Glossary: terms starting with O

Option Based Portfolio Insurance: equities plus a put, or a safe asset plus a call, which can also be replicated with continuously adjusted positions in equities and cash. The protection applies at a fixed end date and costs an option premium.

Source: Bertrand and Prigent (2002); Rubinstein and Leland (1981)

More: CPPI: portfolio insurance with cushion, floor and multiplier

The percentage change in a warrant's price per 1% change in the price of the underlying: delta times simple leverage. Unlike simple leverage, it takes into account that an out-of-the-money warrant moves less than the underlying.

Example: Delta 0.3836, spot $100, ratio 0.1, price $0.53: omega = 0.3836 × 100 × 0.1 / 0.53 = 7.24.

Methodology: Option pricer: how Portfolio Lab values options

The ratio of gains above a threshold to losses below it, weighted by their probabilities. It uses the entire distribution rather than just the mean and variance; above 1 means more gain mass than loss mass.

Source: Bacon (2008)

More: Risk metrics beyond the Sharpe ratio: Treynor, Calmar, Omega, Ulcer Index and more

The forgone return of the best alternative. Equity tied up in a home costs no interest, but it does cost the return it would have earned in a brokerage account.

Example: $120,000 of equity at an expected return of 5% in a brokerage account: $6,000 of opportunity cost a year.

More: Your whole wealth: total wealth from portfolio, home, human capital and car

Roll strategy for commodity futures that does not mechanically switch into the next contract to expire, but instead, for example, picks the contract with the least contango or the strongest backwardation, or shifts the timing of the switch. The basis of many “enhanced” commodity indices.

Source: Mouakhar and Roberge (2009)

More: Active or passive in bonds and commodities: why the rules differ from equities

A physically replicating ETF holds only some of the index constituents, selected so that countries, sectors and metrics match the index. Common for indices with thousands of securities.

More: ETF basics: costs, replication and distributions

The right, but not the obligation, to buy (call) or sell (put) an underlying at a fixed price. The buyer pays a premium for this; the seller (writer) bears the risk.

Source: Black and Scholes (1973)

More: Option pricing: where fair option prices come from · Methodology: Option pricer: how Portfolio Lab values options

Spread of a bond with embedded options, such as an issuer call right, after removing the value of the options; calculated with an interest rate model. Without options, it equals the Z-spread; for callable bonds, it is lower.

More: Bond math: calculating price, yield, duration, convexity and spreads

A service that feeds data from outside the blockchain (prices, interest rates, events) into a smart contract. It is a weak point: if the reported value is wrong or manipulated, the contract calculates with wrong numbers, e.g. for margin calls or liquidations.

More: Digital assets: tokenization, stablecoins, crypto securities and the digital euro

Discount when a loan or bond is paid out: the borrower receives less than face value but repays the full face value. The discount raises the lender's return, spread over the term, and all the more the earlier the loan is repaid.

Example: Paid out at 98, repaid at 100 after four years: roughly 2 / 4 = 0.5 percentage points of extra return a year.

More: Private debt in practice: direct lending, unitranche, mezzanine, loan structure and fund vehicles

A random process that is pulled back toward equilibrium with a force proportional to its distance from it. The standard model for spreads and residuals in statistical arbitrage; in daily data it corresponds to an AR(1) regression, from which the speed of reversion and the half-life follow.

Source: Uhlenbeck and Ornstein (1930); Avellaneda and Lee (2010)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

A measure of forecast quality outside the sample: 1 minus the model's squared error divided by the squared error of the historical mean. A positive value means the model beats the mean; for monthly equity returns, even small positive values are rare.

Example: Mean squared error of 19.90 instead of 20.00 for the historical mean: 1 − 19.90 / 20.00 = 0.5%.

Source: Campbell and Thompson (2008); Welch and Goyal (2008)

More: Return forecasting models: ARIMA, GARCH, LSTM and machine learning

Committing more than the target allocation implies, because the full commitment is never invested at the same time: early funds are already distributing, while late ones have not yet called everything. The overcommitment ratio sets NAV plus unfunded commitments against the target amount; the unfunded commitments must be payable at any time.

Example: Target 15%, unfunded commitments 8.99% of assets: (15 + 8.99) / 15 = 1.60.

More: Takahashi-Alexander model: forecasting the cash flows of private markets funds

Investors believe their knowledge and accuracy are greater than they really are. The result is frequent trading: in a large study, the households with the highest turnover earned considerably lower returns than the market.

Source: Barber and Odean (2000)

A model adapts to the noise of the past rather than to the real relationships. Telltale signs: many parameters, a dazzling backtest, disappointing results afterward.

Source: Bailey et al. (2016); López de Prado (2018)

More: Backtest overfitting: when the past looks too good

Share of two funds that is invested in the same securities: the sum of the smaller of the two weights across all common holdings. What does not overlap is what the second fund genuinely adds to the portfolio.

Example: Fund A holds X at 40% and Y at 30%, fund B holds X at 50% and Y at 20%: overlap 40% + 20% = 60%.

More: Thematic ETFs and hype: what studies, costs and overlaps reveal

Rolling multi-year returns in monthly steps share almost all their months with their neighbors. The number of truly independent observations is much smaller than the number of data points suggests.

Source: Boudoukh et al. (2008)

More: Shiller P/E (CAPE): how expensive is the stock market?

Derivatives, usually futures, swaps or currency forwards, placed on top of an existing portfolio to change exposure or currency risk without buying or selling the securities themselves.

More: Multi-asset attribution: weighting schemes, top-down and bottom-up, currencies and overlays

An apartment or house in which the owner lives. It is investment and consumption at the same time, usually leveraged with a loan, hard to sell, and a concentrated risk in one location.

Source: Flavin and Yamashita (2002); EStG § 23 (2009)

More: Your whole wealth: total wealth from portfolio, home, human capital and car