Utility Adjusted Return vs Roy's Safety First Measure

Couple of questions on the above topic: 1. The utility adjusted return calcs depends on investor’s risk aversion while Roy’s SF measure seems to be neutral to investor’s risk aversion rating. Which is a better method for evaluation when there is a conflict in end result from these two methods? 2. What’s the exact formulae for Roy’s SF measure… I have seen two versions: SF = (Rp - Rmin)/Std Dev of PF SF = (Rp - Rmin)/PF’s downside sigma Can someone clarify which one is more accurate? Thanks, bn

caveat: I’m not studying for this exam. But where angels fear to tread… 1. In general where you get preferences from clients (assuming you’re writing an IPS), I think cfai recommends you respect the client wishes while informing them of other approaches. So if you have an accurate characterization of client’s risk aversion you should use that instead of a more normative approach. 2. I’ve never heard of the downside sigma approach for calculating Roy’s SF. Is that new to the curriculum this year?

Roy’s safety first measure is calculated and is used for investor’s risk aversion SF = (Rp - Rmin)/Std Dev of PF There is another measure called Sortino ratio which uses downside deviation which appears in alternative investments volume 4 reading 34 page 336. That is used in performance evaluation of hedge funds. The Sortino ratio uses (annualised rate of return-annualised risk free rate)/downside deviation.

not 100% sure on this, but downside volatility is mostly useful if you have strong reasons to suspect that the distribution is substantially skewed (i e you think it is not symmetrical). The logic is that investors are more worried about returns less than the expected rate and see anything above that as gravy, therefore downside volatility is most relevant. If returns are symmetrical, however, throwing away roughly had the data points is a little silly and doesn’t buy you much value. On another note, if the formula above is true (I assume it is), then the Sortino ratio is really just the Sharpe ratio using downside volatility only. And the Sharpe ratio is just the Roy’s safety first criterion with the return on cash as the hurdle rate.