Liability Beta vs. Market Beta

Source: Liability Beta vs. Market Beta

Beta is a term first pioneered by PhD. William Sharpe in his 1970 book “Portfolio Theory and Capital Markets”. Here he introduced his famous capital asset pricing model (CAPM) which presented the idea that individual investments contain two types of risk: Systematic and Unsystematic risk.

Systematic risk was deemed to be market risk that cannot be diversified away while unsystematic risk was deemed to be the specific risk of that investment (i.e. credit, features, etc.) that can be diversified away through adding other investments to the portfolio. Modern portfolio theory (MPT) shows that unsystematic risks can be removed or reduced through portfolio diversification. The problem that remains is that of market risk.

The Notre Dame fixed income indexes study of 1986 proved that the market risk for bonds is interest rate risk which is quite dominate. Their calculations showed that interest rate risk explained or accounted for 96% plus of the total return for the major bond index aggregates. This study further proved that interest rate is best measured by a yield curve that is well diversified by maturity or duration (term structure). Any bond index that does not have a distinct term structure is not a good measurement of bond market risk.

Through time, it became obvious how difficult it was for active management to consistently outperform a market index as a benchmark (especially after fees). This led to Index Funds as a major asset management style. The growth in this form of asset management has been dramatic especially when including the explosive growth of exchange traded funds (ETFs).

With the advent of Portable Alpha as a strategy, assets are divided into two groups: Alpha and Beta. A Portable Alpha strategy transfers (ports) the excess return (Alpha) over to the Beta portfolio to secure the victory. The Beta portfolio is considered the portfolio that matches the objective as an index benchmark (i.e. Index Fund) and Alpha is considered the portfolio that outgrows (excess return) the index objective.

Given the currentasset liability management(ALM)or liability driven investment (LDI) trends, it has become obvious that the true objective of a pension is to fund a liability schedule unique to each plan sponsor. Since the objective of a pension (and most institutional objectives) is liability driven shouldn’t the terms Beta and Alpha be redefined for any LDI objective. After communication with PhD. William Sharpe years ago, he suggested I qualify my research as Liability Beta and Liability Alpha to distinguish it from market beta and market alpha. I agree, that makes good sense.

Market Beta and Alpha

Most asset managers are given an index bogey or objective that best represents the asset class risk/reward behavior that the client has chosen as the objective of such asset allocation. Asset consultants are quite diligent in selecting and monitoring the asset managers to perform under these index objectives. The goal could be to either match the risk/reward behavior (Beta portfolio or index fund) or outperform the return behavior (earn Alpha). A few good questions here are: if your asset managers earn market Alpha, does that mean they earned liability Alpha? If all asset managers outperformed their index bogey but total assets underperformed liability growth, did the client win or lose? Did asset allocation create value added (Alpha)?

Liability Beta and Alpha

Several strategies exist to match pension liabilities (cash flow matching, duration matching, derivatives, interest rate swaps, etc.). These liability Beta portfolios are to match the liability cash flow schedule (cash flow matching) or interest rate sensitivity of liabilities (duration matching) or both. Liability Alpha is rarely a consideration yet this is how a pension improves its funding status and reduces pension costs (i.e. contributions). In the end, total assets must outgrow total liabilities over time to earn liability Alpha thereby enhancing the funded status and reduce pension costs.

Custom Liability Index

Given any liability driven objective, the proper index benchmark should be a Custom Liability Index (CLI) that best measures the size, shape and risk/reward behavior of these client specific benefit payment schedules. The Ryan ALM CLI is a monthly report that calculates the present value, growth rate and interest rate sensitivity of liabilities. Client liabilities are like snowflakes… you will never find two alike. Only a CLI could accurately represent the true pension objective. It should be obvious thatthe true objective of a pension is to fund their liabilities in a cost-efficient manner with prudent risk. It is difficult, if not impossible, for asset liability management (ALM) to function effectively without proper knowledge of the liability cash flows. In sports, the scoreboard dictates the strategy. The CLI is the pension scoreboard for liabilities. When compared to assets, the plan sponsor knows every month if they are winning or losing the pension game.

Current accounting rules and actuarial practices price liabilities as a zero-coupon bond portfolio at a single discount rate on an annual basis, months delinquent where the liability cash flow schedule (annual projections of benefits) is rarely seen. Moreover, this single discount rate may not be a market rate (GASB for public plans uses the ROA). Could any asset manager perform versus a generic market index if it came out annually, months delinquent where the index portfolio was not transparent and all issues were priced at the same yield? Sounds ridiculous … well, welcome to the current pension liability world we live in.

The Society of Actuaries (SoA) in their 2004 research paper addressed this situation citing that current accounting rules distort economic reality and urged pensions to create a set of economic books that price liabilities at the market on a frequent and accurate basis. Such economic books are best created and maintained as a Custom Liability Index. Indeed, until a Custom Liability Index is installed, the asset side cannot function effectively towards a liability objective. How could an asset allocation model function without correct input as to the true economic Funded Ratio (assets/liabilities) and the size of the economic deficit or surplus (funded status)? How could performance measurement be calculated quarterly without knowledge of the true economic liability growth rate (total return)? How could you match and fund assets to liabilities without a Custom Liability Index?

I designed the CLI over 32 years ago as the best representation and benchmark for any liability objective. The CLI is a monthly report that prices liabilities at the market (using either the Ryan ALM ASC 715 (AA corporates) discount rates or US Treasury STRIPS). The CLI calculates the true economic present value of liabilities and their growth rate so the funded status and performance measurement of assets versus liabilities can both be ascertained.

Lehman Aggregate and Generic Bond Indexes

As the designer of many of the popular Lehman bond indexes (now Bloomberg Barclay’s), I am honored by the acceptance of these bond indexes. However, it should be obvious that they do not behave like liabilities. All of the popular generic bond indexes are rules based. Such rules only use coupon bonds and do not have zero-coupon bonds. Mathematically, the longest duration of any coupon bond is around 17 years today. As a result, such bond indexes could not be a proxy for long duration liabilities or match these liabilities as an index fund. Furthermore, most pensions are weighted to long durations with an average pension fund in the 10 to 15-year average duration area. The Bloomberg Barclay’s Aggregate’s average duration is usually between four to five years … a definite mismatch to pension liabilities cash flow. Even the long Corporate or Credit index cannot match liabilities. It has two distinct rules based problems. First, it has no issues shorter than 10 years in maturity which leaves out a large and most important segment of liability cash flows. Second, it has no issues with durations longer than 17 years. This is an inappropriate proxy for any pension’s liabilities. It is not the average duration you are trying to match and monitor but the entire liability term structure (liability cash flows). Once again only a Custom Liability Index is the proper fit as a liability benchmark.

Liability Beta Portfolio™ (LBP)

If the Beta portfolio is the portfolio that matches the index objective (Index Fund) then given a liability objective, the proper liability Beta portfolio is … the portfolio that matches the liability objective (Liability Index Fund). To be accurate, you must fund each monthly liability payment.

The Ryan ALM LBP is a cash flow matching portfolio that matches and funds monthly liability cash flows chronologically. Our LBP is a cost optimization model that will produce the optimal lowest cost portfolio to fund the target liability cash flows. Our LBP should reduce funding costs by about 2% per year (1-10 year liability schedule = 20% funding cost savings)! Moreover, the LBP will outyield the CLI thereby providing liability Alpha similar to the yield difference which enhances the funded status. The Ryan ALM LBP should also mitigate interest rate risk (similar duration and term structure matching) and reduce pension expense, the volatility of the funded status and contributions.

The intrinsic value in bonds is the certainty of their cash flows. We urge pensions to use bonds for their value… to match bond cash flows that fund liability cash flows. We do not view bonds as performance vehicles or Alpha assets. They are best as liquidity assets to fund liabilities as they come due. By bifurcating liquidity assets from growth assets (Beta vs. Alpha assets) you BUY TIME for the Alpha assets to grow unencumbered. Many pensions use a “Cash Sweep” where they take away income from all asset classes to fund benefits + expenses (B+E). According to S&P 500 data, dividends reinvested accounted for: 47% of rolling 10 years returns since 1940. So let the bond allocation (liquidity assets) fund B+E which will buy time for the Alpha assets to grow significantly more.

“An error is not a mistake until you refuse to correct it” John F. Kennedy

The Smartest Beta

Source: The Smartest Beta

The term “beta” is credited to William F. Sharpe, Ph.D. in his 1964 work in development of the “Capital Asset Pricing Model (CAPM)”. It means (1) the covariance of the return on a security or portfolio with that of the market portfolio divided by (2) the variance of the return on the market portfolio. Professor Sharpe originally called this “market sensitivity” since you are comparing an investment to the market as defined by a market index. A beta of 1.0 suggests you have no residual risk in that you match the risk/reward behavior of the market index you are being compared against. Ideally, a market index fund should consistently have a market beta of 1.0.

Beta is a measurement based on a market or objective index. Without the index benchmark there is no applicable beta calculation. Traditionally, this has been the popular index benchmarks (i.e. S&P 500, Lehman Aggregate, etc.) but in truth it can be any index that best represents the objective of such funds (i.e. ETFs, index funds). Back in 1964 there was the absence of market indexes so beta was limited mainly to a measurement versus the S&P 500. The first bond index was introduced by Kuhn Loeb in 1973 (merged into Lehman in 1977). Since the advent of ETFs in 1993 there has been numerous new indexes created to feed the explosive growth of ETFs. Such new indexes are the stated objective of these many new ETFs.

Smart Beta

Smart beta is the optimization of the risk/reward behavior of a market index usually by changing the weights. Popular smart beta weighting schemes have been: fundamental weighting, equal-weighting, risk-clusters, and diversity weighting (combines equal and cap weighting). By changing the weights methodology the goal is to enhance returns or reduce volatility or both. Smart beta products have grown well in a short period of time but for the most part are still equity index derivatives. Rob Arnott and Research Affiliates, LLC have been a leader here introducing fundamental weighting for both bond and stock indexes as risk/reward value-added.

There is debate as to whether changing the weight methodology of a market index is really active management or an alpha strategy rather than a beta strategy or discipline. My recommendation is that the objective decides what is beta and alpha. What is important is to have the objective defined by a rules based index. If this reweighted index is the stated objective of an ETF, mutual fund or client then beta is the portfolio that matches the risk/reward of this objective index version. It also follows that alpha is the excess return versus this modified index objective. All comparisons to the traditional generic market index are just good information to know but do not determine the alpha and beta calculations.

Liability Beta Portfolio (The Smartest Beta)

The “smartest beta” portfolio is the portfolio that best matches and achieves the true client objective with the least amount of risk and cost. Risk is best measured as the uncertainty of achieving the objective. Cost is the amount required to fund the objective. The true objective of most institutions and even individuals is some type of liability (annuities, banks, insurance, lotteries, NDT, OPEB, pensions, etc.). The absolute level of volatility of returns is not risk given a liability objective. Indeed a 10-year liability payment is best matched and funded (defeased) by a 10-year Treasury STRIPS which has a certain future value. A three month T-bill would be very risky given this liability objective as it has 39 reinvestment moments of uncertainty. Although the 10-year Treasury STRIPS would be much more volatile in returns, such a return pattern would match the present value behavior of the 10-year liability and thus be low risk or even risk-free (defeasance).

Given a liability objective it is critical to create a custom liability index (CLI) as the proper benchmark. It must be a custom index since liabilities are like snowflakes… you will never find two alike. The CLI is a portfolio of liability payments weighted by the schedule of payments (term structure). Most institutional liabilities are calculated by actuaries who produce an actuarial projection of the liability payment schedule for each client. As such, the CLI is weighted by the actuarial projection in present value dollars. To calculate the present value of each liability payment you need to price liabilities based on a yield curve of discount rates. Depending on the type of liability there are accounting rules (ASC, FASB, GASB, IASB, PPA, etc.) that dictate the discount rate methodology.

Most, if not all, liabilities are priced as zero-coupon bonds since they produce a certain future value. Using U.S. corporate pensions, as an example, they are regulated by ASC 715 (formerly FAS 158) for GAAP accounting purposes. These rules suggest pricing liabilities as if they were AA corporate zero-coupon bonds. Since such bonds are not available in the bond market, they have to be manufactured as hypothetical zero-coupon bonds. As a result, liabilities behave like a yield curve of zero-coupon bonds weighted by the actuarial projections. This means that pension liabilities are extremely interest rate sensitive.

The CLI should calculate all of the necessary statistics to maintain and monitor a liability beta portfolio: term structure weights, total present value, YTM, duration, growth rate, interest rate sensitivity. The CLI is also the proper benchmark to measure liability alpha. If equity assets outperform the S&P 500 but underperform the CLI growth rate… did you earn alpha? In the eyes of the client you lost to liability growth which will damage the funded ratio

(assets/liabilities), credit rating and increase contribution cost. Liability alpha is the excess return versus the CLI return (growth rate) and not versus a market index return. Based on Ryan ALM indexes, liability YTD returns through November 30 should be between 12.7% (10-year duration) and 22.2% (15-year duration). Hard to believe that any pension has earned liability alpha so far in 2014.

The key point here is that the client objective is truly the focus and determinant of relative risk and reward (beta and alpha). The client objective is to fund liabilities in such a way that risk and cost are reduced and stable over a long horizon. Given a long average life (duration) based on the liability payment schedule then the liability beta portfolio needs to match these term structure weights. An S&P 500 index fund or any generic market index fund could never represent the beta portfolio for a liability driven objective. Cash or a money market fund is a very risky investment for most liability objectives that have long average lives (duration).

The most appropriate and smartest beta portfolio is the one that matches the liabilities cash flow as measured by the CLI. In essence, the smartest beta portfolio is a custom liability index fund. Such a portfolio should be the core portfolio for any liability objective. By matching the liability term structure the uncertainty risk of matching liabilities is eliminated and interest rate sensitivity is neutralized. By matching the liability term structure with bonds that have higher yields and lower present values (price) than the discount rates used… you have reduced costs. Since the accounting rules (ASC 715, IASB, and PPA) use AA zero-coupon discount rates then a liability beta portfolio of A and BBB will produce higher yields and lower costs. This should provide significant cost savings of 10% to 15%. This matching process is called cash flow matching. Beware of duration matching strategies (i.e. immunization) which do not match the liability cash flows but just the average duration. This is not an accurate or cost effective way to match liabilities. The smartest beta portfolio is a liability cash flow matched portfolio!