Safety First Ratio

CFA Level III
#1

In the book Roy’s Safety First is defined as: RSF = (Rp - Rmar) / (std. dev portfolio) However, I was just doing some Schweser practice problems and they defined it in the following way in the answer: “The safety first ratio can be calculated as the expected portfolio return minus 2 standard deviations.” ----- Is there a variation of the Safety First ratio that I didn’t read?

#2

“Expected portfolio return minus 2 standard deviation” is the worst case return from a portfolio, at 95% confidence. It cannot to be taken as the “Ratio” itself.

#3

^ correct. a lot of times in essay q’s or whatnot, you’ll get a question like the pension’s min acceptable risk level is E® - 2 std. deviations and you’ll just have to use that as one of the factors to knock out what portfolios may or may not be ideal for the fund if they have too much variation. but your first formula up there is the RSF ratio.

#4

Interesting… thanks for the responses. Not sure why Schweser called that formula what it did.

#5

Thought this thread might be worth a bump as I had the same question and was able to find a past thread on it using the ‘Search’ function in the forum.

I didn’t realize there were two ways to utilize Roy’s safety first criterion:

  • SFRatio = (Expected return on portfolio - Risk threshold level) / Standard deviation of portfolio

AND

  • [Shortfall risk test]: Worse case return on portfolio = Expected return on portfolio - 2 * Standard deviation of portfolio

I see in Reading 18 Asset Allocation that for the second bullet point above, “if the resulting number falls below the client’s threshold, the portfolio does not pass the shortfall risk test. Shortfall probability levels of 5% and 10% translate into 1.65 and 1.28 standard deviations below the mean, respectively, under a normality assumption” (page 190-191).

My question is: Why does the shortfall risk test formula suggest we use 2 times the standard deviation of the portfolio? Won’t our number of standard deviations depend on our shortfall probability level? I understand the 1.65 and 1.28 won’t apply if the return distribution isn’t normal, but is there anything else to this that I’m missing?

Thanks!

OMGMileyCyrus

#6

2times standard deviation assume 95% confidence internal.

#7

Ur maximum acceptable loss is 2x the STD…

#8

Quote from CFA Curriculum, fyi. Given a normal distribution of returns, the probability of a return that is more than two standard deviations below the expected return is approximately 2.5 percent. Therefore, if we subtract two standard deviations from a portfolio’s expected return and the resulting number is above the client’s return threshold, the resulting portfolio passes that shortfall risk test.

#9

Mark it to memoize Kaplan question