A derivative has a value that is derived from the value of another asset or interest rate.

Exchange-traded derivatives, notably futures and some options, are traded in centralized locations and are standardized, regulated, and default risk free.

Forwards and swaps are customized contracts (over-the-counter derivatives) created by dealers and by financial institutions. There is very limited trading of these contracts in secondary markets and default (counterparty) risk must be considered.

A forward commitment is a binding promise to buy or sell an asset or make a payment in the future. Forward contracts, futures contracts, and swaps are all forward commitments.

A contingent claim is an asset that has value only if some future event takes place (e.g., asset price is greater than a specified price). Options are contingent claims.

Forward contracts obligate one party to buy, and another to sell, a specific asset at a predetermined price at a specific time in the future.

Swaps contracts are equivalent to a series of forward contracts on interest rates, currencies, or equity returns.

Futures contracts are much like forward contracts, but are exchange-traded, quite liquid, and require daily settlement of any gains or losses.

A call option gives the holder the right, but not the obligation, to buy an asset at a predetermined price at some time in the future.

A put option gives the holder the right, but not the obligation, to sell an asset at a predetermined price at some time in the future.

Derivative markets are criticized for their risky nature. However, many market participants use derivatives to manage and reduce existing risk exposures.

Derivative securities play an important role in promoting efficient market prices and reducing transaction costs.

Riskless arbitrage refers to earning more than the risk-free rate of return with no risk, or earning an immediate gain with no possible future liability.

Arbitrage can be expected to force the prices of two securities or portfolios of securities to be equal if they have the same future cash flows regardless of future events.

A deliverable forward contract on an asset specifies that the long (the buyer) will pay a certain amount at a future date to the short, who will deliver a certain amount of an asset.

Default risk in a forward contract is the risk that the other party to the contract will not perform at settlement, because typically no money changes hands at the initiation of the contract.

A forward contract with cash settlement does not require delivery of the underlying asset, but a cash payment at the settlement date from one counterparty to the other, based on the contract price and the market price of the asset at settlement.

Early termination of a forward contract can be accomplished by entering into a new forward contract with the opposite position, at the then-current expected forward price. This early termination will fix the amount of the gain or loss at the settlement date. If this new forward is with a different counterparty than the original, there is credit or default risk to consider since one of the two counterparties may fail to honor its obligation under the forward contract.

An end user of a forward contract is most often a corporation hedging an existing risk.

Forward dealers, large banks, or brokerages originate forward contracts and take the long side in some contracts and the short side in others, with a spread in pricing to compensate them for actual costs, bearing default risk, and any unhedged price risk they must bear.

An equity forward contract may be on a single stock, a customized portfolio, or an equity index, and is used to hedge the risk of equity prices at some future date.

• Equity forward contracts can be written on a total return basis (including dividends), but are typically based solely on an index value.
• Index forwards settle in cash based on the notional amount and the percentage difference between the index value in the forward contract and the actual index level at settlement.

Forward contracts in which bonds are the underlying asset may be quoted in terms of the discount on zero-coupon bonds (e.g., T-bills) or in terms of the yield to maturity on coupon bonds. Forwards on corporate bonds must contain special provisions to deal with the possibility of default as well as with any call or conversion features. Forward contracts may also be written on portfolios of fixed income securities or on bond indexes.

Eurodollar time deposits are USD-denominated short-term unsecured loans to large money-center banks outside the United States.

The London Interbank Offered Rate (LIBOR) is an international reference rate for Eurodollar deposits and is quoted for 30-day, 60-day, 90-day, 180-day, or 360-day (1-year) terms.

Euribor is the equivalent for short-term Euro-denominated bank deposits (loans to banks).

For both LIBOR and Euribor, rates are expressed as annual rates and actual interest is based on the loan term as a proportion of a 360-day year.

The payment to the long at settlement on an FRA is:

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The numerator is the difference between the rate on a loan for the specified period at the forward contract rate and the rate at settlement, and the denominator is to discount this interest differential back to the settlement date at the market rate at settlement.

Currency forward contracts specify that one party will deliver a certain amount of one currency at the settlement date in exchange for a certain amount of another currency.

Under cash settlement, a single cash payment is made at settlement based on the difference between the exchange rate fixed in the contract and the market exchange rate at the settlement date.

Compared to forward contracts, futures contracts:

• Are more liquid, trade on exchanges, and can be closed out by an offsetting trade.
• Do not have counterparty risk; the clearinghouse acts as counterparty to each side of the contract.
• Have lower transactions costs.
• Require margin deposits and are marked to market daily.
• Are standardized contracts as to asset quantity, quality, settlement dates, and delivery requirements.

Futures margin deposits are not loans, but deposits to ensure performance under the terms of the contract.

Initial margin is the deposit required to initiate a futures position.

Maintenance margin is the minimum margin amount. When margin falls below this amount, it must be brought back up to its initial level by depositing variation margin.

Margin calculations are based on the daily settlement price, the average of the prices for trades during a closing period set by the exchange.

Trades cannot take place at prices that differ from the previous day’s settlement prices by more than the price limit and are said to be limit down (up) when the new equilibrium price is below (above) the minimum (maximum) price for the day.

Marking-to-market is the process of adding gains to or subtracting losses from the margin account daily, based on the change in settlement prices from one day to the next.

The mark-to-market adjustment either adds the day’s gains in contract value to the long’s margin balance and subtracts them from the short’s margin balance, or subtracts the day’s loss in contract value from the long’s margin balance and adds them to the short’s margin balance.

A futures position can be terminated in the following ways:

• An offsetting trade, entering into an opposite position in the same contract.
• Cash payment at expiration (cash-settlement contract).
• Delivery of the asset specified in the contract.
• An exchange for physicals (asset delivery off the exchange).

Eurodollar futures contracts are for a face value of $1,000,000, are quoted as 100 minus annualized 90-day LIBOR in percent, and settle in cash.

Treasury bond contracts are for a face value of $100,000, give the short a choice of bonds to deliver, and use conversion factors to adjust the contract price for the bond that is delivered.

Stock index futures have a multiplier that is multiplied by the index to calculate the contract value, and settle in cash.

Currency futures are for delivery of standardized amounts of foreign currency.

A call option on a financial or physical asset gives the option’s owner the right, but not the obligation, to buy a specified quantity of the asset from the option writer at the exercise price specified in the option for a given time period. The writer of a call option is obligated to sell the asset at the exercise price if the option’s owner chooses to exercise it.

A put option on a financial or physical asset gives the option’s owner the right, but not the obligation, to sell a specified quantity of the asset to the option writer at the exercise price specified in the option for a given time period. The writer of a put option is obligated to purchase the asset at the exercise price if the option’s owner chooses to exercise it.

The owner (buyer) of an option is said to be long the option, and the writer (seller) of an option is said to be short the option.

American options can be exercised at any time up to the option’s expiration date.

European options can be exercised only at the option’s expiration date.

Moneyness for puts and calls is determined by the difference between the strike price (X) and the market price of the underlying stock (S):

Interest rate option payoffs are the difference between the market and strike rates, adjusted for the loan period, multiplied by the principal amount.

At expiration, an interest rate call receives a payment when the reference rate is above the strike rate, and an interest rate put receives a payment when the reference rate is below the strike rate.

An FRA can be replicated with two interest rate options: a long call and a short put.

Interest rate caps put a maximum (upper limit) on the payments on a floating-rate loan and are equivalent (from the borrower’s perspective) to a series of long interest rate calls at the cap rate.

Interest rate floors put a minimum (lower limit) on the payments on a floating-rate loan and are equivalent (from the borrower’s perspective) to a series of short interest rate puts at the floor rate.

An interest rate collar combines a cap and a floor. A borrower can create a collar on a floating-rate loan by buying a cap and selling a floor.

The payoff to the holder of a call or put option on a stock is the option’s intrinsic value. Payment occurs at expiration of the option.

Payoffs on interest rate options are paid after expiration, at the end of the interest rate (loan) period specified in the contract.

The intrinsic value of an option is the payoff from immediate exercise if the option is in the money, and zero otherwise.

The time (speculative) value of an option is the difference between its premium (market price) and its intrinsic value. At expiration, time value is zero.

Minimum and maximum option values:

Minimum and maximum option values:

Calls with lower exercise prices are worth at least as much as otherwise identical calls with higher exercise prices (and typically more).

Puts with higher exercise prices are worth at least as much as otherwise identical puts with lower exercise prices (and typically more).

Otherwise identical options are worth more when there is more time to expiration, with two exceptions:

• Far out-of-the-money options with different expiration dates may be equal in value.
• With European puts, longer time to expiration may decrease an option’s value when they are deep in the money.

A fiduciary call (a call option and a risk-free zero-coupon bond that pays the strike price X at expiration) and a protective put (a share of stock and a put at X) have the same payoffs at expiration, so arbitrage will force these positions to have equal prices: c + X / (1 + RFR)^T = S + p. This establishes put-call parity for European options.

Based on the put-call parity relation, a synthetic security (stock, bond, call, or put) can be created by combining long and short positions in the other three securities.

• c = S + p − X / (1 + RFR)^T
• p = c − S + X / (1 + RFR)^T
• S = c − p + X / (1 + RFR)^T
• X / (1 + RFR)^T = S + p − c

An increase in the risk-free rate will increase call values and decrease put values (for options that do not explicitly depend on interest rates or bond values).

Increased volatility of the underlying asset or interest rate increases both put values and call values.

Swaps are based on a notional amount of principal. Each party is obligated to pay a percentage return on the notional amount at periodic settlement dates over the life (tenor) of the swap. Percentage payments are based on a floating rate, fixed rate, or the return on an equity index or portfolio.

Except in the case of a currency swap, no money changes hands at the inception of the swap and periodic payments are netted (the party that owes the larger amount pays the difference to the other).

Swaps are custom instruments, are largely unregulated, do not trade in secondary markets, and are subject to counterparty (default) risk.

Swaps can be terminated prior to their stated termination dates by:

• Entering into an offsetting swap, sometimes by exercising a swaption (most common).
• Agreeing with the counterparty to terminate (likely involves making or receiving compensation).
• Selling the swap to a third party with the consent of the original counterparty (uncommon).

In a plain vanilla (fixed-for-floating) interest-rate swap, one party agrees to pay a floating rate of interest on the notional amount and the counterparty agrees to pay a fixed rate of interest.

The formula for the net payment by the fixed-rate payer, based on a 360-day year and the number of days in the settlement period is:

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In an equity swap, the returns payer makes payments based on the return on a stock, portfolio, or index, in exchange for fixed- or floating-rate payments. If the stock, portfolio, or index, declines in value over the period, the returns payer receives the interest payment and a payment based on the percentage decline in value.

In a currency swap, the notional principal (in two different currencies) is exchanged at the inception of the swap, periodic interest payments in two different currencies are exchanged on settlement dates, and the same notional amounts are exchanged (repaid) on the termination date of the swap.

Call option value at expiration is Max (0, S − X) and profit (loss) is Max (0, S − X) − option cost.

Put value at expiration is Max (0, X − S) and profit (loss) is Max (0, X − S) − option cost.

A covered call position is a share of stock and a short (written) call. Profits and losses are measured relative to the net cost of this combination (S₀− premium).

• The purpose of selling a covered call is to enhance income by trading the stock’s upside potential for the call premium.
• The upside potential on a covered call is limited to (X − S₀) + call premium received. The maximum loss is the net cost (S₀ – premium).

A protective put consists of buying a share of stock and buying a put. Profits and losses are measured relative to the net cost (S₀+ premium).

• A protective put is a strategy to protect against a decline in the value of the stock.
• Maximum gains on a protective put are unlimited, but reduced by the put premium paid. Maximum losses are limited to (S₀ − X) + put premium paid.

"Traditional investments" refers to long-only positions in stocks, bonds, and cash. "Alternative investments" refers to some types of assets such as real estate, commodities, and various collectables, as well as some specific structures of investment vehicles. Hedge funds and private equity funds (including venture capital funds) are often structured as limited partnerships; real estate investment trusts (REITs) are similar to mutual funds; and ETFs can contain alternative investments as well.

Compared to traditional investments, alternative investments typically have lower liquidity; less regulation and disclosure; higher management fees and more specialized management; potential diversification benefits; more use of leverage, use of derivatives; potentially higher returns; limited and possibly biased historical returns data; problematic historical risk measures; and unique legal and tax considerations.

Hedge funds are investment companies that use a variety of strategies and may be highly leveraged, use long and short positions, and use derivatives.

Private equity funds usually invest in the equity of private companies or companies wanting to become private, financing their assets with high levels of debt. This category also includes venture capital funds, which provide capital to companies early in their development.

Real estate as an asset class includes residential and commercial real estate, individual mortgages, and pools of mortgages or properties. It includes direct investment in single properties or loans as well as indirect investment in limited partnerships, which are private securities, and mortgage-backed securities and real estate investment trusts, which are publicly traded.

Commodities refer to physical assets such as agricultural products, metals, oil and gas, and other raw materials used in production. Commodities market exposure can provide an inflation hedge and diversification benefits.

Various types of collectibles, such as cars, wines, and art, are considered alternative investments as well.

• Event-drivenstrategies include merger arbitrage, distressed/restructuring, activist shareholder and special situations.
• Relative valuestrategies seek profits from unusual pricing issues.
• Macro hedgestrategies are "top down" strategies based on global economic trends.
• Equity hedge strategies are "bottom up" strategies that take long and short positions in equities and equity derivatives. Strategies include market neutral, fundamental growth, fundamental value, quantitative directional, short bias, and sector specific.

In periods of financial crisis, the correlation of returns between global equities and hedge funds tends to increase, which limits hedge funds' effectiveness as a diversifying asset class.

Due diligence factors for hedge funds are investment strategy, investment process, competitive advantages, track record, longevity of fund, and size (assets under management). Other qualitative factors include management style, key person risk, reputation, investor relations, growth plans, and management of systematic risk.

Leveraged buyouts (LBOs) and venture capital are the two dominant strategies. Other strategies include developmental capital and distressed securities.

Types of LBOs include management buyouts, in which the existing management team is involved in the purchase, and management buy-ins, in which an external management team replaces the existing management.

Stages of venture capital investing include the formative stage (composed of the angel investing, seed, and early stages); the later stage (expansion); and the mezzanine stage (prepare for IPO).

Methods for exiting investments in portfolio companies include trade sale (sell to a competitor or another strategic buyer); IPO (sell some or all shares to investors); recapitalization (issue portfolio company debt); secondary sale (sell to another private equity firm or other investors); or write-off/liquidation.

Private equity has some historical record of potential diversification benefits.

An investor must identify top performing private equity managers to benefit from private equity.

Due diligence factors for private equity include the manager’s experience, valuation methods used, fee structure, and drawdown procedures for committed capital.

Reasons to invest in real estate include potential long-term total returns, income from rent payments, diversification benefits, and hedging against inflation.

Forms of real estate investing:

Real estate investment categories include residential properties, commercial real estate, REITs, mortgage-backed securities, and timberland and farmland.

Historically, real estate returns are highly correlated with global equity returns but less correlated with global bond returns. The construction method of real estate indexes may contribute to the low correlation with bond returns.

Due diligence factors for real estate include global and national economic factors, local market conditions, interest rates, and property-specific risks including regulations and abilities of managers. Distressed properties investing and real estate development have additional risk factors to consider.

The most common way to invest in commodities is with derivatives. Other methods include exchange-traded funds, equities that are directly linked to a commodity, managed futures funds, individual managed accounts, and specialized funds in specific commodity sectors.

Beyond the potential for higher returns and lower volatility benefits to a portfolio, commodity as an asset class may offer inflation protection. Commodities can offset inflation, especially if commodity prices are used to determine inflation indices.

Spot prices for commodities are a function of supply and demand. Global economics, production costs, and storage costs, along with value to user, all factor into prices.

Hedge funds often invest in securities that are not actively traded and must estimate their values, and invest in securities that are illiquid relative to the size of a hedge fund’s position. Hedge funds may calculate a trading NAV that adjusts for the illiquidity of these securities.

A private equity portfolio company may be valued using a market/comparables approach (multiple-based) approach, a discounted cash flow approach, or an asset-based approach.

Real estate property valuation approaches include the comparable sales approach, the income approach (multiples or discounted cash flows), and the cost approach. REITs can be valued using an income-based approach or an asset-based approach.

A commodity futures price is approximately equal to the spot price compounded at the risk-free rate, plus storage costs, minus the convenience yield.

Risk management of alternative investments requires understanding of the unique circumstances for each category.

• Standard deviation of returns may be misleading as a measure of risk.
• Use of derivatives introduces operational, financial, counterparty, and liquidity risks.
• Performance for some alternative investment categories depends primarily on management expertise.
• Hedge funds and private equity funds are less transparent than traditional investments.
• Many alternative investments are illiquid.
• Indices of historical returns and standard deviations may not be good indicators of future returns and volatility.
• Correlations vary across periods and are affected by events.

Key items for due diligence include organization, portfolio management, operations and controls, risk management, legal review, and fund terms.

A commodity futures market is in contango if futures prices are greater than the spot price. The market is in backwardation if futures prices are less than the spot price.

Futures markets that are dominated by long hedgers (users of the commodity who buy futures to protect against price increases) tend to be in contango. Futures markets that are dominated by short hedgers (producers of the commodity who short futures to protect against price decreases) tend to be in backwardation.

The return on a commodity investment includes:

• Collateral yield: the return on the collateral posted to satisfy margin requirements.
• Price return: the gain or loss due to changes in the spot price.
• Roll yield: the gain or loss resulting from re-establishing positions as contracts expire.

Roll yield is positive if the futures market is in backwardation and negative if the market is in contango.

Commodities can provide diversification benefits to a portfolio of securities because commodity returns tend not to be highly positively correlated with securities returns.