Excerpt
Abstract
This thesis examines optimized portfolios of three investor types during four different time intervals ranging from 1998 to 2013 to determine if the inclusion of Treasury Inflation-Protected Securities (TIPS) has benefits for institutional investors such as pension plans, university endowments, foundations and sovereign wealth funds. The three investor types used in this study differ in their risk tolerance, with the more risk-averse investor type choosing not to include certain asset classes in his investment portfolio. The efficient frontier algorithm, developed by Prof. Harry Markowitz, is used to determine whether the inclusion of TIPS improves the risk/return profile of the portfolio. Sharpe ratio, developed by Prof. William Sharpe, is used to measure a portfolio’s risk adjusted performance. The study found that the benefits of the inclusion of TIPS in a portfolio vary by time period and investor type. While all investors were able to improve their risk return profile, the more risk-averse investor type benefits to a larger degree from the inclusion of TIPS. Furthermore, a significant increase in the financial efficiency was only observed in the 1998 to 2002 period. Therefore, the researcher concludes that the TIPS market is quite dynamic and investors need to take into account forward-looking information to profit from the inclusion of TIPS in investment portfolios.
I. Introduction
The U.S. Treasury issues several forms of debt to finance the activities of the government. The most prevalent form of debt issuance is through issuance of U.S. Treasury bills which pay the investor a nominal coupon rate each period and the principal at maturity. Many institutional investors as well as individuals buy this form of sovereign debt and include them within their investment portfolios. While nominal Treasury bills are the most prominent form of government debt and have been issued for decades, the Treasury also issues another, relatively new form of debt: Treasury Inflation-Protected Securities (TIPS). Since the U.S Treasury introduced the first issue of TIPS in 1997, its popularity and uses have evolved. The U.S. government originally decided to issue TIPS because it believed that debt could be issued at a lower borrowing cost, as investors typically do not require much additional yield compensation for future inflation, preferring instead a monthly inflation index reset. Thus, TIPS could be offered with a lower real (after-inflation) coupon interest rate than regular (nominal) Treasuries. In addition, the Treasury believed it can bear and manage the inflation risk better than investors since the U.S. government controls monetary and fiscal policy which are the primary determinants of inflation.
As far back as Keynes, economists have argued that indexed bonds could reduce government borrowing costs (Price, 1997). If the market overestimates future inflation, government will reduce borrowing costs by issuing indexed bonds due to the following reasons:
- The investors’ expectations are not completely forward-looking or rational.
- The government has better information about the future course of inflation due to its ability to influence and contain it through its policies.
- As tax revenues are inflation-sensitive, TIPS also offer better matching of tax income to debt service.
The TIPS market consists of many different types of investors such as portfolio managers, institutional investors, and individuals. Investors are attracted to TIPS for different reasons. Many investors and fund managers use TIPS as a tool for diversifying their portfolio and in asset allocation because credit risk and inflation risk for TIPS is minimal. Like Treasury bills, TIPS are guaranteed by the government and investors do not have to worry about the risk that inflation will outpace and erode their investment returns over time. In principle, TIPS should appeal to risk-averse investors and those who expect the greatest rates of inflation. If the interest rates on conventional bonds and TIPS are regarded as equally attractive by investors who accept the consensus forecast of inflation, then those who expect inflation to exceed the consensus forecast will regard the real yields on conventional bonds to be inadequate compared to those on TIPS.
The current state of the TIPS market is difficult to describe. As inflation remains low, some prominent investors such as Jeffrey Gundlach, head of the investment firm DoubleLine, call TIPS a “disaster” and a “trap.” They have been avoiding indexed bonds because they see no signs of rising inflation expectations. Others, such as investment guru Bill Gross who manages the PIMCO Total Return Fund, have a different view of the TIPS market and see big investment opportunities in TIPS. As a result of prolonged money printing by the Fed, Bill Gross bet on higher future inflation and invested heavily in TIPS in April of 2013. He also predicted that the price of nominal Treasury bills would fall. While his second prediction turned out to be true, his bet on higher inflation turned out to be a mistake. The market’s fear of inflation fell and Gross was faced with huge losses for his $268 billion PIMCO Total Return Fund. Withdrawals in June 2013 totaled $9.9 billion, the most on record (Weiss & Leonidis, 2013).
The main purpose of this paper will be to examine optimized portfolios including TIPS over four different time intervals from 1998 to 2013 in order to determine how indexed bonds should be utilized within the context of asset allocation. Specifically: Do TIPS improve the risk return profile for fund managers who use these types of investments in their portfolios? Furthermore, this paper attempts to answer the question whether TIPS should be assigned a separate asset class status next to stocks, bonds, commodities, real estate, and foreign exchange. Additionally, this paper tackles the question: What are the benefits of TIPS for institutional investors such as pension plans and mutual funds that use these securities strategically or tactically in their portfolios? The analysis of reasons as to why the government commits itself to the issuance of indexed bonds and the demand by the investment community will lead to the understanding of issues related to the use of these securities by institutional as well as individual investors.
II. Features
Treasury Inflation-Protected Securities (TIPS) are U.S. Treasury-issued notes and bonds. Their principal value is adjusted monthly for changes in the level of inflation as measured by the non-seasonally adjusted Consumer Price Index for All Urban Consumers (CPI-U) on a 2-month lag. Inflation-indexed bonds were created to meet the needs of longer-term investors wanting to insulate their investment principal from erosion due to inflation. These bonds have been issued in the United Kingdom (1981), Australia (1985), Canada (1991), the United States (1997) and France (1998).
The basic structure is the same for all US TIPS. A fixed coupon interest rate is paid semi-annually on the inflation-adjusted principal. At maturity, the principal is redeemed at the inflation-adjusted principal amount (but not less than par value). In other words, unlike the Canadian counterparts, TIPS issued in the U.S. are protected against the risk of deflation. The Department of Treasury provides a guarantee (floor) at the par value in a deflationary environment. As a result of this “guaranteed principal floor”, TIPS incorporate a minimal hedge against sustained deflation.
In the event of an absolute decline in the price level; i.e., deflation, over the life of an inflation protected bond, the Treasury will repay the full face value at maturity, insuring a floor for investors. That is, the principal of TIPS is increased by the percentage increase in the CPI or decreased by the percentage decrease in the CPI unless such adjustment would reduce the principal below its initial value. This asymmetric price-level adjustment feature provides TIPS investors with some protection against deflation in addition to the complete inflation protection.
An increase in inflation results in a commensurate increase in outstanding principal payable to the TIPS bondholder at maturity. In mutual funds holding inflation-protected securities, the inflation adjustment to principal is accrued as current income and allocated to shareholders. In order to protect their purchasing power over time, mutual fund investors must reinvest at least the inflation-adjustment portion of the distribution. In other words, investors who spend, rather than reinvest, their entire distribution will defeat the inflation-protection purpose of this fund.
Like all Treasuries, the interest income on TIPS is subject to federal income tax, but is exempt from state and local taxes. The principal inflation adjustment on TIPS is also taxed as ordinary interest income in the year in which the adjustments occur, even though investors will receive no cash from the principal adjustment until maturity or when sold, similar to the imputed (phantom) income derived from zero coupon Treasuries. Investors in TIPS mutual funds who desire real current income have the option to take the inflation adjustment as a monthly dividend distribution with the tax consequences remaining the same as with individual TIPS. Therefore, TIPS contain three distinct components of total return – coupon interest, plus inflation adjustment, plus (or minus) capital gains/losses.
III. TIPS in an Asset Allocation Framework
In the active management of a bond portfolio, a bond fund manager can use the real interest rate view against the market and try to switch effectively between indexed and conventional Treasuries. This could be viewed as an alternative bond strategy to using the portfolio duration as real rates are expected to change in the near term. It could be argued that it is difficult for a bond fund manager to consistently benefit from the perceived market misjudgments about future inflation, nominal and real rates. Even though the public expectations of future inflation could exceed (or lie below) actual future inflation, such forecasting errors cancel out over the long run. Unless bond managers start betting on the apparent systematic irrational behavior in the Treasury markets, the secondary market for indexed bonds will not be as deep as other bonds issued by the U.S. government. However, the combination of indexed and conventional bonds allows bond fund managers to disentangle real interest rate risk and inflation risk. This enables them to either eliminate or bet on a certain risk component that is in line with their risk preferences. To this end, the Treasury creates an environment with a more efficient risk sharing
Why would TIPS be called an “asset class”? Is there a consistent definition of “asset class” used in the industry? Does having very low or negative correlations to U.S. stocks, non-U.S. stocks and Treasuries qualify a fairly new financial instrument to be assigned the “asset class” status? Assuming the same expected return for conventional and indexed bonds, should TIPS become a complement to or replace Treasuries in institutional investment portfolios? This section will try to offer possible explanations to these and other related issues.
Asset classes can only exist if we believe that there is a notion of asset allocation, which will help individuals and institutions to achieve their objectives. They are basically a by-product of the bigger idea of asset allocation. The evolution of the practice hinged upon the technological advancements as to how many securities one could use in an optimization algorithm or computerized systems. An asset class should provide the investor with a distinct risk/return expectation that is in line with his or her risk preferences and time horizon. To be able to define asset classes, one should first list the functional attributes of each along with practical implications. For instance, stocks provide the investors with the ability to grow the market value of the portfolio (growth), bonds are used to provide a stable income stream (stability), and absolute return products are a hedge against the uncertainty in traditional investment vehicles.
In short, an asset class should include a set of securities, marketable or non-marketable, which behave in a consistent manner. The need for asset classes in investment management arises due to the following reasons:
- The process provides a coherent structure whereby the investor matches its liabilities more closely.
- It could be advantageous to allocate funds into specialist portfolio managers, who represent different asset classes and various categories within each class.
- Allocation into multiple asset classes with distinct characteristics and less correlation among themselves could help
- The overall return to flow smoothly.
- The investor hedge risks arising from betting on financial markets.
Besides providing investors with stable income, fixed income as an asset class helps investors hedge against financially difficult times, in other words, provide decent portfolio protection. To this end, high-quality, long-term, non-callable bonds fit the description. If one takes the breakeven inflation as a yardstick to compare the ex-ante performance of nominal versus indexed bonds and feels comfortable in advising people an agnostic view toward the mix of nominal and indexed bonds, long-term investors should have a combination of nominal and indexed bonds to hedge against movements on both sides of the breakeven inflation. If the inflation happens to be greater than the breakeven inflation any time, indexed bonds would outperform and vice versa. An agnostic person would split her bond portfolio between the two.
The correlation statistics of TIPS versus other asset classes has been very appealing from a mean-variance analysis perspective. Due to the fact that inflation impacts traditional bonds quite differently than TIPS, the correlation coefficient between the two is expected to be low. When inflation increases, the prices of both equities and nominal bonds decrease (as investors require higher discount rates for future dividends and coupon payments), whereas the prices of TIPS rise according to increases in inflation. Since their launch in 1997, there has been a low positive correlation between the price change of TIPS and broad market fixed interest securities and a low to negative correlation with the S&P 500, as demonstrated by the correlation matrices in Figures 2 through 5. As TIPS have a low to negative correlation with other asset classes, they provide the investor a tool for diversifying portfolios and are a hedge against inflation. TIPS are a very distinct form of asset because no other asset class provides a complete hedge against inflation. Therefore, they deserve to be assigned “asset class” status.
IV. Literature Review
There are several scholars who have studied the relationship between TIPS and conventional nominal bonds. Hunter and Simon (2005) examine the relationship between TIPS and nominal bonds using weekly data from February 1997 to August 2001, using a bivariate GARCH framework to model the conditional means and volatilities as well as their conditional correlation. Their research resulted in the conclusion that adding TIPS to a portfolio of Treasury bills, nominal bonds, and equities does not significantly enhance the opportunity set for investors. However, since the inflation during the sample period remained relatively low, I argue that extending the data period to include a full business cycle might shed more light on the benefits of TIPS in building more efficient portfolios.
Cartea et al. (2012) draw a distinction between buy-and-hold long term and short-term investors to show that each type benefits differently from the use of TIPS in their portfolios. Specifically, TIPS replace nominal risk-free assets for long term investors, and improve the opportunity set of real returns for short-term investors. They further show that gains from TIPS are tempered by the availability of such alternative assets as gold and real estate, both of which covary with inflation. Moreover, they postulate that when commodities are available, the improvement to highly risk-averse investors decreases due to the fact that commodities are a better hedge against inflation. In their analysis, there is no rebalancing between different asset classes at intermediate points in time.
Daskalaki and Skiadopoulos (2011) investigate whether investors are made better off by including commodities in a portfolio with traditional asset classes, namely stocks, bonds, and cash. They depart from previous research of this question by employing mean–variance and non-mean–variance spanning tests and then forming optimal portfolios by taking into account the higher order moments of the portfolio returns distribution and evaluate their out-of-sample performance. Their conclusion challenges the alleged diversification benefits of commodities and their evidence is robust across a number of performance evaluation measures, utility functions and datasets. However, they note an exception during the 2005-2008 unprecedented commodities boom period.
Chu et al. (2007) investigate whether the inflation protection offered by TIPS occurs in real time, with TIPS prices moving up and down to reflect the flow of CPI information into the market before the CPI announcement, or whether the price adjustment occurs only on or after the monthly public announcement. This is a crucial point for our purposes since we not only analyze diversification benefits of TIPS but also entertain the idea of using them within the “real assets” sub-portfolio, which has been gaining popularity as part of the portfolio construction process. Using pooled time-series, cross-sectional data, the study shows that TIPS prices efficiently aggregate near-term inflation information. Their conclusion is that the market is very efficient at observing and responding to changes in consumer prices as they occur. They also postulate that TIPS prices were distorted before 2004 due to the presence of a significant liquidity premium.
Christensen and Gillan (2011) argue that estimating market expectations for inflation from the yield difference between nominal Treasuries and TIPS is complicated by the liquidity differential between these two types of securities. They show that until the failure of Lehman Brothers, the yield spread between seasoned and newly issued TIPS of comparable maturities was typically negative because deflation risk was negligible. However, in the weeks and months following the Lehman failure, a significant and persistent spread reflected widespread deflation fears.
Kajuth and Watzka propose a new method of correcting break-even inflation rates derived from index-linked bonds for liquidity and inflation risk premia
without resorting to survey-based measures. They have found that in a state-space framework, the difference between break-even inflation rates and unobserved true inflation expectation is explained by measures of time-varying liquidity and inflation risk premia. Their proposed approach has several advantages: Entirely survey-free financial market based measures of inflation expectations can be obtained and the measure yields more exact forecasts for core inflation than the raw break-even rates or the SPF answers.
V. Methodology
The question whether TIPS improve the risk return profile for investors who use them in their portfolios will be answered using efficient frontier analysis. The efficient frontier “is a modern portfolio theory tool that shows investors the best possible return they can expect from their portfolio, given the level of volatility they’re willing to expect.” This concept was introduced by Harry Markowitz in 1952. The efficient frontier is curved and represents an investor’s risk tolerance on the x-axis and rate of return on the y-axis. A portfolio that lies on the efficient frontier offers the highest expected return for a given level of risk. Thus, portfolios that lie below or cluster to the right of the efficient frontier are considered sub-optimal because they offer a lower expected return for a given level of risk tolerance or have a higher level of risk for a defined level of return.
The efficient frontier is computed based on the concepts of Markowitz’s Modern Portfolio Theory model. Modern Portfolio Theory is a formulation of the concepts of diversification. It aims to select different asset classes that collectively have a lower risk than any single asset. This is possible because different asset classes such as stocks, bonds, or commodities have different correlations. If the correlation is negative or slightly positive, a portfolio can be diversified and thus, risk reduced. The model assumes that all investors are risk-averse, meaning that when two portfolios yielding the same return are available, the investor will choose the portfolio that has a lower risk. The model also assumes that all investors act rationally and that the market is efficient. Although there have been many critics since Markowitz introduced this model, mainly coming from behavioral economics, it is still widely used in practice by many institutional investors (Singh, 2012).
In the following section I attempt to construct a classic Modern Portfolio Theory model assuming two or three asset class portfolios (according to Markowitz, 1952):
- Expected return
Abbildung in dieser Leseprobe nicht enthalten (1)
where [Abbildung in dieser Leseprobe nicht enthaltenis] the return on the portfolio, [Abbildung in dieser Leseprobe nicht enthaltenis]the return on asset i and Abbildung in dieser Leseprobe nicht enthaltenis the weighting of component asset Abbildung in dieser Leseprobe nicht enthalten(that is, the proportion of asset "i" in the portfolio).
- Portfolio return variance:
Abbildung in dieser Leseprobe nicht enthalten (2)
where [Abbildung in dieser Leseprobe nicht enthaltenis] the correlation coefficient between the returns on assets i and j. Alternatively the expression can be written as:
Abbildung in dieser Leseprobe nicht enthalten, (3)
where [Abbildung in dieser Leseprobe nicht enthaltenf]or i = j.
- Portfolio return volatility (standard deviation):
Abbildung in dieser Leseprobe nicht enthalten (4)
For a two asset portfolio:
- Portfolio return:
Abbildung in dieser Leseprobe nicht enthalten (5)
- Portfolio variance:
Abbildung in dieser Leseprobe nicht enthalten (6)
For a three asset portfolio:
- Portfolio return:
Abbildung in dieser Leseprobe nicht enthalten (7)
- Portfolio variance:
Abbildung in dieser Leseprobe nicht enthalten
(8)
To calculate the efficient frontier, matrices are used. In matrix form, for a given "risk tolerance" Abbildung in dieser Leseprobe nicht enthalten, the efficient frontier is found by minimizing the following expression:
Abbildung in dieser Leseprobe nicht enthalten (9)
where ·[Abbildung in dieser Leseprobe nicht enthaltenis] a vector of portfolio weights and Abbildung in dieser Leseprobe nicht enthalten (The weights can be negative, which means investors can short a security.);
- [Abbildung in dieser Leseprobe nicht enthaltenis] the covariance matrix for the returns on the assets in the portfolio;
- [Abbildung in dieser Leseprobe nicht enthaltenis] a "risk tolerance" factor, where 0 results in the portfolio with minimal risk and Abbildung in dieser Leseprobe nicht enthaltenresults in the portfolio infinitely far out on the frontier with both expected return and risk unbounded; and
- [Abbildung in dieser Leseprobe nicht enthaltenis] a vector of expected returns.
- [Abbildung in dieser Leseprobe nicht enthaltenis] the variance of portfolio return.
- [Abbildung in dieser Leseprobe nicht enthaltenis] the expected return on the portfolio.
The above optimization finds the point on the frontier at which the inverse of the slope of the frontier would be q if portfolio return variance instead of standard deviation were plotted horizontally. The frontier in its entirety is a parametric of q. Bloomberg’s Asset Allocation Optimizer spreadsheet provides a routine to solve for the efficient frontier and displays the percentage allocation of each asset in order to achieve a certain return given a level of risk.
In order to measure the risk-adjusted return of investment portfolios, the Sharpe ratio is used:
(10) where:
= return of the portfolio
Abbildung in dieser Leseprobe nicht enthalten
[Abbildung in dieser Leseprobe nicht enthalten] standard deviation of the portfolio
The Sharpe ratio indicates whether a portfolio’s return was due to smart investing or excess risk. The higher a portfolio’s Sharpe ratio, the better is its risk-adjusted performance.
For my analysis I compare the performance of portfolios that include TIPS within their asset allocation and portfolios that do not include TIPS. Furthermore, I examine three different investor types. Investor A is considered a “progressive” investor with a much diversified portfolio including all asset classes. Investor B is considered a diversified investor, who excludes commodities and hedge funds. Investor C is considered a “traditional” type of investor whose portfolio is less diversified. Investor C does not include the following asset classes: hedge funds, high yield bonds, commodities, and emerging markets. I use monthly return series from 4 different time periods: (i) 1998 to 2002, (ii) 2003 to 2007, (iii) 2008 to 2013, as well as the whole period from 1998 to 2013. S&P 500 index is used as a proxy for U.S. stock allocation, Barclay’s US Aggregate Bond index for nominal bonds, MSCI EAFE and EM indices for international stocks and emerging markets. Furthermore, Russell 2000, Barclay’s Corporate High Yield, FTSE All Equity REIT, HFRX Global HF, and Barclay’s US Inflation Linked indices will be used as proxies for small-cap stocks, high yield bonds, real estate, hedge funds, and TIPS, respectively. The data is collected from Bloomberg Professional.
Figures 2-5 show correlation matrices for all periods of the study. The correlation matrices show negative correlation between TIPS and most other asset classes. However, the stronger negative correlations are in the period between 1998 and 2002 and with the following asset classes: EAFE international stocks index with a correlation coefficient of -0.171, Russell 2000 small cap index with a cf of -0.164, S&P 500 and Emerging market index with a cf of -0.143. When looking at the correlation matrix for the whole period 1998-2013, it can be observed that the correlations between TIPS and other asset classes are mostly in the lower positive interval. Not surprisingly, two asset classes that have strong positive correlations with TIPS in all periods are US Aggregate Bonds and Mortgage Backed Securities (MBS).
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