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portalpha

Compute risk-adjusted alphas and returns for one or more assets

Syntax

portalpha(Asset, Benchmark)
portalpha(Asset, Benchmark, Cash)
portalpha(Asset, Benchmark, Cash, Choice)
Alpha = portalpha(Asset, Benchmark, Cash, Choice)
[Alpha, RAReturn] = portalpha(Asset, Benchmark, Cash, Choice)

Arguments

Asset

NUMSAMPLES x NUMSERIES matrix with NUMSAMPLES observations of asset returns for NUMSERIES asset return series.

Benchmark

NUMSAMPLES vector of returns for a benchmark asset. The periodicity must be the same as the periodicity of Asset. For example, if Asset is monthly data, then Benchmark should be monthly returns.

Cash

(Optional) Either a scalar return for a riskless asset or a vector of asset returns to be a proxy for a "riskless" asset. In either case, the periodicity must be the same as the periodicity of Asset. For example, if Asset is monthly data, then Cash must be monthly returns. If no value is supplied, the default value for Cash returns is 0.

Choice

(Optional) A number, string, or cell array of numbers or strings to indicate one or more measures to be computed from among a number of risk-adjusted alphas and return measures. The number of choices selected in Choice is NUMCHOICES. The current list of choices is given in the following table:

CodeDescription
'xs'Excess Return (no risk adjustment)
'sml'Security Market Line
'capm'Jensen's Alpha
'mm'Modigliani & Modigliani
'gh1'Graham-Harvey 1
'gh2'Graham-Harvey 2
'all'Compute all measures

Choice is specified by using the code from the table (for example, to select the Modigliani & Modigliani measure, Choice = 'mm'). A single choice is either a string or a scalar cell array with a single code from the table.

Multiple choices can be selected with a cell array of choice codes (for example, to select both Graham-Harvey measures, Choice = {'gh1','gh2'}). To select all choices, specify Choice = 'all'. If no value is supplied, the default choice is to compute the excess return with Choice = 'xs'. Choice is not case sensitive.

Description

Given NUMSERIES assets with NUMSAMPLES returns in a NUMSAMPLES-by-NUMSERIES matrix Asset, a NUMSAMPLES vector of Benchmark returns, and either a scalar Cash return or a NUMSAMPLES vector of Cash returns, compute risk-adjusted alphas and returns for one or more methods specified by Choice.

To summarize the outputs of portalpha:

  • Alpha is a NUMCHOICES-by-NUMSERIES matrix of risk-adjusted alphas for each series in Asset with each row corresponding to a specified measure in Choice.

  • RAReturn is a NUMCHOICES-by-NUMSERIES matrix of risk-adjusted returns for each series in Asset with each row corresponding to a specified measure in Choice.

    Note:   NaN values in the data are ignored and, if NaNs are present, some results could be unpredictable. Although the alphas are comparable across measures, risk-adjusted returns depend on whether the Asset or Benchmark is levered or unlevered to match its risk with the alternative. If Choice = 'all', the order of rows in Alpha and RAReturn follows the order in the table. In addition, Choice = 'all' overrides all other choices.

Examples

See Risk-Adjusted Return.

References

John Lintner, "The Valuation of Risk Assets and the Selection of Risky Investments in Stocks Portfolios and Capital Budgets," Review of Economics and Statistics, Vol. 47, No. 1, February 1965, pp. 13-37.

John R. Graham and Campbell R. Harvey, "Market Timing Ability and Volatility Implied in Investment Newsletters' Asset Allocation Recommendations," Journal of Financial Economics, Vol. 42, 1996, pp. 397-421.

Franco Modigliani and Leah Modigliani, "Risk-Adjusted Performance: How to Measure It and Why," Journal of Portfolio Management, Vol. 23, No. 2, Winter 1997, pp. 45-54.

Jan Mossin, "Equilibrium in a Capital Asset Market," Econometrica, Vol. 34, No. 4, October 1966, pp. 768-783.

William F. Sharpe, "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk," Journal of Finance, Vol. 19, No. 3, September 1964, pp. 425-442.

See Also

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