Add-StdDev-of-Returns-to-a-ScoreCard

Standard deviation of daily/weekly/monthly returns is part of the finantic ScoreCard extension. You're advised to use the already existing feature.

Also, its scriptable performance metrics come to help when you need to restate some existing metric in a way that interests you.

This is a core metric, it should *not* be omitted from WL's own Metrics Report.

Sure, you have the right to have a different opinion but if something is already coded, it's not appreciated to request a remake of the friendly developer's job.

This is a CORE metric. It deserves a place in the software's own Metrics Report.
If other developers want to display it, or a variation thereof, I have no issue with it but that cannot be in lieu of the software's own responsibility.
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I see that this issue has been marked as Declined and removed from the Wishlist.
Kindly restore it to the Wishlist and let users vote on it. If there aren't 10 votes after 6 months you can then mark it as Declined - that would be OK with me.

This is just one of the many metrics. Kudos to @DrKoch who has already implemented it for you.

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QUOTE:
Kindly restore it to the Wishlist and let users vote on it. If there aren't 10 votes after 6 months you can then mark it as Declined - that would be OK with me.

It looks like you're comfortable with setting your own rules. How about fair play so that they work both ways? If a user has submitted 10 feature requests, suspend further petitions from her/him for 6 months or more to let the queue clear up. Our resources shall not belong to a single user repeatedly requesting features to be added to WL8 which appear to have been implemented in 3rd party extensions.

There are some inconsistencies here. You say you'd like the geometric mean, but the Sharpe Ratio uses the arithmetic mean (it's not a Geometric Sharpe Ratio.)

Also our Sharpe Ratio is calculated based on monthly returns, not yearly.

The StdDev on the Periodic Returns tab is calculated on the arithmetic mean of the annual returns.
The proper way is to calculate it on geometric returns - monthly or yearly.

And why is that “proper?”

Different ways to calculate Standard Deviation of Returns

1. StdDev using arithmetic mean of annualized returns
- simple, easy to understand and calculate
- however, using average of annual returns that are compounded, such as investment returns, is not accurate
https://www.investopedia.com/articles/08/annualized-returns.asp
e.g. hypothetically if you have +100% return one year and -100% the next year then the arithmetic mean of returns is: (100 + (-100))/2 = 0% which we all know is wrong.

2. StdDev using Log Returns or Geometric Returns
- StdDev is calculated using either geometric mean (Compound Annual Growth Rate/CAGR, aka APR in WL) or log returns; not sure which one WL uses for calculating the Sharpe Ratio (I suspect it's the latter) but either is preferred over using arithmetic mean.
Furthermore (and simplifying things):
CAGR / StdDev of Returns = Sharpe Ratio
CAGR * (1 - StdDev of Returns) = Risk-adjusted CAGR (https://www.investopedia.com/investing/compound-annual-growth-rate-what-you-should-know/)
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Other useful articles and text snippets from them:

https://www.kitces.com/blog/volatility-drag-variance-drain-mean-arithmetic-vs-geometric-average-investment-returns/
In the investment world, it’s common to discuss average rates of return, both in a backward-looking fashion (e.g., to report investment results), and in a more forward-looking manner (e.g., to project the average growth rate of investments for funding future goals in retirement planning software). However, the reality is that because returns are linked to each other – the return in one year increases or decreases the available wealth to compound in the subsequent year – it’s not sufficient to simply determine an “average” return by adding up all the historical returns and dividing by how many there are.
Instead of this traditional “arithmetic mean” approach to calculating an average, in the case of investment returns, the proper way to calculate average returns is with a geometric mean, that takes into account the compounding effects of a series of volatile returns over time.


https://www.investopedia.com/articles/investing/071113/breaking-down-geometric-mean.asp
- The arithmetic mean can be used to evaluate data, but it doesn't consider compounding.
- A geometric mean helps you evaluate investment returns based on the number of periods you've held it and how much it has returned over time.
- The geometric and arithmetic mean may be similar if investment returns do not fluctuate greatly.
- If investment returns vary highly, the arithmetic and geometric means will be very different.
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Please add StdDev of Returns to the Metrics Report as its a Core metric.

@Glitch
I'm interested as well, as I'm calculating the StdDev by a Custom ScoreCard Control, but using both approaches. Out of your experience, which of the two is the correct one and why?

I don't have any experience with the geometric version, have only ever used the arithmetic. My gut feeling is that since we’re already taking the StdDev of PERCENTAGE returns an arithmetic average and StdDev makes the most sense.

To back up this feeling:

https://machinelearningmastery.com/arithmetic-geometric-and-harmonic-means-for-machine-learning/#:~:text=The%20arithmetic%20mean%20is%20appropriate,with%20different%20measures%2C%20called%20rates.

"The arithmetic mean is appropriate if the values have the same units, whereas the geometric mean is appropriate if the values have differing units."

AND

"The geometric mean does not accept negative or zero values, e.g. all values must be positive."

Let’s take a simple example. If I have three months of returns 5%, 2% and -1% then my arithmetic mean is 2%. What is my geometric mean? It makes no sense to use geometric mean for this purpose.

QUOTE:

"The geometric mean does not accept negative or zero values, e.g. all values must be positive."

This is how I transform negative and zero % values.

CODE:

        private double CalculateGeometricMean(List<double> values)
        {
            double geometricMean, multipliedPl;

            multipliedPl = 1.0;
            foreach (double value in values)
                multipliedPl *= ((value / 100) + 1);

            geometricMean = Math.Pow(multipliedPl, (1.0 / (double)values.Count));
            return geometricMean;
        }

Don’t you need to untransform the result? I’m getting a number that doesn’t make sense for the sample set.

QUOTE:
"The geometric mean does not accept negative or zero values, e.g. all values must be positive."

[link]https://www.investopedia.com/articles/08/annualized-returns.asp[/link]
How to Calculate Your Investment Return:
...
" The Compound (Geometric) Average
Just by noting that there are dissimilarities among methods of calculating annualized returns, we raise an important question: Which option best reflects reality? By reality, we mean economic reality. In other words, which method will show how much extra cash an investor will have in his or her pocket at the end of the period?

Among the choices, the geometric average (also known as the "compound average") does the best job of describing investment return reality. To illustrate, imagine that you have an investment that provides the following total returns over a three-year period:
Year 1: 15%
Year 2: -10%
Year 3: 5%

To calculate the compound average return, we first add 1.00 to each annual return, which gives us values of 1.15, 0.9, and 1.05, respectively.

We then multiply those figures together and raise the product to the power of one-third to adjust for the fact that we have combined returns from three periods.
(1.15)*(0.9)*(1.05)^1/3 = 1.0281

Finally, to convert to a percentage, we subtract the 1 and multiply by 100.
In doing so, we find that we earned 2.81% annually over the three-year period.

Does this return reflect reality? To check, we use a simple example in dollar terms:
Beginning of Period Value = $100
Year 1 Return (15%) = $15
Year 1 Ending Value = $115
Year 2 Beginning Value = $115
Year 2 Return (-10%) = -$11.50
Year 2 Ending Value = $103.50
Year 3 Beginning Value = $103.50
Year 3 Return (5%) = $5.18
End of Period Value = $108.67

If we simply earned 2.81% each year, we would likewise have:
Year 1: $100 + 2.81% = $102.81
Year 2: $102.81 + 2.81% = $105.70
Year 3: $105.7 + 2.81% = $108.67

The Simple Average
The more common method of calculating averages is known as the arithmetic mean, or simple average. For many measurements, the simple average is both accurate and easy to use. If we want to calculate the average daily rainfall for a particular month, a baseball player's batting average, or the average daily balance of your checking account, the simple average is a very appropriate tool.

However, when we want to know the average of annual returns that are compounded, the simple average is not accurate. Returning to our earlier example, let's now find the simple average return for our three-year period:
15% + -10% + 5% = 10%
10%/3 = 3.33%

Claiming that we earned 3.33% per year compared to 2.81% may not seem like a significant difference. In our three-year example, the difference would overstate our returns by $1.66, or 1.5%. Over 10 years, however, the difference becomes larger: $6.83, or a 5.2% overstatement. As we saw above, the investor does not actually keep the dollar equivalent of 3.33% compounded annually. This shows that the simple average method does not capture economic reality."
======================================

[link]https://www.investopedia.com/articles/investing/071113/breaking-down-geometric-mean.asp[/link]
Breaking Down the Geometric Mean in Investing:
...
" Example 2
An investor holds a stock that has been volatile, with returns that varied significantly from year to year. His initial investment was $100 in stock A, and it returned the following:
Year 1: 10%
Year 2: 150%
Year 3: -30%
Year 4: 10%
In this example, the arithmetic mean would be 35% [(10+150-30+10)/4].

However, the true return is as follows:
Year 1: $100 x 1.10 = $110.00
Year 2: $110 x 2.5 = $275.00
Year 3: $275 x 0.7 = $192.50
Year 4: $192.50 x 1.10 = $211.75
The resulting geometric mean, or a compounded annual growth rate (CAGR), is 20.6%, much lower than the 35% calculated using the arithmetic mean."
...
"...the arithmetic mean tends to overstate the actual average return by a greater and greater amount the more the inputs vary."

QUOTE:
If I have three months of returns 5%, 2% and -1% then my arithmetic mean is 2%. What is my geometric mean?

To calculate Geometric Mean
Convert % to decimals:
0.05, 0.02, -0.01

Add 1.00:
1.05, 1.02, 0.99

Multiply and raise to power of 1/3 (as we have 3 values):
(1.05 * 1.02 * 0.99) ^1/3 = 1.06029 ^1/3 = 1.01970

Subtract 1.00:
1.01970 - 1 = 0.01970

Multiply by 100 to get Geom. Mean as % = 1.97%
===============================

Let's verify (numbers rounded to 2 digits for simplicity)
Actual Returns:
100 + 5% = 105
105 + 2% = 107.10
107.10 -1% = 106.03

Returns calculated using Geometric Mean (calculated above):
100 + 1.97% = 101.97
101.97 + 1.97% = 103.98
103.98 + 1.97% = 106.03
===============================

Arithmetic mean = 2.00%
Geometric mean = 1.97%

Thanks for the examples!

Here is a prototype of my Custom ScoreCard Control. This shows the behavior described in "Breaking Down the Geometric Mean". I'm not an expert with such things but fact is, the more volatile the annual profit is, the more deviant the Geo Mean StdDev will be.

CODE:

static double CalculateGeometricMean(List<double> yearlyReturns)
{
    double geometricMean, multipliedPl;
    multipliedPl = 1.0;
    for (int i = 0; i < yearlyReturns.Count; i++)
    {
        Console.WriteLine("Year {0}: {1}", (i + 1), yearlyReturns[i]);
        multipliedPl *= ((yearlyReturns[i] / 100) + 1);
    }
    geometricMean = Math.Pow(multipliedPl, (1.0 / (double)yearlyReturns.Count));
    return geometricMean;
}

static double CalculateStandardDeviation(List<double> yearlyReturns, bool useGeometricMean)
{
    double stdDevOut = 0;
    if (yearlyReturns.Any())
    {
        double avg = 0.00;
        avg = useGeometricMean ? CalculateGeometricMean(yearlyReturns.ToList()) : yearlyReturns.Average();
        double sum = yearlyReturns.Sum(x => Math.Pow(x - avg, 2));
        stdDevOut = Math.Sqrt((sum) / yearlyReturns.Count());
    }
    return Math.Round(stdDevOut,2);
}

static void Main(string[] args)
{
    Console.WriteLine("\nSteady Performance:");
    List<double> steadyReturns = new List<double> { -2.09, 4.55, 4.73, 3.74, 9.11, 5.36 };
    Console.WriteLine("StdDev(G) = {0} \nStdDev(A) = {1}", CalculateStandardDeviation(steadyReturns, true), CalculateStandardDeviation(steadyReturns, false));

    Console.WriteLine("\nVolatile Performance:");
    List<double> volatileReturns = new List<double> { -9.09, 64.55, 194.73, 53.74, 159.11, 75.36 };
    Console.WriteLine("StdDev(G) = {0} \nStdDev(A) = {1}", CalculateStandardDeviation(volatileReturns, true), CalculateStandardDeviation(volatileReturns, false));
}

I'll go ahead and add these to the standard metrics report.

But I'm finding sources saying that Geometric Means/StdDevs are not preferred for Sharpe calculations, arithmetic calculation is the way to go. Let's leave our Sharpe calculations as they are for the time being at least.

https://longspeakadvisory.com/arithmetic-vs-geometric-mean-which-to-use-in-performance-appraisal/#:~:text=As%20a%20result%2C%20for%20measures,arithmetic%20mean%20than%20geometric%20mean.

"Because risk is already being accounted for in the denominator, there is no need to include it in the numerator; in fact, including it would be double-counting the risk taken. As a result, for measures like Sharpe Ratio, it is more appropriate to use the arithmetic mean than geometric mean."

I think some confusion has crept into this thread. Let me try to de-confuse (is that even a word?):

@Springroll
There is actually such a thing as Geometric Standard Deviation (https://en.wikipedia.org/wiki/Geometric_standard_deviation). I think your method CalculateStandardDeviation, when using Geom. Mean, may be calculating that. But that's NOT what I've been talking about, let me clarify.....
StdDev of Returns is calculated around a mean value (say, X) and it uses simple (not geometric) mean to measure variance around this X which is perfectly OK. The central question is which mean do you use for X? The Periodic Returns tab in the Backtest uses the arithmetic mean but the proper way is to use the Geom. mean as only that takes into account the compounding inherent in investment returns.
In other words, StdDev should be calculated around the Geom. mean 'X' value and the averaging inherent in StdDev calculations should use arithmetic (not geometric) mean of deviations from X.
{It is this calculation that I would very much like to be added to the Metrics Report. As for the Periodic Returns tab it can be left as is as an 'alternate' calculation.}


@Glitch
Sharpe Ratio formula (simplified): Portfolio Return / StdDev of Portfolio Return

I looked at your link. The author is an investment advisory firm which naturally has a vested interest in inflating the Sharpe Ratio and as we know well by now for investment returns the arithmetic mean is always >= geom. mean so they're pumping its use in the numerator (incidentally, even they have no issue with the use of geom. mean in the denominator).
But let's pause for a moment. For calculating Sharpe Ratio I believe WLab uses APR (CAGR) in the numerator - and correctly so - so that's not even up for debate (and thus this firm's - already wrong - opinion instantly goes out the window).
Its the denominator we're focused on - and that ought to be calculated around the Geom. mean, not arithmetic.
==============================

Some additional references, completely unbiased:
1) https://quant.stackexchange.com/questions/3607/should-i-use-an-arithmetic-or-a-geometric-calculation-for-the-sharpe-ratio
Should I use an arithmetic or a geometric calculation for the Sharpe Ratio?
Caution: Has a lot of geeky stuff!

2) https://quant.stackexchange.com/questions/21449/risk-adjusted-performance-measurement-log-returns-vs-simple-returns-and-geomet
Risk-adjusted performance measurement: Log returns vs. simple returns and geometric vs. arithmetic mean return
(...since stock prices, and therefore Investment Returns, are lognormally distributed...)
...for calculating risk adjusted measures in your case would be: unless you can prove, graphically or by statistical testing, that your weekly returns are lognormal, go with geometric averaging of simple percent changes. This will allow for (1) compounding and (2) better interpretability. Arithmetic averaging will give you wrong results when compounding.

3) If you love math, this reference is for you!
https://en.wikipedia.org/wiki/Rate_of_return
==============================

Hope I managed to de-confuse. If not, its all on me.

To get back to the original point, was your desire to have the Geometric Mean of annual returns, and the Arithmetic Std Dev in the Metrics report?

Because as of now I added the Geometric Mean and the Geometric Std Dev.

Arithmetic StdDev of Annual % Returns* around the APR - the latter represents the Geometric Return.
And right below the APR, please.

*If APR annualizes partial year's returns then so too should StdDev, o/w not.
Added 7/15/23, 8:15am EST:
All values required for StdDev calculation already exist - APR on the Metrics Report tab and Annual Returns on the Monthly Returns tab.

Thank you so, so much for implementing this in B40 !!!