Fixed-income securities are an important asset class that adds considerable diversification benefits to a portfolio.
The passive strategy known as stratified sampling allows investors to achieve benchmark returns while controlling risk and transaction costs.
This approach can be utilized in a tactical asset-allocation strategy, as it allows for relatively quick changes in portfolio allocations.
Stratified sampling allows for active bets to be integrated into the portfolio by tilting weights in response to forecasted returns.
The use of back-testing will ensure that actual outcomes align with expectations by adequately controlling benchmark risks.
An allocation of investment to fixed-income assets is an important component of any diversified investment strategy. The fixed-income asset class comprises a variety of debt instruments that include government bonds, corporate bonds, municipal bonds, mortgage-backed securities, inflation-indexed debt, and convertible bonds, among others. With such a large number of securities available from which to construct a portfolio, this article reviews the stratified sampling method of replicating the returns of a benchmark portfolio in fixed-income securities. This method is of use to investors who are undertaking both active and passive portfolio management approaches.
Figure 1 shows the daily total returns of the S&P 500 and the MSCI World equity indices as well as fixed-income indices covering a broad-based global benchmark, global high yield, and world corporate debt between February 2002 and February 2012. The impact of the financial crisis is clearly evident in the figure. Interestingly, an investment made in February 2002 in either of the fixed-income indices would be worth more today than either of the equity benchmarks. In terms of risk, the standard deviation of monthly returns is considerably higher for the two equity indices—around 16%. The global broad-based index and the world corporate index have values of 6–7%. An important benefit of including fixed income in a portfolio is the diversification benefit. The correlation coefficients between the five indices are given in Table 1. The global high-yield index is more highly correlated with the equity indices than the other fixed-income indices. Either way, it is clear that fixed income should be included in a diversified portfolio.
|MSCI World Equity||S&P 500||BOFA/ML Global Broad FI||BOFA/ML Global High Yield FI||Citibank World Corporate FI|
|MSCI World Equity||1.000||0.973||0.264||0.755||0.466|
|BOFA/ML Global Broad FI||0.264||0.166||1.000||0.346||0.877|
|BOFA/ML Global High Yield FI||0.755||0.705||0.346||1.000||0.622|
|Citibank World Corporate FI||0.466||0.357||0.877||0.622||1.000|
BOFA/ML: Bank of America Merrill Lynch; FI: fixed income
Risks of Investing in Fixed Income
Despite the lower standard deviation of returns, the recent events of the financial crisis have shown that significant risks are involved in investing in fixed-income securities. As with any financial security, expected returns will vary with risk. Before constructing a portfolio of fixed-income securities, it is important to understand the risks that an investor faces when investing in such securities.
Interest rate risk. There is an inverse relationship between the level of interest rates and bond prices. However, the prices of some bonds are more sensitive to changes in interest rates and are therefore exposed to greater interest rate risk. Reinvestment risk is also related to interest rate risk, as coupon payments received are reinvested at an uncertain interest rate.
Credit risk. This is the risk that the issuer of a bond may not make periodic coupon payments or pay back the full amount of principal at maturity. Credit rating agencies (Standard & Poor’s, Moody’s, and Fitch IBCA) provide ratings on the creditworthiness of bond issuers. These credit ratings allow investors to differentiate between bonds on the basis of the rating agencies’ assessments that an issuer will default and not meet its obligations.
Liquidity risk. This represents the chance that you will not be able to trade the desired quantity of a specific security when you want to trade. Bonds that are more liquid are cheaper to trade. A prime example of liquidity risk is that which occurred in certain collateralized debt obligations and mortgage-backed securities during the financial crisis.
Inflation risk. The chance that inflation will erode the value of investments.
Sovereign risk. This is related to credit risk as it represents the chance that a foreign government will not repay its debts. As the recent sovereign debt crisis has highlighted, it is an important consideration for investors in Portugal, Ireland, Greece, and Spain.
Currency risk. This represents the risk that a domestic investor may purchase a bond that is denominated in a foreign currency. A domestic investor faces uncertainty about the domestic currency value of the coupons and the principal paid in foreign currency.
Call risk. Certain bonds may allow the issuer to call the issue before maturity. This adversely impacts the investor as it introduces uncertainty as to the stream of future cash flows and limits the price appreciation of the security. Generally, these bonds are called when interest rates are low, creating reinvestment risk. Prepayment risk affects mortgage-backed securities and is related to call risk. It reflects the uncertainty surrounding the timing of cash flows to the holders of securitized loans that depend on the mortgage repayments of mortgage holders.
In order to realize a return that is in line with expectations, it is necessary for an investor to adequately monitor and manage these risks.
Active versus Passive Management
Investors in fixed-income assets essentially have two choices as to how to construct their portfolio. First, active management attempts to outperform a selected benchmark index, such as the Barclays Capital US Aggregate Bond Index. In order to outperform the index, an investor needs to either exercise superior security selection or time the market by entering the market before prices rise and exiting the market before prices fall (ignoring coupon payments). Passive portfolio management, on the other hand, aims to provide an investor with a return that matches a selected benchmark index.
There is continued debate in both the industry and academic literature on whether active portfolio management is superior to passive portfolio management. The findings from the most recent academic studies show that in some instances active funds outperform passive funds. However, the fees charged by active funds are higher and they generally erode the additional return they provide. Chen, Ferson, and Peters (2010) show that, after controlling for timing ability, funds outperform benchmarks before fees and costs, but underperform when fees and costs are taken into account. Boney, Comer, and Kelly (2009) find perverse market timing ability for high-quality corporate bond funds. An earlier study by Blake, Elton, and Gruber (1993) found that active funds that performed well in the past did not exhibit continued outperformance in the future. However, there is recent evidence from Huij and Derwall (2008) that past performance predicts future performance.
Thus, the jury is still out on whether an active or passive approach to bond portfolio management is preferable. Active strategies can provide higher returns than the benchmark, but an investor needs to consider the additional risks they are taking and any additional fees charged. All in all, the choice between active and passive investment styles in fixed-income assets is based on the investor’s ability to provide consistent returns above the benchmark after fees. If they are unable to do this, then adopting a passive approach that seeks to provide returns consistent with a benchmark index is a wise decision.
Active managers may also make use of a passive approach for a number of reasons. If they believe that the underlying signals that drive the performance of their active strategy are currently not strong enough, an alternative is to match their portfolio to the index to avoid introducing risk and potentially letting performance deteriorate. A passive approach is also of use if investors are engaging in tactical asset allocation. By building a portfolio that replicates the benchmark return without the need to hold all the constituents of the index, investors can be nimble in response to changes in forecasts of returns across asset classes. Enhanced indexing is another benefit, as it allows for an additional return pickup if an investor has some information about future returns that would allow them to slightly outperform the benchmark.
Finally, an important question to be addressed is whether the investor has the skill in a specific area to undertake active management. Consider an investor who specializes in European corporate debt. It may be prudent for investments in other sectors, such as US mortgage-backed securities, to be based on a passive approach rather than actively trading in mortgage-backed securities and attempting to outperform the benchmark.
Choosing a Benchmark Index
The first decision an investor should make is what benchmark they should target. There are a vast number of fixed-income benchmarks to choose from: Barclays Capital, Merrill Lynch, JP Morgan, and other investment banks all offer benchmark bond indices for investors to track and benchmark their performance against. These bond indices can track the performance of the global bond market, or focus on different sectors of the bond market: US Treasury, corporate, mortgage-backed securities, municipal, inflation-indexed, high-yield, Eurodollar, etc. They can also focus on different geographical areas, such as the United States, Asia, or Europe, and their specific sectors.
The primary concern regarding choice of index is to select a benchmark that has the desired risk and return profile of the investor. For example, investing in emerging market high-yield debt is going to be considerably more risky than investing in US Treasury securities (ignoring currency risk). Certain benchmarks can be selected to avoid exposure to certain risks altogether. For example, if a US investor does not want to be exposed to currency risk in their fixed-income portfolio, they should choose a US bond index. Similarly, if an investor wanted to remove inflation risk, they should select an inflation-indexed benchmark that invests only in inflation-protected securities, such as Treasury Inflation-Protected Securities (TIPS). The nature of the liabilities will also impact the choice of benchmark and could well indicate that a passive approach is unsuitable. Instead, a liabilities-based strategy such as cash flow matching would be more appropriate.
A number of different methods for constructing passive bond portfolios exist: tracking error minimization, factor-based replication, and derivatives-based approaches (see references in the More Info section for a more detailed discussion). One relatively straightforward method of building a portfolio designed to achieve benchmark returns is to use a stratified sampling (or cell-matching) technique. This method allows an investor to control the risk factors which they deem most important in determining returns in the bond market. This approach can be used irrespective of the scale of the portfolio and is flexible enough to be incorporated into an active portfolio management process.
After targeting a benchmark index, an investor then chooses risk factors that they think are important in determining benchmark returns. For example, an investor might choose duration (a measure of interest rate risk), credit ratings, and call risk as being important determinants of bond returns. The investor would then divide the benchmark into a number of different cells based on these three factors. If they partition the index into short, medium, and long duration; AA and above, BBB+ to AA–, and BBB and below; and callable and noncallable debt, they would get a total of 3 × 3 × 2 = 18 cells. The investor then determines the percentage of market value that is contained in each cell. They would then purchase at least one bond from each cell, allocating their capital in proportion to the index weights.
One benefit of this approach is that it allows the investor to incorporate subjective forecasts in their portfolio. They can adjust the weight in each cell, relative to the benchmark index, if they believe that certain factors will provide outperformance. For example, if an investor thinks that interest rates are likely to decrease, then long-duration bond prices will increase by a greater amount than short-duration bonds. As a result, they could take an overweight position in the long-duration cells, compared to the benchmark weights, and an underweight position in the short-duration cells. They may also be underweight the callable bond cells, relative to the benchmark weights, to minimize the adverse impact of bonds being called when interest rates fall.
An important step in forming a passive portfolio is to undertake back-testing of the portfolio based on the choice of cells. This will ensure that unwanted results from omitting an important risk factor do not occur. It will also allow for a better understanding of the trade-off between achieving benchmark returns and minimizing the number of bonds held in the portfolio.
Let us consider the Barclays Capital US Aggregate Bond Index. The index has more than 8,000 constituents, which is clearly too many bonds to hold in a portfolio. First and foremost, a substantial number of these bond issues would be illiquid and very expensive to trade in. By using stratified sampling, it is possible to achieve benchmark returns without holding a large number of bonds in the portfolio.
An investor may decide that maturity and credit risk are the three important risks that they need to take into account. The benchmark can be divided based on the time until maturity of the bonds—short, medium, and long; and credit ratings—AAA, AA, A, and BBB. The investor would obtain a grid like the one in Table 2, with a total of 12 cells.
In this instance, the simplest approach would be to choose 12 bonds and allocate the portfolio investments in proportion to the market value weights in each cell for the index. With only 12 bonds in the portfolio, additional diversification benefits may accrue by including several bonds from within each cell. As mentioned above, a back-testing approach would shed light on what might be a reasonable number of bonds to include in the portfolio. The investor may also want to partition the index based on the various sectors of the market—Treasury, government-related, corporate, and securitized—to increase the number of cells from which to choose bonds.
Advantages and Disadvantages of Stratified Sampling Approach
What are the advantages of pursuing a stratified sampling approach to passive portfolio construction? First, it is straightforward and easy to understand. It matches the risk profile of the index, and therefore the return generated. By reducing the number of bonds in the portfolio and selecting the liquid bonds in each cell, transaction costs can also be reduced. From an asset allocation perspective, the use of stratified sampling makes it relatively easy to adjust holdings in response to changes in forecasted returns. The stratified sampling approach also avoids problems associated with statistical models that rely on historical correlations. After the financial crisis it is clear that these correlations are not always stable. In addition, bonds mature and exit the benchmark index (unlike the case of equity securities), and it can be difficult to estimate correlations on a security that has just been issued.
One disadvantage of the stratified sampling approach is that the investor has discretion as to the number and type of risk factors to focus on, and the number of partitions to divide the index into. Investors face the risk that an omitted risk factor may be a significant driver of index performance. As mentioned above, back-testing of various combinations of risk factors and partition size will alleviate concerns. There is a trade-off between the number of cells chosen and the costs associated with the strategy. An increase in the number of cells will improve the ability of the portfolio to match the index more closely; however, transaction costs are likely to rise. An additional consideration for investors is that passive strategies need to be monitored and rebalanced regularly so that the actual return does not deviate from the benchmark.
Fixed-income assets represent an important component of a diversified investment portfolio. Although debate on the relative merits of active versus passive portfolio management in fixed-income securities has not reached a resolution, indexing can play a significant role in an investment portfolio. Stratified sampling is a method of achieving benchmark risk and return while reducing transaction costs. It can also be incorporated into a tactical asset allocation process, as it allows investors to be more nimble in altering their portfolios. A further benefit of the stratified sampling approach to index replication is that it allows for active bets to be easily incorporated by altering weights in each cell relative to the benchmark weight. Investors using a stratified sampling approach should undertake back-testing to ensure that actual outcomes align with expectations.
Making It Happen
Pick an appropriate benchmark and identify the risk–return profile that you are targeting.
Assess whether you have the skills to undertake active management in a given sector of the bond market.
Determine the risk factors that you consider important in determining the returns of the benchmark index.
Undertake back-testing of the stratified sampling approach. Compare different combinations of risks (interest rate, credit risk, etc) and assess the performance of the strategy based on the number of cells chosen.
Monitor your portfolio and rebalance regularly as the index weights in each cell will change over time.