2. Steps
(I) Find out the excess return to beta ratio
(II) Rank them from highest to lowest
(III) Proceed to calculate c for all the stocks according to
the ranked order using the formula.
σ²m Σ(Ri– Rf ) x βi
σ²ei
C= .
1 + σ²m Σβi²
σ²ei
(IV) The cumulated value of c start declining after certain
point. That stock ratio is cut off ratio.

3. The risk less rate is 5% and market
variance is 10
Security Mean Excess Beta Unsystematic Excess return to
number return return risk beta (Ri– Rf )/ β
Ri– Rf
1 19 14 1 20 14
2 23 18 1.5 30 12
3 11 6 0.5 10 12
4 25 20 2 40 10
5 13 8 1 20 8
6 9 4 0.5 50 8
7 14 9 1.5 30 6

4. Security Excess (Ri– Rf ) x βi Σ(Ri– Rf ) x βi βi² Σβi² Ci
number return to σ²ei σ²ei σ²ei σ²ei
beta
1 14 .7 .7 .05 .05 4.67
2 12 .9 1.6 .075 .125 7.11
3 12 .3 1.9 .025 .15 7.60
4 10 1 2.9 .1 .25 8.29
5 8 .4 3.3 .05 .3 8.25
6 8 .04 3.34 .005 .305 8.25
7 6 .45 3.79 .075 .38 7.90

6. Optimal portfolio with short sales
 In this we use the last point as cut off point and short
sale is done where the result is negative and
proportion is calculated as in case of normal portfolio.