| Another definition of Risk |
There are a jillion definitions of "Risk" and I don't hardly like any of them.
>Don't tell me you're talking about risk again!
I know! I know! I've done it several times before. (Search here for "risk".)
However, I think many would like to think the following:
If stock A is "riskier" than stock B, then you'd expect:
- The probability of getting large returns is higher for stock A
- The probability of getting large losses is also higher for stock A
You'd like to be rewarded for taking a larger "risk", knowing full well that there's also a greater possibility of getting large losses.
>Yeah, so why call it "another definition of risk"? Why not stick with existing definitions like ...?
Like downside risk or standard deviation or value at risk or ... ?
>And they are ...?
Did I mention that you can search ... here?
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Anyway, I was thinking about such a definition and decided it shouldn't be called "risk" (which should imply only losses), but should be based upon both criteria noted above.
That is, the probability of larger gains as well as larger losses.
For example, which of the two stock return distributions would you think is ... uh, "riskier"? >With what definition of "risk"?
>In that case, I'd say the red stock is "riskier" ... but you really should give it another name.
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Which is riskier?
>You mean g-riskier, right? In that case, I'd say red ... that's Microsoft. But I coulda told you that without any g-risk mumbo-jumbo.
Well, yes but ...
>Besides, you're talking history, not future. I suggest you take a look at this.
Thanks ... but don't you think you'd like to avoid investments that are risky unless there's a reasonable chance of making BIG bucks?
>Investments that are risky? Define risky.
Okay, I mean investments that have a higher probability of losing money.
>Higher than what?
Higher than, say, some risk-free rate (like maybe 4%) or maybe higher than some Index, like the S&P500, or maybe ...
>Yeah, I'll go with that. I'd be prepared to accept a greater risk of loss, compared to the S&P, provided there was a good chance of getting a greater return.
Okay, then you'll like g-Risk. It compares the probability of getting a larger return (than some benchmark) to the probability of getting a smaller return.
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For example, Value at Risk or VAR considers the probability of having a return less than some benchmark return.
We want to consider BOTH: less than something and greater than something so maybe we should consider a Ratio.
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>Don't you have to assume some kind of distribution of returns?
Yeah. In VAR it's normal to assume a ... uh, normal distribution. If we continue with that "normal" assumption, but do the Ratio thing, we'd get something like 
... as we did, once upon a time, in a Risk / Reward tutorial. Notice that the integral in the denominator is the probability of getting less than some return. It's subtracted from "1" to get the probability of getting "greater" than something. >And if the returns aren't normally distributed?
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Indeed, we're interested in probabilities of getting less than something (since both integrals in numerator and denominator are animals of this ilk).
That poses the following problem:
| How to generate a mathematical distribution that mimics an actual return distribution vis-a-vis the probabilities of getting less than something |
In other words, we need a mathematically defined distribution that mimics quantiles for some actual, historical distribution.
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>Quantiles?
Yes. Consider a random variable R. We want to have a 70% probability that R is less than something. What's that something? If the distribution satisfies Pr[R < ??] = 0.70
>Huh?
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I'm thinking.
