Roy’s Safety First vs. Worst case return return, which

Viceroy

Roy’s Safety First vs. Worst case return (ie. E(R) - 2σ > worst case return)

Does anyone know when to use which?

NakedPuts2011

Sorry, doesn't display well. retype again.

Worst case return: E(R) - 2(std dev) > Worse case return

IAmNeil

is E(R) - 2(sd) the worst case return?

is this shown in the textbooks?

bkballa

Roy's safety first = (R-Rmin)/sd

This is an access return (over the minimum acceptable return) per unit of risk.. clients might require that their minimum acceptable return is risk-free rate.. in which case, your Roy's safety ratio becomes Sharpe ratio...

You can use either to evaluate which balanced portfolio to choose..

If I say, "I don't want my portfolio fall below -5%", my shortfall risk is -5%.. so you better construct such a portfolio that agrees with my risk tolerance...



Edited 2 time(s). Last edit at Tuesday, May 25, 2010 at 01:16AM by kurmanal.

Valores

Sharpe = [E(R) - RFR]/STD
Roy = [E(R) - MAR]/STD
Sortino = [E(R) - MAR]/DD
Shortfall = E(R) - 2*STD

Analyze_This

In my understanding, a shortfall risk is the risk that the portfolio will fall below its value... normally, if someone mentions that they want to control that risk, she/he exhibits high risk aversion..

Look at it this way.. picture a bell-shaped curve... 2.5% of the left tail has a Z-score of 1.96.. you are essentially saying that I want my returns lay within the curve.. I want to be 97.5% confident that that will happen.. hence, the formula for shortfall risk = R - 1.96*sd (or rounding it to R-2*sd..



Edited 1 time(s). Last edit at Tuesday, May 25, 2010 at 01:34AM by kurmanal.

thommo77

isn't Jensen's alpha is simply that alpha in the regression?

M2 = Rf + SharpeRatio*(SD of market)

Windjam

Jensen's alpha: R-[Rf+(Rm-Rf)*beta]
M2 = Rf+(Rp-Rf)/SDp*SDm

bboo

Sometimes if the question say "I don't want my portfolio fall below -10%"

We use Roy = [E(R) - (-10)]/STD to compare which portfolio is higher.

In CFAI textbook, Vol 2, P.136. The question stated that a worst-case return of -10% would be acceptable.

They use E(R) - 2*STD to calculate the worst-case return for each portfolio and see which portfolio has worst-case return > -10%.

My question is..
The statement "I don't want my portfolio fall below -10%" and "the worst-case return of 10% looks are acceptable" looks similar. How do we distinguish which one to use ? (Worst case return or Roy, both are downside risk measures).

ll11

this downside risk calculation is shown on vol2 pg134 of the curiculum.

it does raise a serious question of what to use on the exam: this downside risk calculation? or Sortino or Roy's first???

I guess the request would be given in the question?