# 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.

**February 9, 2017** - Bonds, Volatility Effects

“Equity Market and Treasuries Variance Risk Premiums as Return Predictors” reports a finding, among others, that the variance risk premium for 10-year U.S. Treasury notes (T-note) predicts near-term returns for those notes (as manifested via futures). However, the methods used to calculate the variance risk premium are complex. Is there a simple way to exploit the predictive power found? To investigate, we test whether a simple measure of the volatility risk premium (VRP) for T-notes predicts returns for the iShares 7-10 Year Treasury Bond (IEF) exchange-traded fund. Specifically we:

- Calculate daily realized volatility of IEF as the standard deviation of daily total returns over the past 21 trading days, multiplied by the square root of 252 to annualize.
- Use daily closes of CBOE/CBOT 10-year U.S. Treasury Note Volatility Index (TYVIX) as annualized implied volatility.
- Calculate the daily T-note VRP as TYVIX minus IEF realized volatility.

VRP here differs from that in the referenced research in three ways: (1) it is a volatility premium rather than a variance premium based on standard deviation rather than the square of standard deviation; (2) it is implied volatility minus expected realized volatility, rather than the reverse, and so should be mostly positive; and, (3) estimation of expected realized volatility is much simpler. When TYVIX has daily closes on non-market days, we ignore those closes. When TYVIX does not have daily closes on market days, we reuse the most recent value of TYVIX. These exceptions are rare. Using daily IEF dividend-adjusted prices since December 2002 and daily closes of TYVIX since January 2003 (earliest available), both through January 2017, *we find that:* Keep Reading

**February 8, 2017** - Bonds, Equity Premium, Volatility Effects

Do bonds, like equity markets, offer a variance risk premium (VRP)? If so, does the bond VRP predict bond returns? In their January 2017 paper entitled “Variance Risk Premia on Stocks and Bonds”, Philippe Mueller, Petar Sabtchevsky, Andrea Vedolin and Paul Whelan examine and compare the equity VRP (EVRP) via the S&P 500 Index and U.S. Treasuries VRP (TVRP) via 5-year, 10-year and 30-year U.S. Treasuries. They specify VRP generally as the difference between the variance indicated by past values of variance (realized) and that indicated by current option prices (implied). Their VRP calculation involves:

- To forecast daily realized variances at a one-month horizon, they first calculate high-frequency returns from intra-day price data of rolling futures series for each of 5-year, 10-year and 30-year Treasury notes and bonds and for the S&P 500 Index. They then apply a fairly complex regression model that manipulates squared inception-to-date returns (at least one year) and accounts for the effect of return jumps.
- To calculate daily implied variances for Treasuries at a one-month horizon, they employ end-of-day prices on cross-sections of options on Treasury futures. For the S&P 500 Index, they use the square of VIX.
- To calculate daily EVRP and TVRPs with one-month horizons, subtract respective implied variances from forecasted realized variances.

When relating VRPs to future returns for both Treasuries and the S&P 500 Index, they calculate returns from fully collateralized futures positions. Using the specified futures, index and options data during July 1990 through December 2014, *they find that:* Keep Reading

**January 25, 2017** - Bonds, Equity Premium, Momentum Investing, Strategic Allocation

“Cross-asset Class Intrinsic Momentum” summarizes research finding that past country stock index (government bond index) returns relate positively (positively) to future country stock market index returns and negatively (positively) to future country government bond index returns. Is this finding useful for specifying a simple strategy using exchange-traded fund (ETF) proxies for the U.S. stock market and U.S. government bonds? To investigate we test the following five strategies:

- Buy and hold.
- TSMOM Long Only – Each month, hold the asset (cash) if its own 12-month past return is positive (negative).
- TSMOM Long or Short – Each month, hold (short) the asset if its own 12-month past return is positive (negative).
- XTSMOM Long Only – Each month hold stocks if 12-month past returns for stocks and government bonds are both positive, and otherwise hold cash. Each month hold bonds if 12-month past returns are negative for stocks and positive for government bonds, and otherwise hold cash.
- XTSMOM L-S-N (Long, Short or Neutral) – Each month hold (short) stocks if 12-month past returns for both are positive (negative), and otherwise hold cash. Each month hold (short) bonds if 12-month past returns are negative (positive) for stocks and positive (negative) for bonds, and otherwise hold cash.

We use SPDR S&P 500 (SPY) and iShares 7-10 Year Treasury Bond (IEF) as proxies for the U.S. stock market and U.S. government bonds. We use the 3-month U.S. Treasury bill (T-bill) yield as the return on cash. We apply the five strategies separately to SPY and IEF, and to an equally weighted, monthly rebalanced combination of the two for a total of 15 scenarios. Using monthly total returns for SPY and IEF and monthly T-bill yield during July 2002 (inception of IEF) through December 2016, *we find that:* Keep Reading

**January 24, 2017** - Bonds, Equity Premium, Momentum Investing, Strategic Allocation

Are stock and bond markets mutually reinforcing with respect to time series (intrinsic or absolute return) momentum? In their December 2016 paper entitled “Cross-Asset Signals and Time Series Momentum”, Aleksi Pitkajarvi, Matti Suominen and Lauri Vaittinen examine a strategy that times each of country stock and government bond (constant 5-year maturity) indexes based on past returns for both. Specifically:

- For stocks, they each month take a long (short) position in a country stock index if past returns for both the country stock and government bond indexes are positive (negative). If past stock and bond index returns have different signs, they take no position.
- For bonds, they each month take a long (short) position in a country government bond index if past return for bonds is positive (negative) and past return for stocks is negative (positive). If past stock and bond index returns have the same sign, they take no position.

They call this strategy cross-asset time series momentum (XTSMOM). For initial strategy tests, they consider past return measurement (lookback) and holding intervals of 1, 3, 6, 9, 12, 24, 36 or 48 months. For holding intervals longer than one month, they average monthly returns for overlapping positions. For most analyses, they focus on lookback interval 12 months and holding interval 1 month. For a given lookback and holding interval combination, they form a diversified XTSMOM portfolio by averaging all positions for all countries. They measure excess returns relative to one-month U.S. Treasury bills. They employ the MSCI World Index and the Barclays Capital Aggregate Bond Index as benchmarks. Using monthly stock and government bond total return indexes for 20 developed countries as available during January 1980 through December 2015, *they find that:* Keep Reading

**January 13, 2017** - Bonds, Momentum Investing

Does the credit premium, measured by the difference in returns between U.S. corporate bonds and duration-matched U.S. Treasuries, exhibit momentum? In his December 2016 paper entitled “Momentum in the Cross-Section of Corporate Bond Returns”, Jeroen van Zundert tests for momentum of the volatility-adjusted credit premium among U.S. corporate bonds via the following methodology:

- Acquire the monthly total credit premium of each corporate bond as the difference in total (coupon-reinvested) returns between the bond and a duration-matched U.S. Treasury instrument.
- For each bond, divide cumulative total credit premium over the last six months by standard deviation of monthly credit premiums over the last 12 months (something like a Sharpe ratio).
- After inserting a skip-month, sort all bonds on this metric into tenths (decile portfolios), with each bond weighted by the inverse of its volatility.
- Hold each portfolio for six months, computing an overall monthly return as the average for portfolios formed within the last six months.
- Calculate volatility-adjusted credit premium momentum as the gross difference in performance between the top (winner) and bottom (loser) decile portfolios.

To estimate portfolio alphas, he adjusts for six factors (equity market, equity size, equity value, equity momentum, bond term and default risk). In robustness tests, he considers past return measurement and holding intervals of one, three, nine and 12 months. Using total credit premiums, trading volumes and characteristics for a broad sample of U.S. investment grade and high yield corporate bonds during January 1994 through December 2015, *he finds that:* Keep Reading

**December 12, 2016** - Bonds, Momentum Investing, Technical Trading

Is there pervasive yield momentum among U.S. corporate bonds? In their November 2016 paper entitled “Is Momentum Spanned Over Corporate Bonds of Different Ratings?”, Hai Lin, Chunchi Wu and Guofu Zhou investigate whether momentum exists in all segments of the U.S. corporate bond market. Their approach to momentum measurement is unconventional, involving cross-sectional regression of bond returns on multiple simple moving averages (SMA) of bond yields. They call their result “trend momentum” to distinguish it from conventional momentum based on simple past return. Specifically, they each month:

- Calculate yield SMAs over the last 1, 3, 6, 12, 24, 36, 48 and 60 months for each bond.
- Regress returns for all bonds on respective prior-month yield SMAs to generate correlations (betas) between returns and past yield SMAs, thereby dynamically determining relative importance of yield SMA measurement intervals.
- Calculate expected (for next month) yield SMA betas as average calculated betas over the past 12 months.
- Estimate expected return (for next month) for each bond based on current yield SMAs and expected yield SMA betas.
- Rank bonds based on expected returns into fifths (quintiles) or tenths (deciles).
- Calculate gross trend momentum factor return as the difference in average (equal-weighted) actual returns between quintiles/deciles with the highest and lowest expected returns.

Using yields, returns, ratings and other characteristics for a broad sample of U.S. corporate bonds during January 1973 through September 2015, *they find that:* Keep Reading

**September 22, 2016** - Bonds, Calendar Effects

Do government bond returns worldwide exhibit seasonal effects analogous to those of stock market returns? In their August 2016 draft paper entitled “Seasonality in Government Bond Returns and Factor Premia”, Adam Zaremba and Tomasz Schabek investigate seasonal patterns in government bond returns across countries, focusing on regression tests of January and sell-in-May (May-October versus November-April) effects. They also examine whether four bond risk premiums (volatility, credit risk, value and momentum), each specified in multiple ways and measured via long-short portfolios formed from monthly sorts, exhibit these two seasonal effects. Using monthly total return bond indexes hedged against the U.S. dollar spanning 25 countries and allocated to five term ranges (1-3 years, 3-5 years, 5-7 years, 7-10 years and 10+ years) during January 1992 through June 2016, *they find that:* Keep Reading

**September 21, 2016** - Bonds, Equity Premium

How (and what) does John Bogle think about the stock and bond markets over the next decade? In their October 2015 article entitled “Occam’s Razor Redux: Establishing Reasonable Expectations for Financial Market Returns”, flagged by a subscriber, John Bogle and Michael Nolan revisit simple models for expected stock market and government bond returns first published in 1991. The stock market model distinguishes between: (1) investment return, defined as initial dividend yield plus expected annual earnings growth rate; and, (2) speculative return, defined as annual percentage change in price-to-earnings ratio (P/E). The government bond model uses the initial interest rate as a reasonable expectation for return over the life of the bond. In both models, the investment horizon is a decade. They update performances of the models to include the 25 years since publication and apply them to determine expectations for stock and bond market returns over the decade ahead. Using data for the stock market since 1871 and for 10-year U.S. Treasury notes (or equivalent) since 1915, both through 2014, *they find that:* Keep Reading

**September 15, 2016** - Bonds, Commodity Futures, Currency Trading, Momentum Investing

Does time series (intrinsic or absolute) momentum work across asset classes prior to the Great Moderation (secular decline in interest rates)? In their August 2016 paper entitled “Trend Following: Equity and Bond Crisis Alpha”, Carl Hamill, Sandy Rattray and Otto Van Hemert test several time series momentum portfolios as applied to groups of bonds, commodities, currencies and equity indexes as far back as 1960. They consider 10 developed country equity indexes, 11 developed country government bond series, 25 agricultural/energy/metal futures series and nine U.S. dollar currency exchange rate series. They calculate return momentum for each asset as the weighted sum of its past monthly returns (up to 11 months) divided by the normalized standard deviation of those monthly returns. They then divide each signal again by volatility and apply a gearing factor to specify a 10% annual volatility target for each holding. Within each of equity index, bond and currency groups, they weight components equally. Within commodities, they weight agriculture, energy and metal sectors equally after weighting individual commodities equally within each sector. They report strategy performance based on excess return, roughly equal to real (inflation-adjusted) return. They commence strategy performance analyses in 1960 to include an extreme bond bear market. Using monthly price series that dovetail futures/forwards from inception with preceding spot (cash) data as available starting as early as January 1950 and as late as April 1990, all through 2015, *they find that:* Keep Reading

**September 13, 2016** - Bonds, Currency Trading, Economic Indicators, Equity Premium

Is global diversification within asset classes disappearing as worldwide economic and financial integration increases? In their August 2016 paper entitled “Globalization and Asset Returns”, Geert Bekaert, Campbell Harvey, Andrea Kiguel and Xiaozheng Wang examine whether economic and financial integration increases global comovement of country equity, bond and currency exchange market returns. They examine three measures of return comovement for each asset class: average pairwise correlation, average beta relative to the world market and average idiosyncratic volatility. They apply these measures separately to developed markets and emerging markets. Using monthly equity, bond and currency exchange market returns in U.S. dollars for 26 developed markets and 32 emerging markets as available from various inceptions through December 2014, *they find that:* Keep Reading