January 8, 2020

Inverse Volatility Position Sizing

Recently I’ve had several of my consulting clients come with a strategy that uses Inverse Volatility Position Sizing. The basic idea is that the more volatile positions have smaller size while the less volatile ones get a larger size. I have always been a fan of equal position sizing for several reasons. One, it is simple to do. Two, it is one less variable to optimize on and thus overfit on. Three, I rarely see much change in the metrics I care about when using more sophisticated algorithms.

Inverse Volatility Position Sizing is said to slightly reduce returns but has a big decrease in drawdowns and an increase in Sharpe Ratio. Time to test and see if that is true.

Recently I wrote about a monthly rotation strategy. I will be using that as a base to compare against.

 

Inverse Volatility Position Sizing Calculation

As a measure of volatility I will be using historical volatility.

  1. Calculate the historical volatility for each stock to get HV
  2. Take the inverse of the HV to get INV_HV. This means INV_HV = 1/ HV
  3. Sum all the INV_HV for the stocks to get TOTAL_IHV
  4. Position size for a stock is its INV_HV/TOTAL_IHV

 

Example

Three stocks in our EXPE, MSFT, NFLX. We will be using 100-day Historical Volatility

Step 1 – Calculate HV

EXPE HV100 = 55

MSFT HV100 = 19

NFLX HV100 = 32

Step 2 – Invert

EXPE INV_HV = 1/55 = .0182

MSFT INV_HV = 1/19 = .0526

NFLX INV_HV = 1/32 = .0313

Step 3- Sum INV_HV

TOTAL_IHV = .0182 + .0526 + .0313 = .1021

Step 4 – Calculate Position Size

Position Size for EXPE = INV_HV/TOTAL_IHV = .0182 / .1021 = 18%

Position Size for MSFT = .0526 / .1021 = 52%

Position Size for NFLX = .0313 / .1021 = 31%

 

With this example, we run into one issue I have with this sizing method. Look at the position size of MSFT vs EXPE. It is 3 times bigger.

 

The Rules

Test date range 1/1/2007 to 11/30/2019.

Buy Rules

  • It is the last day of the month
  • Stock is a member of the Nasdaq 100. I test several others.
  • Close is above the 200-day moving average
  • The close of the $SPX is above the 200-day moving average
  • Buy the top 5 highest priced stocks on the next open

The price I am using is the as traded price. This is the price before it has been adjusted for splits and dividends. This is the price you would have seen on your screen at the end of the day.

Sizing: Equal position sizing (EPS). Inverse volatility sizing (IVS) using [5, 10, 15, 20, 25, 50, 100, 125, 175, 200] day historical volatility.

Sell Rules

  • It is the last day of the month
  • Sell on the next open

 

The Metrics

Since the general claim is that risk is reduced, I will be focusing on Maximum Drawdown, Ulcer Index and Sharpe Ratio. But keeping an eye on Compounded Annual Growth Rate.

Nasdaq 100 Results

The grey row is EPS. Green cells are the best for that metric. The change in results from EPS and IVS are small. EPS had the best drawdown. The Sharpe Ratio improved by 5%, which is noise in my book. I am not seeing any real improvement in the risk numbers for the extra work.

Russell 3000 Results

Maybe a different index would produce different results

Again, seeing very little change in the results. Drawdown is better with EPS. With IVS, Ulcer Index is unchanged and Sharpe Ratio is 2% better. Again, the difference in the results is noise.

Spreadsheet

Fill in the form below to get the spreadsheet with lots of additional information. Included are results for Russell 1000 index and for a maximum positions of 10. See the results of all variations from the optimization run. This includes top drawdowns, trade statistics and more.

Final Thoughts

These results are what I have generally seen in my other tests. Maybe small improvements in the risk metrics but they are often less than 5% better. Is it worth all the extra work? I don’t like that this gives even more variables to potentially overfit the data with. In this example, two, the chosen volatility formula and the length of the lookback.

Another reason I do not like IVS is that even low volatility stocks can quickly crash. Meaning this sizing can get you into a large position in a low volatility stock that then crashes overnight.

Maybe a month Is not enough time for Inverse Volatility Sizing to show its benefits? Maybe a better measure of volatility would help.

Maybe IVS works well with your strategy. As I like to say “test everything.” Share your thoughts below.
Backtesting platform used: AmiBroker. Data provider: Norgate Data (referral link)

Good quant trading,

Fill in for free spreadsheet:

spreadsheeticon

 
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Ryan Watson - January 9, 2020 Reply

I have always preferred equal position sizing and never really understood why volatility position sizing is all the rage in the trading community. I always think that I’m missing something but never see the return versus the extra work (or risk?) as you mention.

There was a brief mention about MSFT v EXPE being 3 x bigger. This is a good example of needing rules with some positions getting really big due to low vol with the risk that those low vol positions could be the high vol positions tomorrow.

I’ll keep looking at vol position sizing but as per your article, I’m still not convinced of significant value add versus extra work required.

Cheers,
Ryan

    Cesar Alvarez - January 9, 2020 Reply

    I am hoping someone points out a situation where there is a big improvement. Because like you, I have not found a case where the extra work and complexity seem to make it worthwhile.

MARCO SIMIONI - January 10, 2020 Reply

I agree with you Ryan and Cesar, I would expect greater results too! Anyway backtesting work many times results in unexpected outcomes. The Turtles used an ATR based position sizing strategy. That was good.
But it was ATR not volatility.
Thanks Cesar,
Marco Simioni
https://nightlypatterns.blog

Rick - January 12, 2020 Reply

Hi Cesar,

It is impossible this strategy for Nasdaq 100 and with EPS has CAR 19.29% in the period of your test.

You are either not using delisted securities correctly or something else is wrong.

Why are you starting test in 2007? If you have delisted series you can start earlier say in 2000. The longer the test the better.

In process of contacting a few quants to have them check your results. I like to think they are correct but a quick test with current Nasdaq series shows 19% CAR so the delisted cannot be that high also.

    Cesar Alvarez - January 12, 2020 Reply

    It is always possible that I made a coding mistake. I am using delisted stocks. Why did I start in 2007? I wanted to cover a bear market and a bull market. Why did I not go back farther in time? I believe that farther you go back the more markets are different from how they are today. You suggested 200. Why not 1990?

    I have seen using delisted stock increase and decrease results.

    If you find significantly different results, I would love to know.

James - February 6, 2020 Reply

Hi Cesar,

Thank you for your blog articles, always great to read.

Two areas that I found inverse volatility increased the risk-adjusted returns were on fixed income ETFs across short, intermediate and long-term fixed income markets and on tactical asset allocations strategies across equity, fixed income, commodity and alternative ETFs. This might be something worth looking at, in my experience the improvement on fixed income only ETFs was greater than on the tactical asset allocation ETFs.

In my testing for individual equities, I found that inverse volatility had little impact, perhaps because equity volatility within an equity index might be very similar whereas the volatility between short, intermediate and long-term fixed income may be greater.

Cheers,

James

    Cesar Alvarez - February 6, 2020 Reply

    Thanks for sharing where this has worked for you. I will have to test that.

Dario Martinelli - May 18, 2020 Reply

Can you please share the custom backtester algorithm to recreate ivs on amibroker? I am a novice and I am learning cbt and I cannot imagine how to correct the weight of the trades in ivs mode. Thanks in advance.

    Cesar Alvarez - May 19, 2020 Reply

    This is complicated code to do. You can use my consulting services to get the code. Click here for more info

Ken - April 25, 2024 Reply

Hi Cesar:

I have long enjoyed your thoughtful approaches to trading.

Position sizing is an art in itself. I use IVP to rank order trade vehicles (i.e. ETF’s and individual stocks) and size them using Linear Sized trades (A,B,C,D = 4,3,2,1) or Exponential Sized Trades (A,B,C,D = 8,4,2,1). This is a little simpler approach to position sizing and has worked for me.

Regards,
KEN

    Cesar Alvarez - April 26, 2024 Reply

    Thank you for sharing. I will have to get it a try.

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