# Roy's Safety First & Min Accepted Return

So schweser uses a minimum accepted return that is negative in one test (book 2 Exam 1 Am Q 1C), but at the 3 day review Lefebvre told us to use the risk free rate if the minimum accepted return is below the rf rate. What would you do?

CFAI will specify which rate to use

No they will not, passme…

This is what the book says:

The oldest shortfall risk criterion is Roy’s safety-first criterion. Roy’s safety- first criterion states that the optimal portfolio minimizes the probability over a stated time horizon that portfolio return, RP , will fall below some threshold level RL that the investor insists on meeting or exceeding. The safety-first optimal port-folio maximizes the safety-first ratio (SFRatio):

SFRatio = [E(RP) - RL] / σP

Equation 2 gives the distance from the expected return to the shortfall level in the numerator. The denominator converts the result into units of the portfo- lio’s standard deviation of return. If a portfolio’s expected return were many standard deviations above the threshold return, the chance that the threshold would be breached would be relatively small.17 There are two steps in choosing among risky portfolios using Roy’s criterion (assuming normality):

1. Calculate each portfolio’s SFRatio. 2. Choose the portfolio with the highest SFRatio.

If there is an asset offering a risk-free return for the time horizon being con- sidered, and if RL is less than or equal to that risk-free rate, then it is safety-first optimal to be fully invested in the risk-free asset. Holding the risk-free asset in this case eliminates the chance that the threshold return is not met. Example 4 illustrates a use of Roy’s safety-first criterion.

It is right there in the curriculum. Pg 235, Vol 3.

Schweser has got it backwards and completely wrong.

agreed

if u use the rfr is it just not the sharpe ratio. i fo not think that is the intention

Thank you CPK!

Roy becomes a boy named Sharpe if RL = RFR, so yes.