Pre-tax return for Roy's Safety First Ratio? (Schweser Exam)

In Schweser Exam Volume 2 Page 14, the after tax return is given in the asset allocation table.

To choose the asset allocation, the after tax return is used (which makes sense, since expenses are given in after tax dollars).

But to calculate Roy’s Safety First Criterion, the after tax return is grossed up to a pre tax return.

Is there something specific about RSF that requires a pre tax return to be used? If not, can anyone explain the inconsistency? Thanks.

The only thing I can think of is that the denominator of Roy’s is std dev of the port and you are using an after tax return figure on top. After tax return volatility would be lower than total volatility (total risk as measured by Std Dev). Using lower return figures in the numerator and a larger risk measure in the denominator would artificailly lower your Roy’s.

I wonder if instead you adjusted to an after tax std dev on the bottom if Roy’s would then be the most accurate since this is for an after tax investor?

On a similar note, sometimes I get tripped up when they say something like “the Wayne’s will not tolerate a loss of more than 5% annually”

I fall into the trap of using (Rp-5%) / SD when i guess its really [RP - (-5%)] / SD because the MAR is a loss not a minimum positive return. This always mindfucks me because the RSF ends up being higher and higher the greate the loss is, which intuitively doesn’t make sense.

It seems that the formula should not work when MAR <= 0, any insight from anybody here?

Wait, why doesn’t that make sense? The more of a loss someone is willing to accept, the “safer” they are in terms of risky investments. If I’m willing to accept some huge loss, then the # of std devs from the mean it would take before I risk exceeding that loss will be pretty damn high (aka. high Roy Safety-First Criterion).

I guess it’s confusing to me because I think of the number it puts out as a “larger is better” more than thinking of it as "this is the # of std dev’s from the MAR they will tolerate.

It is hard for me to associate “better” with “massive allowance for losses”.

Ah, I see. It’s interesting, because I still think of higher Roy Safety number as “better” because the higher it is, the better my portfolio is at achieving its intended goal. It just so happens that the goal in this case is to not make a huge loss rather than shoot for a specific gain lol. But I see what you’re saying.

ITs because I am so conditioned to the sharpe ratio interpretation of “this is how much excess return i get for each unit of risk” That when I think of a high RSF that is due to large allowance for losses, it just messes with my head.

No-one wants a negative return . Do you want a negative return?

M.A.R. being negative makes no sense at all , so let’s not get into useless discussion with 25 days to go

It’s not a useless discussion ace. I have taken more than one test where they used RSF and the client stated they didn’t want to “lose more than x% a year”, so the formula was minus a negative.

OK sorry , you are right.

If MaR is negative RSF increases over Rsf when MaR is zero. That is correct.

If you’re comapring two strategies or managers , its just a number to denote how much each provides by way of cushion per unit of risk

back to the original question, can anyone help understand why the expected return is grossed up to a pretax return?

FinNinja: im not sure i understand your explanation. if you return is after tax, then your standard deviation is after tax as well. so why would you start to mix a pretax return with an after tax standard deviation?

I don’t know what the actual Schweser question is, but one suggestion is that maybe the MAR is pre-tax, meaning the actual return should be pre-tax as well as the std. dev for the purposes of the calculation. If the MAR in this case is the risk-free rate, I bet they quote the risk-free rate as pre-tax.

you got it, thats the right answer.

the MAR is the tbill rate. it doesnt say that this rate is pretax but i take it that we should assume so since tbills are taxed.

then since the return is given as after tax, we gross up the return to pretax to match the MAR.

sharpe ratio is given and then you solve for the pre tax SD.

i guess the only question is why you dont instead alternatilvey decrease the risk free rate to an after tax return (youd get different answers if u did), but i guess its not important–exam wouldnt have a question this open ended i think.

I believe that was what I was trying to say - if you have pretax returns you would use a pretax std dev. If they provided the std deviation in the problem it is probably pretax (using the actual returns of the portfolio), unless they specify otherwise. If you calculated the std deviation yourself then you could calculate the after tax std dev if you use the after tax returns in your calculation.

In my original answer I was assuming that they gave you a before tax std deviation for the denominator, and you used an after tax return for the numerator. It was just a guess though.

Hmmm… I see the logic but i don’t think i would gross it up on the exam. I don’t recall problems where they say that the MAR is “pre tax” or “after tax”, they just give a number, and the answer doesn’t gross up the portfolio return or mess with the SD.

Feel free to correct me or provide examples to the contrary.

Ah nice! And to answer your last part, I bet it’s because the standard deviation is based on pre-tax returns. If it were adjusted for after-tax returns, I imagine (not sure whatsoever, though) that the resulting ratio should be the same.

I had the same thought, but I haven’t spent time to try and test it. Although, different portfolios may rank differently after tax depending on whether it is a taxable, TDA, or Tax Exempt account.

Well said and I agree.

Hey guys, Schweser has made a correction to that particular question. Basically, there’s no need to gross up the after tax returns.