The formula for both is the same: Excess return over risk free rate (minimum acceptable return) per unit of standard deviation. Can someone confirm if the concept (like the formula) for both Sharpe ratio and Roy Safety First ratio is the same?
They are not the same. Sharpe uses the risk free rate. Roy’s safety use’s MAR which the investor would choose.
cfasf1 Wrote: ------------------------------------------------------- > They are not the same. Sharpe uses the risk free > rate. Roy’s safety use’s MAR which the investor > would choose. +1
So, yes… the concept is the same, but the actual formula is NOT. Unless, of course, the risk free rate is your minimum acceptable return. Roy’s safety first ratio should probably be around 2 for an acceptable portfolio - depending on the specification of the investor, of course. But a Roy’s measure of 2 would imply that the minimum acceptable return is about 2 standard deviations away (under) the acceptable return. This is the best way to think about Roy’s measure – it really just tells you how many standard deviations away from the expected return an investor’s minimum acceptable return is. If you had a Roy’s measure of .5, well then you would have a very high likelihood of breaching that MAR. If you are 2 std dev away from the MAR, then your odds are only about 2.5% (I think…). Sharpe ratios are more typically around .3 to .6 range and measure the excess return per unit of risk the investor can attain. The Sharpe ratio of the tangency portfolio also gives us the slope of the capital allocation line. I hope this helps.
Good explanation plyon.
good stuff to know, plyon. thanks. better than just knowing the formula.
plyon Wrote: ------------------------------------------------------- > So, yes… the concept is the same, but the actual > formula is NOT. Unless, of course, the risk free > rate is your minimum acceptable return. > > Roy’s safety first ratio should probably be around > 2 for an acceptable portfolio - depending on the > specification of the investor, of course. But a > Roy’s measure of 2 would imply that the minimum > acceptable return is about 2 standard deviations > away (under) the acceptable return. This is the > best way to think about Roy’s measure – it really > just tells you how many standard deviations away > from the expected return an investor’s minimum > acceptable return is. If you had a Roy’s measure > of .5, well then you would have a very high > likelihood of breaching that MAR. If you are 2 > std dev away from the MAR, then your odds are only > about 2.5% (I think…). > > Sharpe ratios are more typically around .3 to .6 > range and measure the excess return per unit of > risk the investor can attain. The Sharpe ratio of > the tangency portfolio also gives us the slope of > the capital allocation line. > > I hope this helps. Pylon, you could be vey sophiticated sometime 
plyon Wrote: ------------------------------------------------------- > So, yes… the concept is the same, but the actual > formula is NOT. Unless, of course, the risk free > rate is your minimum acceptable return. > > Roy’s safety first ratio should probably be around > 2 for an acceptable portfolio - depending on the > specification of the investor, of course. But a > Roy’s measure of 2 would imply that the minimum > acceptable return is about 2 standard deviations > away (under) the acceptable return. This is the > best way to think about Roy’s measure – it really > just tells you how many standard deviations away > from the expected return an investor’s minimum > acceptable return is. If you had a Roy’s measure > of .5, well then you would have a very high > likelihood of breaching that MAR. If you are 2 > std dev away from the MAR, then your odds are only > about 2.5% (I think…). > > Sharpe ratios are more typically around .3 to .6 > range and measure the excess return per unit of > risk the investor can attain. The Sharpe ratio of > the tangency portfolio also gives us the slope of > the capital allocation line. > > I hope this helps. Pylon, you could be very sophiticated sometime
good explanation pylon, Thanks!
Wow…thanks to all for the value add. I asked this as i came across a question where the MAR is the risk free rate. And to add to the confusion, there is another formula which is the same, the shortfall risk. Shortfall risk = (Rp – Rmin)/ óp.
shortfall risk is a probability measure, isn’t it? the probability that you will lose more than an acceptable dollar limit?
I think there is two ways to look at shortfall risk, in term of return or in term of loss. For return, it is the probability of the actual return will be less than the target return. For measurement of loss, it is the risk that the loss will exceed the maximum acceptable dollar loss. Just for info, there is another diff betw Sharpe and Roy Safety Ratio. For Safety Ratio the MAR can be negative (not possible for risk free rate). For example if the question says that the investor would like to see the portfolio lose not more than 2% etc.