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Greetings

So, as we discussed in the previous newsletter, I’ve been neck deep in the idea of weighting a portfolio for weeks now. That trend is going to continue today, undeterred. If any of you have explored the depths of the random threads of the server recently, you’ll see that I posted this spreadsheet recently. For those who’ve attended the calls Garen has been hosting recently, you’ll be able to piece together what it’s doing rather quickly. If you haven’t attended any of the calls (I don’t blame you, they’re in the middle of the business day) you can try to get on the list for one here if signups are still open when you read this.

Now, have you got the spreadsheet open? Good, lets take a dive through it and discuss what its doing as well as its goals.

But first, a short commercial break!

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Welcome back!

First things first, let’s cover what weighting by volatility actually means. If you've taken a high school-level statistics class, this should sound familiar, but it can serve as a good refresher. We'll be calculating Daily Volatility over the duration of the backtest. This will give us the 1 Standard Deviation, or 1Σ, value which can be used on its own or alongside the dollar value of your portfolio and the maximum amount you're willing to risk in a day. With these numbers, you can limit the "average" gains or losses your portfolio experiences to a more predictable range.

Sound good? Lets dive in!

We’ve got 2 calculators in this document. A simple strategy level, one off calculator without the frills, bells and whistles, and a much more in depth portfolio level calculator. Lets cover the “simple” one really quick, as a primer for page 2.

The “Simple Volatility Weight Calculator” is, as its name implies, simplified for use with 1 strategy at a time. All you need to give it is the Annualized Volatility of your strategy, how many dollars per day you’re willing to see it swing, the total amount you want to allocate to it. With those three, it’ll provide you with an allocation that you can use to help determine a percentage to split your allocation in to between a cash equivalent and the risk-on strategy of choice.

Now, some bullet points

Required Stats

• Annualized Volatility, AKA Standard Deviation. - This is the statistic that Composer gives you, if you don’t want to use Quantstats yet.

• Risk per day $- Money you want to risk daily OR % move you're willing to risk daily.

• Total Strategy Allocation - Total dollars you want to allocate to the strategy.

Outputs

• Daily Volatility - 1 Standard Deviation, measured per day instead of per year. This is also known as the amount that the strategy will how much your strategy will move 68% of the time.

• Allocation to Strategy $ - The dollar value you should weight to cash when you create your strategy. Mostly here as an input for the 3rd output.

• Allocation to Strategy % - The percentage you need to allocate to cash in your end strategy to achieve the desired volatility level.

So, hows the thing work?

The bullet points cover the inputs well enough, so lets focus on outputs.

Daily Volatility - This converts the Volatility Annualized metric to daily volatility by dividing the VA by √252 (square root of the average # of trading days in a year), which is approximately 15.87.

Allocation to strategy $- Take the dollars you want to risk per day, and divide it by your daily volatility. If you play around with the “Dollars to Risk per day” metric, you’ll start to see the relation between the two. It’s relatively easy (with some strategies that aren’t all that volatile) to have such a low risk appetite relative to the total amount that you want to invest that you end up not needing to have a permanent cash allocation at all. I’ve put an example of this in the stock calculator, as an example.

Allocation to Strategy % - When you go to make a strategy that is weighted like this, this is going to be the number that you paste directly into the allocation percentage of your cash equivalent of choice.

Pause, you’re using confusing math words. Explain yourself.

Gladly. If you’re on my level, its probably the Σ or standard deviation that’s getting you. Let me clarify. Σ stands for Sigma, and contrary to what the kids say these days, Sigma is shorthand for “Standard Deviation”, or volatility in this context. Standard deviation describes, roughly, the range of movement a variable stays within. 1 standard deviation is the range that the strategy will move within ~68% of the time. 2.5 standard deviation, ~95% of the time. 3 Standard deviation moves, or moves that are your defined limit x 3, will be exceeded .3% of the time. If you assume 252 days in a trading year, this works out to once every 1.3 years. So just don’t sell on your one really bad day and you’ll be fine, you pansy.

The circle with a hat is apparently lowercase sigma, with uppercase being the Σ. I learned something in the process of writing this, and hopefully you did too.

Jake, there’s a whole second page, it’s got way more inputs, and it scares me. Help

Since you asked so nicely, sure thing buddy.

Portfolio Level Assignment

Assigning a dollar amount to a single strategy is cool and all, but this math makes more sense to run on a portfolio level, at least to me. That’s where this second, far bigger and cooler calculator comes in.

Bullet points again

Required Stats

• Portfolio Amount - How much are you trying to assign across all your strategies?

• Portfolio Risk Per Day $ - How much do you want the total portfolio to move on a daily basis?

• Number of strategies in portfolio - self explanatory, how many strategies are in the spreadsheet?

• Smart Sharpe - Run a quantstats report, paste the value in here. Link to a loose explanation of the statistic.

• Smart Sortino - Run a quantstats report, paste the value in here. Link to a loose explanation of the statistic.

• Volatility Annualized, AKA Standard Deviation. - This is the statistic that Composer gives you, if you don’t want to use Quantstats yet.

• Worst Day - A statistic specifically from the Quantstats Report. The single worst day that the strategy has suffered.

Outputs

• Daily Volatility - 1 Standard Deviation, measured per day instead of per year. This is also known as the amount that the strategy will how much your strategy will move 68% of the time.

• Allocation to Strategy $ - The dollar value you should weight to cash when you create your strategy. Mostly here as an input for the 3rd output.

• Allocation to Strategy % - The percentage you need to allocate to cash in your end strategy to achieve the desired volatility level.

• Portfolio Risk per day % - What percentage move are you willing to enact? This is calculated off your total portfolio dollar value and your Portfolio Risk per Day $. This can be for the illustration of your risk, otherwise this is here mostly for calculation purposes.

• Strategy Daily Move $- The volatility normalized dollar value that represents 1 SD of daily movement for each strategy. Again, not a super important number to look at (unless you’re a total nerd like me), but is used in further calculations.

• Daily volatility - The daily move for each individual strategy, calculated from the Annualized Volatility.

• Max Allocation to strategy - This field displays the “Maximum” amount that you can allocate to the strategy and still have it move at “maximum,” the value that gets defined in B7, the “Strategy Daily Move.” This number will not add up to your defined Portfolio Allocation, this is purely an upper limit.

• Max loss from Worst Day - Finally, something important to look at. Taking the “Worst Day” statistic and the volatility-weighted allocation, we arrive at the theoretical amount your strategy would have been down on the historic worst day the strategy has had. Please, keep in mind that records exist to be broken. The more overfit, the shorter the backtest, and generally questionable the strategy is, the less you can trust this number going forward. This warning applies to all the numbers in this calculator, however.

• Portfolio Weighted Allocation - Need to work on the name, but this is the previous number, allocation to strategy, [redacted] calculated out to add up to the amount you’ve defined. This is one of the end products, the amount of money you want to assign to the individual strategies.

Now, on to the highly theoretical stuff. These columns, 3 currently, but more as I start to make use of the “Optional Stats,” are the product of a couple months of brainstorming and testing with Garen, Dereck, and myself. Dereck came up with the hypothesis that the gap between the Smart Sortino and Smart Sharpe is indicative of a frequency or tendency of a strategy to deviate to the upside. I set out to prove or disprove the idea, and thus far, I can say a couple things definitively .First, it does increase risk to reward metrics like Calmar ratio in many situations, but not all. Almost universally however, it improves things like Serenity Index, Ulcer Index, max and average drawdown, as well as many of the other less obvious downside metrics you can see in a Quantstats report. It doesn’t always make the strategy better on a pure “make me more money” basis, but if you find yourself constantly looking at your portfolio thinking you made a mistake because it’s moving 5% a day every day, this process was basically developed for you. Now, on to the columns.

• Smart Sharpe - A variation of the Sharpe Ratio that takes into account the length of the backtest. The formula is set up in such a way that as your backtest length grows, your Smart Sharpe and Sharpe will become much closer. Additionally, it takes into account the Skew and Kurtosis, two statistics that measure outliers and tail distribution, to try to normalize a stat that is likely to be skewed to the upside.

• Smart Sortino - Exactly the same explanation as above, but downside deviation instead of overall volatility.

• Smart Sharpe/Smart Sortino Weight (S/S Weight)- So this is where it gets fun. When you divide the Sharpe ratio by the Sortino, it gives you a number that centers around .5. The further above .5, the less the strategy deviates to the upside as opposed to overall volatility. The further below, the more it deviates to the upside. This gives you a way to weight your strategies according to how much they move up compared to move overall.

• S/S Weighted Allocation - After converting the above number to a percentage, this number is a product of your Volatility Weighted Allocation to Strategy divided by the S/S weight. We’re no longer limiting the strategy to the maximum volatility defined previously, but we’re continuing to refine and direct the returns upward rather than downward, but the core still effects of each strategy being brought in line remain. The more volatile a strategy overall, the lower its allocation. The less volatile, the higher. After the S/S Weight is applied, the disparity between the . Trade offs.

• S/S Portfolio Weighted Allocation - Takes the previous number and makes it add up to your defined portfolio allocation. Now, as an added bonus after this, you can take the strategies that you’ve allocated like this (assuming they all fit into a Master Symphony, you’re beat if they don’t.,) and re-run the statistics to weight for volatility and end up with both your volatility capped, and your potential for upside deviation amplified!

  Now, with the overview of the sections, what they mean, and how they work laid out, lets show off some strategies, shall we? Lets start with Page 1, strategy volatility weighting.

Now, with the overview of the sections, what they mean, and how they work laid out, lets show off some strategies, shall we? Lets start with Page 1, strategy volatility weighting.

Lets compare to the original;

Now, as you can see, huge reduction in returns, but also a massive reduction in volatility and drawdown. If you’re here for the same reasons I am, throwing as large a chunk of your money into these strategies as possible, this is exactly what I’m looking for. I’m fine with giving up some risk-adjusted returns on paper if it helps reduce the biggest risk of all.

Being a paper-handed bitch.

Seriously, I can’t handle volatility to save my life. This is going to be immensely helpful in my quest to just invest in a strategy and forget about it. I can’t stand seeing red, and big red numbers are even worse!

Now, second page.

Lets start with the fancy one first. Sharpe/Sortino ratio weighting.

With zero effort to find a basket of uncorrelated strategies to work with, it hits the 10 Calmar mark. Now lets show the comparisons.

And there we have it from the perspective of the Equal Weight version, and the trend continue. We trade returns for downside protection and stability. Is the tradeoff worth it for you? It is for me, but the final decision is yours to make.

Hopefully you found this helpful!

If you get use out of this, make sure you post the strategy up in the server, and tag me in it! I want to see the creationsyou come up with.

If you’ve made it this far, thank you for reading.

Time for some shameless plugs!

Want a one on one coaching session with Garen?

For the next few months, we’re running free one on one coaching sessions! If you’ve got questions, a topic you want to discuss, or anything to do with your algorithmic investment portfolio, pick a timeslot and schedule it!

We’re working on running strategy creation contests!

Check out the announcement post on Discord for more details!

And finally, thanks again to this weeks sponsor!

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