# 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.

**March 17, 2021** - Bonds, Economic Indicators

A subscriber asked (years ago): “Everyone says I should not invest in bonds today because the interest rate is so low (and inflation is daunting). But real bond returns over the last 30 years are great, even while interest rates are low. Could you analyze why bonds do well after, but not before, 1981?” To investigate, we consider the U.S. long-run interest rate and the U.S. Consumer Price Index (CPI) series from Robert Shiller. The long-run interest rate is the yield on U.S. government bonds, specifically the constant maturity 10-year U.S. Treasury note after 1953. We use the term “T-note” loosely to name the entire series. We apply the formula used by Aswath Damodaran to the yield series to estimate nominal T-note total returns. We use 12-month change in CPI. We subtract inflation from T-note nominal total return to get T-note real total return. Using annual Shiller interest rate and CPI data for 1871 through 2020, *we find that:* Keep Reading

**February 16, 2021** - Bonds, Economic Indicators, Equity Premium

Investors arguably expect that investments generate returns in excess of the inflation rate. Do different measures of the inflation rate indicate materially different yield discounts? To investigate, we relate 12-month trailing S&P 500 annual operating earnings yield (E/P), S&P 500 12-month trailing annual dividend yield, 10-year U.S. Treasury note (T-note) yield and 3-month U.S. Treasury bill (T-bill) yield to four measures of annual U.S. inflation rate:

- Non-seasonally adjusted inflation rate based on the total Consumer Price Index (CPI) from the Bureau of Labor Statistics (retroactive revisions of seasonal adjustments interfere with historical analysis).
- Non-seasonally adjusted inflation rate based on core CPI from the Bureau of Labor Statistics.
- Inflation rate based on the Personal Consumption Expenditures: Chain-type Price Index (PCE) from the Federal Reserve Bank of St. Louis.
- Trimmed mean PCE from the Federal Reserve Bank of Dallas.

Using monthly data for all variables during March 1989 (limited by earnings data) through December 2020, *we find that…* Keep Reading

**January 14, 2021** - Bonds, Calendar Effects, Equity Premium

A subscriber requested evaluation of three retirement investment alternatives, assuming a constant increment invested at the end of each month, as follows:

- 50-50: allocate each increment via fixed percentages to stocks and bonds (for comparability, we use 50% to each).
- Seasonal 1: during April through September (October through March), allocate 100% of each increment to stocks (bonds).
- Seasonal 2: during April through September (October through March), allocate 100% of each increment to bonds (stocks).

The hypothesis is that seasonal variation in asset class allocations could improve overall long-term investment performance. We conduct a short-term test using SPDR S&P 500 ETF Trust (SPY) as a proxy for stocks and iShares iBoxx $ Investment Grade Corporate Bond ETF (LQD) as a proxy for bonds. We then conduct a long-term test using Vanguard 500 Index Fund Investor Shares (VFINX) as a proxy for stocks and Vanguard Long-Term Investment-Grade Fund Investor Shares (VWESX) as a proxy for bonds. Based on the setup, we focus on terminal value as the essential performance metric. Using total (dividend-adjusted) returns for SPY and LQD since July 2002 and for VFINX and VWESX since January 1980, all through December 2020, *we find that:* Keep Reading

**January 13, 2021** - Bonds, Political Indicators, Size Effect

“Exploiting the Presidential Cycle and Party in Power” summarizes strategies that hold small stocks (large stock or bonds) when Democrats (Republicans) hold the U.S. presidency. How has this strategy performed in recent years? To investigate, we consider three strategy alternatives using exchange-traded funds (ETF):

- D-IWM:R-SPY: hold iShares Russell 2000 (IWM) when Democrats hold the presidency and SPDR S&P 500 (SPY) when Republicans hold it.
- D-IWM:R-LQD: hold IWM when Democrats hold the presidency and iShares iBoxx Investment Grade Corporate Bond (LQD) when Republicans hold it.
- D-IWM:R-IEF: hold IWM when Democrats hold the presidency and iShares 7-10 Year Treasury Bond (IEF) when Republicans hold it.

We use calendar years to determine party holding the presidency. As benchmarks, we consider buying and holding each of SPY, IWM, LQD or IEF and annually rebalanced portfolios of 60% SPY and 40% LQD (60 SPY-40 LQD) or 60% SPY and 40% IEF (60 SPY-40 IEF). We consider as performance metrics: average annual excess return (relative to the yield on 1-year U.S. Treasury notes at the beginning of each year); standard deviation of annual excess returns; annual Sharpe ratio; compound annual growth rate (CAGR); and, maximum annual drawdown (annual MaxDD). We assume portfolio switching/rebalancing frictions are negligible. Except for CAGR, computations are for full calendar years only. Using monthly dividend-adjusted closing prices for the specified ETFs during July 2002 (limited by LQD and IEF) through December 2020, *we find that:*

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**December 31, 2020** - Bonds, Equity Premium, Momentum Investing, Strategic Allocation

Are the “Simple Asset Class ETF Value Strategy” (SACEVS) and the “Simple Asset Class ETF Momentum Strategy” (SACEMS) mutually diversifying. To check, based on feedback from subscribers about combinations of interest, we look at three equal-weighted (50-50) combinations of the two strategies, rebalanced monthly:

- 50-50 Best Value – EW Top 2: SACEVS Best Value paired with SACEMS Equally Weighted (EW) Top 2 (aggressive value and somewhat aggressive momentum).
- 50-50 Best Value – EW Top 3: SACEVS Best Value paired with SACEMS EW Top 3 (aggressive value and diversified momentum).
- 50-50 Weighted – EW Top 3: SACEVS Weighted paired with SACEMS EW Top 3 (diversified value and diversified momentum).

We consider as a benchmark a simple technical strategy (SPY:SMA10) that holds SPDR S&P 500 ETF Trust (SPY) when the S&P 500 Index is above its 10-month simple moving average and 3-month U.S. Treasury bills (Cash, or T-bills) when below. We also test sensitivity of results to deviating from equal SACEVS-SACEMS weights. Using monthly gross returns for SACEVS, SACEMS, SPY and T-bills during July 2006 through November 2020, *we find that:* Keep Reading

**December 30, 2020** - Bonds, Fundamental Valuation

How does the Cyclically Adjusted Price-to-Earnings ratio (CAPE, or P/E10) behave during the COVID-19 pandemic? What are its current implications? In the November 2020 revision of their paper entitled “CAPE and the COVID-19 Pandemic Effect”, Robert Shiller, Laurence Black and Farouk Jivraj examine behavior of CAPE during 2020 in the U.S., UK, Europe, Japan and China, highlighting the impact of the pandemic. They apply CAPE to generate current 2-year, 5-year and 10-year equity return forecasts based on full-sample regressions. They then extend the CAPE forecasting approach to forecast changes in excess real return of stocks over bonds (see the chart below) to explore why investors strongly prefer equities over bonds during the pandemic. Finally, they look at sector dynamics within each economy. Using Shiller data during January 1871 through September 2020, *they find that:* Keep Reading

**December 29, 2020** - Bonds, Equity Premium, Real Estate, Strategic Allocation

What happens if we extend the “Simple Asset Class ETF Value Strategy” (SACEVS) with a real estate risk premium, derived from the yield on equity Real Estate Investment Trusts (REIT), represented by the FTSE NAREIT Equity REITs Index? To investigate, we apply the SACEVS methodology to the following asset class exchange-traded funds (ETF), plus cash:

3-month Treasury bills (Cash)

iShares 20+ Year Treasury Bond (TLT)

iShares iBoxx $ Investment Grade Corporate Bond (LQD)

SPDR Dow Jones REIT (RWR) through September 2004 dovetailed with Vanguard REIT ETF (VNQ) thereafter

SPDR S&P 500 (SPY)

This set of ETFs relates to four risk premiums, as specified below: (1) term; (2) credit (default); (3) real estate; and, (4) equity. We focus on effects of adding the real estate risk premium on gross compound annual growth rates (CAGR), maximum drawdowns (MaxDD) and annual Sharpe ratios of the Best Value (picking the most undervalued premium) and Weighted (weighting all undervalued premiums according to degree of undervaluation) versions of SACEVS. Using lagged quarterly S&P 500 earnings, monthly S&P 500 Index levels and monthly yields for 3-month U.S. Treasury bill (T-bill), the 10-year Constant Maturity U.S. Treasury note (T-note), Moody’s Seasoned Baa Corporate Bonds and FTSE NAREIT Equity REITs Index since March 1989 (limited by availability of earnings data), and monthly dividend-adjusted closing prices for the above asset class ETFs since July 2002, all through November 2020, *we find that:* Keep Reading

**December 23, 2020** - Bonds, Equity Premium, Strategic Allocation

“Simple Asset Class ETF Value Strategy” (SACEVS) finds that investors may be able to exploit relative valuation of the term risk premium, the credit (default) risk premium and the equity risk premium via exchange-traded funds (ETF). However, the backtesting period is limited by available histories for ETFs and for series used to estimate risk premiums. To construct a longer test, we make the following substitutions for potential holdings (selected for length of available samples):

To enable estimation of risk premiums over a longer history, we also substitute:

As with ETFs, we consider two alternatives for exploiting premium undervaluation: Best Value, which picks the most undervalued premium; and, Weighted, which weights all undervalued premiums according to degree of undervaluation. Based on the assets considered, the principal benchmark is a monthly rebalanced portfolio of 60% VFINX and 40% VFIIX. Using monthly risk premium calculation data during March 1934 through November 2020 (limited by availability of T-bill data), and monthly dividend-adjusted closing prices for the three asset class mutual funds during June 1980 through November 2020 (40+ years, limited by VFIIX), *we find that:*

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**December 21, 2020** - Bonds, Equity Premium, Strategic Allocation

Is there a better way than the Fed model to measure relative attractiveness of equities and bonds. In his October 2020 paper entitled “Towards a Better Fed Model”, Raymond Micaletti examines seven Fed Model alternatives, each comparing a 10-year forward annualized estimate of equity returns to the yield of 10-year constant maturity U.S. Treasury notes (T-note). The seven estimates of future equity returns are based on autocorrelation-corrected quarterly regressions using 10 years of past quarterly data for one of: (1) Aggregate Investor Allocation to Equities (AIAE); (2) Cyclically-Adjusted Price-to-Earnings Ratio (CAPE); (3) Tobin’s Q (QRATIO); (4) Market Capitalization-to-Nominal GDP (MC/GDP); (5) Market Capitalization-to-Adjusted Gross Value Added (MC/AGVANF); (6) Market Capitalization-to-Household and Non-Profit Total Assets (MC/HHNPTA); and, (7) Household and Non-Profit Equity Allocation-to-Nominal GDP (HHNPEQ/GDP). He calculates AIAE as total market value of equities divided by the sum of total market value of equities and total par value of bonds, approximated by adding the liabilities of five categories of borrowers. He then tests for each alternative a tactical asset allocation (TAA) strategy that each month weights equities and bonds based on a modified z-score of the forecasted 10-year equity risk premium (equity return minus T-note yield) computed by subtracting the median and dividing by the standard deviation of actual monthly premiums over the past 10 years. If modified z-score is greater than 1 (less than -1), the strategy is 100% in equities (0% in equities). In between those thresholds, weights are based on linear interpolation. Using quarterly data from the Archival Federal Reserve Economic Database (ALFRED) and Robert Shiller’s data library and daily U.S. equity market returns and U.S. Treasury bond/note roll-adjusted futures returns as available from the end of the fourth quarter of 1951 through the end of the third quarter of 2020, *he finds that:* Keep Reading

**December 16, 2020** - Bonds, Equity Premium, Gold, Technical Trading

A subscriber asked about a strategy that switches between an equal-weighted portfolio of Invesco QQQ Trust (QQQ) and iShares Russell 2000 ETF (IWM) when the S&P 500 Index is above its 200-day simple moving average (SMA200) and an equal-weighted portfolio of SPDR Gold Shares (GLD) and iShares 20+ Year Treasury Bond ETF (TLT) when below. Also, more generally, is an equal-weighted portfolio of GLD and TLT (GLD:TLT) superior to TLT only for risk-off conditions? To investigate, we (1) backtest the switching strategy and (2) compare performances of GLD:TLT versus TLT when the S&P 500 Index is below its SMA200. We consider both gross and net performance, with the latter accounting for 0.1% portfolio switching frictions 0.001% daily portfolio rebalancing frictions (rebalancing one hundredth of portfolio value). As benchmarks, we consider buying and holding SPDR S&P 500 ETF Trust (SPY) and a strategy that holds SPY (TLT) when the S&P 500 Index is above (below) its SMA200. Using daily S&P 500 Index levels starting February 5, 2004 and daily dividend-adjusted levels of QQQ, IWM, GLD, TLT and SPY starting November 18, 2004 (limited by inception of GLD), all through November 25, 2020, *we find that:*

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