Why a Decision Maker May Prefer a Seemingly Unfair Gamble

Prakash, Arun J.; Chang, Chun‐Hao; Hamid, Shahid; Smyser, Michael W.

doi:10.1111/j.1540-5915.1996.tb00852.x

Cited by 5 publications

(8 citation statements)

References 21 publications

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“…The Prakash et al (1996) paper contains some minor errors, such as the sign on the right-hand side of inequality (1 0) and the comparable signs on page 250, none of which negate their results. More critical, however, the left-hand side of equation (6) may be written where t is the random payoff in a lottery.…”

Section: The Gamblementioning

confidence: 66%

“…and In essence, Prakash et al (1996) show that even when Ipe -1 + [pe(0-2) + 11 ml / 2} < 0 it will always be possible to find a value ofp, for a given 8 and ml < 0,…”

Section: The Gamblementioning

confidence: 97%

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mentioning

confidence: 98%

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Will a Risk‐averse Decision Maker Ever Really Prefer an Unfair Gamble?*

Horowitz

1998

Decision Sciences

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Prakash, Chang, Hamid, and Smyser (1996) purport to show that with sufficient preference for positive skewness, risk-averse managers might elect to engage in unfair gambles. Their "proof' of the impossible assumes the existence of a differentiable risk-preference function that satisfies certain assumptions about the first three derivatives. The fundamental flaw in their argument is that no differentiable function exists for which risk aversion and the participation in an unfair gamble are compatible.

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Section: The Gamblementioning

confidence: 66%

“…and In essence, Prakash et al (1996) show that even when Ipe -1 + [pe(0-2) + 11 ml / 2} < 0 it will always be possible to find a value ofp, for a given 8 and ml < 0,…”

Section: The Gamblementioning

confidence: 97%

See 1 more Smart Citation

Will a Risk‐averse Decision Maker Ever Really Prefer an Unfair Gamble?*

Horowitz

1998

Decision Sciences

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“…For the risk-averse trader, we add the [24] function, to the left side of Equation (10). This function describes the probability of a risk-averse trader earning a profit with a high-risk gamble.…”

Section: Single Asset Cryptocurrency Portfoliosmentioning

confidence: 99%

The Valuation of Cryptocurrencies in Single-Asset and Multiple-Asset Models

Abraham¹,

Tao²

2019

TEL

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Cryptocurrencies are virtual currencies employed in blockchain transactions. They are particularly worthy of theoretical examination, given the limited academic literature on the subject. This paper constructs valuation models of bitcoin and altcoins, both as single investments and components of mutliple-asset portfolios. As single investments, cryptocurrencies are valued at the confluence of Legendre utility functions, with Esscher transformed Geometric Levy pricing processes. As part of portfolios, cryptocurrencies are contained in traditional Markowitz portfolios which are varied by increasing the proportion of the riskless asset, shorting the risky asset, or adding currency options. Theoretical formulations show that Markowitz models combined with bitcoin, located on the Capital Market Line (which we term CML portfolios), have low returns, mainly due to the presence of the riskless asset. Such portfolios are appropriately suited to the investment goals of risk-averse traders, while overlooking the preferences of risk-takers. To satisfy less riskaverse investors, we propose a high-return portfolio with 9 asset choices, consisting of risky assets, cryptocurrencies, US dollars, soybean futures, Treasury bond futures, oil futures, currency options on the US dollar, currency options on the Mexican peso, and technology, or biotechnology stocks. Laplace transforms are employed to suppress volatility, skewness, or kurtosis of returns, which empirical studies have found to contribute to tail risk contained in outliers in fat-tailed distributions.

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“…C t = Value of Call Option in Foreign Currency at time t, S t = Spot Echange Rate at time t, (T − t) = Time to maturity, , [38] derived utility functions in which managers, who were offered windfall profits in an unexpected opportunity, accepted them in utility functions with decreasing absolute risk aversion.…”

Section: Put Currency Optionsmentioning

confidence: 99%

The Valuation of Currency Put Options

Abraham¹

2018

TEL

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Investors who seek to profit from depreciating currencies may invest in put options. Upon option exercise, the currency is sold at a high price, and then purchased at the lower future currency value, resulting in a gain for the put buyer. A series of such transactions yields a stream of income for the put investor. Alternatively, the investor could short sell the currency, reaping gains from the difference between the high short sale price and the low future purchase price. This paper derives the theoretical formulations for combined short sale and puts purchase strategies for the US dollar, the Euro, the Australian dollar and the New Zealand dollar, and the Mexican peso. Utility functions are based upon an assumption of declining risk aversio with negative rescale factors and positive threshold factors in a hyperbolic cosine distribution. This distribution intersects with the cosine distribution of short sale prices on the U. S. dollar, the lognormal distribution of short sale prices on the Euro, the Weiner process for shorts on the Australian dollar and the New Zealand dollar, and the Laplace currency distribution for peso shorts. Similar utility functions intersect with Levy-Khintchine jump processes to provide put option prices for each type of foreign currency.

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Why a Decision Maker May Prefer a Seemingly Unfair Gamble

Cited by 5 publications

References 21 publications

Will a Risk‐averse Decision Maker Ever Really Prefer an Unfair Gamble?*

Will a Risk‐averse Decision Maker Ever Really Prefer an Unfair Gamble?*

The Valuation of Cryptocurrencies in Single-Asset and Multiple-Asset Models

The Valuation of Currency Put Options

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