*Warning. This post is kind of a finance geek out. I’ll try and keep it as basic as possible but I apologize in advance if I cause any heads to hit the keyboard…*

In this post I’ll take a look at impact and potential benefits of adding volatility weighting and mean-variance optimization to tactical asset allocation portfolios similar to the IVY (GTAA) portfolios I discuss frequently on the blog. Most of the data and theory I present here comes from this great paper on Adaptive Asset Allocation. If you have any interest in applying the concepts here to your portfolio it’s a must read.

The basic theory here is the short-run estimates of returns, volatility, and correlation are better predictors than longer term estimates of the same parameters over most investor time frames. By using these short run estimates, portfolios can exhibit much better results than otherwise. For example, on the return side GTAA portfolios use momentum to weight the portfolio towards assets that are currently outperforming. This in contrast to having a constant weight to stocks, say 60%, because long term estimates of returns say that this is where we should be invested. We can use similar concepts for volatility and correlation to achieve better results. Lets begin.

The diversified portfolios used for this study all consist of 10 assets classes studied from 1995 to 2012: US stocks, European stocks, Japanese stocks, Emerging market stocks, US REITs, International REITs, US intermediate treasuries, US long treasuries, Commodities, and Gold. The first optimization is to use momentum to weight the portfolio to the best recent performing asset classes. Here only 6 month returns are used as opposed to average momentum used by the IVY portfolios. Momentum is a very strong factor and works when applied in many ways. The top 5 assets classes by 6 month return are bought each month in equal weights. Lets look at these results first.

As with the IVY portfolios, just using momentum works exceedingly well to increase returns and lower risk. But we still have quite a bit of volatility and drawdowns. Volatility weighting uses short run estimates of volatility to change the weights of the assets in the portfolio. The simplest method, without using leverage, is to reduce the weighting of the assets when they exhibit large volatility. Here we use daily returns over the last 60 days to generate our short term volatility estimates. The calculation is pretty simple and is included in the paper. I’ve also added it to my GTAA 13 portfolio tracking sheet which you can find here. Basically, the target is a 1% daily volatility for each asset class. If the asset class exhibits higher volatility over the preceding 60 days it’s weight is reduced in the portfolio. In the results below, I show a pure comparison of volatility weighting with equal weighting and then show volatility weighting combined with momentum.

Impressive results. As the table above shows volatility weighting alone mainly improves risk, sharpe ratios and drawdowns. Combined with momentum you get slightly lower returns than pure momentum alone but with lower drawdowns and a higher sharpe ratio as well. But we can do even better, albeit with an add in complexity. Volatility of assets classes matters, but in portfolios what matters even more is how assets move together, or the correlation of returns among the assets. This is the whole theory of diversification. Certain assets like stock and bonds tend to move in opposite directions. But just like returns and volatility these correlations can change and vary wildly over time so we’re better off using shorter term estimates of correlations to weight asset classes. Let’s see how we go about doing that.

Just like with volatility, we need to look at the last 60 days of returns for the asset classes. Then for whichever assets are in the portfolio we need to put together a covariance matrix, a table that tells us how these assets have ‘moved’ together over the last 60 days. Then we use these covariances to calculate the volatility of the overall portfolio. I’ve done this for the GTAA AGG3 and AGG6 portfolios that I track in the spreadsheet I linked to above. Here is the most recent snapshot.

For the AGG3 portfolio the most recent 60 day covariances yield a portfolio volatility of 6.8% annualized with an equal weight of the top 3 asset classes. This will change every month. Now, we can do a couple of things. We can use Solver in excel (unfortunately the Google Sheets version won’t work for this) to either calculate the portfolio weights that give us the minimum volatility or better yet we can choose an acceptable level of volatility we’re willing to take and calculate the portfolio weights that yield this volatility. For example, if I put the above covariances for AGG3 into solver and target an 8% annual portfolio volatility I get portfolio weights of 58.5% for VNQ, 20.2% for VGLT, and 21.3% for MTUM. Quite different from an equal weighting. How does this kind of optimization perform over time. Below I’ve summarize all the optimizations we’ve discussed.

The mean variance optimization gives us similar risk to the volatility weighting but about 1.6% extra points in annual returns. Is it worth it? That’s a very personal decision and is up to the individual investor. The good thing is once you master these calculations these changes are applied only once a month just like the all the GTAA signals and triggers.

That’s about it. Here I’ve showed how incorporating short term estimates of volatility and correlations can be used with the well known momentum factor to increase returns and reduce risk in portfolios.

*Full Disclaimer - Nothing on this site should ever be considered advice, research or the invitation to buy or sell securities. These are my personal opinions only.*

Bringing it to a whole new level Paul, I love it. Seems like the extra effort up front is totally worth the increase to Sharpe ratio. Great work and it intuitively makes sense, which is also reassuring. I think I’ll give it a go!

I figured you would Jeff.

Paul

Nice work. I have just recently discovered your blog and it is a fantastic resource that has really opened up my eyes to ETF rotation strategies.

I think I may have fixed a small bug in your spreadsheet on the voltable on the GTAA 13 AGG page -:

https://docs.google.com/spreadsheet/ccc?key=0Ao9NNtrFQP_zdEFUWDhzTGdaUWNQc0t2RlctYnBoWGc&usp=sharing

Thanks David. I’ve made a couple of changes and moved the vol table to another location.

Paul

I appreciate the research that Mike, Adam and Rodrigo have published over the past few years. However, for my own ETF momentum model an equal weight (1/n) weighting works better than a MVO weighting. A number of academic papers reach the same conclusion. The difference in findings may lie in the assets used and the timeframe. In your analysis, you used a timeframe in which interest rates were falling and bond prices were rising. I suspect that the weighting process you used resulted in higher weights for bonds than a 1/n weighting.

In my opinion, you have to go back to at least the early 1970’s and run this analysis to determine if anything beats a 1/n weight.

All good points. I’m skeptical of anything that doesn’t go back to prior to the great depression, 1929ish. All modern asset allocation decisions are done with data that at best goes back to 1973ish. Bar the first few years, the entire period was one of falling rates, and exceptional stock returns to boot. We’re all swimming at least half blind….

Personally, I also use 1/n weighting as well in my real money momentum portfolios and am just tracking vol and mov weighting.

I use an moving average overlay as well which I think may make at least vol weighting moot. Moving average overlays are a function of momentum but have some differing characteristics as well.

Paul

Great post again , Thanks for all the hard work. When looking at your last 2 post ; Bond and using momentum and Ivy Agg(3) or Here with a choice of 10 Diversified portfolio Sectors , is there a good way from a more Marco view to choice how to allocate your total portfolio ? Or do you equal weight the best 4 or 5 systems and rebalance yearly .?

thanks

John, great question. And I don’t have a systematic answer. My approach evolves over time. Currently, I run AGG3/6 systems, several quant stock models, a passive bond portfolio, Bond momentum model, plus a cash allocation for short term purposes. My plan is to migrate all my bond allocation to the bond momentum model over time and use automatic systems for 100% of my portfolio. My overall goal is to have a portfolio that targets approx 10-15% is maximum annual drawdowns since that’s what matters for retiree portfolios.

Paul

Hi Paul,

been following your blog (quietly on the sidelines) since i stumbled into your WheelingIt site last year. I have a financial background and am impressed by your research and knowledge, along with the ability to clearly explain fairly complex financial jargon. I have been studying Adaptive Asset Allocation lately and am impressed with how it improves returns, while mitigating risk. You did a great job of condensing and explaing Butler’s 29-page white paper into your blog. Curious why you left off the last model with a target volatility (8%) with the portfoloio being rebalanced on a weekly basis (exhibit 6). Assuming the weekly was not mentioned to avoid trading costs, but the increase in CAGR to 16.91% and max daily drawdown to -9.56% were impressive changes. Interested in your thoughts.

Keep up the great work!

Thanks

Mark

Thanks Mark. I left the last model out for a few reasons. One, the weekly rebalance I don’t think is appropriate for most investors. But that was a minor issue. My bigger issue was that Butler didn’t make clear what all the rules were for this new model. He describes ‘A true AAA framework would address issues around specific look-back periods for the generation of parameter estimates and assemble optimal portfolios without constraints on portfolio size. Further, volatility would be managed at the portfolio level to maintain a stable risk profile. … along with some engineering improvements to improve the signal-to-noise ratio of parameter estimates, and more frequent rebalancing to better control…’ Since I didn’t know the rules to generate this portfolio outcome I chose to put it in the post.

But I would definitely be interested in that model.

Paul

Appeared he was taking the same approach as the Exhibit 5 model, but doing on a weekly basis vs. monthly. Also, he added the target volatility (8%) in that last model. I have a sizeable 401K that I need to get more aggressive with while limiting my risk, so interested in looking at the weekly model if “we” can figure it out, and duplicate his findings. 🙂

Mark

I hear ya. The messing around with look-back periods is what really gave me pause. But the model I put on in my GTAA spreadsheet can just be used on a weekly basis. Then take the covariance matrix and use Excel solver to solve for portfolio weights with an 8% target annual vol (which is 0.5% daily).

Paul

Hey Paul…sorry to be monopolizing your time here. I have just started looking more in depth at your Excel models after reading almost all of your quant posts over the last couple days. Your spreadsheets and formulas are impressive. It has been interesting to watch your opinion about quants change over the time you have been blogging. In my earlier days I built many Excel spreadsheets and have forgot more than I know now (sadly). I was going to re-create what you did in Excel, but after looking at what you have built, no need to re-invent the wheel here if these are working for you and others. However, I am failing to see where you do the following in the model quoted from you above — “For example, if I put the above covariances for AGG3 into solver and target an 8% annual portfolio volatility I get portfolio weights of 58.5% for VNQ, 20.2% for VGLT, and 21.3% for MTUM.”

Where did you do this in the model? I need a jump off point to start managing my 401K, so need to determine where best to jump in for each model. Also, what if I want to go with a less aggressive approach (AGG6 or 13), where are the weighted averages for those? Maybe these have to be calculated, but in the brief time I have spent looking at your model, I didn’t see them. Appreciate you clarifying if you don’t mind.

I am going to go through your model more tomorrow, I like to understand and confirm what formulas do. Not that I don’t trust your model, just like to know how things work.

Thanks

Mark

Mark, no problem. The solver in Google sheets doesn’t work when trying to solve for portfolio weights with a target volatility. You need to take the appropriate covariance table and formulas for standard deviations I have in the GTAA spreadsheet, copy them to excel, and run Solver there to figure out the portfolio weights.

Paul