What are some alternative, numerical proxies for risk besides volatility?

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foodhype
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What are some alternative, numerical proxies for risk besides volatility?

Post by foodhype » Mon Jan 22, 2018 8:45 am

Academic papers often refer to volatility and risk as if they are the same thing, although volatility does not capture the whole picture. Assets that have high volatility tend to be more risky, but that is not always the case. There is no perfect measure for risk, but what are some alternative numerical proxies for risk besides volatility? And what do they capture that volatility doesn't?

golfCaddy
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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by golfCaddy » Mon Jan 22, 2018 11:10 am

In the retirement phase, SWR tells you what is the least risky strategy. Probability of running out of money seems like the best measure of risk to me.

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by dcabler » Mon Jan 22, 2018 11:17 am

Max-Drawdown is another numerical proxy for risk that is often used as is the closely related "ulcer-index".

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by willthrill81 » Mon Jan 22, 2018 11:24 am

dcabler wrote:
Mon Jan 22, 2018 11:17 am
Max-Drawdown is another numerical proxy for risk that is often used as is the closely related "ulcer-index".
Maximum drawdown is far superior, IMHO, to standard deviation as a measure of risk. The more that time goes on, the less I think that standard deviation is relevant for most investors.

People don't say "I can't take this volatility! My standard deviation was 12% last year!" Rather, they say "My portfolio dropped 22% last year!"
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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by alex_686 » Mon Jan 22, 2018 11:36 am

First, let's talk about the advantages of standard deviation. It is a generic robust theoretically solid tool. It can be used with multiple different asset classes, time frames, or secular conditions. It puts out actionable and useful predictions. It has flaws but the flaws are well known.

Semi-var, or downward volatility, is popular. Power Law and Fractal Math are other options. There is Monte Carlo, but that is more of an art than a science. However, all of these are specialized applications. i.e., for these types of assets under these types of conditions we get results. Please don't use them under other circumstances. As such there is not much academic interest in them.

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by Regressor » Tue Jan 23, 2018 8:46 am

Value at risk is one of them (often calculated as 95th percentile of the simulated pnl vector i.e. how much are you expected to lose approximately once per month if history repeats itself). Also, lower standard deviation is another, calculated similarly as standard deviation but the positive values are skipped in the calculations.

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by Valuethinker » Tue Jan 23, 2018 9:08 am

alex_686 wrote:
Mon Jan 22, 2018 11:36 am
First, let's talk about the advantages of standard deviation. It is a generic robust theoretically solid tool. It can be used with multiple different asset classes, time frames, or secular conditions. It puts out actionable and useful predictions. It has flaws but the flaws are well known.

Semi-var, or downward volatility, is popular. Power Law and Fractal Math are other options. There is Monte Carlo, but that is more of an art than a science. However, all of these are specialized applications. i.e., for these types of assets under these types of conditions we get results. Please don't use them under other circumstances. As such there is not much academic interest in them.
Does Power Law tell us anything useful? Isn't the point of a Power Law there is no scale? For any given asset both -100% and +thousands of a per cent are possible outcomes and much more frequently than the normal distribution implies?

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by Valuethinker » Tue Jan 23, 2018 9:09 am

willthrill81 wrote:
Mon Jan 22, 2018 11:24 am
dcabler wrote:
Mon Jan 22, 2018 11:17 am
Max-Drawdown is another numerical proxy for risk that is often used as is the closely related "ulcer-index".
Maximum drawdown is far superior, IMHO, to standard deviation as a measure of risk. The more that time goes on, the less I think that standard deviation is relevant for most investors.

People don't say "I can't take this volatility! My standard deviation was 12% last year!" Rather, they say "My portfolio dropped 22% last year!"
This is consistent with Actuarial Risk.

Actuarial Risk is the risk that your assets do not meet your liabilities (in the future).

It's Actuarial Risk that we all bear. (There's a mirror, the risk that we die with too much money, but for most people, that's not a big worry).

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by Theoretical » Tue Jan 23, 2018 9:54 am

Drawdowns/ulcer index for me.

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by dbr » Tue Jan 23, 2018 10:27 am

foodhype wrote:
Mon Jan 22, 2018 8:45 am
Academic papers often refer to volatility and risk as if they are the same thing, although volatility does not capture the whole picture. Assets that have high volatility tend to be more risky, but that is not always the case. There is no perfect measure for risk, but what are some alternative numerical proxies for risk besides volatility? And what do they capture that volatility doesn't?
Academic papers do not refer to volatility and risk as if they are the same thing. Academic papers define the word "risk" to mean volatility, specifically the standard deviation of returns, and they use that definition consistently from there on. Academics do not actually talk about risk "risk" in the sense of a danger or a concern at all.

I hate these discussions because everyone wants to offer their own version of what risk is without acknowledging that "risk" is a word to be defined according to what best suits the needs of a particular discussion. Academics define risk they way they do because what they are concerned with is the statistical distribution from which annual returns can be imagined to be a sample. Many such distributions are defined by naming the functional form and then can be specified exactly by putting numbers to the two parameters of mean and standard deviation. Our unloved normal distribution is one of those. A Poisson distribution does not even need a standard deviation because the SD is determined once the mean is set. Other distributions can be specified by two parameters, three, or more, and some distributions don't have a mean or a standard deviation.

Once the distribution is defined all other consequences of variability for that distribution can be calculated. That is why in this context such things as largest draw down, semi (downside) variance, etc. are actually already defined once the SD is known. It is just a question of what one wants to calculate. As far as that goes you can compute the CAGR for that portfolio, the SWR, etc. Defining risk as volatility does not prevent you from computing the output for all kind of other things if you want to, and you can hypothesize any distributions you want if you don't like the one you have.

Probably the biggest departure from doing these statistics at all is illustrated by such methodology as FireCalc, CFireSim, Otar's calculator, and some others that evaluate retirement withdrawal prospects (I will ban use of the word "risk" altogether) by just plugging in historical annual data in a list whatever the statistics of that list might be.

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by inbox788 » Tue Jan 23, 2018 11:02 am

Regressor wrote:
Tue Jan 23, 2018 8:46 am
Value at risk is one of them (often calculated as 95th percentile of the simulated pnl vector i.e. how much are you expected to lose approximately once per month if history repeats itself). Also, lower standard deviation is another, calculated similarly as standard deviation but the positive values are skipped in the calculations.
I don't understand these or know how to use them, but I've seen it reported on IB (interactive brokers) Risk Navigator page. It shows both VAR and ES, which I just looked up and is also known as CVaR (Conditional Value at Risk).

https://www.investopedia.com/terms/c/co ... t_risk.asp

I'm not sure how any of these statistical measures including standard deviation is really meaningful since we don't really have sufficient understanding or enough data. Sure, we fool ourselves thinking we have decades of data or millions of trading points, but there's a reason the disclaimer that past performance is not indicative of future results is constantly used. One market is not the same as another and one trade isn't identical to another. Sure, they are similar, sometimes for long periods of time, but then one day, it's different. We worry about outliers and want to use a measure of risk to quantify something that is inherently chaotic, and it's risky to do so.

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by JoMoney » Tue Jan 23, 2018 11:26 am

I think there are some good alternative non-numerical, less abstracted, more qualitative ideas about risks.
Having some idea of the typical price volatility has some usefulness to it... but understanding the problems of combined custody and decision making, and having independent auditors, would have helped someone looking at investing with Bernie Madoff more than knowing the Sharpe ratio of his returns.
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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by staythecourse » Tue Jan 23, 2018 11:40 am

I don't really care what academia considers risk. The only definition of risk for me is not having dollars when I need it to pay for my monthly liabilities. That's it.

For me risk gas nothing to do with what the markets do. It has all to do with not losing my job. The paycheck I get prevents anxiety about paying the mortgage or groceries or xyz.

Good luck.
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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by dbr » Tue Jan 23, 2018 11:50 am

There is nothing wrong with talking about all sorts of concerns and hazards that relate only vaguely or even not at all to the prices of investments on a market, but that is a different conversation from one about how prices of investments on a market do affect things that concern us. Both kinds of conversations can be relevant on this Forum, though being that this is a Forum about investing in a certain way in mutual funds, it would seem the concerns that relate to pricing of investments in a market would most often be the subject of conversation.

Again, it is not about disputing what is risk; it is about each specific conversation making clear what concern one wants to talk about.

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by Rowan Oak » Tue Jan 23, 2018 3:16 pm

foodhype wrote:
Mon Jan 22, 2018 8:45 am
Academic papers often refer to volatility and risk as if they are the same thing, although volatility does not capture the whole picture. Assets that have high volatility tend to be more risky, but that is not always the case. There is no perfect measure for risk, but what are some alternative numerical proxies for risk besides volatility? And what do they capture that volatility doesn't?
"Market losses are the one constant that don’t change over time — get used to it."

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by alex_686 » Tue Jan 23, 2018 3:56 pm

Valuethinker wrote:
Tue Jan 23, 2018 9:08 am
Does Power Law tell us anything useful? Isn't the point of a Power Law there is no scale? For any given asset both -100% and +thousands of a per cent are possible outcomes and much more frequently than the normal distribution implies?
I am working off of memory here. Benoit Mandelbrot, of fractal frame, came up with a power law distribution framework. He did quite a bit of fininical modeling stuff. His distribution handled fat tails better than a normal distribution. I think you are right that part of the trick is that it doen't have a traditional scale. The time from the last crisis does and does not matter.

He wrote a books and papers and got a fair amount of traction. The problem was the math was harder and the results were less universial. So better art, worse science.

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by jalbert » Tue Jan 23, 2018 5:25 pm

Volatility is not a single measure. It is the variance (or standard deviation) of return, but you have to put a timeframe on it. You can talk about variance of 1 month nominal return or variance of 40-year real return. The less one's need for portfolio liquidity, the longer the horizon in the risk measure.

Variance of 40-year real returns is probably more relevant to a retirement saver. A retirement saver hopefully requires minimal liquidity from a retirement portfolio during accumulation.

A retiree cares about shorter-term variances because they affect portfolio liquidity and avoiding withdrawals at unfavorable valuations.

Most academic work on asset returns uses fairly short term sample variance most likely because it is easy to measure, though that is unlikely to be the stated reason.
Risk is not a guarantor of return.

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by willthrill81 » Tue Jan 23, 2018 5:32 pm

Part of the problem is that measuring risk or volatility with something like standard deviation is that it can be misleading for those not familiar with its nuances.

For instance, those that say stocks are just as risky in the long-term as the short-term are referring to the standard deviation of returns*. However, many take this statement to mean that they would have been just as likely to lose money in stocks over 20 years as they would have been over one year, which is completely false.

The volatility of long-term returns is basically the difference between "Well, that wasn't as good as I hoped for, but it's still okay" and "Holy *#!%, we hit the mother-load!"

*Note: I disagree with this even as it is put forth though because mean reversion begins to level out the returns over the long-term, assuming we're talking about time-weighted returns.
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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by dbr » Tue Jan 23, 2018 5:38 pm

willthrill81 wrote:
Tue Jan 23, 2018 5:32 pm

For instance, those that say stocks are just as risky in the long-term as the short-term are referring to the standard deviation of returns*. However, many take this statement to mean that they would have been just as likely to lose money in stocks over 20 years as they would have been over one year, which is completely false.
It's a classic case of the problem can't be made simpler than it is. It is also testimony to why a statement like "Stocks are just a risky in the long term as in the short term" are useless for understanding investments or actually devising a financial plan. A statement like that is not a fact but a reference to a discussion.

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by nisiprius » Tue Jan 23, 2018 7:55 pm

I think I see consensus above, and I personally agree, with the idea that "maximum drawdown" is a better measure of risk for most investors (certainly for me) than "standard deviation." That interests me because it's easy to get both risk measures, quickly, from PortfolioVisualizer.

But is "standard deviation" a bad measure?

Do we make seriously bad judgements if we look at standard deviation, if what we are interested in is maximum drawdown?

To answer this, I'm going to try a simple experiment. Off the top of my head, I'm going to list a few funds/ETFs and ticker symbols in various categories, I'm going to choose ones that go back at least to 1/2007, and I'm going to use PortfolioVisualizer to give me the standard deviation and max drawdown for each one, and plot the two measures of risk against each other.

Here are my top-of-the-head choices. Any others?

GLD (gold ETF)
PCRIX (commodities fund)
VTSMX (total stock)
DFSTX (small cap value fund)
ULPIX (2X daily-leveraged S&P 500 fund)
FNMIX (EM bond fund)
VEIEX (emerging markets)
VGTSX (global ex-US, international stocks)
FJPNX (Fidelity Japan fund)
VBMFX (Vanguard Total Bond)
VWEHX (junk bonds)
LMVTX (Legg Mason Value Trust, once-legendary active fund)
COIN (Bitcoin ETF) -- just kidding
"CASHX" (PortfolioVisualizer's "ticker symbol" for one-month Treasury bills)

Dec 2004 - Dec 2017
Standard deviation, max drawdown

St. dev. Max drawdown
CASHX 0.50% 0.00%
VBMFX 3.22% -3.99%
VWEHX 8.19% -28.90%
FNMIX 9.59% -26.04%
VTSMX 14.18% -50.89%
VJPNX 16.80% -54.96%
VGTSX 17.65% -58.50%
LMVTX 18.04% -68.91%
GLD 18.21% -42.91%
DFSTX 18.79% -55.02%
PCRIX 19.87% -63.49%
VEIEX 22.29% -62.70%
ULPIX 27.79% -81.36%

And here's the result.

Image

The two points that are a bit off the main sequence are GLD (lower drawdown relative to standard deviation) and LMVTX (Legg Mason fund, higher drawdown relative to standard deviation).

That's a 92% correlation coefficient.

That's about as close to a perfect linear relationship as you're ever likely to see in investing data, and to me what it says is that even if maximum drawdown is a better proxy for psychological risk, the relationship between standard deviation and max. drawdown is so close that standard deviation is a perfectly good measure. To find out if you have a fever, purists may prefer rectal temperature, but temperature by mouth is a very good substitute.

Provisionally, I think standard deviation is a perfectly reasonable measure of "risk."

I think that there is a lot of deliberate obfuscation surrounding the word risk, and that very likely a more thorough examination would show that, regardless of conceptual differences, most measures of "risk" are pretty closely correlated; risk is risk.
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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by dbr » Tue Jan 23, 2018 8:17 pm

What a strange result that SD and max drawdown would be highly correlated. I would never have imagined.

PS Thanks for the data. That is very helpful.
Last edited by dbr on Tue Jan 23, 2018 8:24 pm, edited 1 time in total.

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by willthrill81 » Tue Jan 23, 2018 8:20 pm

nisiprius wrote:
Tue Jan 23, 2018 7:55 pm
I think I see consensus above, and I personally agree, with the idea that "maximum drawdown" is a better measure of risk for most investors (certainly for me) than "standard deviation." That interests me because it's easy to get both risk measures, quickly, from PortfolioVisualizer.

But is "standard deviation" a bad measure?
Thanks for the very interesting analysis.

Even though max drawdown and std. dev. are highly correlated, I'd still gravitate toward max drawdown as a preferable measure simply because it's far easier for most investors to interpret and plan accordingly.

It's like the difference between covariance and correlation. The information is the same, but correlations are far easier to interpret than covariances.
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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by AlohaJoe » Tue Jan 23, 2018 9:17 pm

foodhype wrote:
Mon Jan 22, 2018 8:45 am
what are some alternative numerical proxies for risk besides volatility? And what do they capture that volatility doesn't?
One common example of the failure of volatility as a measure of risk is someone who is using a short volatility investing strategy; using options, swaps, options on swap, and convertibles bonds and notes. A volatility strategy has the same exact mean return as the S&P 500. And the same exact standard deviation as the S&P 500. But even on Bogleheads I don't think you'll find anyone who thinks a short volatility strategy is exactly the same as just buying a S&P 500 ETF....because everyone intuitive understands the limitations of using volatility as your only definition of risk.

In most economics and finance people's preferences are represented by utility and "risk" is about maximizing that utility. (Well, it is probably better to say that risk is about minimising the times of high marginal utility. A time of high marginal utility is when you really, really care about that extra $1 and you want to minimise those times in your life.) There are different definitions of utility and those differences are captured in different utility functions.

Some of the main problems with using volatility as risk:

1. It treats upside and downside the same.
2. Only the first two moments are used. That is the mathematical way of saying that only the mean and volatility get counted, even though there are third & fourth moments like skewness that we know people also care about. This is often talked about as "tail risk" or "black swans".
3. It ignores the fact that subjective probabilities matter. I'd wager that the vast majority of Boglehead posts are about people struggling to come to terms with their subjective probabilities. ("I think the market is going to crash this year.")
4. There are "bad times" other than just being rich or poor in an absolute sense. (Say you inherit $100,000 from your mom, invest it all in Russian oil futures, and lose it all. You'll probably feel bad even if $100,000 isn't a big part of your personal wealth.)

Alternative definitions of "risk" try to handle one or more of these problems in their utility functions.

One common utility function is Constant Relative Risk Aversion (CRRA), which the "risk" is relative to your wealth. The more wealth you have, the more risk you can take because you are more financially secure. One benefit of CRRA is that is explicitly takes into account diminishing marginal utility of wealth (volatility does not).

Safety First is one of the oldest definitions of risk -- it was formalised even before mean-variance and modern portfolio theory. Liability Matching Portfolio design takes this definition of risk as its main building block. If you meet a given liability you are 100% happy. If you don't meet the liability entirely then you are 100% unhappy.

Quantile Utility Maximization is similar and what most "Safe Withdrawal Rate" backtesting is doing. Pick a percentile (say the 90th percentile) and use the results from that to inform your portfolio design. In this case you are saying "my definition of risk is that the 1 in 100 event happens again".

Loss Aversion (aka Prospect Theory) takes into account that (based on empirical research) people care about losses more than they care about gains. Obviously this is very different from volatility which treats gains and losses the same. (I believe most research suggests that losses are about 7 times more painful than gains.) There's actually a lesser known second part of Prospect Theory about decision weights which are similar to but not quite probabilities. A decision weight could be: "I assign a weight of 0.6 that it will rain tomorrow and a weight of 0.6 that is does not rain tomorrow". That doesn't add up to 1.0, so it doesn't obey the laws of probability but research shows that's how many people often think. (The way this happens in most people is they say/think/believe something like: I have a 20% chance of winning the lottery, a 20% chance of the market crashing and losing everything, and an 80% chance of just being average. That is, they overweight extreme results on both the positive and negative side.)

Disappointment Aversion is similar to loss aversion but a bit more "rational" (and mathematically better defined; using loss aversion sometimes leads to unbounded results). Upside outcomes are "elating" and downside outcomes are "disappointing" and there is some kind of endogenous reference point.

Habit Utility is a relative kind of risk. It is what most retirement planning conversations implicitly revolve around. It is also shares some similarities to loss aversion. The amount of wealth you have isn't important, only your wealth relative to a reference point. (Maybe your portfolio value on the day you retire? Maybe the value of the portfolio that you inherit?) It also captures lifestyle escalation. As wealth levels get close to the "habit level" the investor becomes more risk averse. Since the "habit level" changes over time (e.g. as you get raises, move into a bigger home, etc) then the point at which you experience risk aversion changes.

Catching Up With the Joneses is another kind of relative risk aversion. Recently there are many good examples of it with coworkers and friends telling you about all the money they made in Bitcoin and other cryptocurrencies. With this utility function what matters isn't some absolute level of return, it return relative to some peer group. (Many fund managers have a variant of this when they do closet indexing or buy all the same stocks all the other fund managers do.) This kind of utility function explains why a group of friends will all invest in some private REIT together or everyone at the country club will buy the same pharmaceutical stock.

Uncertainty Aversion is a move away from a single probability distribution to a whole universe of them. Not only do we not know the future returns...we don't even know what probability function they will be drawn from. Here we care about uncertainty and ambiguity. Using uncertainty aversion leads to significantly more conservative portfolios than many other kinds of risk. (Given how individual investors almost universally underweight equities relative to what they are "supposed" to hold, that suggests that this definition of risk is actually much more common in the real world than, say, volatility.)

In the academic literature all of these have formal mathematical definitions.

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by nisiprius » Wed Jan 24, 2018 2:30 pm

"And now for my next act..." The Sharpe ratio is sometimes criticized for measuring bidirectional risk, while the Sortino ratio measures only downside volatility. How much does it matter? How far wrong will we go using the Sharpe ratio if we don't think we should care about uncertainty in the positive direction?

Same set of funds (except CASHX for which no ratios can be calculated), same years, data from PortfolioVisualizer.

Dec 2004 - Dec 2017
St. dev. Max drawdown Sharpe Sortino
CASHX 0.50% 0.00%
VBMFX 3.22% -3.99% 0.88 1.52
VWEHX 8.19% -28.90% 0.64 0.91
FNMIX 9.59% -26.04% 0.76 1.05
VTSMX 14.18% -50.89% 0.58 0.86
FJPNX 16.80% -54.96% 0.27 0.39
VGTSX 17.65% -58.50% 0.35 0.5
LMVTX 18.04% -68.91% 0.21 0.29
GLD 18.21% -42.91% 0.47 0.75
DFSTX 18.79% -55.02% 0.51 0.76
PCRIX 19.87% -63.49% -0.03 -0.05
VEIEX 22.29% -62.70% 0.42 0.61
ULPIX 27.79% -81.36% 0.44 0.62

Image

The last point, not quite an "outlier," is VBMFX, total bond, which, relative to the Sharpe ratio has a higher Sortino ratio than the others. But... it's an 0.97 correlation between the two.

It's the commodities fund, PCRIX that has the slightly negative Sharpe and Sortino ratios, by the way.
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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by rbaldini » Wed Jan 24, 2018 4:18 pm

Someone may have already said this, but...

One measure that is somewhat useful is Probability of Loss Over [some time frame]. E.g. what's the probability that I'll have less money than I have now in 1 year? 5 years? etc. Generally speaking, the longer the timeframe, the smaller the number is - hence buy and hold. Savings account will have effectively 0 probability, bonds will have less than stocks, both less than, say, cryptocurrency. This value will tend to be correlated with the std dev but not determined by it.

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by alex_686 » Wed Jan 24, 2018 4:28 pm

rbaldini wrote:
Wed Jan 24, 2018 4:18 pm
Someone may have already said this, but...

One measure that is somewhat useful is Probability of Loss Over [some time frame]. E.g. what's the probability that I'll have less money than I have now in 1 year? 5 years? etc. Generally speaking, the longer the timeframe, the smaller the number is - hence buy and hold. Savings account will have effectively 0 probability, bonds will have less than stocks, both less than, say, cryptocurrency. This value will tend to be correlated with the std dev but not determined by it.
Question - how does one calculate this number? I would suspect that it would be with standard deviation. So while it might be presented differently we are stuck with the same old number.

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by rbaldini » Wed Jan 24, 2018 4:30 pm

nisiprius wrote:
Tue Jan 23, 2018 7:55 pm
Provisionally, I think standard deviation is a perfectly reasonable measure of "risk."

I think that there is a lot of deliberate obfuscation surrounding the word risk, and that very likely a more thorough examination would show that, regardless of conceptual differences, most measures of "risk" are pretty closely correlated; risk is risk.
For the most part, in practice, you're right. But of course in theory one could be misled by std dev.

Consider two investments. Both are normally distributed in returns, and uncorrelated random walks. Investment A returns mean of 20% with 8% standard deviation annually. Investment B returns mean of 5% with 4% deviation annually. What's less risky?

You might say "Investment A has twice the standard deviation of Investment B. More volatility. It's riskier." But by the assumptions I wrote, Investment A will only lose money 0.6% of the time, whereas Investment B would lose money 10.5% of the time. There's basically no downside risk to A, despite the greater volatility. A is the better investment, hands down.

Now, in reality, if this were true, then Investment B would surely cease to exist, because no one would make that investment. So it seems unlikely that such a scenario would ever arise. Your analysis of the data demonstrates this.

rbaldini
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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by rbaldini » Wed Jan 24, 2018 4:34 pm

alex_686 wrote:
Wed Jan 24, 2018 4:28 pm
Question - how does one calculate this number? I would suspect that it would be with standard deviation. So while it might be presented differently we are stuck with the same old number.
Measure it empirically. Look at a bunch of years in the past, count up the number that are below 0, and divide by total number of years.

Calculating quantiles from a standard deviation requires that you make an assumption about the distribution of the data. A common one is normality, but that may not be valid. The empirical method above doesn't require that assumption - it's an estimate that is reasonably appropriate regardless of the distribution. (That doesn't mean it will be "right" or "good" - just that it doesn't imply extra assumptions - well, apart from the assumption that "the future will be something like the past", of course).

Even if you do assume normality, the probability of loss isn't determined solely by the standard deviation. It's also determined by the mean. So it wouldn't be just the same old number. Though, in reality, it may be that these things are strongly correlated, as others have shown.

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patrick013
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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by patrick013 » Wed Jan 24, 2018 4:38 pm

While price beta and standard deviation are quite pragmatic
in measuring common volatility or at least getting a numerical
measure.....here is some other related theory.


When you create negative correlation in your portfolio, you have
done what's called “portfolio hedging.” Hedging can result in the
most effective way to reduce risk. However, it can also produce
negative returns in profitable times. The most diversified port-
folio consists of securities with the greatest negative correlation,
with perfect negative correlation risk in theory would be eliminated.

A diversified portfolio can also be achieved by investing in a
portfolio of uncorrelated assets, but there will be times when the
securities will be both up or down, and therefore, a portfolio of
uncorrelated assets will have a higher degree of risk than a port-
folio of negatively correlated assets, but it is still significantly
less than positively correlated investments.

Positively correlated investments will be less risky than single
assets or investment groups that are perfectly positively correlated.
There is no reduction in risk with portfolio assets that are per-
fectly correlated.
age in bonds, buy-and-hold, 10 year business cycle

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Re: What are some alternative, numerical proxies for risk besides volatility?

Post by foodhype » Wed Jan 31, 2018 10:57 pm

I think nispirius's argument is the most compelling. Even though volatility may not be as "meaningful" or intuitive to an investor as something like maximum drawdown or the ulcer index, it is so highly correlated with the other risk metrics in the real world that it's "good enough" as a measure of risk. If the maximum drawdown is high, so is the volatility in the overwhelming majority of cases. If the ulcer index is high, so is the volatility in the overwhelming majority of cases.

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