Toronto Team  

  • T416.203.0067
  • 1.866.242.0203
  • F416.203.0544
  • 8 Wellington Street East
    3rd Floor
  • Toronto, Ontario M5E 1C5

Momentum: The 4th Factor?

Forget everything you’ve read about “past performance not predicting future performance”. Momentum investing is a well-documented phenomenon, in which winning stocks continue to be winners, and losing stocks remain losers (at least in the very short term). The very existence of momentum appears to challenge the Efficient Market Hypothesis (EMH), which asserts that stock prices instantly change to reflect new information.

Construction of a Momentum Index
The construction of a momentum index is surprisingly straightforward and transparent.  I have included the methodology for momentum indices constructed by AQR Capital Management below:
  • Rank the stocks in the investment universe by their total return over the prior twelve months (excluding the last month)
  • The top 33% of stocks with the highest rank are included, and weighted based on their market capitalization
  • The index is reconstituted quarterly
Momentum as a Complement to Value
In a 2009 white paper published by AQR Capital Management, they studied the annual excess returns (relative to the Russell 1000 Index) from the AQR US Large Cap Momentum Index and found them to be negatively correlated to excess returns from the Russell 1000 Value Index. This would imply that one could increase the diversification of a portfolio by combining the two strategies.
Tracking Error Relative to the Market
Momentum and value strategies have both experienced prolonged periods of underperformance relative to the market. This tracking error may cause investors to lose faith and abandon their original plan. A balanced portfolio combining these two factors has historically resulted in lower tracking error relative to a balanced market portfolio.  
In Table 1 below, I’ve created four balanced portfolios: Market, Momentum, Value, and Value + Momentum.  In Table 2, I’ve illustrated the historical 3-year rolling tracking error relative to the Market portfolio for each of the remaining three portfolios. As we can see, the tracking error is reduced significantly by combining Value + Momentum in a portfolio (dark blue line).

Sources:  AQR Capital Management, Dimensional Returns 2.0


Sources:  AQR Capital Management, Dimensional Returns 2.0

Risk-adjusted Returns
Although the Momentum and Value portfolios had higher risk-adjusted returns (i.e. Sharpe Ratio) than the Market portfolio, combining Value + Momentum in a portfolio actually increased the risk-adjusted returns further.  

Sources:  AQR Capital Management, Dimensional Returns 2.0

Transaction Costs
AQR Capital Management estimates the transaction costs of their large cap U.S. momentum strategies to be around 0.70% annually. This would decrease some of the benefit associated with implementing a momentum strategy in a portfolio.
AQR Capital Management estimates the annual turnover of their large cap U.S. momentum strategies to be in excess of 100%. For taxable investors, the constant buying and selling of stocks may result in additional realized capital gains. To counter this potential drawback, they have recently introduced “tax-managed” momentum funds.
Incorporating momentum into a portfolio appears to have significant diversification benefits for investors. As more low-cost and tax-efficient momentum products are released, adding momentum stocks to a portfolio may become as common as adding small cap and value stocks.


By: Justin Bender | 0 comments

The Variable Maturity Approach to Fixed Income Investing (Part I)

The variable maturity approach to fixed income investing is based on research by Eugene Fama and Robert Bliss. They concluded that the current yield curve is the best estimate of future yield curves. In other words, if the current yield on a two-year bond is 2%, the best estimate for what a two-year bond will be yielding next year is also 2%.

Dimensional Fund Advisors use this approach with their DFA Five-Year Global Fixed Income Fund. If the yield curve is positively sloped, they will invest in longer-dated bonds (with five years to maturity or less) as long as the additional term risk is compensated for with higher expected returns (longer maturities must provide at least 20 additional basis points per year).

For example, suppose a four-year bond is yielding 2.10% and a similar five-year bond is yielding 2.30%. In this case, since the bond with one year of additional term risk is being compensated for with 20 additional basis points of expected return (2.30% - 2.10% = 0.20%), the four-year bond would be sold and the five-year bond would be purchased.

To illustrate this concept further, I’ve adapted an example from Larry Swedroe’s book, “The Only Guide to a Winning Bond Strategy You’ll Ever Need.”

Suppose we have the choice to invest in either a one-year bond yielding 1% or a two-year bond yielding 2%. Assuming that we do not have superhuman interest rate forecasting abilities (a reasonable assumption), and also assuming that the current yield curve is the best estimate of future yield curves, how would we implement a variable maturity approach?

Step 1: Buy the two-year bond at the beginning of year 1 for $100
Since we receive a full 100 basis points of additional expected return for extending the bond maturity one further year out on the yield curve, we would purchase the two-year bond. At the end of year 1, we are paid the annual interest of $2 and the market value of our bond is now $101.

*Please see below for an explanation of why our two-year bond is now worth $101 at the end of year 1

Why has the value of our bond increased to $101 at the end of year 1? Remember that our main assumption is that the yield curve has not changed after one year. We currently hold a bond that matures at $100 in one year’s time (when it would pay us $2 of interest). Another one-year bond that currently trades in the marketplace is identical in every way to our bond except that it will pay its holder only $1 of interest at the end of the year. How much more could we reasonably expect to sell our bond for (relative to a similar one-year bond trading at par)? The answer is, of course, $1. The purchaser of our bond would receive $1 of additional interest income. Therefore, they would be willing to pay up to $1 more for our bond.

Step 2: Sell the two-year bond at the end of year 1 for $101
Assuming we sell our bond for $101 at the end of year 1 (and realize a capital gain of $1 in the process), we now have a total return of $3 ($2 from the annual interest and $1 from the realized capital gain from the sale of our bond at a premium).

Step 3: Repeat the process
Assuming the yield curve has not changed, we would repeat the process, again buying the two-year bond at the beginning of year 2 (earning a total return of $3 when we sell it at the end of year 2).

In Part II of this blog, I will show investors how they can implement a similar variable maturity approach, using some common fixed income exchange-traded funds (ETFs).


By: Justin Bender | 0 comments

Should you avoid long term bonds?

In a 2009 article written by Larry Swedroe and Kevin Grogan called, “The Maturity of Fixed-Income Assets and Portfolio Risk”, the authors examined the impact of extending bond maturities for various equity allocations. They found that at low fixed income (high equity) allocations, the equities were the dominating factor in the portfolio’s volatility. In other words, investors with high equity allocations could extend the maturities of their fixed income (increasing their expected returns) without significantly increasing the volatility of their portfolio. The reverse was also true; at high fixed income (low equity) allocations, the fixed income was the dominating factor in the portfolio’s volatility. Investors looking to reduce the volatility of their portfolio would be required to reduce the maturities of their fixed income.

I ran a similar analysis from 1980 to 2011 using historical Canadian fixed income and equity index returns. The equity allocation for each portfolio was split evenly between the S&P/TSX Composite Index, the S&P 500 Index and the MSCI EAFE Index. I used the following bond indices to demonstrate the impact of extending maturities:

  • DEX Short Term Bond Index (Short Term Bonds)
  • DEX Universe Bond Index (Broad Market Bonds)
  • DEX Long Term Bond Index (Long Term Bonds)

The analysis produced similar results to the above study. For higher equity allocations (i.e. 80% equity / 20% fixed income), extending the maturities of the fixed income did not drastically increase the volatility of the portfolio. For lower equity allocations (i.e. 20% equity / 80% fixed income), extending the maturities increased the volatility of the portfolio dramatically. I’ve illustrated the results in the graph below:

Standard Deviation of Various Equity Allocations: 1980–2011

Sources:  Dimensional Fund Advisors, Morningstar EnCorr


When deciding on how far to extend your fixed income maturities, your risk tolerance should be the main driving factor.  However, if your tolerance is high (and you also have a relatively high equity allocation), you should consider taking more maturity risk with your fixed income allocation.


By: Justin Bender | 0 comments