hotseat. We've prepared a guide if you'd like to read more about how it works.

Figure 6.2 page 14

0 votes
asked Feb 23 in BUS 4028F - Financial Economics by anonymous

One of the emails sent earlier said we were not allowed to send pictures of ActEd notes. However my question is related to Figure 6.2 on page 14. (I've been to the physical hotseat but each time I look at this, I get more questions). 

My questions are:

1. What do we mean by negative /positive holdings of S1 and S2 in terms of the diagram. According to the diagram, how do I deduce that when \rho =-1 we have positive holdings of both securities. How do we conclude the when \rho = 1 we have a negative holding of S2 and a positive holding of S1?

2. I understand the opportunity set to be the set of all portfolios available to the investor(i.e efficient and inefficient). On this diagram, does this mean only the points along the lines comprise the opportunity set or am I right to think that the opportunity set would be all the points within/between the the lines(eg for when \rho\ =1 that's all the points within the two lines corresponding to \rho\ =1 ). 

1 Answer

0 votes
answered Feb 23 by Mufaro (520 points)


I don't have access to the diagram you're referring to but hopefully this will still help.

1. I think you're referring to variance minimising portfolios:

When rho = -1 we have two perfectly negatively correlated holdings. If you wanted to minimise the risk of your portfolio then you would hold an equal weighting in the two, S1 and S2. This is because as one increases, the other decreases. For example, if S1 increases by 10% then S2 would decrease by 10% (perfectly correlated). If you held equal weight in the two then the increase and decrease would cancel each other out each time leaving no risk.

Similarly, if rho = 1 we have perfectly positively correlated holdings. If you want to minimise risk then you can again get to zero risk. Considering S1 and S2 as the holdings again: if S1 were to increase by 10% you know that S2 will increase by 10%. Therefore, if you had shorted S2 then the gain from S1 would be offset by the 'loss' due to your negative position in S2. If you are holding the same positive quantity in S1 as your negative quantity in S2 then any gains/losses will always cancel each other out, leading to zero risk.

2. Please post the diagram (the copyright shouldn't be an issue for this).