To my mind, a good use for risk parity is for assigning allocations to long-only funds in order to balance volatility. My goal is to maintain a relatively smooth return over a few years; the moving 3-year CAGR is about the right duration for assessing performance for my purposes.
The figure below is my attempt at developing a risk parity portfolio. It's basically minimum variance except that the risk assigned to equities is 60 percent in aggregate and to LTT is 40 percent; minimum variance would assign equal risk to each component. This method does not include return estimates when developing weights.
Each month the portfolio weights are recalculated with a two-month lookback for the correlation matrix. Note that the average weight for LTT is roughly 50 percent, but it bounced around considerably.
I have 4 equities (S&P 500, NASDAQ, utilities, and real estate) plus long-term treasuries.
- The top plot shows the portfolio value, adjusted to 1 at the start, and the components adjusted to their fraction of the portfolio.
- The second plot shows the moving 3-year CAGR.
- The third plot shows the allocation for each fund.
- The fourth plot shows the ulcer index for the components and the portfolio.
The portfolio only roughly follows the components; it does not track the peak performer. However, it does back down the allocations of components that are not doing well. Over this period the CAGR was 10 percent.
Exactly the same method is used for 2x LETFs in the next figure. The early part of some LETFs are synthetic, based on leveraging the corresponding fund in the first figure, and may be optimistic with respect to expenses. All of the LETFs start before 2/2007 except UBT (2010).
The key here is that the funds again balanced out very nicely, even though some of the individual 2x funds had bad patches. The calculated CAGR for the period was 19 percent, again probably a bit optimistic from the first few years. The portfolio oscillations are a bit bigger than the unleveraged version.
I find that the 3x version also behaved nearly as smoothly, but all funds are synthetic prior to 2009 and the synthetic versions are probably quite optimistic so I'm not showing it. The CAGR from 2009 on was roughly 25-30 percent.
As a bit further backtest, the following figure does just the 2x S&P500 and NASDAQ, and 3x LTT. These have synthetic daily data, although the values are increasingly questionable the further back in time. However, UOPIX was actually in existence starting in 1998, so it gives an idea of responses during the 2000 period and the 2008 period. The 3x LTT has a proportionately smaller fraction of the portfolio than a 2x LTT would occupy (but the same risk fraction), so overall returns are a bit bigger than a pure 2x-only portfolio.
I've delayed posting this until now, because I wanted to verify the behavior accounting for correlations. It turns out that I don't see a very big difference in returns and volatility using the minimum variance approach (considering the correlations) or just inverse variance weighting, even though the weights vary somewhat. I expect that picking funds that have relatively low correlations probably is partly responsible, and probably explicitly assigning risk fractions to each fund also is partly responsible. I realize that the correlations are not very accurate, but (i) recalculating correlations each month also will tend to even out estimation errors from one month to the next and (ii) the results aren't sensitive to the correlation matrix anyway.
I've tried other funds and combinations, in particular considering TNA/URTY, UMDD, CURE, SOXL, EDC, EURL, UGL, commodities, and TYD. I don't see any particular benefit to adding these other funds, but the methodology seems to work pretty well. I discarded 2x LETFs and TYD because they need too much of the portfolio in order to balance volatility. I discarded commodities, EDC, and EURL for low returns. I discarded TNA/URT, UMDD, CURE, and SOXL mainly for simplicity.
I am not currently using the unemployment index as an indicator, which I had discussed before. I think that it won't be useful until the COVID shock has worked its way out of the system.
I am still considering the possibility of using TMV instead of TMF if there comes a time with steadily rising interest rates, such as the period from 1955 to 1982.
I've done some backtesting trying to predict market movements based on moving averages and volatility. In common with much that I've read, I wasn't able to see any predictive capability in these indicators, so I will not be using them.
This is the type of strategy that I will be following with my HEDGEFUNDIE adventure going forward. It's only practical in tax protected, because of the monthly rebalancing. I'm planning to test drive this for at least five years with five percent of my current portfolio, and consider a larger fraction if it goes well (especially if it goes well under adverse conditions).