When we talked about Sortino Ratios we noted that it was a ratio of Reward to Downside Risk.
The Reward was the excess of the average return R (over the last umpteen months) over some (monthly) risk-free rate: R_f.
The Downside Risk was the standard deviaton of those monthly returns which were less than R_f.

Because standard deviation measures volatility (not "risk" in the usual, garden-variety, everyday-person, comman-man/woman, non-guru sense),
we've decided to adopt a dictionary definition of "risk", namely:

  Risk n The probability of Loss.

To that end we might consider, for example VAR so that ...

>Huh?
Read all about it, here.

Here's what we'll do: Download two years worth of monthly asset returns. Calculate the Mean and Standard Deviation: R and S. Calculate the excess return, above some risk-free return Rf. That's R - Rf. With R and S in hand, generate a normal cumulative distribution: F(x,R,S) Take as our "downside" risk Sd = F(Rf,R,S). This gives the probability of having a return less than Rf, assuming returns are normally distributed. Calculate the Ratio: (R - Rf) / Sd.

Figure 1

>That's it? That's your new ratio? New? I have no idea if'n it's new ... but it's interesting, no? >So what's it called? I was thinking Ponzorino Ratio. Like it? >No! It was your suggestion. Anyway, the idea is to use a downside risk which (I think) is more reasonable than standard deviation. One that incorporates real, live, down-home risk (and not "volatility" or "uncertainty"). >You mean one that doesn't use standard deviation, right? Right, so we can ... >Where's the spreadsheet? Patience ... but here's an example The idea is to look for stocks (or other assets) with large Ponzorinos. (Gee, that sounds good; Ponzorino, Ponzorino, Ponzorino.) >And, for short, you call it the Ponzi? Very funny ...

Figure 2

Figure 3 has a bunch of DOW stocks with their Ponzorino Ratios (using the data for a 2-year period ending Jan 1, 2006). You can click on the stock symbol and get a Yahoo chart for the last year ... to see how they performed. Arranged from bestest to worstest (as per Ponzorino Ratio, expressed as a percentage), they are:

BA 0.067 MO 0.043 CAT 0.037 XOM 0.035 MCD 0.033 HPQ 0.023 AXP 0.017 UTX 0.015 JNJ 0.014 PG 0.014 GE 0.012 HD 0.011 HON 0.011 JPM 0.010 MSFT 0.004 C 0.003 DIS 0.002 AIG 0.002 T -0.001 DD -0.003 MMM -0.007 VZ -0.008 IBM -0.010 WMT -0.011 KO -0.016 AA -0.016 INTC -0.017 MRK -0.019 PFE -0.026 GM -0.054 Figure 3

>And the best Ponzorino is the best stock? Is that it?
You want the best performing stock ... in the future? Wait till I check

> I look at the "best" Ponzorino stocks in Jan/06 and they didn't do that well since then and the worst is up 35% and in nine months and ...
Okay, so Ponzorinos aren't that good ... but remember we're talking Reward and, especially Risk.
Here's the big question:

1. How should we define "risk" and, in particular "downside risk" ... given a bunch of returns: r₁, r₂, ... r_n?
2. It should clearly depend, as well, upon some risk-free return, r_f ... which will be our Minimum Acceptable Return.
3. Call this risk-function: R[r₁, r₂, ... r_n, r_f]
4. It should have the property that, if any return is increased by h > 0, "risk" should decrease:
   R[r₁, ... r_k+h, ... r_n, r_f] < R[r₁, ... r_k, ... r_n, r_f] ... if h > 0.
   And, of course, R should increase if h < 0 ... and returns are smaller.
5. Further, R should increase if r_f is increased (since it's harder to achieve that larger minimum acceptable return).
6. And, if r_k > 0, then λr_k should give a smaller risk if λ > 1 ... since that kth return is increased.
   And, of course, R should increase if λ < 1 ... since that kth return is decreased.
7. And ...

>But what about a Sortino spreadsheet?

Almost forgot. It's here ... somewhere.
I'll give you a hint. It starts with sortino2.

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