Beta coefficient (β)

Beta shows how strongly one asset's price responds to systemic volatility of the entire market. Beta measures an asset's non-diversifiable systematic risk — its market exposure — not its idiosyncratic, asset-specific risk. Upside Beta (Beta+) and Downside Beta (Beta-), popularized by Harry M. Markowitz, are also included. Beta+ and Beta- capture asymmetric sensitivity during rising and falling markets. [Discuss] 💬

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// C# usage syntax
IReadOnlyList<BetaResult> results = barsEval
  .ToBeta(barsMarket, lookbackPeriods, type);

Parameters

param	description
sourceEval IReadOnlyList<IReusable>	Historical price bars used as the evaluation subject. You must have the same number of periods as sourceMrkt.
sourceMrkt IReadOnlyList<IReusable>	Historical price bars used as the benchmark basis for comparison. This is usually market index data. You must have the same number of periods as sourceEval.
lookbackPeriods int	Number of periods (N) in the lookback window. Must be greater than 0 to calculate; however we suggest a larger period for statistically appropriate sample size and especially when using Beta +/-.
type BetaType	Type of Beta to calculate. Default is BetaType.Standard. See BetaType options below.

Historical price bars requirements

You must have at least N periods of sourceEval and sourceMrkt to cover the warmup periods. More than the minimum is typically provided, since a larger sample improves statistical quality — especially when using Beta +/-.

sourceEval and sourceMrkt must have consistent frequency (day, hour, minute, etc). Mismatch histories will throw InvalidBarsException. See the Guide for more information.

BetaType options

type	description
BetaType.Standard	Standard Beta only. Uses all historical price bars. (default)
BetaType.Up	Upside Beta only. Uses market up bars only.
BetaType.Down	Downside Beta only. Uses market down bars only.
BetaType.All	Returns all of the above. Required for Ratio and Convexity values. Note: 3× slower.

✨ Pro tip

Financial institutions often depict a single number for Beta on their sites. To get that same long-term Beta value, use 5 years of monthly bars for bars and a value of 60 for lookbackPeriods. If you only have smaller bars, use the Aggregate() utility to convert it.

Alpha is calculated as R – Rf – Beta (Rm - Rf), where Rf is the risk-free rate.

Response

IReadOnlyList<BetaResult>

• This method returns a time series of all available indicator values for the bars provided.
• It always returns the same number of elements as there are in the historical price bars.
• It does not return a single incremental indicator value.
• The first N-1 periods will have null values since there's not enough data to calculate.

BetaResult

property	description
Timestamp DateTime	Date from evaluated TBar
Beta double?	Beta coefficient based
BetaUp double?	Beta+ (Up Beta)
BetaDown double?	Beta- (Down Beta)
Ratio double?	Beta ratio is BetaUp/BetaDown
Convexity double?	Beta convexity is (BetaUp-BetaDown)2
ReturnsEval double?	Returns of evaluated bars (R)
ReturnsMrkt double?	Returns of market bars (Rm)

Utilities

• .Condense()
• .Find(lookupDate)
• .RemoveWarmupPeriods()
• .RemoveWarmupPeriods(removePeriods)

See Utilities and helpers for more information.

Chaining

This indicator may be generated from any chain-enabled indicator or method.

// example
var results = barsEval
    .Use(CandlePart.HL2)
    .ToBeta(barsMarket.Use(CandlePart.HL2), ..);

🚩 Matching inputs required

Both eval and market arguments must contain the same number of elements and be the results of a chainable indicator or .Use() method.

Results can be further processed on Beta with additional chain-enabled indicators.

// example
var results = barsEval
    .ToBeta(barsMarket, ..)
    .ToSlope(..);

See Chaining indicators for more.

Streaming

Use the buffer-style List<T> when you need incremental calculations without a hub. Add each series separately as its values arrive; either one may run ahead, and a result is added once both hold the same timestamp:

BetaList betaList = new(lookbackPeriods, type);

// call from each series' message handler
void OnEvalReceived(IReusable value) => betaList.AddSource(value);
void OnMarketReceived(IReusable value) => betaList.AddOther(value);

// the list itself holds the results; fills as the handlers run
IReadOnlyList<BetaResult> results = betaList;

A timestamp that only one series holds produces no result, where the Series method throws. Each series must arrive in strictly increasing order: an older or equal timestamp on a side throws an InvalidOperationException. Each side stages at most MaxListSize values, so a side that falls further behind than that loses the pairs the leading side has dropped.

Subscribe to a BarHub for each series for advanced streaming scenarios:

BarHub evalHub = new();
BarHub marketHub = new();
BetaHub observer = evalHub.ToBetaHub(marketHub, lookbackPeriods, type);

// call from each series' message handler
void OnEvalReceived(IBar bar) => evalHub.Add(bar);
void OnMarketReceived(IBar bar) => marketHub.Add(bar);

// results fill as the handlers run
IReadOnlyList<BetaResult> results = observer.Results;

A result is added once both providers hold the same timestamp. A value that arrives late, or is revised or removed, on either side is handled by the usual rebuild. Timestamps match exactly: each return is measured from the previous matched timestamp, and the lookback window spans N matched returns. Drive both providers from one thread at a time.

See Buffer lists and Stream hubs for full usage guides.