# 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.

**June 28, 2021** - Bonds, Economic Indicators, Equity Premium, Gold

How sensitive are returns of stocks, bonds and gold to levels real interest rates (nominal rates minus inflation)? To investigate, we consider three nominal interest rates and two measures of inflation, as follows:

These choices offer six alternative real interest rates. We use end-of-month interest rates and inflation measures lagged by one month to account for release delay. We use the S&P 500 Index (SP500) capital gain only, the 10-year yield (with bond prices moving inversely) and spot gold price, all measured end-of-month, to represent returns for stocks, bonds and gold. We then relate monthly changes in real interest rates to asset class monthly returns in two ways: (1) calculate correlations of monthly real interest rates to asset class returns for each of the next 12 months to get a sense of how real rates lead asset returns; and, (2) calculate average asset class monthly returns by ranked tenths (deciles) of prior-month real interest rates to discover any non-linear relationships. Using monthly PCEPI and Core PCEPI since January 1961, interest rates since January 1962, SP500 level since December 1961 and spot gold price since December 1974 (when controls are removed), all through May 2021, *we find that:*

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**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

**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

**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 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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**November 19, 2020** - Bonds, Equity Premium

“Market Impacts of Growth in Target Date Funds” summarizes research on potential market-wide effects of periodic rebalancing actions of Target Date Funds (TDF), which trade against momentum. One piece of evidence is that monthly autocorrelation of S&P 500 Index returns is significantly negative during 2010-2019 but not during 1986-1995 or 1996-2005. Another is that TDFs accomplish most of quarterly rebalancing within the next quarter. To assess how convincing autocorrelation findings are, we calculate rolling 5-year monthly (60-month) and quarterly (20-calendar quarter) autocorrelations of returns for:

Using monthly total (dividend-reinvested) returns for these three assets through October 2020, *we find that:* Keep Reading

**November 18, 2020** - Bonds, Equity Premium, Strategic Allocation

Are aggregate periodic stocks-bonds rebalancing actions of Target Date Funds (TDF), which trade against momentum, increasingly affecting U.S. stock market dynamics? In their October 2020 paper entitled “Retail Financial Innovation and Stock Market Dynamics: The Case of Target Date Funds”, flagged by a subscriber, Jonathan Parker, Antoinette Schoar and Yang Sun examine market impacts of Target Date Funds (TDFs), assets of which have grown from less than $8 billion in 2000 to more than $2.3 trillion (of roughly $21 trillion in U.S. mutual funds) in 2019. Using quarterly data on TDF holdings, monthly U.S. stock market and Vanguard Total Bond Market Index Fund (bond market) returns and monthly data for stocks held by and similar to those held by TDFs during the third quarter of 2008 through the fourth quarter of 2018 (excluding three quarters with suspect data), *they find that:*

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**July 16, 2020** - Bonds, Equity Premium, Strategic Allocation

How should investors think about the interactions between working years (retirement account contributions) and retirement years (retirement account withdrawals)? In his June 2020 paper entitled “Retirement Planning: From Z to A”, Javier Estrada integrates working and retirement periods to estimate how much an individual should save and how they should invest to achieve a desired retirement income and ultimate bequest to heirs. He illustrates his analytical solution empirically for U.S. stocks and bonds, first using a base case plus sensitivity analysis and then using Monte Carlo simulations. His base case assumes:

- Work will last 40 years with a 60%/40% stocks/bonds retirement portfolio.
- Retirement will last 30 years with beginning-of-year real (inflation-adjusted) withdrawals of $60,000 from a 40%/60% stocks/bonds retirement portfolio and ultimate bequest $300,000.

Using annual data for U.S. stocks (the S&P 500 Index total return), bonds (10-year U.S. Treasury notes) and U.S. inflation during 1928 through 2019, *he finds that:* Keep Reading