First, we talk about the - We look at a the average annual return of some asset (say, R = 9%) and compare it to some risk-free return
(say R
_{f}= 4%, so R - R_{f}= 5%). Our "Reward" is the excess return:**R - R**._{f} - That excess return may look pretty good, but the asset has volatility (or Standard Deviation, say SD = 25%).
That's our "Risk". It measures how far our annual returns deviate from their average. In our example, we might expect most returns to vary between R - SD = 9 - 25 = -16% and R + SD = 9 + 25 = 34%. - We consider the Sharpe Ratio:
**(R - R**( In our example, it's: 5/25 = 0.20_{f}) / SD
Yes, so we might look for assets with large Sharpe Ratios. However, if the returns get really large compared to R >Then don't buy the asset!
If we
where SD is the "downside volatility" and the sum includes only returns
for which r < R_{d}_{f}.
If we take
Define "better". One thing is for sure: Sortino doesn't penalize an asset for "upside" volatility ... which is a "good" volatility. However, there's a problem with Sortino. It may happen that no returns are less than R in which case
_{f}SD = 0 and Sortino = ∞
_{d}
Well ... I used ten years worth of monthly returns and used (as Rf) 1/12 of the annual risk-free rate (or MAR). >Ain't that cheating? Define "cheating". >Where's the spreadsheet and what did you do when Sortino = ∞ and ... ? The spreadsheet will look like this: but it isn't finished ... yet. In fact, I keep playing with it and it keeps getting bigger and bigger. When it's finished, you can download three assets (from Yahoo) and compare Sortino and Sharpe and ...
Okay, so here's what I did with the spreadsheet: I used monthly returns instead of annual returns ... since there are so many more of those available >Huh?
(1/n) Σ (r - R,
becomes _{f})^{2}(1/n) Σ (λr -λR
= _{f})^{2}λ.
^{2}(1/n) Σ (r -R_{f})^{2}Hence the downside volatility SD gets multiplied by _{d}λ as well.
(Indeed, any standard deviation gets multiplied by that parameter ... which is one reason I don't like standard deviation as a measure of "risk".)
That'd change (λR - λR
= _{f}) / λSD_{d}(R - R.
_{f}) / SD_{d}In other words, the Sortino Ratio don't change at all
!Okay, so I just forgot about any effort to change monthly to annual, and just used monthly returns.
One other thing.
>And what about years when Yeah, sure ... so pick a more reasonable Rf. >And is that spreadsheet ready yet?
Almost forgot this, too.
That means the Sortino and Sharpe ratios get multiplied by SQRT(12) ... since 12/SQRT(12) = SQRT(12). The spreadsheet will do that if'n you ask nice. Just say y:
It will give ratios which are more like the ones you might see in the literature or on the internet (even tho' the increased values don't change the look of the charts). >Didn't you say you did >Then why don't you invent your own Sortino ratio, with your own measure of risk? You could call it ... uh, the |