# Thread: the minimum variance of the profit rate

1. ## the minimum variance of the profit rate

There are one riskless bond and a bunch of stocks with risk in the market. For the expected profit r>1 (or r=1) the minimum variance of the profit rate for the risk papers is

σ^2(r)=r^2-2r+2.

Let's asume that we have a portfolio with both riskless bonds and stocks with risk. When expected profit r=8, the variance of the profit rate is 45. What is the minimum variance of the profit rate when r=2?

Is there anyone who could help me with this? I have tried to solve this in many ways, but I never get the answer.

2. is that the entire question, as printed, with no changes or omissions?

if it is, i am stumped. You are presumably expected to use the first scenario to deduce the return on the bonds; this will let you work out the proportion of the portfolio in bonds and stocks in the second scenario; then you can just plug numbers in to get the variance.

However, i dont see how to deduce the return on the bonds from the information you posted.

3. Yes, it is unfortunately all the information I have

4. Is this the proper way to approach this problem:

1) Given $\sigma^2_{min} = 45$ for $r=8$ implies 7.633% of the return is from stocks and 0.367% is from bonds (i.e. riskless, so contribute zero to the variance).

2) To have portfolio returning r=2, with bonds only able to contribute 0.367, the stock portion must be 2 - 0.367 = 1.633, thus r=1.633, so $\sigma^2_{min}=1.4$

?

5. 1.4 was my answer on the exam and I got 0 points. I calculated it differently though.