Trading Cases: F2 & H1

The quick and dirty on H1

Symbol?

What's notable about the asset?


 

RTX

  • index future for 100 largest companies
  • index value at start is 1050
  • contract multiplier is 250
  • no dividends, \(r_0=0\)

What is your task?
 

  1. hedge portfolio of 10 stocks worth $100M
  2. buy or sell RTX to hedge stock risk

Forward (OTC)

  • Bilateral contract to buy/sell at price K on date T
  • Fully customized (size, date, settlement)
  • No daily settlement; full counterparty risk

Futures (Exchange-Traded)

  • Standardized contracts cleared through an exchange
  • Daily mark-to-market: profits/losses settled each day
    → losing side pays, winning side receives variation margin
  • Key standardized terms:
    • Contract size (e.g., 1,000 barrels WTI; 50× S&P index)
    • Tick size and tick value
    • Delivery months (Mar/Jun/Sep/Dec)
    • Settlement type (cash vs physical)
  • Exchanges:
    • US: CME Group, ICE Futures U.S., Cboe Futures Exchange
    • Canada: Montréal Exchange (MX)
  • Risks: liquidity gaps, margin calls, basis risk, and clearing-member operational risk

Forwards \(\to\) Futures: Definitions

Spot Move Leverage Change in Futures P&L on Margin Comment
+5 % 1× +5 % Same as spot
+5 % 5× +25 % Gains magnified
+5 % 10× +50 % Gains amplified further
–5 % 10× –50 % Same magnification on losses
–10 % 10× –100 % Position wiped out (liquidation)
  • Futures returns scale roughly linearly with leverage until margin exhaustion.
  • Both long and short must post initial margin.

Why trade with futures? Profit and Leverage Basics

for this case...

  • relevant here: you can hedge easily:
    • you can be short in the future (you "write" the future or sell it to someone betting on a rise in the index)
    • if the index rises, you lose
    • if the index falls, you gain
    • hedge = offset loss in one dimension with gain in another
    • here: implies that you are willing to give up upside

Background on futures

  • index future notional value = index future price \(\times\) contract size
     
  • How many do you have to buy or sell to match exposure?
     
  • Naive approach:
    • you want \[\text{dollar value of portfolio} = \text{notional dollar value of hedge}\]
    • then compute \[\#\text{contract}\times\text{notional}=\text{\$ portfolio}\]

\[\#\text{contracts}=\frac{\text{\$ portfolio}}{\text{notional}}=\frac{\$100M}{1050\times 250=\$262,500}\approx 381\]

But this approach is naive!

  • your holdings are not the index
  • \(\to\) your holdings' risk may be different from index!
  • Scenario:
    • if risk portfolio > index risk \(\to\) short more futures
    • if risk portfolio < index risk \(\to\) short fewer futures
    • if risk portfolio \(\nearrow\) (\(\searrow\)) \(\Rightarrow\) index \(\searrow\) (\(\nearrow\)) then hedge need to be inverse (must be long index)
  • So how do you measure risk ... ?
  • Beta of the portfolio!!!

Use the provided data!

  • So how do you measure risk ... ?
  • Beta of the portfolio!!!
    • Use the data to calculate the betas of the stocks
      \[\beta=\frac{cov(\text{stock},\text{index})}{Var(\text{stock})}\]
    • calculate the weight of stocks in portfolio
      \[w_i=\frac{\$\text{value of stock }i}{\$\text{value of portfolio}}.\]
    • calculate portfolio beta
      \[\beta_p=\sum_{i=1}^{10}w_i\cdot \beta_i\approx 1.18\]

\[\#\text{contracts}=\frac{\beta_p\times\text{\$ portfolio}}{\text{notional}}=\frac{1.18\times\$100M}{\$262,500}\approx 449\]

The quick and dirty on F1

Symbols?

What's notable about the assets?




 

CL-1F and CL

  • 1mo futures contract on crude oil CL-1F
  • CL-1F is for 1000 barrels each
  • spot crude CL price per barrel
  • storage container for 10,000 barrels costs $1,000 per day
  • interest rate is 0.

What is your task?
 

take advantage of any arbitrage opportunity that you might see

What is "basis", what is contango?

  • Basis (traditional usage): the difference between the futures price and the spot (index) price. \[\text{Basis} = F - S\]

    • Positive basis (futures > spot) → market in contango.

    • Negative basis (futures < spot) → market in backwardation.

  • In dated futures, the basis reflects carry costs over time until expiry.

Historical origin of "Contango"

  • In the London Stock Exchange of the 1800s, many trades were financed on margin.

  • Traders who wanted to roll their long positions forward to the next settlement day had to pay a continuation fee to their brokers.

  • The slang pronunciation of “continuation” became contango, and the fee itself was called the contango charge.

  • When futures markets later formalized, the term stuck — describing a situation where the futures price exceeds the spot price, i.e. when carrying (storage + financing) costs make deferred delivery more expensive.

Why backwardation?

  • Traders who wanted to postpone delivery pay a contango fee, while those who wanted early delivery sometimes received a backwardation allowance.

  • Backwardation → “inventory value dominates” → futures below spot.

  • happens when convenience yield  is high

    • = value of holding the physical good

What is cost of carry, what is convenience yield?

  • Commodity futures are associated with, duh, commodities, the storage of which is costly.
    • That storage cost is the "cost of carry[ing an inventory]"
  • What is convenience yield?
    • The value of holding the physical good
    • for stock indices you earn dividends from stocks but not from the index so then convenience yield = dividend yield
  • They are both expressed as percentages
  • Together they give you a formula for the price of the future relative to spot

    \[F_t=S_t\cdot e^{(r+c-y)(T-t)}.\]

for this case...

  • relevant here: 
    • no interest => ignore \(r\)
    • no convenience yield mentioned => just contango applies
    • So we can simplify

      \[F_t=S_t+\text{daily cost}\times (T-t).\]
       
    • Contango means price should follow a step function.

$100

crude spot

futures

expiration

MGT435: Futures F2 and H1

By Andreas Park

MGT435: Futures F2 and H1

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