Creating Equity Out of Cash
A fund manager is planning to equitize CNY 200 million for three months, using the following information:
| Description | Value |
|-----|-----|
| Futures price | 18,000 |
| Multiplier | CNY 10 |
| Dividend yield | 4.0% |
| Risk-free rate | 2.5% |
The position will create approximately how many shares of synthetic stock?
Incorrect.
This is possibly the result of failing to use the risk-free rate in the first step in order to determine the number of futures contracts needed, leading to 1,111. But there should be 1,118 futures contracts purchased in this scenario.
Incorrect.
This is possibly the result of getting to the correct number of futures contracts of 1,118, but not accounting for the time period of 0.25 years when adjusting the value invested for the dividend yield.
Correct!
The number of futures contracts can be calculated as follows:
$$\displaystyle N_f = \frac{V(1 + r)^T}{(Multiplier)F} = \frac{200,000,000(1 + 0.025)^{0.25}}{10 \times 18,000} = 1,117.99 \approx 1,118 $$
This number of contracts, along with the multiplier, can then be adjusted by the gross dividend yield to calculate the synthetic number of stock units created:
$$\displaystyle \frac{N_f \times (Multiplier)}{(1 + \delta)^T} = \frac{1,118 \times 10}{(1 + 0.04)^{0.25}} = 11,070.91 $$
This is closest to 11,071 units of stock or stock index.
10,683
10,750
11,071
