DERIVATION needed. No numeric answer. There's no additional data. Just written equation is needed with many variables

Problem 1-CAPM For this question, we are using the assumptions from what we have introduced in Lecture 4. Suppose you currently hold the market portfolio. You would like to invest a small additional fraction a of your wealth in the market portfolio. If you are assumed to borrow at rate of rb: a) Find the expected return and variance of your portfolio after the change. b) Compare the newly derived return and variance with the ones of market portfolio, indicate the changes. c) What is the marginal price of risk (defined as the ratio of incremental risk premium and incremental risk)? Now, suppose you would like to invest a small additional fraction a of your wealth in some financial security i instead of the market portfolio. It is still the case that you are borrowing at the rate rb. d) Find the expected return and variance of your portfolio after the change. e) Compare the change with the market portfolio one, find the changes in the expecta- tion and variance. f) Find the marginal price of risk (defined as the ratio of incremental risk premium and incremental risk). g)Before we go to the last step, we need to make some further require- ment for a. Do you know what kind of requirement we should have and in which step we apply that requirement? h) What is the intuition of the last step in CAPM model. (Hint: if you let two terms equal to each other, why they are equal to each other?) i) With part g) and part h), can you finally derive the SML for CAPM? j) If the borrowing rate ry is 0.04, can you construct a linear model that will help us to estimate CAPM? k) What are the known variables (you have data for them) and unknown variables (you want to estimate them) in your constructed model? Problem 1-CAPM For this question, we are using the assumptions from what we have introduced in Lecture 4. Suppose you currently hold the market portfolio. You would like to invest a small additional fraction a of your wealth in the market portfolio. If you are assumed to borrow at rate of rb: a) Find the expected return and variance of your portfolio after the change. b) Compare the newly derived return and variance with the ones of market portfolio, indicate the changes. c) What is the marginal price of risk (defined as the ratio of incremental risk premium and incremental risk)? Now, suppose you would like to invest a small additional fraction a of your wealth in some financial security i instead of the market portfolio. It is still the case that you are borrowing at the rate rb. d) Find the expected return and variance of your portfolio after the change. e) Compare the change with the market portfolio one, find the changes in the expecta- tion and variance. f) Find the marginal price of risk (defined as the ratio of incremental risk premium and incremental risk). g)Before we go to the last step, we need to make some further require- ment for a. Do you know what kind of requirement we should have and in which step we apply that requirement? h) What is the intuition of the last step in CAPM model. (Hint: if you let two terms equal to each other, why they are equal to each other?) i) With part g) and part h), can you finally derive the SML for CAPM? j) If the borrowing rate ry is 0.04, can you construct a linear model that will help us to estimate CAPM? k) What are the known variables (you have data for them) and unknown variables (you want to estimate them) in your constructed model