en>UKoch: /* Characterization */ added an explanation (sort of), formatting of formula, TeX, no links in headings

2014-11-30T18:36:40Z

Characterization: added an explanation (sort of), formatting of formula, TeX, no links in headings

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en>Mojdadyr: /* Special cases */

2014-02-18T16:32:38Z

Special cases

← Older revision		Revision as of 18:32, 18 February 2014
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	~~{{Refimprove\|date=December 2006}}~~		33 year-old Psychiatrist Leif from Windsor, has many interests including quilting, ganhando dinheiro na internet and sleeping. Has travelled since childhood and has visited many destinations, as an example Church of the Ascension.<br><br>My website; [http://comoficarrico.comoganhardinheiro101.com ganhe dinheiro]
	~~'''Roy's safety~~-first criterion''' is a [[risk management]] technique that allows an investor to select one portfolio rather than another based on the criterion that the probability of the portfolio's return falling below a minimum desired threshold is minimized.<ref>{{cite journal\|last=Roy\|first=Arthur D.\|year=1952\|title=Safety First and the Holding of Assets\|journal=Econometrica\|volume=1952\|issue=July\|pages=431–450}}</ref>

	~~For example~~, ~~suppose there are two available investment strategies - portfolio A and portfolio B~~, and ~~suppose the investor's threshold return level (the minimum return that the investor is willing to tolerate) is -1%~~. ~~then the investor would choose the portfolio that would provide the maximum probability of the portfolio return being at least as high~~ as ~~−1%.~~

	~~Thus, the problem of~~ an ~~investor using Roy's safety criterion can be summarized symbolically as:~~

	~~::<math>\underset{i}{\min}\Pr(R_{i}<\underline{R})</math>~~

	~~where <math>\Pr(R_{i}<\underline{R})</math> is the probability~~ of ~~<math>R_{i}</math> (the actual return of asset i) being less than <math>\underline{R}</math> (~~the ~~minimum acceptable return)~~.

	~~==Normally distributed return and SFRatio==~~
	~~If the portfolios under consideration have [[normal distribution\|normally distributed]] returns, Roy's safety-first criterion can be reduced to the maximization of the safety-first ratio, defined by:~~

	~~::<math>SFRatio_{i}=\frac{E(R_{i})-\underline{R}}{\sqrt{Var(R_{i})}}</math>~~

	~~where~~ <~~math~~>~~E(R_{i})~~<~~/math~~> is the [[expected value\|expected]] return (the mean return) of the portfolio, <math>\sqrt{Var(R_{i})}</math> is the standard deviation of the portfolio's return and <math>\underline{R}</math> is the minimum acceptable return.

	~~===Example===~~
	If [[Portfolio (finance)\|Portfolio]] A has an expected return of 10% and [[standard deviation]] of 15%, while portfolio B has a mean return of 8% and a standard deviation of 5%, and the investor is willing to invest in a portfolio that maximizes the [[probability]] of a return no lower than 0%:

	~~: SFRatio(A) = [10 &minus~~;~~ 0]/15 = 0.67,~~
	~~: SFRatio(B) =~~ [~~8 − 0]/5 = 1.6~~

	~~By Roy's safety-first criterion, the investor would choose portfolio B as the correct investment opportunity.~~

	~~==Similarity to Sharpe Ratio==~~
	~~Under normality,~~

	: ~~SFRatio = (expected return − minimum return)~~/~~(standard deviation of return).~~

	~~Recall that [[Sharpe ratio]] is defined as excess return per unit of risk, or in other words:~~

	~~: Sharpe ratio = [Expected return − Risk-Free Return]~~/~~(standard deviation of [Expected return − Risk-Free Return]).~~

	~~SFRatio has a striking similarity to Sharpe ratio~~. Thus for normally distributed returns, Roy's Safety-first criterion - with the minimum return equal to the risk-free rate - provides the same conclusions (about which portfolio to invest in) as if we were picking the one with the maximum Sharpe Ratio.

	~~== See also ==~~
	* [[Value at Risk]]

	~~==References==~~
	~~{{Reflist}}~~

	~~{{DEFAULTSORT:Roy's Safety-First Criterion}}~~
	~~[[Category:Financial risk]]~~
	~~[[Category:Portfolio theories]~~]

en>Leonsoftware: /* References */ Corrected Reference

2013-12-12T21:47:55Z

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2012-05-08T04:34:45Z

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Generalized Pareto distribution - Revision history

en>UKoch: /* Characterization */ added an explanation (sort of), formatting of formula, TeX, no links in headings

en>Mojdadyr: /* Special cases */

en>Leonsoftware: /* References */ Corrected Reference

en>Helpful Pixie Bot: ISBNs (Build KE)