A Note on Geometric Mean Portfolio Selection and the Market Prices of Equities

Litzenberger, Robert H.; Budd, Alan

doi:10.2307/2329861

Cited by 17 publications

(10 citation statements)

References 12 publications

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“…The log‐utility CAPM was developed by Litzenberger and Budd (1971), Roll (1973) and Rubinstein (1976). See Rubinstein (2006), pages 258–261, for further background.…”

Section: Log‐utility Capital Asset Pricing Modelmentioning

confidence: 99%

Log-Optimal Economic Evaluation of Probability Forecasts

Johnstone

2012

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary. The commercial test of an expert's probability assessments is not that they are accurate in an abstract sense, but that they yield financial returns to decision makers. From this utilitarian standpoint, a model or forecaster is merely a font of cash pay-offs, like any other form of asset or security. The modern perspective in finance theory is that individual 'securities' (sources of cash pay-offs) must be valued in portfolio rather than of themselves. Applying portfolio methods to forecast evaluation, the theoretical worth of a forecast depends on its marginal contribution to the best available portfolio of securities. When considered within a log-optimal (maximum E[log.wealth/]) portfolio, the value of an individual forecast (or forecaster) depends on both its expected cash pay-off and the covariance of its pay-off with those from all other available securities. In effect, portfolio theory rewards forecasters more for making accurate forecasts when other forecasters (or, more broadly, other sources of pay-offs) perform badly than when all or most forecasters do well. Conversely, the penalty for being wrong is reduced when other forecasters are right. This has the effect of promoting original thinking and unique (idiosyncratic) forecasting expertise. Herding by resort to industry standard models or routines is discouraged.

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“…The log‐utility CAPM was developed by Litzenberger and Budd (1971), Roll (1973) and Rubinstein (1976). See Rubinstein (2006), pages 258–261, for further background.…”

Section: Log‐utility Capital Asset Pricing Modelmentioning

confidence: 99%

Log-Optimal Economic Evaluation of Probability Forecasts

Johnstone

2012

Journal of the Royal Statistical Society Series A: Statistics in Society

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“…These results may also be extended to other classes of utility functions. Lintner [6] has shown that for negative exponential utility functions (i.e.,

{normalU}_{normalk} ({normalY}_{normalk}) = - exp - {normala}_{normalk} {normalY}_{normalk}

λ = {(\underset{normalk}{normalΣ} {normala}_{normalk}^{- 1})}^{- 1} = {[\underset{normalk}{normalΣ} (\frac{1}{{normalR}_{normalk}})]}^{- 1} .

More recently Litzenberger and Budd [7] have shown that for Bernoulli or logarithmic utility functions (i.e.,

{normalU}_{normalk} ({normalY}_{normalk}) = ln {normalY}_{normalk}

)

λ = \frac{1}{{normalμ}_{normaln}} = {[\underset{normalk}{normalΣ} E (\frac{1}{{normalR}_{normalk}})]}^{- 1} .

While under logarithmic utility functions single period decision rules are completely myopic, the quadratic and negative exponential utility functions are partially myopic and the parameters of the investor's “indirect” single period utility functions (4a) and (4b) are derived from his utility function of final wealth and expectations of future interest rates [8]. Except under quadratic utility functions, the above derivation requires the further assumption that the end of period national wealth is normally distributed 1 .…”

Section: Changes In Risk Premium Through Timementioning

confidence: 99%

Secular Trends in Risk Premiums

Litzenberger

Budd

1972

The Journal of Finance

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“…Under the conventional set of assumptions of portfolio theory and for specific utility functions, the market value of the firm may be derived. Mossin [13] derived results for a quadratic utility function, Lintner [6] for an exponential utility function and Litzenberger and Budd [8] for a Bernoulli or logarithmic utility function. These results take the interest rate as exogenously determined and derive conditions for partial equilibrium in the market for risk and safe assets.…”

mentioning

confidence: 99%

“…Using an approximation to a Bernoulli or logarithmic utility function