An investor has a portfolio of n different stocks. He has bought s_i shares of s

Question

An investor has a portfolio of n different stocks. He has bought s_i shares of stock i at price p_i, i = 1,..., n. The current price of one share of stock i is q_i. The investor expects that the price of one share of stock i in one year will be r_i. If he sells shares, the investor pays transaction costs at a rate of 1% of the amount transacted. In addition, the investor pays taxes at the rate of 30% on capital gains. For example, suppose that the investor sells 1,000 shares of a stock at $50 per share. He has bought these shares at $ 30 per share. He receives $ 50,000. However, he owes 0.30(50000-30000) = 6000 dollars on capital gain taxes and 0.01(50000) = 500 dollars on transaction costs. So, by selling 1,000 shares of his stock he nets $ 43,500.

Formulate the problem by selecting how many shares the investor needs to sell in order to raise an amount of money K, net of capital gains and transaction costs, while maximizing the expected value of his portfolio next year.

Explanation / Answer

LET INVESTOR WILL SELL` N1` STOCK OF `S1` SHARE WHICH HE HAS PURCHASED EACH FOR $ P1 N2 NUMBERS OF S2 SHARE WHICH HE HAS PURCHASED EACH FOR $ P2 N3 NUMBERS OF S3 SHARE WHICH HE HAS PURCHASED EACH FOR $ P3 AND SO ON .................................................

NN NUMBERS OF SN   SHARE WHICH HE HAS PURCHASED EACH FOR $ PN

NOW TOTAL PURCHASING COST = N1P1+N2P2+N3P3+.....................+NNPN TOTAL AMOUNT EXPECTED BY SELLING THESE SHARES NEXT YEAR = N1R1+N2R2+N3R3+..........+NNRN TOTAL TAX PAYMENT = [(N1R1+N2R2+N3R3+..........+NNRN ) - (N1P1+N2P2+N3P3+.....................+NNPN )] X 30%

AND TOTAL TRANSACTION COST = ( N1R1+N2R2+N3R3+..........+NNRN ) X 1%  

HENCE TOTAL GAIN` K `= [ N1R1+N2R2+N3R3+..........+NNRN] - [  [(N1R1+N2R2+N3R3+..........+NNRN ) - (N1P1+N2P2+N3P3+.....................+NNPN )] X 30%  - ( N1R1+N2R2+N3R3+..........+NNRN ) X 1%

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.