Foundations

Weighting on a friend

Our last few posts on portfolio construction have simulated various weighting schemes to create a range of possible portfolios. We’ve then chosen portfolios whose average weights yield the type of risk and return we’d like to achieve. However, we’ve noted there is more to portfolio construction than simulating portfolio weights. We also need to simulate return outcomes given that our use of historical averages to set return expectations is likely to be biased.

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.

Discounted expectations

After our little detour into GARCHery, we’re back to discuss capital market expectations. In Mean expectations, we examined using the historical average return to set return expectations when constructing a portfolio. We noted hurdles to this approach due to factors like non-normal distributions, serial correlation, and ultra-wide confidence intervals. While we highlighted these obstacles and offered a few suggestions to counteract such drawbacks, on first blush it didn’t seem like historical averages were all that satisfactory.

Mean expectations

We’re taking a break from our extended analysis of rebalancing to get back to the other salient parts of portfolio construction. We haven’t given up on the deep dive into the merits or drawbacks of rebalancing, but we feel we need to move the discussion along to keep the momentum. This should ultimately tie back to rebalancing, but from a different angle. We’ll now start to examine capital market expectations.

Rebalancing history

Our last post on rebalancing struck an equivocal note. We ran a thousand simulations using historical averages across different rebalancing regimes to test whether rebalancing produced better absolute or risk-adjusted returns. The results suggested it did not. But we noted many problems with the tests—namely, unrealistic return distributions and correlation scenarios. We argued that if we used actual historical data and sampled from it, we might resolve many of these issues.

Rebalancing ruminations

Back in the rebalancing saddle! In our last post on rebalancing, we analyzed whether rebalancing over different periods would have any effect on mean or risk-adjusted returns for our three (equal, naive, and risky) portfolios. We found little evidence that returns were much different whether we rebalanced monthly, quarterly, yearly, or not at all. Critically, as an astute reader pointed out, if these had been taxable accounts, the rebalancing would likely have been a drag on performance.