You decide to sell short 100 shares of Charlotte Farms when it is selling at its yearly high of $56. Your broker tells you that your margin requirement is 45% and that the commission on the purchase is $155. While you are short the stock, Charlotte pays a $2.50 per share dividend. At the end of 1 year, you buy 100 shares of Charlotte at $45 to close out your position and are charged a commission of $145 and 8% interest on the money borrowed. What is your rate of return on the investment?
Your rate of return on the investment is -7.5%.
Calculation:
Profit/Loss = (Sale Price - Purchase Price - Commission - Interest - Dividend) x Number of Shares
Profit/Loss = ($45 - $56 - $155 - ($45 x 0.45 x 0.08) - ($2.50 x 100)) x 100
Profit/Loss = -$1,050
Rate of Return = (Profit/Loss / Initial Investment) x 100
Rate of Return = (-$1,050 / ($56 x 100 + $155)) x 100
Rate of Return = -7.5%
To calculate the rate of return on your investment, we need to calculate the total gain or loss incurred during the investment period.
First, let's calculate the initial investment:
1. Selling Price: $56 per share
2. Number of shares sold short: 100
3. Initial investment: 100 shares x $56 per share = $5,600
Now let's calculate the commission on the purchase:
1. Commission on the purchase: $155
Next, let's calculate the dividend received:
1. Dividend per share: $2.50
2. Number of shares: 100
3. Total dividend received: $2.50 per share x 100 shares = $250
Now let's calculate the cost to close out the position:
1. Purchase price: $45 per share
2. Number of shares bought: 100
3. Closing out cost: 100 shares x $45 per share = $4,500
Now let's calculate the commission on closing out the position:
1. Commission on closing out: $145
Next, let's calculate the interest on the money borrowed:
1. Margin requirement: 45%
2. Borrowed amount: (100 shares x $56 per share) x (1 - 45%) = $3,080
3. Interest rate: 8%
4. Interest paid: $3,080 x 8% = $246.40
Now let's calculate the total gain or loss:
1. Initial investment: $5,600
2. Commission on purchase: $155
3. Dividend received: $250
4. Closing out cost: $4,500
5. Commission on closing out: $145
6. Interest paid: $246.40
Total gain or loss = $5,600 - $155 + $250 - $4,500 - $145 - $246.40 = -$2,196.40
Finally, let's calculate the rate of return:
Rate of return = (Total gain or loss / Initial investment) x 100
Rate of return = (-$2,196.40 / $5,600) x 100
Rate of return = -39.21%
Therefore, the rate of return on your investment is approximately -39.21%.
To calculate the rate of return on this investment, you need to consider several factors:
1. Initial short position:
- Short selling 100 shares of Charlotte Farms at $56 per share results in a short position of (100 * $56) = $5,600.
2. Margin requirement:
- Your broker requires a margin of 45%, which means you need to have 45% of the short position as collateral.
- The margin required is (45% * $5,600) = $2,520.
3. Commission on the purchase:
- The commission on the purchase of 100 shares is $155.
4. Dividend while short:
- Charlotte Farms pays a dividend of $2.50 per share while you are short.
- The dividend payment you receive is (100 * $2.50) = $250.
5. Cost to close the short position:
- At the end of 1 year, you decide to buy 100 shares of Charlotte Farms at $45 per share to close out your position.
- The cost to close the short position is (100 * $45) = $4,500.
6. Commission on closing the position:
- The commission on closing the position is $145.
7. Interest on borrowed money:
- You need to consider the interest charged on the money borrowed for the short position.
- The interest charge will be 8% of the margin requirement, which is (8% * $2,520) = $201.60.
Now, let's calculate the overall rate of return:
Initial investment = Margin requirement + Commission on the purchase
= $2,520 + $155
= $2,675
Final investment = Cost to close the short position + Commission on closing the position + Interest charged
= $4,500 + $145 + $201.60
= $4,846.60
Net investment = Final investment - Dividend received
= $4,846.60 - $250
= $4,596.60
Rate of return = (Net investment - Initial investment) / Initial investment
= ($4,596.60 - $2,675) / $2,675
= $1,921.60 / $2,675
= 0.718 (approximately) or 71.8% (approximately)
Therefore, the rate of return on the investment is approximately 71.8%.