# Bonds

Bonds have two price components, yield and response of price to prevailing interest rates. How much of a return premium should investors in bonds expect? How can investors enhance this premium? These blog entries examine investing in bonds.

**September 16, 2019** - Bonds

Does the term premium as measured by returns to zero-coupon U.S. Treasury notes (T-notes) concentrate during some part of the monthly cycle? In their August 2019 paper entitled “Predictable End-of-Month Treasury Returns”, Jonathan Hartley and Krista Schwarz examine the monthly cycle of excess returns on 2-year, 5-year and 10-year T-notes. Specifically, they calculate average excess return by trading day before end-of-month (EOM), with excess return measured as raw T-note return minus general collateral repo rate. Using modeled daily prices for the specified T-notes and daily general collateral repo rate during January 1990 through December 2018, *they find that:* Keep Reading

**August 30, 2019** - Bonds, Equity Premium, Momentum Investing, Strategic Allocation

“SACEMS-SACEVS for Value-Momentum Diversification” finds that the “Simple Asset Class ETF Value Strategy” (SACEVS) and the “Simple Asset Class ETF Momentum Strategy” (SACEMS) are mutually diversifying. Do longer samples available from “SACEVS Applied to Mutual Funds” and “SACEMS Applied to Mutual Funds” confirm this finding? To check, we look at the following three equal-weighted (50-50) combinations of the two strategies, rebalanced monthly:

- SACEVS Best Value paired with SACEMS Top 1 (aggressive value and aggressive momentum).
- SACEVS Best Value paired with SACEMS Equally Weighted (EW) Top 3 (aggressive value and diversified momentum).
- SACEVS Weighted paired with SACEMS EW Top 3 (diversified value and diversified momentum).

Using monthly gross returns for SACEVS and SACEMS mutual fund portfolios during September 1997 through July 2019, *we find that:*

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**June 24, 2019** - Bonds, Equity Options, Gold, Momentum Investing, Strategic Allocation

What steps should investors consider to mitigate impact of inevitable large U.S. stock market corrections? In their May 2019 paper entitled “The Best of Strategies for the Worst of Times: Can Portfolios be Crisis Proofed?”, Campbell Harvey, Edward Hoyle, Sandy Rattray, Matthew Sargaison, Dan Taylor and Otto Van Hemert compare performances of an array of defensive strategies with focus on the eight worst drawdowns (deeper than -15%) and three NBER recessions during 1985 through 2018, including:

- Rolling near S&P 500 Index put options, measured via the CBOE S&P 500 PutWrite Index.
- Credit protection portfolio that is each day long (short) beta-adjusted returns of duration-matched U.S. Treasury futures (BofAML US Corp Master Total Return Index), scaled retrospectively to 10% full-sample volatility.
- 10-year U.S. Treasury notes (T-notes).
- Gold futures.
- Multi-class time-series (intrinsic or absolute) momentum portfolios applied to 50 futures contract series and reformed monthly, with:
- Momentum measured for 1-month, 3-month and 12-month lookback intervals.
- Risk adjustment by dividing momentum score by the standard deviation of security returns.
- Risk allocations of 25% to currencies, 25% to equity indexes, 25% to bonds and 8.3% to each of agricultural products, energies and metals. Within each group, markets have equal risk allocations.
- Overall scaling retrospectively to 10% full-sample volatility.
- With or without long equity positions.

- Beta-neutral factor portfolios that are each day long (short) stocks of the highest (lowest) quality large-capitalization and mid-capitalization U.S. firms, based on profitability, growth, balance sheet safety and/or payout ratios.

They further test crash protection of varying allocations to the S&P 500 Index and a daily reformed hedge consisting of equal weights to: (1) a 3-month time series momentum component with no long equity positions and 0.7% annual trading frictions; and, (2) a quality factor component with 1.5% annual trading frictions. For this test, they scale retrospectively to 15% full-sample volatility. Throughout the paper, they assume cost of leverage is the risk-free rate. Using daily returns for the S&P 500 Index and inputs for the specified defensive strategies during 1985 through 2018, *they find that:*

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**June 12, 2019** - Bonds

Is there a straightforward way to model the returns on U.S. Corporate bond indexes? In his April 2019 paper entitled “Give Credit Where Credit is Due: What Explains Corporate Bond Returns?”, Roni Israelov models returns on these indexes based on four intuitive factors:

- Positive exposure to government bond yields, quantified via duration-matched government bonds.
- Negative exposure to rate volatility from bond call provisions (uncertainty in duration), quantified via delta-hedged options on 10-year Treasury note futures.
- Positive exposure to firm values due to default risk, quantified via index constituent-weighted equities.
- Negative exposure to firm stock volatility due to default risk, quantified via index constituent-weighted delta-hedged single-name equity options.

Exposures 1 and 2 are general (systematic), while exposures 3 and 4 contain both systematic and firms-specific (idiosyncratic) components. He tests this 4-factor model on six Bank of America Merrill Lynch U.S. corporate bond indexes: Investment Grade, High Yield, 1-3 Year Corporate, 3-5 Year Corporate, 5-10 Year Corporate, and 10+ Year Corporate. All duration-specified indexes are investment grade. He also tests two Credit Default Swap (CDS) indexes: investment grade and high yield. He further devises and tests a Risk-Efficient Credit strategy on the six bond indexes that isolates and exploits compensated risk premiums by buying bond index futures, buying equity index futures, selling delta-hedged equity index options and selling delta-hedged options on bond index futures, with allocations sized to match respective historical exposures of each index. Using monthly data for the eight bond/CDS indexes and the four specified factors and their components during January 1997 through December 2017, *he finds that:*

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**May 16, 2019** - Bonds, Investing Expertise

Did Bill Gross, the Bond King, generate significantly positive alpha during his May 1987 through September 2014 tenure as manager of PIMCO Total Return Fund (Fund)? In their March 2019 paper entitled “Bill Gross’ Alpha: The King Versus the Oracle”, Richard Dewey and Aaron Brown investigate whether Bill Gross generates excess average return after adjusting for market exposures over this tenure. They further compare evaluation of bond market alpha for Bill Gross to evaluation of equity market alpha for Warren Buffett. Following the explanation given by Bill Gross for his outperformance, their factor model of Fund returns includes three long-only market factors: interest rate (Merrill Lynch 10-year Treasury Index), credit (Barclays U.S. Credit Index) and mortgage (Barclays U.S. MBS Index). It also includes a fourth factor that is long U.S. Treasury 5-year notes and short U.S. Treasury 30-year bonds, with weights set to eliminate coupon and roll-down effects of their different durations. Using monthly returns for the Fund and the four model factors, and monthly 1-month U.S. Treasury bill yield as the risk-free rate during June 1987 (first full month of the Fund) through September 2014 (when Gross left the Fund), *they find that:* Keep Reading

**March 20, 2019** - Bonds, Economic Indicators

A subscriber asked about the validity of the assertion in “The Daily Shot” of February 26, 2019 (*The Wall Street Journal*) that “recent weakness in the ISM [Institute for Supply Management] Manufacturing PMI [Purchasing Managers’ Index] index points to downside risks for high-yield debt.” Such a relationship might support a strategy of switching between high-yield bonds and cash, or high-yield bonds and U.S. Treasuries, based on PMI data. To investigate, we consider the following two pairs of funds:

- Vanguard High-Yield Corporate (VWEHX) and Vanguard Long-Term Treasury (VUSTX) since May 1986 (limited by VUSTX).
- iShares iBoxx High Yield Corp Bond (HYG) and iShares 7-10 Year Treasury Bond (IEF) since April 2007 (limited by HYG).

We consider both statistical tests and strategies that each month (per the PMI release frequency) holds high-yield bonds or cash, or high-yield bonds or Treasuries, according to whether the prior-month change in PMI is positive or negative. We use the 3-month U.S. Treasury bill (T-bill) yield as a proxy for return on cash. Using fund monthly total returns as available and monthly seasonally adjusted PMI data for January 1950 through January 2016 from the Federal Reserve Bank of St. Louis (discontinued and removed) and from press releases thereafter, all through February 2019, *we find that:* Keep Reading

**January 24, 2019** - Bonds, Equity Premium, Strategic Allocation

Failure rate, the conventional metric for evaluating retirement portfolios, does not distinguish between: (1) failures early versus late in retirement; or, (2) small and large surpluses (bequests). Is there a better way to evaluate retirement portfolios? In their December 2018 paper entitled “Toward Determining the Optimal Investment Strategy for Retirement”, Javier Estrada and Mark Kritzman propose coverage ratio, plus an asymmetric utility function that penalizes shortfalls more than it rewards surpluses, to evaluate retirement portfolios. They test this approach in 21 countries and the world overall. Coverage ratio is number of years of withdrawals supported by a portfolio during and after retirement, divided by retirement period. The utility function increases at decreasing rate (essentially logarithmic) as coverage ratio rises above one and decreases sharply (linearly with slope 10) as it falls below one. They focus on a 30-year retirement with 4% initial withdrawal rate and annual inflation-adjusted future withdrawals. The portfolio rebalances annually to target stocks and bonds allocations. They consider 11 target stocks-bonds allocations ranging from 100%-0% to 0%-100% in increments of 10%. When analyzing historical returns, the first (last) 30-year period is 1900-1929 (1985-2014), for a total of 86 (overlapping) periods. When using simulations, they draw 25,000 annual real returns for stocks and bonds from two uncorrelated normal distributions. For bonds, all simulation runs assume 2% average real annual return with 3% standard deviation. For stocks, simulation runs vary average real annual return and standard deviation for sensitivity analysis. Using historical annual real returns for stocks and bonds for 21 countries and the world overall during 1900 through 2014 from the Dimson-Marsh-Staunton database, *they find that:* Keep Reading

**December 27, 2018** - Bonds, Commodity Futures, Currency Trading, Equity Premium

Should investors rely on aggregate positions of speculators (large non-commercial traders) as indicators of expected futures market returns? In their November 2018 paper entitled “Speculative Pressure”, John Hua Fan, Adrian Fernandez-Perez, Ana-Maria Fuertes and Joëlle Miffre investigate speculative pressure (net positions of speculators) as a predictor of futures contract prices across four asset classes (commodity, currency, equity index and interest rates/fixed income) both separately and for a multi-class portfolio. They measure speculative pressure as end-of-month net positions of speculators relative to their average weekly net positions over the past year. Positive (negative) speculative pressure indicates backwardation (contango), with speculators net long (short) and futures prices expected to rise (fall) as maturity approaches. They measure expected returns via portfolios that systematically buy (sell) futures with net positive (negative) speculative pressure. They compare speculative pressure strategy performance to those for momentum (average daily futures return over the past year), value (futures price relative to its price 4.5 to 5.5 years ago) and carry (roll yield, difference in log prices of nearest and second nearest contracts). Using open interests of large non-commercial traders from CFTC weekly legacy Commitments of Traders (COT) reports for 84 futures contracts series (43 commodities, 11 currencies, 19 equity indexes and 11 interest rates/fixed income) from the end of September 1992 through most of May 2018, along with contemporaneous Friday futures settlement prices, *they find that:* Keep Reading

**November 26, 2018** - Bonds, Calendar Effects, Equity Premium, Momentum Investing, Size Effect, Strategic Allocation, Value Premium

Is the U.S. equity turn-of-the-month (TOTM) effect exploitable as a diversifier of other assets? In their October 2018 paper entitled “A Seasonality Factor in Asset Allocation”, Frank McGroarty, Emmanouil Platanakis, Athanasios Sakkas and Andrew Urquhart test U.S. asset allocation strategies that include a TOTM portfolio as an asset. The TOTM portfolio buys each stock at the open on the last trading day of each month and sells at the close on the third trading day of the following month, earning zero return the rest of the time. They consider four asset universes with and without the TOTM portfolio:

- A conventional stocks-bonds mix.
- The equity market portfolio.
- The equity market portfolio, a small size portfolio and a value portfolio.
- The equity market portfolio, a small size portfolio, a value portfolio and a momentum winners portfolio.

They consider six sophisticated asset allocation methods:

- Mean-variance optimization.
- Optimization with higher moments and Constant Relative Risk Aversion.
- Bayes-Stein shrinkage of estimated returns.
- Bayesian diffuse-prior.
- Black-Litterman.
- A combination of allocation methods.

They consider three risk aversion settings and either a 60-month or a 120-month lookback interval for input parameter measurement. To assess exploitability, they set trading frictions at 0.50% of traded value for equities and 0.17% for bonds. Using monthly data as specified above during July 1961 through December 2015, *they find that:*

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**November 1, 2018** - Bonds, Equity Premium, Strategic Allocation

How does use of actuarial estimates of retiree longevity and empirical mean reversion of stock market returns affect estimated retirement portfolio success rates? In the October 2018 revision of his paper entitled “Joint Effect of Random Years of Longevity and Mean Reversion in Equity Returns on the Safe Withdrawal Rate in Retirement”, Donald Rosenthal presents a model of safe inflation-adjusted retirement portfolio withdrawal rates that addresses: (1) uncertainty about the number of years of retirement (rather than the commonly assumed 30 years); and, (2) mean reversion in annual U.S. stock market returns (rather than a random walk). He estimates retirement longevity as a random input based on the Social Security Administration’s 2015 Actuarial Life Table. He estimates stock market real returns and measures their mean reversion using S&P 500 Index inflation-adjusted total annual returns during 1926 through 2017. He models real bond returns using 10-year U.S. Treasury note (T-note) total annual returns during 1928 through 2017. He applies Monte Carlo simulations (3,000 trials for each scenario) to assess retirement portfolio performance by:

- Assuming an initial retirement portfolio either 100% invested in stocks or 60%/40% in stocks/T-notes (rebalanced at each year-end).
- Debiting the portfolio each year-end by a fixed, inflation-adjusted percentage of the initial amount.
- Calculating percentage of simulation trials for which the portfolio is not exhausted before death (success) and average portfolio terminal balance for successful trials.

He considers two benchmarks: (1) no stock market mean reversion (random walk) and fixed 30-year retirement; and, (2) no stock market mean reversion and actuarial estimate of retirement duration. He also runs sensitivity tests to see how changes in assumptions affect success rate. Using the specified data, *he finds that:*

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