# Roy's safety -first measure

The excess return in Roys measure (numerator) is the expected return in excess of the investors minimum acceptable return. Dividing excess retun by the portfoli standard deviation tells us HOW MANY STANDARD DEVIATIONS THE MINIMUM ACCEPTABLE RETURN LIES BELOW THE PORTFOLIO ACCEPTABLE RETURN. short: for roys’s safety measure we know that we take the portfolio with the larger measure. it’just seems counterintuitve withe the explanation above. wouldnt we want to choose a portfolio where the standard dev. is small? sorry im confused.

different portfolio can have different std deviations. by doing (Rp - Rmin)/sp (where p = portfolio) --> you are able to determine in a normalized manner - how far away in terms of Standard deviations of that portfolio - the portfolio lies from your Rmin (min reqd return). a higher roy’s safety first measure gives you more area to play with in terms of the std dev of that portfolio. you are surer of meeting the rmin requirements with a portfolio with a higher roy measure.

Safety First measures the excess return (above a minimum level) per unit of risk (st. dev.), so the higher the variable, the better. I think your explanation refers to something else. Let’s you are evaluating whether a portfolio (A) is appropriate for the client or not. The portfolio (A) has an expected return of 10% and st. dev. of 8%. The client can only tolerate a volatility of 5%. So portfolio (A) has a 2.5% chance (2 st. dev. away from the mean) to have a return below -6%. Since the client can only tolerate 5% volatility, portfolio (A) is not appropriate. This process explains what you are referring to as “HOW MANY STANDARD DEVIATIONS THE MINIMUM ACCEPTABLE RETURN LIES BELOW THE PORTFOLIO ACCEPTABLE RETURN”. But this is NOT the Safety First formula.

right if you think about it Sharpe ratio is really just a specific version of Roy’s Safety first in which the mimimum value is the mean

Sharpe Ratio is a special case of SF forumula, in which the minimum required level of return is the rfr.

brain fart ur right i meant the rfr…thanks mik82

It is a downside measure. As a result, the larger the cushion the better.

yes but whats the measure ? i mean if I divide return divided by risk. what do i get? my explanation in terms of HOW MANY STANDARD DEVIATIONS THE MINIMUM ACCEPTABLE RETURN LIES BELOW THE PORTFOLIO ACCEPTABLE RETURN…comes from schweser. so if the minimum return lies 1 standard dev- away from the portfolio return vs. the minimum return lies 0.5 standard dev. away, which one do i prefer?

where do you have a bigger cushion? (in terms of the std deviation)?

On what page is that Schweser definition of SF?

Wouldn’t you want your minimum return to lie as far away from your mean return as possible? That would mean that you have a lower chance of hitting that minimum or below. Therefore you should choose the higher number in a SF calculation which indicates that the mean return is further away from the minimum return you would accept. Right?

yellayella Wrote: ------------------------------------------------------- > yes but whats the measure ? i mean if I divide > return divided by risk. what do i get? That’s the crux of it, your dividing the expected return (high = good), by a measure of variance, aka, uncertainty (high = BAD) … Step back a bit and think about *what* a std dev actually represents. Go back to level 1 and specify the following in words: >>>>> Expected return 10%, std dev 8%. To me, that says: expected return is 10% 68% of returns will be within 1 standard deviation (ie, 10 +/- 8 = 2 to 18%) 95% of returns will be within 2 standard deviations (ie, 10 +/- 2*8 = -6 to 26%) Now, to take this to extremes, what would you prefer out of: Expected return = 10%, std dev = 0 (ie, 100% of returns = 10%) and Expected return 10%, std dev = 1000000 (ie, 65% of returns in -999990% to 1000010%) So, regarding: yellayella Wrote: ------------------------------------------------------- > yes but whats the measure ? i mean if I divide > return divided by risk. what do i get? You get a measure of how much of a comfort factor you can expect.

In short, it is a risk adjusted return. Return per unit of risk. you want to max it out.