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As inflation moderates at higher than optimal levels and real rates on 5-year Treasury inflation-protected securities (TIPS) are above 2 percent, TIPS become increasingly relevant. This column examines important issues associated with TIPS. Since TIPS are marked-to-market, their returns are much noisier than inflation bond returns. Clients can invest directly or indirectly in TIPS, and each has important advantages. Investors must be careful when comparing TIPS funds because reported yields sometimes include inflation and fund expenses (i.e., there is no uniformity among funds). Lastly, duration interpretation is a bit different for TIPS versus nominal bonds. [ABSTRACT FROM AUTHOR]

This paper presents a computationally tractable optimization model for cashflow-driven investment where the aim is to find asset portfolios whose future payouts cover given liability payments as well as possible. While current industry solutions are largely based on expected future cash flows, we use a stochastic optimization model that seeks portfolios that give the best possible match across time as well as scenarios. Cashflow matching across scenarios is controlled by risk aversion while the timing is driven by illiquidity of money markets. When illiquidity increases, the hedging strategy quickly shifts towards portfolios suggested by deterministic models, but significant uncertainty remains. The model can incorporate hundreds of quoted instruments in the construction of optimal hedging strategies. The hedging strategies are able to employ any statistical connections between the liabilities and publicly quoted assets. The model is solved with simple Monte Carlo approximations and off-the-shelf convex optimization software. Besides optimal hedging strategies, we find the least cost of hedging which provides a market-consistent valuation based on the current quotes and the liquidity factors as well as the views and risk preferences of the investor/regulator. The approach is illustrated by pricing and hedging defined benefit pension liabilities which depend on uncertain longevity developments and the consumer price index. The hedging strategies are constructed from 128 publicly quoted instruments including index-linked bonds and equities. We find that the optimized hedging strategies achieve lower risk at a lower cost than the strategies obtained by matching expected cashflows. The hedging-based liability valuations are robust with respect to model parameters and the additional risk reduction achieved by optimization does not add much to the overall hedging cost. [ABSTRACT FROM AUTHOR]

In this column, I discuss how I bonds work and demonstrate effective ways to use them. Many planners seldom deal with I bonds and thus don’t know much about them. From 1990 through 2021, the average inflation rate was a bit above 2 percent, and it rarely moved above 4 percent. Inflation was under control and many investors didn’t pay much attention to it. This is not the case today although it seems as if inflation is moderating. [ABSTRACT FROM AUTHOR]

We decompose long-term nominal bond yields into real and inflation components in an international context using inflation-linked and nominal bonds. In contrast to extant results, real rate variation dominates the variation in inflation-linked and nominal yields. Cross-country nominal and inflation-linked yield correlations have declined since the Great Recession. Real rates are the main source of the correlation between nominal yields. Our results are robust to various alternative measurements of inflation expectations and the liquidity premium. They continue to hold when a no-arbitrage term structure model with real, nominal, and inflation factors is used to effect the yield decomposition. [ABSTRACT FROM AUTHOR]

When financial contracts are not fully enforceable and firms observe their own nominal sales before the observation of the aggregate nominal price, the optimal financial contract is not fully indexed to inflation. Because of the limited nominal indexation, which is endogenous in the model, unanticipated inflation affects aggregate investment and future economic activity. The macroeconomic volatility induced by price uncertainty, however, is not monotone: It first increases and then decreases with nominal price uncertainty. We also show that the degree of nominal indexation declines with real idiosyncratic volatility and the impact of an inflation shock decreases with nominal indexation. Using firm-level data from Canada, we find that both predictions are supported by the data. [ABSTRACT FROM AUTHOR]

Defined benefit (DB) pension plans are a primary type of pension schemes with the sponsor assuming most of the risks. Longevity-indexed bonds have been used to hedge or transfer risks in pension plans. Our objective is to study an aggregated DB pension plan's optimal risk management problem focusing on minimizing the solvency risk over a finite time horizon and to investigate the investment strategies in a market, comprising a longevity-indexed bond and a risk-free asset, under stochastic nominal interest rates. Using the dynamic programming technique in the stochastic control problem, we obtain the closed-form optimal investment strategy by solving the corresponding Hamilton–Jacobi–Bellman (HJB) equation. In addition, a comparative analysis implicates that longevity-indexed bonds significantly reduce solvency risk compared to zero-coupon bonds, offering a strategic advantage in pension fund management. Besides the closed-form solution and the comparative study, another novelty of this study is the extension of actuarial liability (AL) and normal cost (NC) definitions, and we introduce the risk neutral valuation of liabilities in DB pension scheme with the consideration of mortality rate. [ABSTRACT FROM AUTHOR]

This paper studies optimally defined contribution (DC) pension investment problems under the expected utility maximization framework with stochastic income and inflation risks. The member has access to a financial market consisting of a risk-free asset (money account), an inflation-indexed bond, and a stock. The market price of volatility risk is assumed to depend on an affine-form, Markovian, square-root factor process, while the return rate and the volatility of the stock are possibly given by general non-Markovian, unbounded stochastic processes. This financial framework recovers the Black–Scholes model, constant elasticity of variance (CEV) model, Heston model, 3/2 model, 4/2 model, and some non-Markovian models as exceptional cases. To tackle the potentially non-Markovian structures, we adopt a backward stochastic differential equation (BSDE) approach. By solving the associated BSDEs explicitly, closed-form expressions for the optimal investment strategies and optimal value functions are obtained for the power, logarithmic, and exponential utility functions. Moreover, explicit solutions to some special cases of our portfolio model are provided. Finally, numerical examples are provided to illustrate the effects of model parameters on the optimal investment strategies under the 4/2 model. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an optimal investment strategy for defined-contribution (DC) pension plan under hybrid stochastic volatility (Heston--Hull--White) model, taking account of the inflation risk and the stochastic salary. The fund wealth is invested in financial market consisting of a risk-free asset, an inflation-indexed bond and a stock with hybrid Heston--Hull--White model. The goal of the pension fund manager is to maximize the expected utility of the terminal real wealth. We derive the Hamilton--Jacobi--Bellman (HJB) equation through the dynamic programming principle, under the constant relative risk aversion (CRRA) utility function, the optimal investment strategy is obtained. Finally, a numerical example is presented to characterize the impacts of financial parameters on the optimal investment strategy. [ABSTRACT FROM AUTHOR]

This paper investigates the robust time-consistent investment strategy for the defined contribution pension plan with a minimum guarantee in a stochastic interest rate and stochastic inflation environment under the mean-variance criterion. To protect the purchasing power of pension members after retirement, the amount of the minimum guarantee is assumed to be adjusted with the stochastic interest rate and inflation level in the model. The fund manager is considered as ambiguity averse, and her objective is to prevent herself from the worst-case scenario and ensure that the fund wealth exceeds the minimum guarantee at retirement. The ambiguity-averse manager is allowed to invest in a financial market consisting of four assets: a risk-free asset, a nominal zero-coupon bond, an inflation-indexed bond and a stock. The nominal zero-coupon bond and the inflation-indexed bond are designed to hedge against interest rate risk and inflation risk. Following the robust optimal control theory, both the robust time-consistent strategy and the equilibrium value function are derived by an introduction of an auxiliary problem. Some degenerate cases are also provided. Finally, a numerical simulation demonstrates the results obtained. [ABSTRACT FROM AUTHOR]

Most of the literature exploring the relationship between inflation and asset prices focuses on inflation hedging from the perspective of a static, buy-and-hold investor. Few studies consider potential strategies for dynamically hedging inflation risk. In this article, the authors use high-frequency inflation indexes derived from the websites of multichannel retailers around the world. The authors first show that these series contain information about future official government inflation releases and find that online inflation predicts changes in the breakeven inflation spread between nominal and inflation-linked Treasury bond yields in the United States. The authors then test an investment strategy to allocate dynamically between Treasury Inflation-Protected Securities and nominal Treasury bonds with the goal of earning a higher yield during periods of low inflation and benefiting from inflation protection during periods of high inflation. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the asset allocation problem for a DC pension plan with minimum guarantee constraint in a hidden Markov regime-switching economy. Suppose that four types of assets are available in the financial market: a risk-free asset, a zero-coupon bond, an inflation-indexed bond and a stock. The expected return rate of the stock depends on unobservable economic states, and the change of states is described by a hidden Markov chain. In addition, the CIR process is used to describe the evolution of the nominal interest rate. The contribution rate is also assumed to be stochastic. The goal of investment management is to minimize the convex risk measure of the terminal wealth in excess of the minimum guarantee constraint. First, we transform the partially observable optimization problem into the one with complete information using the Wonham filtering technique and deal with the minimum guarantee constraint by constructing auxiliary processes. Furthermore, we derive the optimal investment strategy by the BSDE approach. Finally, some numerical results are presented to illustrate the impacts of some important parameters on investment behaviors. [ABSTRACT FROM AUTHOR]

We construct recursive solutions for, and study the properties of the dynamic equilibrium of an economy with three types of agents: (i) household/investors who supply labor with a finite elasticity, consume a large variety of goods that are not perfect substitutes and trade government bonds; (ii) firms that produce those varieties of goods, receive productivity shocks and set prices in a Calvo manner; (iii) a government that collects an income-driven fiscal surplus and acts mechanically, buying and selling bonds in accordance with a Taylor policy rule based on expected inflation. In this setting, we show that stock market returns are much less than one-for-one related to inflation over a 1-year holding period, which means that stock securities have a strong nominal character. We also show that their nominal character diminishes as the length of the stock-holding period increases, in accordance with empirical evidence. [ABSTRACT FROM AUTHOR]

This paper studies the dynamically optimal consumption, investment and life-insurance strategies for a wage earners under inside information and inflation. Assume that the wage earner can invest in a risk-free asset, a risky asset and an inflation-indexed bond and that the wage earner can obtain some additional information on the risky asset from the financial market. By maximizing the expected utility of the wage earner's consumption, inheritance and terminal wealth, we obtain the dynamically optimal consumption, investment and life-insurance strategies for the wage earner. The method of this paper is mainly based on (dynamical) stochastic control theory and the technique of enlargement of filtrations. Moreover, sensitivity analysis is carried out, which reveals that a wage earner with inside information tends to increase his/her consumption and investment, while reducing his/her purchase of life insurance. [ABSTRACT FROM AUTHOR]

This paper examines the optimal asset allocation for defined-contribution pension plans in an inflationary economy under money illusion. The financial market consists of nominal bonds, inflation-linked bonds, and a stock index. The objective of the pension plan is to maximize the expected utility of a mixture of nominal and real wealth at retirement, as the plan member partially overlooks inflation and tends to think in terms of nominal rather than real monetary values. We obtain the optimal strategy and demonstrate the impacts of money illusion on asset allocation. In particular, money illusion significantly reduces investment in inflation-linked bonds. We also show that (even partially) overlooking inflation can lead to considerable welfare losses. [ABSTRACT FROM AUTHOR]

Purpose: The aim of the article is to examine whether inflation-indexed treasury bonds issued by the Polish Minister of Finance protect investors’ capital against the negative consequences of an increase in the price level. Design/methodology/approach: The condition which has to be met in order to achieve a positive net rate of return in real terms has been established. The historical and current rates of return on investment in the inflation-indexed treasury bonds issued by the Polish Minister of Finance were analysed to check whether they meet this condition. Findings: Own research has shown that in general, operation principle of bonds indexed to inflation should allow the investor to gain protection from negative effects of price changes. Yet, the example of Polish treasury bonds shows that systematic reduction of interest premiums for the subsequent series of issued instruments, changes in the operation principles, negative effect of taxation and materialisation of the defined in article time-shift mismatch risk – in the high-inflation environment results in significantly negative values of the current net rates of return in real terms of the latest series of COI and EDO bonds. This means that these bonds have not protected investors from the negative effects of price increases and loss of purchase power of invested capital. Research limitations/implications: The levels of real rates of return calculated in the way presented in the article, i.e. based on official data of the Statistics Poland, are representative for the entire economy, yet do not have to translate into the same value for the individuals – real rates of return calculated appropriately for the individual investor may vary in both ways and therefore be more or less favourable than presented in the article. Originality/value: The demand for these investment products is increasing, which is surprising in the light of the article’s findings. That may, result from investors’ expectations regarding a decrease in inflation in the coming periods, as well as the fact that, despite the negative profitability in real terms, these instruments can more effectively minimize the real-term losses stemming from inflation than other types of investments of a similar risk level (deposits, savings accounts) what can be furtherly reviewed in the next research. [ABSTRACT FROM AUTHOR]

This paper investigates the impact of the introduction of inflation-linked bonds, which incur transaction costs when traded, on the monetary economy with sunspots. This paper shows that there always exists a certain range of positive transaction costs, where both monetary and bond markets are active. This implies that on top of governments, profit-seeking financial entrepreneurs also have the incentive to issue these bonds. This paper also displays how financial innovation on the indexed bond can be Kaldor improving, even if not necessarily Pareto improving. This finding indicates that together with lump-sum tax policies, the government can attain consensus among consumers on bond issuance. [ABSTRACT FROM AUTHOR]

This paper offers a detailed investigation of the foreign‐exchange risk premium using a structural relationship in the inflation‐index bond market, first introduced by Clarida. Unlike the conventional vector autoregressive (VAR) approach, this approach estimates risk premium through the non‐arbitrage relationship between investing in inflation‐indexed bonds from two countries and works in the market information set. A rise in the estimated foreign‐currency risk premium helps to forecast dollar depreciation in subsequent periods. And the forecasting power is stronger than that of the other existing VAR approaches. [ABSTRACT FROM AUTHOR]

This paper studies the optimal consumption, investment, and life insurance choices for a wage earner with subjective survival beliefs and habit formation types. The wage-earner has access to a risk-free asset, an index bond, and a stock in a financial market. Introducing subjective survival beliefs describes the wage earner's optimistic or pessimistic attitude towards the longevity risk. Two types of habit formation are considered: one depends on real past consumption; the other is incited by money illusion and depends on nominal past consumption. The aim is to maximize the expected utility of real consumption, total legacy, and terminal wealth, where the utility of consumption comes from the part of real consumption that exceeds real habit level. Using the dynamic programming method, we provide and prove a verification theorem and obtain the closed-form solution of the optimization problem. Numerical results reveal that subjective survival beliefs and habit formation types play important roles in the financial behaviors of the wage-earner. Detailed results are exhibited. Especially, subjective survival beliefs, the existence of habit formation, and the relative risk aversion coefficient affect the demand for life insurance. [ABSTRACT FROM AUTHOR]

The high energy consumption and carbon footprints have raised environmental and sustainable concerns of green investors and policymakers. This study explores comovements between three green and socially responsible financial assets, S&P global clean energy index (GCEI), S&P green bonds index (GB), DJ sustainability world index (DJSWI) and four cryptocurrency uncertainty/attention indices cryptocurrency policy uncertainty index, Central Bank Digital Currencies Uncertainty Index, Central Bank Digital Currencies Attentions Index and Index of Cryptocurrency Environmental Attention using the bivariate wavelet coherence approach. The findings show that GCEI, GB, DJSWI returns have consistent positive comovement with all cryptocurrency uncertainty/attention indices in the medium‐term, suggesting their time‐varying leading role. Evidence of negative coherences shows that higher cryptocurrency uncertainties/attentions lead to lower green financial asset returns, reflecting the adverse impact of higher uncertainties/attention on the trust of green and sustainable investors. The above empirical findings offer up‐to‐date insights for guiding policymakers, and regulators, enabling them in environmental policy development. Furthermore, socially responsible investors can make better investment judgments by considering the environmental concerns in the cryptocurrency marketplaces. [ABSTRACT FROM AUTHOR]

Wavelet power spectrum (WPS) and wavelet coherence analyses (WCA) are used to examine the co-movements among oil prices, green bonds, and CO2 emissions on daily data from January 2014 to October 2022. The WPS results show that oil returns exhibit significant volatility at low and medium frequencies, particularly in 2014, 2019–2020, and 2022. Also, the Green Bond Index presents significant volatility at the end of 2019–2020 and the beginning of 2022 at low, medium, and high frequencies. Additionally, CO2 futures' returns present high volatility at low and medium frequencies, expressly in 2015–2016, 2018, the end of 2019–2020, and 2022. WCA's empirical findings reveal (i) that oil returns have a negative impact on the Green Bond Index in the medium term. (ii) There is a strong interdependence between oil prices and CO2 futures' returns, in short, medium, and long terms, as inferred from the time–frequency analysis. (iii) There also is evidence of strong short, medium, and long terms co-movements between the Green Bond Index and CO2 futures' returns, with the Green Bond Index leading. [ABSTRACT FROM AUTHOR]

Treasury Inflation-Protected Securities (TIPS) are frequently thought of as risk-free real bonds. Using no-arbitrage term structure models, we show that TIPS yields exceeded risk-free real yields by as much as 100 basis points when TIPS were first issued and up to 300 basis points during the 2007-2008 financial crisis. This spread predominantly reflects the poorer liquidity of TIPS relative to nominal Treasury securities. Other factors, including the indexation lag and the embedded deflation protection in TIPS, play a much smaller role. Ignoring this spread also significantly distorts the informational content of TIPS break-even inflation, a widely used proxy for expected inflation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a robust optimal investment problem for a defined contribution (DC) pension plan with a return of premiums clause, taking account of the inflation risk and the salary risk. The members in the pension plan continuously contribute a fixed proportion of their stochastic salaries into the pension fund and receive the benefits at retirement time. Due to a return of premiums clause, the members who die in the accumulation phase have the right to withdraw their accumulated premiums. The pension fund manager can invest the wealth of the fund into a financial market consisting of a risk-free asset, an inflation-indexed bond and a stock. The manager is assumed to be ambiguity-averse and attempt to maximize the expected utility of the terminal wealth in each alive member's pension account under the worst-case scenario. By adopting a new state variable which represents the accumulated premiums and using dynamic programming approach, we derive the robust optimal investment strategy and the corresponding value function. Finally, the effects of the stochastic salary, the return of premiums clause and the attitude about the model uncertainty on the robust optimal investment strategy are illustrated by mathematical and numerical analysis. [ABSTRACT FROM AUTHOR]

This paper investigates an optimal investment problem for a defined contribution pension plan member who receives a stochastic salary, and considers inflation risk and stock return predictability. The member aims to maximize the expected power utility from her terminal real wealth by investing her pension account wealth in a financial market consisting of a risk-free asset, an inflation-indexed bond and a stock. The expected excess return on the stock can be predicted by both an observable predictor and an unobservable predictor, and the member has to estimate the unobservable predictor by learning the history information. By using the filtering techniques and dynamic programming approach, the closed-form optimal investment strategy and the corresponding value function are derived. Finally, with the help of numerical analysis, we explore the impact of model parameters on the optimal investment strategy, and analyze the welfare benefits from leaning and using inflation-indexed bond to hedge the stock return predictors. [ABSTRACT FROM AUTHOR]

The purpose of the article is to justify the feasibility of creating new financial instruments in the Ukrainian economic space. In particular, it is about the introduction of state securities indexed to inflation, the identification of issuance conditions that will be mutually beneficial for investors and the issuing state. The regularities of the dynamics of the annual consumer price index in Ukraine are analyzed. The feasibility of introducing bonds indexed to inflation was evaluated by calculating their yield and comparing it with the yield of traditional government bonds. A comparison was made of the costs of repayment and servicing of the state debt issued in 2009 and 2016 under different options for issuing 3-year domestic state loan bonds. The thesis is that the issue of securities indexed to inflation can create budget savings and at the same time be beneficial not only to the state, at also to financial companies working in the field of non-state pension provision. Calculations have proven that the introduction of medium-term indexed bonds with a maturity of about 3 years is beneficial to the state if the bond is issued in a period that coincides with a decline in inflation. Calculations based on the examples of the periods 2009-2011 and 2016-2018 showed that mutually beneficial conditions for the issuance of new financial instruments for the state as a borrower and for buyers of these securities arise after a certain time. This is due to the fact that a wave-like change in inflation is periodically generated in the Ukrainian economic environment. In particular, a new inflationary slump may form after the Russian Federation’s armed aggression against Ukraine is repelled. The dynamics of NPF assets and life insurance companies in Ukraine, private pension assets in some European countries and Ukraine, as well as the share of pension fund assets in the GDP of Ukraine and neighboring countries were analyzed. It is shown that the improvement of s ecurities that will s timulate the increase in the amount of “long money” is relevant because the development of non-state pension provision in Ukraine is at the initial stage, and the amount of accumulated pension assets is too small compared to neighboring countries. [ABSTRACT FROM AUTHOR]

Considering market-based inflation expectations, we show that investors' forecasts are non-linear. We capture this non-linear behavior with a Markov-switching model that allows us to identify a regime of high uncertainty, and a regime of low uncertainty and low concern about inflation. Using a complete cross-asset panel of equity sectors, bonds, and commodities, we perform regressions in both regimes including several control variables, and show that the exposure of European assets returns to implied inflation is regime-dependent. We show that inflation-indexed government bonds and oil are the best way to get exposure to slow upward revisions of future inflation that correspond to periods of rallying inflation. We thus identify alternatives to hedge oneself against revisions in inflation forecasts when inflation is considered as a variable of interest by market participants, which, in fact, corresponds to periods of breaks in the trend of realized inflation. In particular, we provide empirical evidence that some equity sectors exhibit good inflation-hedging properties. [ABSTRACT FROM AUTHOR]

Cryptocurrencies have been the subject of much scholastic research in the last few years with many still fascinated with the phenomenon. This is especially so in the case of Bitcoin, arguably the most influential one. Some of these papers look at the market efficiency of such quasi-currencies while others hypothesise on the very definition of such assets, with many concluding their existence to hover between being a full-fledged currency and an investment asset. In this paper, we use several robust volatility estimators to compare the volatility and returns of Bitcoin vis-à-vis a selected number of other traditional assets and currencies to ascertain its risk diversification capability relative to these other assets and currencies. Further, we measure the risk per unit of return of the assets using the volatility estimates generated. We find Bitcoin to be one of the more attractive investment tool and test its risk diversification capabilities using the Markowitz Portfolio Theory. We propose an optimal portfolio allocation consisting of Bitcoin, stock and bond index. [ABSTRACT FROM AUTHOR]

The authors investigate the capital-protection property of inflation-linked bonds in an international context during the period 2012 to 2022. Inflation-linked bonds compensate domestic investors for loss of local purchasing power. Whether the bonds protect foreign investors effectively depends on the inflation levels they endure and on the currency hedging costs. The authors study the case of an American investor who considers allocating inflation-linked bonds to emerging markets rather than to US bonds in view of reaping higher inflation compensation. Their results suggest that during the past decade such allocation would have been worthwhile, even when taking latent risks, notably country default, into account. [ABSTRACT FROM AUTHOR]