CFA Level 3 Application of Derivatives: Forwards, Futures, Options, and Swaps

Below, you’ll find my personal CFA level 3 application of derivatives notes…

You can find a list of the other categories here: CFA Level 3 Notes, Formulas, and Weights.

Forwards and Futures are similar but… Forward Contracts are customized agreements between two parties. Futures Contracts are standardized, trade on exchanges, and limit credit risk with clearinghouses. Both types of contracts have a starting value of zero and a linear payoff.

Short-term futures tend to have higher liquidity than long-term futures.

Forward Rate Agreement Formula


Number of Future Contracts Duration Formula

Ex-Post Duration is calculated by finding aggregate return % (include derivative gains and losses) divided by yield change.

Stock Beta Formula
Number of Stock Future Contracts Formula

S = Market Value of Stock Portfolio

Long Stock = Long Risk-Free Bond + Long Futures

Synthetic Index Fund Formulas

T = Time to Futures Expiration
V = Amount of Money to be Invested
f = Futures Price
d = Dividend Index Yield
r = Risk-Free Rate
q = Multiplier
Nf= Number of Futures
ST = Futures Price at Expiration

Payoff = Nf × q(ST – f)

Synthetic Equity and Cash Formulas

Nf*q / (1 + d)T= Number of Stocks Units Equivalent to Buying V*in Bonds and Nf*in Futures

Important to note that futures strategies will only be effective if the futures are priced correctly.

The synthetic fund approach is useful for Equitizing Cash. The bonds and futures are liquid and can be closed out (assuming again that the futures are priced correctly).

If a firm wants to Create Cash out of Equity it can use the same formulas to determine the number of futures to short (-Nf*).

Bull Spreads involve buying a call option and selling a call option at a higher price. Invert buying and selling for a bear spread with calls.

Bear Spreads involve buying a put option and selling a put option at a lower price. Invert buying and selling for a bear spread with puts.

Butterfly Spreads combine a bull and a bear spread. With low to high strike prices of X1, X2, and X3… buy a call at X1, sell two calls at X2, buy a call at X3. This pays off when realized volatility is lower than expected. Butterfly Spreads with puts also buy outside strikes (X1, X3) and sell inside strikes (X2) twice.

Option Collars (aka range forwards and risk reversals) combine Protective Put and Covered Call options. If the premiums net to zero, it’s a Zero-Cost Collar.

Black-Scholes-Merton Formula

Straddles involve buying both a call and put at the same strike price. Straddles profit when realized volatility is higher than expected. The strategy is useful when direction is unknown. Directional bets can be placed by adding an additional call (strap) or put (strip).

Strangles are similar to Straddles but have different strike prices. The initial outlay is lower but needs even more volatility to profit.

Box Spreads combine a bull and bear spread but with only two strike prices. Buy a call at X1 and sell a call at X2… buy a put at X2 and sell a put at X1. If the options are correctly priced with Black-Scholes, then the payoff is the difference of the strike prices divided by the risk-free rate over the timeframe. Box spreads are arbitrage opportunities when option mispricing occurs.

Delta tends to be above 0.5 if the option is in-the-money and below 0.5 if out-of-the-money. Approaching expiration, the delta moves closer to 1 (in-the-money) or 0 (out-of-the-money).

Currency Exchange Risks

Economic Exposure refers to risks from exchange rate impact on price competitiveness relative to other countries.

Translation Exposure refers to risks from exchange rate changes being reflected on accounting statements.

Transaction Exposure refers to exchange rate risk from needing to convert currency to another in the future when the exchange rate is uncertain.

[Review Interest Rate Option Strategies… and Swap Strategies]

Please comment below if you have any suggestions or questions. Also, the next category in my CFA level 3 study list is Trading and Rebalancing.

Invest mindfully,

Brian Kehm

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