Bonds

What is the best mix of stocks and bonds to hold during retirement worldwide? In his January 2015 paper entitled “The Retirement Glidepath: An International Perspective”, Javier Estrada compares outcomes for different stocks-bonds allocation strategies during retirement from a global perspective. He considers declining equity, rising equity and static glidepaths with an annual withdrawal rate of 4% (of the portfolio value at retirement) and annual rebalancing during a 30-year retirement period. He tests the following glidepaths:

• Four declining equity strategies that begin with 100%-0%, 90%‐10%, 80%‐20% and 70%‐30% stocks-bonds allocations and shift toward bonds linearly via annual rebalancing.
• Four mirror-image rising equity strategies that begin with 0%-100%, 10%-90%, 20%-80% and 30%-70% stocks-bonds allocations and shift toward stocks linearly via annual rebalancing.
• Eleven static allocations ranging from 100%-0% to 0%-100% stocks-bonds allocations maintained via annual rebalancing, with focus on conventional or near-conventional 60%-40%, 50%-50% and 40%-60% allocations.

He focuses on the failure rate of these strategies during 81 overlapping 30-year retirement periods during 1900-2009. He also considers average and median terminal wealth/bequest, tail risk, annual volatility (standard deviation of annual returns) and upside potential. He defines tail risk (downside risk) as average terminal wealth for the 1%, 5% or 10% lowest values from the 81 periods. Using annual total real returns for stocks and government bonds for 19 countries (in local currency adjusted by local inflation) and for the world market (in dollars adjusted by U.S. inflation) during 1900 through 2009 (110 years), he finds that: Keep Reading

In reference to “Optimal Monthly Cycle for Simple Asset Class ETF Momentum Strategy?”, a subscriber asked about an optimal monthly cycle for the “Simple Debt Class Mutual Fund Momentum Strategy”. This latter strategy each month allocates the entire portfolio value to the one of the following 12 debt class mutual funds with the highest past total return (optimally over the last two months):

T. Rowe Price New Income (PRCIX)
Thrivent Income A (LUBIX)
Vanguard GNMA Securities (VFIIX)
T. Rowe Price High-Yield Bonds (PRHYX)
T. Rowe Price Tax-Free High Yield Bonds (PRFHX)
Vanguard Long-Term Treasury Bonds (VUSTX)
T. Rowe Price International Bonds (RPIBX)
Fidelity Convertible Securities (FCVSX)
PIMCO Short-Term A (PSHAX)
Fidelity New Markets Income (FNMIX)
Eaton Vance Government Obligations C (ECGOX)
Vanguard Long-Term Bond Index (VBLTX)

To investigate, we compare 21 variations of the strategy based on shifting the monthly return calculation cycle relative to trading days from the end of the month (EOM). For example, an EOM+5 cycle ranks funds based on closing prices five trading days after EOM each month. We use the historically optimal two-month fund momentum measurement interval. Using daily dividend-adjusted closes for the 12 funds during mid-December 1994 through mid-January 2015 (241 months), we find that: Keep Reading

Do factor models predict returns for corporate bonds as they do for stocks? In their October 2014 paper entitled “Factor Investing in the Corporate Bond Market”, Patrick Houweling and Jeroen van Zundert develop and test a four-factor (size, low-risk, value and momentum) model of future corporate bond returns. Each month for investment grade and high yield bond market segments separately, they construct an equally-weighted long-only portfolio consisting of the 10% of bonds with the highest exposure to each factor. They hold portfolios for 12 months, resulting in 12 overlapping portfolios for each segment and factor. Specifically, the factor portfolios are:

1. Size – the 10% of bonds with the smallest company index weights, calculated as the sum of market value weights of all company bonds in the index that month.
2. Low-risk – a combination of rating and maturity. For investment grade, the portfolio holds the 10% of bonds rated AAA to A- and having the shortest maturities. For high yield, the portfolio holds the 10% of bonds rated BB+ to B- and having the shortest maturities. On average, the maturity threshold is 2.8 (3.7) years for investment grade (high yield).
3. Value – the 10% of bonds with the largest percentage gaps between actual credit spread and credit spread indicated by monthly regressions of credit spread on rating.
4. Momentum – the 10% of bonds with the highest return relative to duration-matched U.S. Treasuries from six months ago to one month ago (with a skip-month to avoid reversal).

They evaluate factor portfolio performance based on excess return of constituent corporate bonds versus duration-matched U.S. Treasuries (thereby focusing on the default premium component of corporate bond returns). To estimate trading frictions, they model bid-ask spreads based on maturity and rating (the longer maturity or the lower the rating, the larger the estimated trading friction). Portfolio-level trading frictions are sums of frictions for all bonds traded. Using monthly data for all bonds in the Barclays U.S. Corporate Investment Grade index and the Barclays U.S. Corporate High Yield index during January 1994 through December 2013 (about 800,000 investment grade and 300,000 high yield bond-month observations), they find that: Keep Reading

How much performance improvement comes from rebalancing a stocks-bonds portfolio, and what specific rebalancing approach works best? In their August 2014 paper entitled “Testing Rebalancing Strategies for Stock-Bond Portfolios Across Different Asset Allocations”, Hubert Dichtl, Wolfgang Drobetz and Martin Wambach investigate the net performance implications of different rebalancing approaches and different rebalancing frequencies on portfolios of stocks and government bonds with different weights and in different markets. With buy-and-hold as a benchmark, they consider three types of rebalancing rules: (1) strict periodic rebalancing to target weights; (2) threshold rebalancing, meaning periodic rebalancing to target weights if out-of-balance by 3% or more; and, (3) range rebalancing, meaning periodic rebalancing to plus (minus) 3% of target weights if above (below) target weights by more than 3%. They consider annual, quarterly and monthly rebalancing frequencies. They use 30 years of broad U.S., UK and German stock market, bond market and risk-free returns to construct simulations with 10-year investment horizons. Their simulation approach preserves most of the asset class time series characteristics, including stocks-bonds correlations. They assume round-trip rebalancing frictions of 0.15% (0.10% for stocks and 0.05% for bonds). Using monthly returns for country stock and bonds markets and risk-free yields during January 1982 through December 2011 to generate 100,000 simulated 10-year return paths, they find that: Keep Reading

Do new funds have the latitude to concentrate in the best opportunities while they remain small? In his June 2014 presentation package entitled “How Long Might An Active Bond ETF’s ‘Best Ideas’ Outperformance Window Last?”, Claude Erb compares the performance of the PIMCO Total Return ETF (BOND), an exchange-traded fund (ETF) introduced in March 2012, to that of its parent mutual fund PIMCO Total Return Institutional Class (PTTRX). Using monthly total returns for BOND and PTTRX during March 2012 through May 2014, he finds that: Keep Reading

Does the reward for taking the risk of holding stocks exhibit any long-term trend? In his April 2014 presentation package entitled “The Incredible Shrinking ‘Realized’ Equity Risk Premium”, Claude Erb examines the trend in the realized U.S. equity risk premium (ERP) since 1925. He defines this ERP as the retrospective difference in 10-year yield between the broad U.S. stock market and the 10-year yield on safe assets such as U.S. Treasury bills or intermediate-term U.S. Treasury notes. Using 10-year returns for U.S. stocks and various alternative safe assets (bills, notes and bonds) during 1925 through 2013, he finds that: Keep Reading

Does stock market timing based on simple moving average (SMA) and time-series (intrinsic or absolute) momentum strategies really work? In the November 2013 version of his paper entitled “The Real-Life Performance of Market Timing with Moving Average and Time-Series Momentum Rules”, Valeriy Zakamulin tests realistic long-only implementations of these strategies with estimated trading frictions. The SMA strategy enters (exits) an index when its unadjusted monthly close is above (below) the average over the last 2 to 24 months. The intrinsic momentum strategy enters (exits) an index when its unadjusted return over the last 2 to 24 months is positive (negative). Unadjusted means excluding dividends. He applies the strategies separately to four indexes: the S&P Composite Index, the Dow Jones Industrial Average, long-term U.S. government bonds and intermediate-term U.S. government bonds. When not in an index, both strategies earn the U.S. Treasury bill (T-bill) yield. He considers two test methodologies: (1) straightforward inception-to-date in-sample rule optimization followed by out-of-sample performance measurement, with various break points between in-sample and out-of-sample subperiods; and, (2) average performance across two sets of bootstrap simulations that preserve relevant statistical features of historical data (including serial return correlation for one set). He focuses on Sharpe ratio (including dividends) as the critical performance metric, but also considers terminal value of an initial investment. He assumes the investor is an institutional paying negligible broker fees and trading in small orders that do not move prices, such that one-way trading friction is the average bid-ask half-spread. He ignores tax impacts of trading. With these assumptions, he estimates a constant one-way trading friction of 0.5% (0.1%) for stock (bond) indexes. Using monthly closes and dividends/coupons for the four specified indexes and contemporaneous T-bill yields during January 1926 through December 2012 (87 years), he finds that: Keep Reading

Do economic indicators usefully predict government bond returns? In the January 2014 version of their paper entitled “What Drives the International Bond Risk Premia?”, Guofu Zhou and Xiaoneng Zhu examine whether OECD-issued leading economic indicators predict government bond returns at a one-month horizon. They focus on a four-country (U.S., UK, Japan and Germany) aggregate leading economic indicator (LEI4). They test whether LEI4 outperforms historical averages and individual country LEIs in predicting term premiums (relative to a one-year bond) for U.S., UK, Japanese and German government bonds with terms of two, three, four and five years. Their test methodology employs monthly inception-to-date regressions of annual change in LEI4 versus next-month bond return for an out-of-sample test period of 1990 through 2011. Using end-of-month total return data for 1-year, 2-year, 3-year, 4-year and 5-year government bonds since 1962 for the U.S., 1970 for the UK, 1980 for Japan and 1975 for GM, all through 2011, they find that: Keep Reading

Do low-risk bonds, like low-risk stocks, tend to outperform their high-risk counterparts? In their September 2013 paper entitled “Low-Risk Anomalies in Global Fixed Income: Evidence from Major Broad Markets”, Raul Leote de Carvalho, Patrick Dugnolle, Xiao Lu and Pierre Moulin investigate whether low-risk beats high-risk for different measures of risk and different bond segments. They consider only measures of risk that account for the fact that the risk of a bond inherently decreases as it approaches maturity, emphasizing duration-times-yield (yield elasticity). They focus on corporate investment grade bonds denominated in dollars, euros, pounds or yen, but also consider government and high-yield corporate bonds worldwide. Each month, they rank a selected category of bonds by risk into fifths (quintile portfolios). For calculation of monthly quintile returns, they weight individual bond returns by market capitalization. They reinvest coupons the end of the month. They focus on quintile portfolio Sharpe ratios to test the risk-performance relationship. Using monthly risk data and returns for 85,442 individual bonds during January 1997 through December 2012 (192 months), they find that: Keep Reading

What initial retirement portfolio withdrawal rate is sustainable over long horizons when, as currently, bond yields are well below and stock market valuations well above historical averages? In their June 2013 paper entitled “Asset Valuations and Safe Portfolio Withdrawal Rates”, David Blanchett, Michael Finke and Wade Pfau apply predictions of bond yields and stock market returns to estimate whether various initial withdrawal rates succeed over different retirement periods. They define initial withdrawal rate as a percentage of portfolio balance at retirement, escalated by inflation each year thereafter. They simulate future bond yield as a linear function of current bond yield with noise, assuming a long-term average of 5% and bounds of 1% and 10%. They simulate future U.S. stock mark return as a linear function of Cyclically Adjusted Price-to-Earnings ratio (CAPE, or P/E10), the ratio of current stock market level to average earnings over the last ten years, assuming P/E10 has a long-term average of 16.4 with noise (implying average annual return 10% with standard deviation 20%). They simulate inflation as a function of bond yield, change in bond yield, P/E10 and change in P/E10 with noise. They assume an annual portfolio management fee of 0.5%. They run 10,000 Monte Carlo simulations for each of many initial withdrawal rate scenarios, with probability of success defined as the percentage of runs not exhausting the portfolio before the end of a specified retirement period. Using initial conditions of a government bond yield of 2% and a P/E10 of 22 as of mid-April 2013, they find that: Keep Reading