Additional Factor-Based Investing
These notes are a continuation of the notes primarily based on the ideas and leanings from "Your Complete Guide To Factor-Based Investing, The Way Smart Money Invests Today", 1st Edition, by Andrew Berkin and Larry Swedroe in 2016. Other additional considerations are presented, such as reasonable expectations around the performance of factors in the future and expanded definitions of several factors. Moreover, as with the factors which were previously mentioned for equities, asset pricing models have been created using factors which are relevant to the relationship of risk within bonds. As before, there needs to be the establishment of unique criteria and characteristics in the definition of a factor as persistent, pervasive, robust, investible and intuitive. Other miscellaneous points are further considered.
Expectations After Publication
An important aspect of factors is whether their relationships and premiums are affected by the publication of the research identifying the factors. If the anomalies causing a factor are the result of behavioural-based reasons or even simple preferences unrelated to the fundamentals of the assets, the publication of the factors would alert the attention of sophisticated investors who can arbitrage the premiums until they disappear. In other words, it would be expected for this information to be incorporated into the market, such that the anomalies would be reduced relative to the limits of arbitrage (regulations against short positions, interest costs of borrowing, limited supply of shares for shorting, re-calling of shorts before strategies are compensated, triggering of liquidation in the short-term, and potentially unlimited losses from shorting). These limits to arbitrage may allow for the factor to remain in a less prominent form, but the premium from the factor would have been significantly reduced. In a sense, the market is becoming more efficient over time (documented as the Adaptive Markets Hypothesis by Paul Calluzzo, Fabio Moneta, and Selim Topaloglu - anomalies are publicized broadly, institutions trade accordingly, and returns decay correspondingly). Thus, a lesser emphasis should be placed on factors which rely solely on behavioural-based reasons. Regardless, the efficiency of the market is increasing and this is favourable for the average investors (who must hold the market in aggregate).
With regard to risk-based reasons, it is still possible for the premiums realized from factors to be reduced in the future. This is evident, as the publication of the factors can lead to the creation of specialized funds which attempt to optimally capture the premium from the factors directly (as opposed to previous funds which may have captured the factors indirectly or sub-optimally by coincidence). As a result, the premiums from the factors must be reduced as the size of the fund increases, as there are potentially more investors who are willing to accept the higher risks associated with the factors, thus reducing the expectations for compensation from these risks. Therefore, it should still be expected for these factors to remain in moderately relevant forms, but the premiums from the factors may be somewhat reduced. For a conservative estimation, it can be projected for the premiums from the factors to half in extreme circumstances and depending on the factor (for example, this may be less applicable to market beta but possibly more applicable to the size factor or momentum factor (especially due to the high turnover)). As mentioned, there is always still the chance of an adverse outcome, as nothing can be guaranteed otherwise there would be no risk.
It should also be recognized that there are external reasons for the possibility of premiums from the factors to be reduced. For example, specifically in the United States, the Securities Exchange Commission (SEC) has strengthened regulations and protections for investors and reduced the risk of investing in certain equities. Since the Great Depression in 1929, the Federal Reserve has been able to intervene to dampen economic volatility and reduce the risk of investing in equities. There is also greater opportunity and wealth, such that capital has become less scarce and assets have become more accessible, such that the valuations of equities have increased - in other words, there are more investors willing to accept the risks associated with factors. Finally, there has been the development of new structures for investments, such as Exchange Traded Funds (ETFs), which assist in increasing the liquidity of assets, as assets with low liquidity can be held indirectly by assets with higher liquidity, such that the price of the illiquid asset is not the only avenue of pricing for that asset - in other words, the asset does not have to be traded to update its effective price at which it would be traded.
Post-Publication Returns
Examining the changes to the premiums from the size, value, and momentum factors (market beta is not considered due to its prolonged and continuous history, while the profitability factor is not considered due to the recency of its discovery with publication in 2013), it is evident that these premiums have decreased but still exist with significance after publication. However, in most cases, a definitive and statistically significant conclusion can only be made as more data becomes available over time with multiple market cycles in the post-publication period.
Considering the size factor, Rolf Banz published a paper in 1981 highlighting the anomaly, relative to the Capital Asset Pricing Model (CAPM), which existed for equities with small market capitalizations compared to equities with large market capitalizations. The pre-publication premium from the size factor between 1927 and 1981 was 4.7% per year, while the post-publication premium from the size factor between 1982 and 2015 was 1.0% per year. Understandably, this reduction is mostly logical due to advancements by brokerages and reductions in trading costs for equities. This has led to narrower bid-ask spreads and commissions, which then increased the liquidity of equities with small market capitalizations. In addition, the introduction of market making and high-frequency trading as data became more widely and instantaneously available has helped to decrease implementation costs. However, if the period is considered in more detail, there may be inconsistencies which should be highlighted. From 1975 to 1983, the premium from the size factor was 13.8% per year, which unevenly increased the pre-publication average to a benchmark which would be difficult to repeat. Unfortunately, from 1984 to 1990, the premium from the size factor was -7.1% per year, which decreased the post-publication average to a baseline which would be difficult to recover. So, it could be that the date of publication is coincidentally at an infliction point between periods of differing performance. For example, from 1991 to 2015, the premium from the size factor was 2.5% per year (from 2000 to 2015, the premium from the size factor was 3.7%).
Considering the value factor, Barr Rosenberg, Kenneth Reid, and Ronald Lanstein published a paper in 1985 highlighting the anomaly which existed for equities with cheap valuations compared to equities with expensive valuations based on their book-to-market ratios. The pre-publication premium from the value factor between 1927 and 1985 was 5.8% per year, while the post-publication premium from the value factor between 1986 and 2015 was 2.8% per year. This reduction could be attributed to the wider distribution and availability of information, which has had the potential to reduce inefficiencies and mitigate mispricing. However, if the period is considered in more detail, it is seen that the Technology Bubble in the 1990s and Financial Crisis in 2007 contributed to the premium from the value factor being negative for brief periods. This would have had an impact on the overall average throughout the period and, if these events were irrational exuberance or anomalies, they should not really be expected to repeat frequently.
Considering the momentum factor, Narasimhan Jegadeesh and Sheridan Titman published a paper in 1993 highlighting the anomaly which existed for equities with high recent returns compared to equities with low recent returns. The pre-publication premium from the momentum factor between 1927 and 1993 was 10.9% per year, while the post-publication premium from the momentum factor between 1994 and 2015 was 5.5% per year. If the period is considered in more detail, this reduction is primarily due to the Financial Crisis in 2007, where the momentum factor experienced a -82.9% drawdown due to the sudden collapse followed by the unexpected recovery in 2009 with equities with low recent returns (due to the collapse) rising dramatically. As mentioned, this potential for very large drawdowns during periods with high volatility is one of the risk-based reasons for the momentum factor - it just happens that the largest of these drawdowns happened in the post-publication period. Again, more data is needed in the post-publication period to make other conclusions (especially if the factor is to be discarded as an insignificant result from random chance).
Size Factor Re-Evaluation
As it was originally constructed, the size factor considers market capitalization, where equities with large market capitalizations are defined to be within the upper 50% of equities with the largest market capitalization, while equities with small market capitalizations are defined to be within the lower 50% of equities with the smallest market capitalizations - in other words, all equities are included in the consideration. This is in contrast to other factors which typically consider equities divided into the upper 30% of equities relative to a metric and lower 30% of equities relative to a metric - in other words, there is a middle portion considered to be core, blend, or neutral. As an implication, it can appear as though the premium from the size factor is lesser than the premium from other factors, but this is primarily due to the premium from the size factor being diluted from a less extreme and more lenient metric. This is clear when deciles based on market capitalization are viewed in isolation, where the premium increases as the market capitalization decreases.
| Period From 1927 To 2015 | Market Capitalization Deciles (1 = Large, 10 = Small) | |||
|---|---|---|---|---|
| 1-2 | 3-5 | 6-8 | 9-10 | |
| Annualized Return | 9.47% | 10.99% | 11.39% | 11.98% |
| Period From 1927 To 2015 | Upper Percentage / Lower Percentage | |||
|---|---|---|---|---|
| 50% / 50% | 30% / 30% | 20% / 20% | 10% / 10% | |
| Size Factor | 3.28% | 5.22% | 6.15% | 7.65% |
| t-Statistic | 2.22 | 2.34 | 2.27 | 2.44 |
Therefore, using stricter definitions of the size factor, it is possible to evaluate how the premium from the size factor changes based on its definition. From 1927 to 2015 and in the domestic market, the annual premium was 3.28% with a t-statistic of 2.22 using the upper 50% and lower 50% of equities based on market capitalization, annual premium was 5.22% with a t-statistic of 2.34 using the upper 30% and lower 30% of equities based on market capitalization, annual premium was 6.15% with a t-statistic of 2.27 using the upper 20% and lower 20% of equities based on market capitalization, and annual premium was 7.65% with a t-statistic of 2.44 using the upper 10% and lower 10% of equities based on market capitalization. Examining the results of funds from 1998 to 2015, the DFA U.S. Micro-Cap Fund (DFSCX) had loadings of 1.01, 0.82, 0.73, or 0.64 compared to the DFA U.S. Small-Cap Fund (DFSTX) with loadings of 0.83, 0.65, 0.56, or 0.48 when the size factor is more narrowly defined with groups of 50%, 30%, 20%, and then 10% of equities.
Dividend Irrelevance
It should be emphasized that dividends are not a factor driving expected returns and are not expected to have any predictive ability of future returns. In 1961, Merton Miller and Franco Modigliani published a paper on capital structure which established that dividend policy should be irrelevant to the returns from equities, as the value of a company is the present value of expected future cash flows (future earnings and change in book value) and is unaffected by and not directly related to how the company is financed (in other words, the value of a company is independent of its capital structure). This has to be the case, as a dividend must always result in a decrease in the price of an asset by an amount equal to the dividend. For example, if there is Company A with a share price of $10, Company B with a share price of $10, and both companies earn $2 per share but Company A distributions 50% of these earnings while Company B retains 100% of these earnings, then the final share price will be $11 for Company A with a distribution of $1 and $12 for Company B without any distributions - in either case, the total return would be $2 per share. The total return of an asset should be the focus for any investor without an immediate preference for dividends or capital gains (unless the investor needs a psychological benefit from receiving income, although this would be an irrational preference).
To be clear, equities with identical exposure to the factors in an asset pricing model have the same expected return regardless of their dividend policy - in other words, the returns of a strategy targetting equities with high dividends are completely explained by their exposure to the factors in an asset pricing model (particularly the value and profitability factors) with statistically insignificant alphas. This is an important consideration, as a strategy targetting equities with high dividends will inevitably be less diversified due to the exclusion of equities which do not pay dividends (about 60% of domestic equities and 40% of international equities), subsequently leading to a higher potential dispersion of returns and lower reliability or certainty in the likely outcome. In addition, dividends should probably be viewed negatively, as they essentially lead to more transaction costs if re-invested and are a taxable event which cannot be controlled.
Low-Volatility Factor
Put forward in 1972 by Fischer Black, a contrasting finding to conventional expectation, that there is a positive relationship between risk and return, was that the relationship between risk and return was actually often flat or negative (when risk was measured using volatility relative to mean-variance analysis from the CAPM). For example, over the last 50 years, the most defensive equities with low volatility have delivered higher returns and higher risk-adjusted returns than the most aggressive equities with high volatility. These defensive equities are referred to as low-beta equities, as they have less volatility than the market, while aggressive equities are referred to as high-beta, as they have more volatility than the market. Strategies targeting low-beta equities would have also generated alphas relative to the FF3 and FF3 with momentum models. This result has also been found in international equities, as well as in various bond markets.
A possible, although counter-intuitive, explanation for this anomaly is that, in order to increase their exposure to market beta and generate higher expected returns, investors are willing to hold high-beta equities and avoid low-beta equities (similar to a form of leverage without borrowing). As a result, the price of high-beta equities is increased by more than their appropriate proportion relative to their exposure to market beta and, as a consequence, these high-beta equities become overpriced relative to their fundamentals. This is also heightened due to constraints and frictions in correcting mispricing due to the limits to arbitrage, transaction costs, taxes, and regulations. This can also be understood through the winner's curse, where, in a market with little or no shorting, the demand for a particular equity comes from the minority who hold the most optimistic expectations about it and, as divergence of opinion is likely to increase with risk, high-risk equities are more likely to be overpriced than low-risk equities due to the greater bias from the minority (after the majority have withdrawn from participating in setting the price (without yet resorting to shorting)). Alternative explanations are centred around the irrationality of investors and their arbitrary preferences or tastes.
However, the majority of high-beta equities tend to be equities with small market capitalizations, expensive valuations, and low quality. Interestingly, profitability is actually the most significant predictor of volatility with high profitability corresponding with low volatility and low profitability corresponding with high volatility. When considering a portfolio with a long portion in low-beta equities and short portion in high-beta equities, it is evident that over 80% of the premium from this surmised low-volatility factor actually comes from the short portion of the portfolio. If profitability is included as a factor in the asset pricing model used to evaluate performance, the performance of strategies targeting low-beta equities can then be mostly explained by the known factors without statistically significant alphas. Thus, especially for long-only portfolios, a low-volatility factor would not be a reliable factor, as an independent driver of cross-sectional variation in returns, once there is already consideration for profitability within the asset pricing model.
To illustrate the reliance on equities with small market capitalizations, expensive valuations, and low quality, a strategy targeting low-beta equities can be created independently in the universes of small-cap growth, small-cap value, large-cap growth, and large-cap value between 1968 and 2015 with a long portion in low-beta equities and short portion in high-beta equities. For small-cap growth, this strategy would have had a cumulative return of 43,000%; for small-cap value, this strategy would have had a cumulative return of 179%; for large-cap growth, this strategy would have had a cumulative return of 23%; and, for large-cap value, this strategy would have had a cumulative return of -73%. In contrast, the 1-month U.S. Treasury bill had a cumulative return of 930%. Thus, it is clear that the effects of low volatility are not universal and primarily the overall result of indirectly avoiding equities with small market capitalizations, expensive valuations, and low quality - it would be more efficient to exclude these equities directly instead of using a low-volatility factor.
Term Factor
Just as the mentioned factors primarily focus on equities (although they are also applicable to other asset classes under similar but adapted definitions), other factors have been developed to primarily focus on bonds. By definition, the term factor expresses the degree or sensitivity to which an asset tends to move with the difference between bonds with a high duration compared to bonds with a low duration. The duration of an asset can be measured as the expected percentage change in price given a percentage change in yield and may be implicitly related to the time until maturity, where long-term bonds typically have a maturity of 20 years with high durations (greater sensitivity in price to changes in interest rates) and short-term bonds typically have a maturity of 1 month with low durations (lesser sensitivity in price to changes in interest rates). For context, another definition of duration and why it is usually quoted in years is that the duration provides a measure of how long it would take for a bond to repay its price with its cash flow based on the present value of future coupon payments and maturity value. The expected component of return of an asset due to its exposure to the term factor is equal to the product of the sensitivity of the asset to the term factor and the difference between the annual average return of bonds with high durations and annual average return of bonds with low durations.
So, it can be said that the return from bonds with high durations offers a premium above the return from bonds with low durations - in other words, this is the return which would be realized by a long/short portfolio (it should be noted that the use of a long/short portfolio eliminates effects from other possible factors, where it is assumed that any effects affect both the long portion and short portion equivalently). From 1927 to 2015 and in the domestic market, when subtracting the annual average return of bonds with low durations (represented by the 1-month U.S. Treasury bill) from the annual average return of bonds with high durations (represented by the 20-year U.S. Government bond), the premium from the term factor has been 2.5% as compensation. This has also been robust to various definitions of time until maturity, where the premium from the term factor always increases as the duration of the bond increases - for example, the difference in annual average return of the 5-year U.S. Treasury note and 1-month U.S. Treasury bill has been 1.8%.
Considering the persistence of the term factor, it has been found that, from 1927 to 2015 and in the domestic market, the premium has been positive in 64% of calendar years and, over longer periods, the odds of outperformance by bonds with high durations of bonds with low durations become even greater. As with other factors, there is always still the chance of an adverse outcome with a negative premium no matter how long the period. Over this same period, the Sharpe ratio of the term factor was 0.25 for bonds in the domestic market.
| Factor | Rolling Periods From 1927 To 2015 | ||||
|---|---|---|---|---|---|
| 1 Year | 3 Year | 5 Year | 10 Year | 20 Year | |
| Term | 64% | 74% | 80% | 88% | 95% |
Considering the pervasiveness of the term factor, there is evidence that the premium from the term factor has been positive with regard to global bonds (although the length of the period of consideration is partially insufficient). Using the difference in return between the Barclays Global Treasury Index and 1-month U.S. Treasury bill, the premium from the term factor has been 3.2%. Considering the investability of the term factor, the bond market is fairly liquidity with low trading costs, especially for government bonds and in the domestic market. Considering the intuitiveness of the term factor, there are obvious risk-based reasons for an investor to expect an excess return through a premium from the term factor. The most prominent reasons is that an investor holding bonds with high durations ultimately faces a greater risk of unexpected inflation compared to an investor holding bonds with low durations, since the period over which the bond is susceptible to the uncertainty of inflation is longer. From a similar perspective, an investor holding bonds with high durations also faces higher volatility compared to an investor holding bonds with low durations, since the period over which the bond is susceptible to the uncertainty of interest rate changes is longer.
An interesting aspect of the term factor is that it has historically had low to negative correlations with other factors. For example, its correlations have been 0.12 with market beta, -0.12 with the size factor, 0.01 with the value factor, 0.08 with the momentum factor, 0.06 with the profitability factor, and -0.42 with the default factor. This provides the additional benefit of diversification with the possibility of reduced volatility and improved return for a portfolio which is able to successfully capture these factors in combination.
Carry Factor
By definition, the carry factor expresses the degree or sensitivity to which an asset tends to move with the difference between bonds with a higher effective yield compared to bonds with a lower effective yield. The effective yield of an asset can be measured as the return an investor would receive if the price of the asset were to remain the same, which is classically applied in currencies by going long currencies with the highest interest rates and short currencies with the lowest interest rates (in a sense, currencies can be seen as very liquid and short-term bonds). In other words, carry can be defined as the expected return on an asset assuming its price does not change, where the carry factor is then related to the effective yield of bonds assuming their prices do not change. However, it should be emphasized that this only works as long as the short asset remains stable, depreciates, or does not appreciate by more than the interest rate differential relative to the long asset. The expected component of return of an asset due to its exposure to the carry factor is equal to the product of the sensitivity of the asset to the carry factor and the difference between the annual average return of bonds with high effective yields and annual average return of bonds with low effective yields.
So, it can be said that the return from bonds with high effective yields offers a premium above the return from bonds with low effective yields - in other words, this is the return which would be realized by a long/short portfolio (it should be noted that the use of a long/short portfolio eliminates effects from other possible factors, where it is assumed that any effects affect both the long portion and short portion equivalently). From 1983-11 to 2012, when subtracting the annual average return of bonds with high effective yields (from the collection of 10-year global bonds) from the annual average return of bonds with low effective yields (from the collection of 10-year global bonds) the premium from the carry factor has been 3.9% as compensation. Likewise, from 1983-11 to 2012, when subtracting the annual average return of currencies with high interest rates from the annual average return of currencies with low interest rates the premium from the carry factor has been 5.3% as compensation.
Considering the persistence of the carry factor, it has been found that, from 1983-11 to 2015 and based on 10-year global bonds, the premium has been positive in 70% of calendar years and, over longer periods, the odds of outperformance by bonds with high effective yields of bonds with low effective yields become even greater. As with other factors, there is always still the chance of an adverse outcome with a negative premium no matter how long the period. Over this same period, the Sharpe ratio of the carry factor was 0.52 based on 10-year global bonds. Similarly, with regard to currencies, the premium has been positive in 75% of calendar years and the Sharpe ratio of the carry factor was 0.68.
| Factor | Rolling Periods From 1983-11 To 2012 | ||||
|---|---|---|---|---|---|
| 1 Year | 3 Year | 5 Year | 10 Year | 20 Year | |
| Carry | 70% | 81% | 88% | 95% | 99% |
| Factor | Rolling Periods From 1983-11 To 2012 | ||||
|---|---|---|---|---|---|
| 1 Year | 3 Year | 5 Year | 10 Year | 20 Year | |
| Carry | 75% | 88% | 94% | 98% | 100% |
Considering the pervasiveness of the carry factor, the concept of carry can be applied to other assets, such as equities and commodities. For example, with equities, the carry trade is determined by the dividend yield (long equities with high dividend yield and short equities with low dividend yield) and the Sharpe ratio has been 0.88 based on global equities; or, with commodities, the carry trade is determined by the roll yield or roll return (difference between the spot rates and future rates) and the Sharpe ratio has been 0.60 based on various resources. With regard to equities, the carry factor shares many similarities with the value factor, since a high dividend yield may be associated with a low price and low dividend yield may be associated with a high price (although the value factor is a more reliable indicator, as some equities do not distribute dividends or prefer to purse share buybacks). Thus, the presence of the carry factor in association with other asset classes shows that the carry factor has been reasonably pervasive.
| Factor | Rolling Periods From 1988-03 To 2012 | ||||
|---|---|---|---|---|---|
| 1 Year | 3 Year | 5 Year | 10 Year | 20 Year | |
| Carry | 81% | 94% | 98% | 100% | 100% |
| Factor | Rolling Periods From 1988-03 To 2012 | ||||
|---|---|---|---|---|---|
| 1 Year | 3 Year | 5 Year | 10 Year | 20 Year | |
| Carry | 72% | 85% | 91% | 97% | 100% |
Considering the investability of the carry factor, the markets in which the carry factor is most applicable are highly liquid with low trading costs - specifically with regard to bonds, currencies, and commodities. This is especially relevant in developed markets without restrictions or controls on foreign exchange - it should also be emphasized that the applicability of the carry factor is relevant to assets with the same or similar credit ratings (it is not associated with credit risk, which has actually been found to have a negative premium with research suggesting that currencies of countries with high credit risks tend to generate lower returns than currencies of countries with low credit risks). In addition, the correlations of the carry factor across asset classes have been low and, as a result, this substantially reduces the volatility of and mitigates the risk from skewness for a strategy pursing the carry factor in a diversified portfolio relative to pursing the carry factor in a concentrated portfolio. Thus, it is possible to construct a strategy focussed on reliably capturing the carry factor.
Considering the intuitiveness of the carry factor, there is a simple risk-based reasons which arises from the long-established concept that prices balance out the supply and demand for capital across markets. In this sense, high interest rates can signal an excess demand for capital not satisfied by local savings, while low interest rates can signal an excess supply of capital already satisfied by local savings. From traditional economic theory, uncovered interest rate parity states that there should be an equality of expected returns on otherwise comparable assets denominated in two different currencies. In other words, any interest rate differentials should be offset by appreciation or depreciation of the associated assets, such that the total returns to an investor would be equivalent across markets. However, there is overwhelming empirical evidence contradicting the predictions of uncovered interest rate parity. This anomaly may be due to the obstacles of the flow of capital from the trading activity of participants in the market who are not seeking a profit and have other intentions, like central banks, government interventions, and corporate hedging programs.
An additional risk-based explanation for the carry factor is related to economic cycles, since it is common for capital to flow into bonds or currencies which are viewed as safe during recessions and usually have low effective yields. In other words, bonds and currencies which are viewed as safe during recessions tend to be stable or appreciate when equities realize poor performance, but bonds and currencies which are viewed as unsafe tend to depreciate when equities realize poor performance (in a sense, bonds and currencies can be seen to have an exposure to equities markets and this exposure is related to their level of safety, although this correlation is usually only seen on the downside under adverse economic conditions but not on the upside under favourable economic conditions). This allows bonds and currencies which are safe to offer a lower effective yield, but forces bonds and currencies which are unsafe to offer a higher effective yield. Therefore, in order to be willing to hold bonds or currencies with high effective yields which are viewed as unsafe, an investor would expect the possibility of a sizable premium to be compensated for accepting the risks of potential depreciation during economic turmoil (similar to the term factor, where bonds with high durations usually have higher effective yields than bonds with low durations in order to convince investors to accept the increased risk - except the carry factor is associated with bonds with the same duration).
Default Factor
The default factor is related to the credit rating of the issuer of a bond. By definition, the default factor expresses the degree or sensitivity to which an asset tends to move with the difference between bonds with low credit ratings compared to bonds with high credit ratings. The credit rating of a bond is associated with the reliability of the issuer of the bond to repay the bond and is usually differentiated between government bonds and investment-grade corporate bonds. Clearly, this should be assumed to be naturally intuitive, as, for example, it would be expected for a higher risk of default to be associated with a bond issued by a company, rather than a bond issued by the government which has more avenues available for financing (such as control of the money supply and tax collection) - there should be a risk premium.
However, from 1927 to 2015 and in the domestic market, when subtracting the annual average return of bonds with high credit ratings (represented by long-term bonds from the U.S. government, U.S. government agency (such as the Federal Home Loan Bank and Tennessee Valley Authority), or government-sponsored entities (such as Fannie Mae and Freddie Mac)) from the annual average return of bonds with low credit ratings (represented by long-term investment-grade corporate bonds), the premium from the default factor has been only 0.3% as compensation. In addition, the t-statistic was unreliable at only 0.61 and not statistically different from random noise. Furthermore, this does not account for the higher transaction costs for trading investment-grade corporate bonds compared to government bonds which are usually more liquid. While investment-grade corporate bonds usually have higher yields than government bonds of the same maturity, the incremental yield historically has been offset by credit losses, typically higher expense ratios of investment-grade bond funds relative to government bond funds (resulting from the need to analyze the credit risk of the company issuing the bond), and other features incorporated into investment-grade corporate bonds (such as call options which give the issuer the right to pre-pay the bond early (usually done if interest rates drop sufficiently to warrant the expense of the recall and re-issuance of new bonds at the then-prevailing lower rate), where investors holding the original bond will have to purchase a new bond at the new lower rates).
Considering the persistence of the default factor, it has been found that, from 1927 to 2015 and in the domestic market, the premium has only been positive in 53% of calendar years and, over longer periods, the odds of outperformance by bonds with high credit ratings of bonds with low credit ratings do not change, as would be anticipated without statistical significance. This further highlights the unreliability of and skepticism with which the default factor should be viewed. Over this same period, the Sharpe ratio of the default factor was only 0.06 for bonds in the domestic market.
| Factor | Rolling Periods From 1927 To 2015 | ||||
|---|---|---|---|---|---|
| 1 Year | 3 Year | 5 Year | 10 Year | 20 Year | |
| Default | 53% | 54% | 56% | 58% | 61% |
Considering the pervasiveness of the default factor, it is possible to consider the Barclays Global Treasury Index and Barclays Global Aggregate Corporate Index (although the length of the period of consideration is relatively short and partially insufficient from 2001 to 2015). The premium from the difference in the average annual returns between these indices was 0.9%, while still neglecting actual implementation costs. Moreover, an additional issue with investment-grade corporate bonds is that they tend to have a higher correlation with equities than government bonds and, in terms of diversification, this decreases the ability of the bonds to affect the risk characteristics of the overall portfolio (expectations for companies to default increase during economic adversity) - it has even been demonstrated that a substantial portion of the credit spread is attributable to factors related to the premium from market beta, as either owning shares of or bonds from a company are both effectively investments in the company.
In more detail, a corporate bond is a combination of a pure interest rate instrument and short position in a put on the equity of the issuer. The put is triggered by a decline in the value of the assets of the issuer to less than the value of the liabilities of the issuer. A default, in other words, results in the holders of shares putting the equity to the holders of bonds, who then become the effective owners of the company. For a highly-rated company with investment-grade bonds, the put is well out of the money and is not likely to be exercised. The option consequently has a negligible impact on the price movement of the bonds, which is more sensitive to interest rate fluctuations. However, in the case of a non-investment-grade corporate bond, default is a realistic enough prospect to enable the equity put to materially affect the price of the bond. With the equity-related option exerting a greater influence on its price movement, the non-investment-grade corporate bond is bound to track government bonds less closely than the investment-grade corporate bond. It should be noted that government bonds can be seen as pure interest rate instruments.
There is recent research which adjusts the comparison between investment-grade corporate bonds and government bonds to, among other things, consider matching duration rather than maturity, as investment-grade corporate bonds tend to have higher effective durations than government bonds for the same maturity, such that any effects from the term factor or others are removed. These modifications result in a premium from the default factor of 1.4% with a Sharpe ratio of 0.37 from 1936 to 2014 and in the domestic market. It was also found that the premium from the default factor varies over time with economic growth and is subject to tail risk, negative skewness, and excess kurtosis. Regardless, once accounting for implementation costs and other considerations, it is still not recommended to favour investment-grade corporate bonds over government bonds.