Invaluable Information For Portfolio Rebalancing

Includes: BND, EEM, EFA, GSG, IWV, RWO
by: Viziphi


If you're a financial advisor (or a sophisticated investor), you know that the pains of portfolio management persist long after a portfolio has gone through its initial allocation. Take the example where you've put to work client's (or your own) funds based on a pristine allocation that incorporated a well-devised Investment Policy Statement ("IPS"), current market dynamics, and client goals and objectives (e.g. future need). The funds have been fully allocated now for about 6 months, and you're faced with the challenging task of "is it time to rebalance?" You might simply employ an interval-based rebalancing framework, (such as annual rebalancing) to ensure allocation weights don't drift too far afield, but if you're a student of capital markets, you know there's more information that you might want to incorporate in your decision-making process. In this post, I go over some high level considerations and even summarize a back-of-the envelop calculation you can use if you don't have access to tools like Viziphi.

Drifting Weights & Risk Contributions

At the time of portfolio implementation (or throughout the Dollar Cost Averaging process), dollars allocated to a specific asset or asset class are neatly apportioned based on some pre-defined weighting schema. If you're implementing asset allocations that take tactical tilts based on your "view" of capital markets, then you're likely quite interested in a deeper layer: how each asset/asset class is contributing to the risk of the entire portfolio over time. Moreover, as asset price fluctuations and underlying market dynamics change, there's the possibility that drift and market dynamic have coalesced to expose the portfolio to far greater risk from a given asset/asset class than was originally intended. One terrific, easy to understand concept (and visualization corollary) is "Contribution to Risk." There are different ways to do this calculation, however at Viziphi, we adhere to best practices of looking at assets' contribution to tail loss, showing how risks within the portfolio have changed irrespective to, and including asset drift. With this information, advisors and investors can make fully informed decisions about whether it makes sense to rebalance to IPS risk allocations or stay put until the next rebalancing period arises.

An Example Scenario

I've created a 60-40 portfolio that incorporates alternative asset classes such as Commodities and REITs, using the following broadly diversified and deeply liquid ETFs:

Asset Class Ticker Weight
US Fixed Income BND 40%
US Equity IWV 25%
Foreign Developed Equity EFA 15%
Foreign Emerging Equity EEM 10%
Global REITs RWO 5%
Commodities GSG 5%
Click to enlarge

Assuming this is an annually rebalanced portfolio, here are the asset allocation weights on 1-4-2016 - the last date of rebalancing - and as of March 22nd, 2016, the close of the last trading day, assuming no trading activity during this time interval occurred.

Click to enlarge

From the image above, it's clear that not much asset drift has occurred since the start of the year. The greatest drift has taken place in Foreign Developed Equities (NYSEARCA:EFA) by falling nearly 0.5% and Foreign Emerging Equities by increasing nearly 0.5%. With a clear view on asset drift since the time of rebalancing, we can add a further layer of information by examining how risk contributions have changed.

When looking at how asset contributions to risk have changed, it's valuable to look at two different pieces of information: irrespective of weighting allocation and current (or past) weighting allocation. Equal-weighting allocation provides an understanding of how assets and their risk attributes have evolved in aggregate, whereas risk contribution using current/past allocation weights provides actual information about sources of risk and their magnitudes in the specific portfolio being analyzed.

Click to enlarge

From the above chart, it's clear that there haven't been dramatic shifts in how each asset is contributing to the risk of the entire portfolio. US equities and commodities (IWV and GSG respectively) represent the biggest changes with about a -3% and 3% change, respectively. Examining each asset's contribution incorporating the weights, e.g. the asset's drift is illustrated below.

Click to enlarge

Note that the decrease in contribution to risk for US equity (ticker IWV) has been reduced even further by asset drift. If the advisor/investor believes that US equities are likely to outperform, this combination of asset drift and change in capital market dynamic could serve as a missed opportunity to gain the desired level of exposure. Even if the result is to maintain the current allocation, the advisor/investor has done one of the most important parts in the investment management process, which is to extensively test and understand how portfolio dynamics have changed and the potential impact of rebalancing or non-action. When an advisor validates investment decisions using a consistent and measurable investment process, the value they provide through their investment decisions is not only defensible, it's irreplicable.

Back-of-the-Envelope Estimate

For users looking to do a quick estimate of this same calculation, here's something that will get you fairly close (however, unfortunately, this does not take into account tail risk, but rather assumes returns are normally distributed):

  1. Take the log returns of the portfolio and each asset since the portfolio was last rebalanced
  2. Calculate the correlation of the log returns of each asset and the log returns of the portfolio
  3. Calculate the volatilities of each asset
  4. Multiply the correlation value of an asset with the volatility of the asset
  5. Sum all of the values from step (3) and then calculate the proportion that each asset represents of the total (that's your marginal contribution to risk)
  6. Multiply the marginal contribution to risk in (5) against:
    a. Equal weights, that gives you your "contribution to risk" irrespective of weight
    b. Actual weights, that provides the "contribution to risk" based on actual holdings