Question

a) A stock has traded at an average price of $50 over the course of a trading day. The covariance of successive transaction price changes (trade-by-trade changes in price) is about -0.06. Using the Roll model, what is the estimate of the bid-ask spread of the stock (measured in percent of the average price of $50)?

b) The market index has average return 7% and standard deviation 30%. The risk-free rate is 3%. A portfolio has beta 1.4, unsystematic variance of 0.03,and an M2-measure of -0.01. What is the average return on the portfolio?

Answer 1

a)

A stock has traded at an average price of = $50.

covariance of successive transaction price changes = 0.06.

Calculating estimate of the bid-ask spread of the stock.

Formula = 2(- Covariance)^1/2

= 2(0.06)^0.5

=(0.12)^0.5

=0.48989794856

or

= 0.4899

Calculating the percentage or % of price == 0.4899 / 50

=0.9798%

b)

Market index has average return = 7%.

Standard deviation = 30%

The risk-free rate is = 3%

A portfolio has beta = 1.4

Unsystematic variance of= 0.03,

M2-measure of= -0.01.

Calculating average return on the portfolio

A portfolio has beta^2 x market variance^2 + Unsystematic variance.

= 1.4^2*0.3^2+0.03

=1.96 x 0.09 +0.03

= 0.1764 + 0.03

= 0.2064

Standard Deviation

= 0.2064^0.5

= 0.4543

or 45.43%

Calculating M2

= (R-0.03)*0.3/0.4543 - (0.07-0.03) = -0.01

(R-0.03) = 0.03*0.4543/0.3 = 0.04543

R = 7.543%

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