To date, the majority of corporate bond benchmarks use a market capitalization weighting approach to determine the size of the constituent holdings. This methodology has been borrowed from the equity space where it has been the norm for decades. Market capitalization may make complete sense in equities, where it is a reasonable proxy for overall market wealth. However, in the case of bonds, capitalization is not a measure of wealth. In fact, it could be quite the opposite – the more a company borrows, the more indebted it becomes and thus the worse its income position could become. Higher corporate leverage generally induces higher volatility in returns. From a credit index perspective, a market capitalization weighted index would, by construction, overweight highly indebted issuers. This has the unintended consequence of greatly exacerbating index return drawdowns during a credit crisis. Given these inherent flaws, is a market capitalization weighting scheme necessarily the best metric for benchmarking the performance of active corporate credit mandates? Some of our longer term institutional clients have asked us whether there are alternative weighting schemes that one could explore, and if so, what their benchmark performance characteristics would look like? This blog addresses some of these questions.

Methodology

Starting with the US dollar denominated constituents of the ICE BofAML Global Corporate Index (G0BC), we explore applying two alternative risk-based weighting methodologies: (i) a bond equal-weighted scheme and (ii) different risk parity weighting schemes, in which the weights are related to the volatility of the underlying bonds. Whilst the former scheme is self-explanatory, the volatility dependent methodologies perhaps require some further clarification.

Defining a coherent measure of volatility for bonds is not straightforward, as bond risk is derived via a number of distinct risk factors. Normally, one would need to use a factor risk modelling framework to remove the systematic sources of volatility and thereby isolate the excess return volatility. In practical terms, Duration Times Spread (DTS) is often used as a proxy measure of bond volatility, as it has been shown to be a good estimator of corporate bond excess return volatility in academic research[1]. We calculate DTS by multiplying a bond’s credit spread by its spread duration[2]. For the risk parity weighted index, we calculate the weight of each bond as an inverse proportion of the DTS (i.e. 1/DTS) and then re-weight to make sure the portfolio sums to 1 for each month. This is a purely theoretical index as in practice there could be a situation where a bond has a very low DTS and very low debt issuance, in which case it would be very difficult to purchase the required amount. We then take our risk parity weighted index a step further, by combining the approach with market capitalization. This is done quite simply by reweighting the original risk parity weights to give the same risk contributions as the market capitalization index across multiple dimensions, or risk cubes, such as sector and issuer[3].

Empirical results

Below, we present our back test results for the following four weighting schemes:

1. Market capitalization weighted;
2. Equal weighted;
3. Risk parity weighted;
4. Risk parity weighted, with sector and issuer neutrality maintained to G0BC;

The key performance characteristics which would be of interest to investors are: returns, volatility, drawdown risk and turnover[4]. In Figure 1 and Table 1, we show the performance of these various indices from January 2000 to May 2018. The risk parity weighted index has the best risk-adjusted returns and the lowest maximum drawdown. When we neutralize this index, we still maintain better risk-adjusted returns and maximum drawdown characteristics than the market capitalization and equal weighted indices. Both risk parity indices have over double the annualized turnover of the market capitalization index. Interestingly, the equal weighted construction also displays better performance characteristics than the market capitalization approach, with only a very slight increase in turnover from 60% to 65%.

We also investigated the impact of transaction costs on our results. Applying our proprietary historical transaction cost model gave us broadly similar conclusions to those presented here. Finally, we performed a return correlation analysis of these custom credit indices versus the S&P 500 equity index. The last line in Table 1 shows that the correlation pertaining to the risk parity index is by far the lowest of the four – in other words, this particular construction generally provides the greatest degree of portfolio diversification in a multi-asset setting.

Liquidity considerations

An important consideration for indices is liquidity. Whilst larger market capitalization bonds are generally more liquid, we investigated whether larger risk parity weights had any particular liquidity bias. Interestingly, our analysis of forward traded volumes in different risk parity quintiles found no bias either way – i.e. the top risk parity weight quintile had the same forward traded volume in March 2018 as the average of all the other risk parity weight quintiles.

Concentration risk implications

Another key concern for indices is concentration risk. To measure concentration risk, we use the Herfindahl-Hirschman Index which is computed as the sum of squared weights per issuer. The lower the value the less concentrated the portfolio is. From Figure 2, we can see that the equal weighted index is the least concentrated portfolio through time. Additionally, the risk parity weighted index has been consistently less concentrated than the market capitalization index since 2007. Also note that the market capitalization index had the highest levels of concentration risk during the global financial crisis. Finally, as we would expect, the neutralized version of the risk parity weighted index has the same concentration risk through time as the market capitalization index.

Summary

Benchmarks are thought to be an efficient representation of “the market”. More importantly, the choice of benchmark by investors is representative of their investment style. Consequently, the benchmark tends to be the starting point for portfolio construction for active mandates. It is clear that not all investment styles seek to be fully consistent with market capitalization weighting – for example, there are longer term buy and maintain styles that actively seek to capture illiquidity premia, or even fundamental quality styles that weight issuers from a balance sheet perspective. We will explore some of these in future blogs. In this piece we have focused on risk-based styles, which are about mitigating volatility and limiting drawdowns during credit crises. It is worth noting that not every investor, when specifying an active mandate, wants to necessarily start with the universe of the most heavily indebted companies or sectors. Some of our longer term institutional clients have specifically wanted to discuss the merits of equal weighted and risk parity related performance benchmarks. The thoughts and empirical results presented in this blog are a starting point for such a discussion.

1. “The Risk Parity Principle Applied to a Corporate Bond Index”, L. Stagnol, Journal of Fixed Income, 2017.
2. When doing this calculation we cap the minimum and maximum DTS values in our dataset at 0.01 and 1, respectively.
3. In the empirical results this version is labelled “Risk parity index (sector and issuer neutral)”.
4. Our calculations of turnover include a number of factors and counts both sides of each buy and sell transaction as well as reinvesting cash from coupon payments, amortizations and maturities. Other factors driving turnover include: fallen angels, rising stars, maturities of less than 1 year, new issues, existing bonds, and other index entrants and leavers (including bonds that are called by the issuer or other corporate actions that force bonds out of the index).