Suppose that you have just started your first job as a junior investment analyst at a hedge fund. You have the data on average annual returns (yield), risk and liquidity levels for the following five securities (e.g Bonds):

Security #	Return (%)	Risk index	Liquidity index
1	7.6	8.6	4.4
2	7.4	7.4	3.8
3	3.0	3.9	7.7
4	5.1	6.6	8.0
5	1.5	1.7	1.9

Table 1: risk, return and liquidity characteristics of five securities

Suppose that you wish to use these data to estimate the following regression model

For where is return, is risk index and is the liquidity index for security

a) Rewrite model ( in the matrix-vector form. Show the contents, and the dimensions, of all the vectors and matrices.

b)Use the vector OLS to obtain the estimate (by hand) of the coefficients vector with the help of formula:

Carefully show your work. Hint: you may use the fact that here,

c) Using your estimate , what is the expected annual return to a bond with the risk index of and liquidity index of

d) Youre considering purchasing a bond that yields 8%, has the risk index of but its liquidity is unknown. Using your estimate , what is the value of the liquidity Index that you can expect to be associated with this bond?

e) Which of these securities appear under/ over-valued relative to their risk, liquidity and return characteristics, and why?

f) In class we saw the estimate of the variance-covariance Matrix of can be found using , where . Use these formulas to find the variance-covariance matrix of .