# Follow up FAQ: “Forecast-Free” Algorithms and Minimum Correlation Algorithm

With so many comments and questions regarding the last post https://cssanalytics.wordpress.com/2011/08/09/forecast-free-algorithms-a-new-benchmark-for-tactical-strategies/ , I decided to take the unusual but more functional approach of writing a FAQ to address these issues for both those that were kind enough to make intelligent contributions and to new readers. Note that it was brought to my attention that fellow blogger Quantivity has written an excellent series of posts on a similar topic: http://quantivity.wordpress.com/2011/04/10/portfolio-theory-is-dead-now-what/

**What is a “Forecast-Free” Algorithm?**

I should have clarified as this is somewhat of a misnomer. Strom Macro http://strommacro.wordpress.com/ posted some comments regarding this issue on a recent blog. “Forecast-Free” in CSS parlance refers to an approach that does not estimate expected returns. In a portfolio algorithm context, this means that we do not care about either relative or absolute conclusions drawn about how an asset class (or stock) should perform. *This does not mean that we do not estimate either correlations or volatility—in fact these estimations are critical to the algorithm*. Estimation error has been shown to be much lower for correlations and volatility than it is for return inputs. This is why financial engineers spend so much time on the latter rather than the former ( engineers are generally more interested in the most predictable components of time series).

2) **How is the algorithm constructed?**

At this point, I should mention that I am in the process of compiling a white paper on this topic (forthcoming). The Minimum Correlation Portfolio (MCP) will be the topic of this article, and the benchmark construction will be laid out in complete detail. It uses a more conventional optimization/iterative approach with some interesting twists. In contrast the Minimum Correlation Algorithm (MCA) is an algorithm— it is a heuristic/computational solution designed to be faster and more robust, but is also proprietary. That said, the MCP performance is very close to MCA, and both are based on the same concept.

3) **Is the algorithm highly sensitive to the choice of asset classes or markets?**

No. This is what differentiates a “forecast-free” approach– both the choice of markets and parameter lengths show substantially less variability than classic “GTAA” approaches. This is because: a) they produce less concentrated portfolios with less correlated constituents b) volatility and correlations can be extrapolated well from almost any time frame, while trends in prices or returns or relative returns/ranks tend to perform best at longer intervals. So while relative strength/momentum and trend-following are robust approaches, I would argue that “forecast-free” algorithms are even more robust.

4) **Is the Minimum Correlation Algorithm a variant of risk-parity?**

No. A risk-parity approach assumes equal risk contributions to portfolio risk, it is a hybrid between a minimum variance approach and an equal weight approach. The MCA seeks to optimize risk contributions to reduce portfolio risk with the view of isolating risk reduction associated with diversification only. That is the best I will say until it is explained in more detail in the paper.

Thank you for all the excellent comments and feedback– I will be releasing a paper on the topic soon enough. For those that wish to receive the paper directly when it is completed I will post an email address on the blog where you can request a first copy.

Ah! Understood. Thanks for the clarification.

-Ström

no problem! it was a good point to raise either way.

best david

Nice post, David. Correlation is sufficiently interesting as to potentially warrant a follow-up post to original minvar series.

hi quantivity, good to see you back to posting and some excellent material. im sure you have a lot of interesting material on the topic. I look forward to reading it.

best

david

Thanks, David. Would love to read your paper when it comes out!

thanks Wilson! Im looking forward to finishing it soon.

best

david

On the surface it seems like your Minimum Correlation Portfolio is similar or would wind up being highly correlated (no pun intended) to Falkenstein’s Minimum Variance Portfolio. The end result appears to be targeting the same idea: that there is no risk premium in variance.

Hi ZDH, there are linkages between the minimum correlation portfolio and the minimum variance portfolio but there are also key distinctions. I am not familiar with Falkenstein’s work but will be sure to take a look.

best

david

@ZDH: depends on how David is defining correlation in this context (which he does not explain), as we recall Pearson correlation is defined as covariance scaled by marginal standard deviations. Thus, equivalence comes down to mathematical formulation and choice of estimators (e.g. shrinkage). Also, note that Falkenstein did not originate MVPs (as he acknowledges).

To add to the conversation regarding minimum variance portfolio, here is the result of trading a classical MVP portfolio over the the same 8 ETFs as those used by David:

To be roughly consistent with David’s original experiment, the portfolio is rebalanced weekly, and the covariance matrix is estimated using last 16 weekly returns. The Sharpe is annualized using weekly returns. I think shrinkage is less important in this case since we only have 8 assets.

Hi Wilson, how did you compute cumulative performance for 1/N? I get somewhat different results using adjusted close data from Yahoo. For example, just glancing at the snapshot you posted, the equity curve for 1/N never crosses 1.6 level. However, using adjusted close data from Yahoo for the Mar 14th,2005 to Aug 1st,2011 the equity curve for 1/N goes above 1.8 level. Here is the sample workbook with all data and computations.

http://dl.dropbox.com/u/39051249/minvar.xls

Please have a look. Thanks

Hi Mike, the discrepancy in results arises from how single-period returns are computed: discrete returns are used in your spreadsheet, while I used log returns.

hi wilson, thanks very much for sharing this. we used weekly rebalancing, but daily data over 1 quarter. for some reason, the classic MVP presented here has a much higher sharpe than we are seeing using the traditional quadratic optimization. did you adjust the sizing of the underlying assets for their relative variance?

best

david

Hi David, the posted result is of the most simplistic case where the only constraint is that all weights sum to one. In this case, there can be some extreme positions on both long and short sides, so the costs of borrowing is a real concern. If I run the experiment with short-sale constrained (i.e., all weights sum to one, and non-negative), the performance is significantly handicapped, as shown here:

Although short-sale constrained version (MVP-SC) has worse returns, the rebalancing costs are much lower. It also has an additional benefit of producing sparse portfolios. In this particular case, MVP-SC has the lowest volatility, so I think it has some merits given its conservative nature.

I quickly ran a test using daily data. My result is consistent with yours in that the Sharpe of the MVP is much lower than using weekly data, while the Sharpe of the 1/N remains the same. Since the performance of the strategy depends highly on the quality of the covariance estimation, it may be because that the weekly data gives a slightly less “noisy” covariance matrix.

David,

Thank you for your work on this subject. I would love to read your white paper on the subject.