Finance-Theory · Unit 11 · Video 7 · Interactive Practice

Futures Leverage, Margin Risk and What Prices Reveal

IKey Formulas

Formula	Name	What it says
$L = \dfrac{\text{notional}}{\text{margin}}$	Leverage	Exposure controlled per dollar deposited; 5% margin means 20 times leverage
$r_{\text{margin}} = \dfrac{\Delta F}{F} \times \dfrac{\text{notional}}{\text{margin}} = L \cdot \dfrac{\Delta F}{F}$	Return on margin	Every 1% move in the futures price is an $L\%$ move in the account, gains and losses alike
$\dfrac{\Delta F}{F} = -\dfrac{\text{margin}}{\text{notional}} \;\Rightarrow\; r_{\text{margin}} = -100\%$	Wipe-out move	With 7% margin, a 7% fall in the futures price erases the whole margin account
$\text{implied chance} \approx \dfrac{\text{price}}{\text{payoff}}$	Event-contract price	A contract paying $1 on a win that trades at 60 cents puts the chance near 60%

Key Insight: Daily marking to market lets margin cover only about one day's price move, so a few percent of notional controls the whole position, and a move of that same few percent can take the entire deposit.

IIA Small Price Move, a Large Return on Margin

With margin a fraction $m$ of notional, every futures price move reaches the account multiplied by $1/m$ .

Margin (% of notional) 5% One-day futures price move −2.5%

💡 Margin can be this small because futures are marked to market daily, so it has to cover only about one day's price move; an ETF on the same index needs the full exposure in cash, with no leverage.

IIISwings Within a Single Session

A leveraged account feels every swing inside the trading day, not just the move from open to close.

Margin Time 9:30

IVWhat an Event-Contract Price Says

A contract paying $1 if a candidate wins trades at a price that reads, roughly, as the traders' chance of a win.

Price (cents) 60¢

💡 A price is only as informative as the traders behind it: poorly informed traders give poorly informed prices, sharp and sophisticated traders give highly informative ones. Prices are the best guide we have but not perfect, and in some periods, such as autumn 2008, they are less reliable than in others.

VQuiz Questions

Problem 1 · Return on the Margin Posted

Given: A trader posts $120,000 of margin on a long futures position with $1,500,000 of notional exposure. The futures price falls 2% in one day. Find the return on the margin.

✅ Correct! The loss is 2% of the whole $1,500,000, that is $30,000, and it comes out of the $120,000 you put down: a quarter of your investment gone in one day.

❌ Not quite. −2% is the return on the notional. You only paid $120,000, so the $30,000 loss is measured against that.

❌ Not quite. Multiplying the margin rate by the move (

8 \times 2 = 16

) is not leverage. Leverage is notional divided by margin, so the move gets divided by the 8% margin rate.

❌ Close, but that is what is left. $90,000 of the $120,000 remains, which is 75% of the deposit. The return is the change,

-30{,}000/120{,}000

❌ Not quite. Compute the dollar loss on the notional, then divide by the margin.

Show solution

The price move applies to the whole notional exposure:

\text{loss} = 0.02 \times 1{,}500{,}000 = 30{,}000.

Measured against the margin, which is the investment:

r_{\text{margin}} = \frac{-30{,}000}{120{,}000} = -0.25 = -25\%.

Equivalently, the leverage is $L = 1{,}500{,}000 / 120{,}000 = 12.5$ and $12.5 \times (-2\%) = -25\%$ . The return on margin is −25%.

Problem 2 · How Far Is Wipe-Out?

Given: A broker requires margin of 4% of notional on a long futures position. Find the one-day move in the futures price that wipes out the entire margin account.

✅ Correct! A 4% fall costs 4% of notional, which is exactly the 4% of notional you deposited.

❌ Not quite. 25 is the leverage,

1/0.04

, not a price move. A 25% fall would cost more than six times the margin.

❌ Not quite. The margin is not the part of the price you are allowed to lose; it is the whole deposit. The loss is taken on the full notional.

❌ Not quite. That is the limit for someone who paid the full price, like an ETF holder. With 4% down, the account is gone long before the price reaches zero.

❌ Not quite. Set the loss on the notional equal to the margin.

Show solution

With margin $= 0.04 \times \text{notional}$ , a price fall of $x$ loses $x \times \text{notional}$ . The account is empty when

x \times \text{notional} = 0.04 \times \text{notional} \iff x = 4\%.

Through leverage: $L = 1/0.04 = 25$ , and $25 \times (-4\%) = -100\%$ . A fall of just 4% takes the whole deposit.

Problem 3 · Setting Margin for a Risk Limit

Given: A fund plans a long futures position with $4,000,000 of notional exposure. Its risk rule: a 3% one-day fall in the futures price must cost no more than 30% of the margin posted.

What does a 3% one-day fall cost?

What is the smallest margin that satisfies the rule?

✅ Correct! The $120,000 loss must be at most 30% of the margin, so the margin must be at least $400,000: 10% of notional, a leverage of at most 10.

❌ Not quite. $36,000 is 30% of the loss. First find the loss itself: 3% of the notional.

❌ Not quite. That is 30% of the notional. The price fall is 3%.

❌ Check the loss. The price move applies to the full $4,000,000 of notional.

❌ Not quite. With $120,000 of margin, the 3% fall would take 100% of it, not 30%.

❌ Check the direction. The loss must be at most 30% of the margin, so the margin is the loss divided by 0.30, not multiplied.

❌ Not quite. 30% of notional is far more margin than the rule needs; the rule is about the loss relative to the margin.

❌ Check the margin. Solve

\text{loss} \le 0.30 \times \text{margin}

for the margin.

Show solution

Loss from a 3% fall:

0.03 \times 4{,}000{,}000 = 120{,}000.

Smallest margin $M$ : the rule requires

120{,}000 \le 0.30\,M \iff M \ge \frac{120{,}000}{0.30} = 400{,}000.

So the margin must be at least $400,000, which is 10% of notional. Check: the leverage is $4{,}000{,}000 / 400{,}000 = 10$ , and $10 \times (-3\%) = -30\%$ , exactly the limit. Any less margin means more leverage and a bigger hit from the same fall.

Problem 4 · Reading an Election Contract

Given: A contract pays $1 if a candidate wins the election and nothing otherwise. It trades at 35 cents.

Roughly what chance of a win does the price imply?

When does that 35-cent price say the most about the candidate's real chances?

✅ Correct! The price reads as a chance near 35%, but that reading is only as good as the traders who produce it: sharp, sophisticated traders make it highly informative.

❌ Not quite. 65% is the implied chance that the candidate loses, the event the contract does not pay on.

❌ Not quite.

35/65 \approx 0.54

is a ratio of price to profit, not a chance. The price is compared with the $1 payoff.

❌ Check the scale. Divide the price by the payoff: 35 cents out of 100 cents.

❌ Not quite. Poorly informed traders produce poorly informed prices; the price is only as good as the market behind it.

❌ Not quite. Prices are the best guide to the future we have, but they are not perfect, and in some periods they are less reliable than in others.

❌ Not quite. Autumn 2008 is the video's example of prices being less reliable: markets swung wildly because people were reacting emotionally.

❌ Check the second part. Ask who produces the price.

Show solution

Implied chance: the contract pays 100 cents on a win, so a price of 35 cents reads roughly as

\frac{35}{100} = 35\%.

What the price is worth: the reading is only as good as the market that produces it. Poorly informed traders give poorly informed prices; sharp, sophisticated traders give highly informative ones. Prices are the best guide we have but not perfect, and in periods such as autumn 2008, when markets swung wildly on emotion, they are less reliable. The answer is ≈ 35%, most informative when the traders are sharp and sophisticated.

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