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.