Machines

Testing expectations

In our last post, we analyzed the performance of our portfolio, built using the historical average method to set return expectations. We calculated return and risk contributions and examined changes in allocation weights due to asset performance. We briefly considered whether such changes warranted rebalancing and what impact rebalancing might have on longer term portfolio returns given the drag from taxes. At the end, we asked what performance expectations we should have had to analyze results in the first place.

Performance anxiety

In our last post, we took a quick look at building a portfolio based on the historical averages method for setting return expectations. Beginning in 1987, we used the first five years of monthly return data to simulate a thousand possible portfolio weights, found the average weights that met our risk-return criteria, and then tested that weighting scheme on two five-year cycles in the future. At the end of the post, we outlined the next steps for analysis among which performance attribution and different rebalancing schemes were but a few.

Portfolio simulations

In our last post, we compared the three most common methods used to set return expectations prior to building a portfolio. Of the three—historical averages, discounted cash flow models, and risk premia models—no single method dominated the others on average annual returns over one, three, and five-year periods. Accuracy improved as the time frame increased. Additionally, aggregating all three methods either by averaging predictions, or creating a multivariate regression from the individual explanatory variables, performed better than two out of the three individual methods.

Mad methods

Over the past few weeks, we’ve examined the three major methods used to set return expectations as part of the portfolio allocation process. Those methods were historical averages, discounted cash flow models, and risk premia models. Today, we’ll bring all these models together to compare and contrast their accuracy. Before we make these comparisons, we want to remind readers that we’re now including a python version of the code we use to produce our analyses and graphs.

Implied risk premia

In our last post, we applied machine learning to the Capital Aset Pricing Model (CAPM) to try to predict future returns for the S&P 500. This analysis was part of our overall project to analyze the various methods to set return expectations when seeking to build a satisfactory portfolio. Others include historical averages and discounted cash flow models we have discussed in prior posts. Our provisional analysis suggested that the CAPM wasn’t a great forecasting model.

Machined risk premia

Over the last few posts, we’ve discussed methods to set return expectations to construct a satisfactory portfolio. These methods are historical averages, discounted cash flow models, and risk premia. our last post, focused on the third method: risk premia. Using the Capital Asset Pricing Model (CAPM) one can derive the required return for a particular asset based on the market price of risk, the asset’s risk, and the asset’s correlation with the market.

Risk premia

Our last post discussed using the discounted cash flow model (DCF) as a method to set return expectations that one would ultimately employ in building a satisfactory portfolio. We noted that if one were able to have a reasonably good estimate of the cash flow growth rate of an asset, then it would be relatively straightforward to calculate the required return. The problem, of course, is figuring out what the cash flow growth rate should be.

OMG O2G!

The oil-to-gas ratio was recently at its highest level since October 2013, as Middle East saber-rattling and a recovering global economy supported oil, while natural gas remained oversupplied despite entering the major draw season. Even though the ratio has eased in the last week, it remains over one standard deviation above its long-term average. Is now the time to buy chemical stocks leveraged to the ratio? Or is this just another head fake foisted upon unsuspecting generalists unaccustomed to the vagaries of energy volatility?

SKEWed perceptions

The CBOE’s SKEW index has attracted some headlines among the press and blogosphere, as readings approach levels not see in the last year. If the index continues to draw attention, doomsayers will likely say this predicts the next correction or bear market. Perma-bulls will catalogue all the reasons not to worry. Our job will be to look at the data and to see what, if anything, the SKEW divines. If you don’t know what the SKEW is, we’ll offer a condensed definition.

Null hypothesis

In our previous post we ran two investing strategies based on Apple’s last twelve months price-to-earnings multiple (LTM P/E). One strategy bought Apple’s stock when its multiple dropped below 10x and sold when it rose above 20x. The other bought the stock when the 22-day moving average of the multiple crossed above the current multiple and sold when the moving average crossed below. In both cases, annualized returns weren’t much different than the benchmark buy-and-hold, but volatility was, resulting in significantly better risk-adjusted returns.