Sharpe’s Optimal Portfolio


Sharpe’s Optimal Portfolio

Sharpe had provided a model for the selection of appropriate securities in a portfolio. The selection of any stock is directly related to its excess return- beta ratio.
Ri-Rf / βi
Where, Ri= the expected return on stock i
Rf= the return on a riskless asset
βi= the expected change in the rate of return on stock i associated with one unit change in the market return
the excess return is the difference between the expected return on the stock and the riskless rate of interest such as the rate offered on the govt security or treasury bill. The steps for finding out the stocks to be included in the optimal portfolio are given below:
1.      Find out excess return to beta ratio for each stock under consideration.
2.      Rank them from the highest to the lowest.
3.      Proceed to calculate Ci for all the stocks according to the ranked order.
The cumulated values Ci starts declining after a particular Ci and that point is taken as the cut off and that stock ratio is the cut off ratio C.
Construction of the optimal portfolio:
After determining the securities to be selected, the portfolio manager should find out how much should be invested in each security. The percentage of funds to be invested in each security can be estimated 

Thus, the proportion to be invested in different securities are obtained.
Optimum portfolio with short sales: the procedure used to calculate the optimal portfolio when short sales are allowed is, more or less similar to the procedure adopted for no short sales, except the cut off point concept. At first, the stocks have to be ranked by excess return to beta. Here, all the stocks are added to the portfolio. They are either held long or short. All the  stocks affect the curt off point. The Z value has to be calculated for each stock. If the Z value is positive, the stock will be held long and if negative, will be sold short. Stocks which are having excess return to beta above C* are sold short.



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