Busıness Decısıon Models Deneme Sınavı Sorusu #1400226
An investor has $1,000 to invest in bonds and stocks of a company. A bond costs $5 and pays $1 coupon annually. The expected one-year yield on this bond is 25%. A stock costs $10 per share and pays $0.8 dividend. The total rate of return expectation for stock B is 50%. For liquidity reasons, investor demands at least $80 of cash from dividends (or coupons) at the end of the year. So as to manage the risk of the portfolio, investor sets an upper and lower limit to the percentage of the funds to be invested in stocks, which are 40% and 20%, respectively. The investor has to decide the optimal amount of shares which makes the total rate of return for the portfolio is maximum.
According to the information above, what are the decision variables?
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Maximize Z = (5 × 0.25)x1 + (10 × 0.50)x2 |
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The quantities, x1 for bonds and x2 for stocks |
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x1 + 0.8x2 ≥ 80 |
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5x1 + 10x2 ≤ 1000 |
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6x2 – 2x1 ≤ 0 and 8x2 – x1 ≥ 0 |
The decision variables are The quantities, x1 for bonds and x2 for stocks. The objective function seeks to maximize total yields of the holdings and is thus expressed as Maximize Z = (5 × 0.25)x1 + (10 × 0.50)x2 A constraint of the model reflects the liquidity requirements at the end of the year x1 + 0.8x2 ≥ 80 Another constraint is about the size of the portfolio and related to prices of the securities 5x1 + 10x2 ≤ 1000 Percentage limits of the funds to be invested in stocks should not be less than 20% and more than 40%. That means the money spent on stocks cannot exceed the %40 of the total amount of money spent on both types of security. On the other side, the money spent on stocks cannot drop down under %20. These constraints are 10x2 ≤ 0.40 (5x1 + 10x2 ) 10x2 ≥ 0.20 (5x1 + 10x2 ) Simplified expressions of these are 6x2 – 2x1 ≤ 0 and 8x2 – x1 ≥ 0. The correct answer is B.
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