Could anybody explain this? Thanks. Portfolio A has a safety-first ratio of 1.3 with a threshold return of 2%. What is the shortfall risk for a target return of 2%? A. 90.3% B. 40.3% C. 9.68% D. 49.68%
look up -1.3 on the Z-table and subtract from 1 = C.
We dont use SF ratio formula here?
they already gave you the answer you would be getting by using the sf ratio formula (1.3).
It’s usually the lowest probabilty given anyway That is the function of the equation
-1.3 on the Z-table = 0.0968 => 9.68% I dont think you need to subtract anything. Incase if you look for +1.3 on the Z-table, you get 0.9032. Hence, you have to do 1- 0.9032 = 0.0968 to get the value for -1.3
Bit confused about this.
Calculating the SFRatios is easy enough. I don’t understand what they mean.
If you have a non standard normal distribution you need to convert it to a standard normal distribution in order to be able to use the tables to determine probabilities since otherwise we would require an infinite number of tables for all the possible unique standard deviations. This makes sense. We thus get a value on the standard normal distribution equivalent to the original normal distribution in terms of the probabilities.
With SFRatios however, the formula is E(Rp-Rl)/SDp. So we’re not standardising yet we input the value into a Z table and get the probability??? I don’t understand how the book gets ~23% under section 3.3 Reading 9. Or indeed why we put in 1.3 directly into the tables as per the OP???
You ARE standardizing (in a sense). All standardizing means is that you are expressing values in terms of how many standard deviations they are from some benchmark value (in a standard normal, it’s SDs from the mean, which is zero).
In the SFR ratio, you are calculating how many standard deviations you are from the RF rate. Then you’re implicitly assuming that the resulting ratio is a standard normal variate.
And the implication is that the more standard deviations your mean return is above your threshold return, the safer the investment.
As an aside, you can view many statistics (t-statistics, z-statistics, RSF) that involve “number of standard deviations” as telling you how far away some point is from some other point (the mean, the benchmark, the minimum acceptable return, etc…). So, they’re really just measures of “Statistical distance.”
Thanks, starting to piece this together now.
Glad to help.