Leveraged Positions
An investor purchased stock on margin and holds it for one year. Data from this transaction are shown (amounts in GBP):
| Item | Amount |
|-----------------------|----------|
| Purchase price/share | 100 |
| Sale price/share | 120 |
| Shares purchased | 100 |
| Leverage ratio | 2.5 |
| Brokers interest rate | 5% |
| Dividend | 1 share |
The total return on this investment is _closest_ to:
Incorrect.
Actually, 40% is the margin percentage, not the return.
Correct.
Initial investment is calculated as
$$\displaystyle \frac{1}{\text{Leverage Ratio}}$$,
where the leverage ratio is 0.40 times the 100 shares at 100, or
$$\displaystyle 0.40 \times 100 \times 100 = 4{,}000$$.
The formula for the end position is then
$$\displaystyle \text{Initial Investment + Trading Gains + Dividends - Interest on Funds}$$
$$\displaystyle 4{,}000 + (20 \times 100) + 120 - (5\% \times 6{,}000)$$
$$\displaystyle 4{,}000 + 2{,}000 + 120 - 300 = 5{,}820 $$ .
Total gain is
$$\displaystyle 5{,}820 - 4{,}000 = 1{,}820 $$
$$\displaystyle \frac {1{,}820} {4{,}000} = 45.5 \% $$
Incorrect.
Simply multiplying the gain by 2.5 doesn't take into account other items, like the interest on the loan.
40%.
45%.
50%.
