CFA L1 Derivatives Flashcards
What is arbitrage?
- Opportunity for riskless profit
- Derivatives are priced so that there is no possibilty for arbitrage on it
2025 L1 DE LM4 - Arbitrage, Replication, and the Cost of Carry
What is discrete compoundign versus continuous compounding?
- Discrete compounding defines a set number of periods
- Continuous compounding is continous, so no number of periods.
- CC formula is e^(rT)
2025 L1 DE LM4 - Arbitrage, Replication, and the Cost of Carry
What is continuous compounding used for?
- Forex portfolios, and indices for equity, fixed income, and commodities
2025 L1 DE LM4 - Arbitrage, Replication, and the Cost of Carry
What rate is used to calculate derivative price?
- Strictly speaking interbank offered rates are used (SOFR). This is continuously compounded already
- However in the curriculum risk free rate is used
- Therefore in the curriculum risk free rate needs to be continously compounded to arrive at derivative pricing rate (MRR)
2025 L1 DE LM4 - Arbitrage, Replication, and the Cost of Carry
What return would a trader earn if they perfectly matched off a long position with a short position?
- The risk-free rate
- If you hedge perfectly you remove all risk
- Therefore rate earned would be risk free rate
2025 L1 DE LM4 - Arbitrage, Replication, and the Cost of Carry
What is the cost of carry?
- The net of costs and benefits of holding the underlying asset for a specified period of time
- If the benefits (ie convenience, dividend) outweigh costs, cost of carry is negative
- Therefore futures price will be LESS than the spot price
- If the benefits are less than the costs (ie high storage, transportation, insurance costs, like gold) the futures price will be MORE than the futures price, and cost of carry is positive
2025 L1 DE LM4 - Arbitrage, Replication, and the Cost of Carry
How you do you find the continuously compounded rate?
- Add 1 to the rate
- use ln()
- So: ln(1 + rate) = continuously compounded rate
2025 L1 DE LM4 - Arbitrage, Replication, and the Cost of Carry
What is the difference between long and short?
- Long means you take delivery of the underlying asset
- Short means you deliver the underlying asset
- So traditionally, to be short you would have to own the underlying asset, and be creating a contract to give it away
2025 L1 DE LM4 - Arbitrage, Replication, and the Cost of Carry
What does it mean to say the base trades at a discount or premium?
- base trades at a discount = forward price is less than spot price
- base trades at a premium = forward price is higher than the spot price
2025 L1 DE LM4 - Arbitrage, Replication, and the Cost of Carry
How do you calculate currency price?
- Spot price of two currencies
- Interest rates on the two currencies
- Spot price x (yield1/yield2) = forward price
2025 L1 DE LM4 - Arbitrage, Replication, and the Cost of Carry
How do interest rate differences between currencies affect FX forward rate value?
- Higher interest rate in currency A means FX forward will show devaluation
- Lower interest rate in currency B means FX forward will show appreciation
- This is because less of currency A will be needed to buy a given amount of currency B in future
Forward Rate = Spot Rate x (1 + Foreign Interest Rate) / (1 + Domestic Interest Rate)
What do contango and backwardation imply?
- Contango = well functioning market.
- Convenience yield is low since supply is unconstrained. Market is well supplied
- Storage costs are greater than convenience yield
- Therefore, spot prices are below forward prices
- Backwardation implies poorly functioning market
- Convenience yield is high since supply is constrained
- Market is is poorly supplied, therefore spot price high and storage costs comparatively lower than convenience yield
- Futures trade at a discount
2025 L1 DE LM4 - Arbitrage, Replication, and the Cost of Carry
What is the value of a derivative after issue before maturity?
- For short derivatives Value at maturity T = spot price - payoff amount
- For long derivatives, reverse: Value at maturity T = payoff amount - spot price
- At time t after issue, Value = spot price - [payoff amount / (1+r)^(T-t)
So divide payoff amount by rate compounded by time left before expiration
2025 L1 DE LM5 Pricing and Valuation of Forward Contracts with Varying Maturities
How do you calculate value of a derivative involving income?
- Discount all income back to start point
2025 L1 DE LM5 Pricing and Valuation of Forward Contracts with Varying Maturities
What is the value of a future or forward contract at issue?
Zero
2025 L1 DE LM6 Pricing and Valuation of Futures Contracts
What is the difference between value of forward and futures contracts?
- Futures value is 0 at the end of each day
- Because difference between price and value is settled every day
- Forward contrast is not settled every day, it is settled at maturity
- So forward value changes over life of contract, is only 0 at issue
2025 L1 DE LM6
What conditions would create indifference between forward and futures contracts for investors?
- Interest rate is constant, not changing over life of contracts, as interest rate effects cancel out
- If futures prices and interest rates are uncorrelated
2025 L1 DE LM6 Pricing and Valuation of Futures Contracts
How would we use futures or FRA to hedge interest rates?
- Short futures or long FRA to hedge against increasing interest rates
- Long futures or short CFA to hedge against decreasing rates
- If interest rates go up, borrowing costs go up, and futures prices will go down. A short future will earn gains under increasing rates
- If interest rates go up, borrowing costs increase, but gains on an FRA offset higher costs, as you pay a fixed rate and pay a floating rate
2025 L1 DE LM6 Pricing and Valuation of Futures Contracts
What is a swap?
- Agreement to exchenge a series of cash flows whereas a forward contract involves a single exchange
- In an interest rate swap, there are multiple payments that occur at the end of each interest rate period
2025 L1 DE LM7 - Pricing and Valuation of Interest Rates and Other Swaps
How does time to expiration affect value of an option?
- Longer time to expiration increases option value
- For any option and for any given strike price
- Because the option has more time to perform, as the underlying has greater volatility
2025 L1 DE LM8 - Pricing and Valuation of Options
How does an underlying that pays dividends or income put pressure on call options?
- Each time income is paid out the call value decreases, since the option doesn’t earn income whereas owning the underlying does
- Put value increases however
2025 L1 DE LM8 - Pricing and Valuation of Options
What is a synthetic forward?
- Creating a forward position using options
- Remember, a forward is an agreement to buy/sell the underlying at time T
- Using options can replicate that without you having to buy or sell the underlying
2025 L1 DE LM9 - Option Replication using Put-Call Parity
How are synthetic forwards constructed?
- Long call short put is a synthetic long forward position
- ## Short call long put is a synthetic short forward position
2025 L1 DE LM9 - Option Replication using Put-Call Parity
What is the gain-to pain ratio?
- Either Calmar ratio or MAR
- Used instead of Sharpe ratio since Sharpe ratio requires noramlly distributed returns
- Alternatives tend to have asymmetric and skewed returns profiles so SR doesn’t work well
- Still, SR of 1-2 is targeted, higher indicating significant volatility smoothing
- Treynor ratio also has performance appraisal issues: measures excess average return relative to beta to a relative benchmark
- However Beta is historical and may be different in future
2025 L1 AI LM1 - Alternative Investment Performance and Returns
How to calculate Calmar ratio?
Avg annual compounded return over 3y / maximum drawdown
2025 L1 AI LM1 - Alternative Investment Performance and Returns
Why is IRR used for alternatives returns?
- Timing is very important for evaluating returns, not just magnitude of returns
2025 L1 AI LM1 - Alternative Investment Performance and Returns
Why are quartile ranking used to rank alternative investment funds?
- It’s not fair to compare investment portfolios started in different years
- So compare portfolios started in same year
- Quartile ranking gives relative performance based on market conditions from that year onwards over the duration of the fund
2025 L1 AI LM1 - Alternative Investment Performance and Returns
What is money-weighted rate of return?
- Calculated similarly to IRR
- Depends on how much money you put in at each time period
- Accurately reflects what a specific investor earned, but lacks comparability
- By investing less per period when market is up, and more per period when market is down, you can achieve higher returns
2025 L1 PM LM1 - Portfolio Risk and Return: Part I
What is time weighted rate of return?
Returns based on the timing of cash flows invested
2025 L1 PM LM1 - Portfolio Risk and Return: Part I
