Effect Of Commissions On Gross Profits
Transaction costs are part of the equation and must be considered. As with securities brokerage, futures brokerage commissions range from "full service" to discount. A spread will likely be more expensive, but not necessarily twice as expensive, even though it is, in effect, two trades.

Any futures transaction carries at least two costs: one to open a position and another to close it.

LOOK OUT!
Read carefully how the exam words the question: does it state that you need to account for "\$60 per commission" â€“ in which case you count it twice â€“ or "\$60 in commissions" â€“ in which case you count it once?

There are other carrying costs to consider as well: delivery costs for agricultural commodities, wire transfer and record keeping costs for financial instruments. In Treasury markets, incidentally, an investor may need to borrow the underlying asset to satisfy the exchange's requirement. This could add another 50 bps to the cost of the futures contract.

Unless otherwise instructed, assume these costs are figured into the commission or are negligible.

Return On (Margin) Equity Calculations
Ultimately, the speculator is not interested in how much money she made in raw terms. Rather, she is interested in how much she made as a proportion of how much money she invested. This is generally expressed as a percentage rather than a dollar figure.

The amount invested is not the original value of the contract, remember; it is mainly the margin. So say that the investor in the example we've been following had to put up 20% margin for an uncovered position or 5% for a spread. But there is another component of the investment: the commissions and associated transaction costs. Let us also assume she paid \$25 per trade in commissions for uncovered positions or \$40 per trade for spreads.

Formula 8.1
Amount invested = margin requirement + commissions

In the uncovered example, she would have had to lock in \$1,942.95 (\$9,464.75 for 100 contracts at \$94.6475 each times 20%, plus \$50 for two \$25 trades).

Formula 8.2
(gross profit â€“ amount invested) / amount invested = return on equity

In the winning case, her gross profit was \$62,500. Her return on equity, then, would be 31.17% ([\$62,500 â€“ \$1,942.95] / \$1,942.95). Potential returns such as these with little investment out of pocket are the attraction of the futures market.

Now let us see what happens when things go wrong. The investment remains the same: \$1,942.95 but now the gross profit is -\$137,500. Her return on equity in this case would be -71.77% ([-\$137,500 - \$1,942.95] / \$1,942.95), which will be awfully hard to explain to her boss.

How does spreading improve her position? First, as we have already seen, it reduces the swing between the upside and the downside, bracketing the price movements. But it will also tend to decrease the margin, more than offsetting any slightly higher commission fee, thus bringing down the amount invested.

In our example, the winning spread gave our speculator a gross profit of \$25,000. Her amount invested would be \$553.24 (\$9,464.75 for 100 contracts at \$94.6475 each times 5%, plus \$80 for two spread trades). Her return on equity would be 4,418.83% ([\$25,000 - \$553.24] / \$553.24). This is actually higher than the return on the uncovered position.

Now let's look at the losing spread that afforded a gross loss of -\$6,250 for the same \$553.24 investment. The return would be -1,229.71% ([-\$6,250 - \$553.24] / \$553.24), still not pretty, but she could show her boss that it was much less painful than the -71.77% return she would have had with an uncovered position.

Tips & Tricks
You will almost certainly see a question about this is on the Series 3 exam. It could be about grains, livestock, foodstuffs, metals, energy, lumber, long-term interest rates, short-term interest rates, municipal bonds, currencies or stock indices. The theory (and the equation) remains the same: How much did the investor make (or lose) as a percentage of her initial investment?

Bear in mind that this is the pre-tax return on equity that we have learned about. For most purposes, this is as far as you need to go. However, you might see a question on the Series 3 exam that is asks you to compare a trade in a taxable eurodollar contract with a trade in tax-exempt municipal bond (muni) contracts. If you are given a taxable instrument and asked to compute at which tax-free rate the muni contract becomes favorable, the following calculation would apply.

1. Determine the yield for the taxable transaction. Let's say that's given as 10%.
2. Determine your client's income tax rate. Let's say that's given as 40%.
3. Subtract the tax rate from 1. In this case, that gives us 0.6 (1.0 â€“ 0.4).
4. Multiply the taxable yield from Step 1 by the result of Step 3. To keep going with this example, the result is 6%.

.1 x (1-.4) = .06 tax-exempt yield

This means that a muni future need return only 6% to be as favorable, after tax, as the 10%-taxable yielding future. If the muni future yields more than 600%, it is more favorable; if it yields less than 600%, it is less favorable.

Alternately, the exam might ask for the equivalent taxable yield given the yield from the muni contract. Essentially, you do the above calculation backward:

1. Determine the tax-exempt yield for the muni contract transaction. To keep the analysis symmetrical, let's say that's 6% (.06).
2. Determine your client's income tax rate. Again, let's call that 40% (.4).
3. Subtract the tax rate from 1. Again, that's 0.6
4. Divide the tax-exempt yield from step 1 by the result of step 3. Our final result is 10%.

.06/(1-.4)=.10 tax-equivalent yield

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