- A Pricing of nominal and inflation-linked bonds We derive the nominal prices of both nominal and inflation-linked bonds in the financial market described in Section 2, following the results on affine term structure models in, for instance, Duffie and Kan (1996), Sangvinatsos and Wachter (2005), and Koijen et al. (2006). To that extent, we assume that both nominal and inflation-linked bond prices are smooth functions of time and the term structure factors X, which satisfy dXt = −KXdt + ΣXdZt. (A.1) Denote the price of a nominal bond at time t that matures at time T by P(Xt, t, T). Since nominal bonds are traded assets, we must have that ÆtP(Xt, t, T) is a martingale, where Æ is given in (7). This implies16 −PXKXX + Pt + tr Σ′ XPXXΣX
Paper not yet in RePEc: Add citation now
- Ang, A., and Bekaert, G., 2006, Stock Return Predictability: Is It There?, forthcoming Review of Financial Studies.
Paper not yet in RePEc: Add citation now
Blake, D., 1999, Annuity Markets: Problems and Solutions, The Geneva Papers on Risk and Insurance 24, 3, 358-375.
Blake, D., Cairns, A.J.G., and Dowd, K., 2003, Pensionmetrics 2: Stochastic Pension Plan Design during the Distribution Phase, Insurance: Mathematics and Economics 33, 29-47.
Bodie, Z., and Pesando, J., 1983, Retirement Annuity Design in an Inflationary Climate, in Z. Bodie and J. Shoven, eds., Financial Aspects of the U.S. Pension System, University of Chicago Press: Chicago, IL. Boulier, J.-F., Huang, S., and Taillard, G., Optimal Management under Stochastic Interest Rates: The Case of a Protected Defined Contribution Pension Fund, Insurance: Mathematics and Economics 28, 2, 173-189.
Bodie, Z., Merton, R.C., Samuelson, W.F., 1992, Labor Supply Flexibility and Portfolio Choice in a Life Cycle Model, Journal of economic dynamics & control 16, 3-4, 427-449.
Brandt, M.W., 1999, Estimating Portfolio and Consumption Choice: A Conditional Euler Equations Approach, The Journal of Finance 54, 5, 1609-1645.
Brandt, M.W., Goyal, A., Santa-Clara, P., and Stroud, J.R., 2005, A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability, Review of Financial Studies 18, 3, 831-874.
Brennan, M.J., and Xia, Y., 2000, Stochastic Interest Rates and the Bond-Stock Mix, European Finance Review 4, 197-210.
Brennan, M.J., and Xia, Y., 2002, Dynamic Asset Allocation under Inflation, The Journal of Finance 57, 3, 1201-1238.
- Brennan, M.J., and Xia, Y., 2005, Persistence, Predictability, and Portfolio Planning, working paper.
Paper not yet in RePEc: Add citation now
Brown, J.R., 2001, Private Pensions, Mortality Risk, and the Decision to Annuitize, Journal of Public Economics 82, 1, 29-62.
- Brown, J.R., and Poterba, J.M., 2000, Joint Life Annuities and Annuity Demand by Married Couples, The Journal of Risk and Insurance 67, 4, 527-554.
Paper not yet in RePEc: Add citation now
Brown, J.R., Mitchell, O.S., and Poterba, J.M., 2001, The Role of Real Annuities and Indexed Bonds in an Individual Accounts Retirement Program, in J.Y. Campbell and M. Feldstein, eds., Risk Aspects of Investment-Based Social Security Reform. University of Chicago Press: Chicago, IL, 321-360.
Browne, S., Milevsky, M.A., and Salisbury, T.S., 2003, Asset Allocation and the Liquidity Premium of Illiquid Annuities, The Journal of Risk and Insurance 70, 3, 509-526.
Buraschi, A., and Jiltsov, A., 2005, Inflation risk premia and the expectations hypothesis, Journal of Financial Economics 75, 429-490.
Cairns, A.J.G., Blake, D., and Dowd, K., 2006, Stochastic Lifestyling: Optimal Dynamic Asset Allocation for Defined Contribution Pension Plans, forthcoming Journal of Economic Dynamics and Control.
Campbell, J.Y., and Thompson, S.B., 2005, Predicting the Equity Premium Out of Sample: Can Anything Beat the Historical Average?, working paper, Harvard University.
Campbell, J.Y., and Viceira, L.M., 1999, Consumption and Portfolio Decisions When Expected Returns Are Time Varying, Quarterly Journal of Economics 114, 2, 433-496.
Campbell, J.Y., and Viceira, L.M., 2001, Who Should Buy Long-Term Bonds?, The American Economic Review 91, 1, 99-127.
Campbell, J.Y., Chan, Y.L., and Viceira, L.M., 2003, A Multivariate Model of Strategic Asset Allocation, Journal of Financial Economics 67, 1, 41-80.
Carroll, C.D., 2006, The Method of Endogenous Gridpoints for Solving Dynamic Stochastic Optimization Problems, forthcoming Economics Letters.
Charupat, N., and Milevsky, 2002, M.A., Optimal Asset Allocation in Life Annuities: A Note, Insurance: Mathematics and Economics 30, 2, 199-209.
Cocco, J.F., Gomes, F.J., and Maenhout, P.J., 2005, Consumption and Portfolio Choice over the Life Cycle, Review of Financial Studies 18, 2, 491-533.
Cochrane, J.H., and Piazzesi, M., 2005, Bond Risk premia, The American Economic Review 95, 1, 138-160.
Deelstra, G., Grasselli, M., and Koehl, P.-F., 2003, Optimal Investment Strategies in the Presence of Labor of a Minimum Guarantee, Insurance: Mathematics and Economics 33, 1, 189-207.
- Diamond, P.A., 1997, Macroeconomic Aspects of Social Security Reform, Brookings papers on economic activity 2, 1-87.
Paper not yet in RePEc: Add citation now
Duffie, D., and Kan, R., 1996, A Yield-Factor Model of Interest Rates, Mathematical Finance 6, 4, 379-406.
- Farhi, E., and Panageas, S., 2005, Saving and Investing for Early Retirement: A Theoretical Analysis, forthcoming Journal of Financial Economics.
Paper not yet in RePEc: Add citation now
Friedman, B.M., and Warshawsky, M.J., 1990, The Cost of Annuities: Implications for Saving Behavior and Bequests, Quarterly Journal of Economics 105, 1, 135-154.
Goyal, A., and Welch, I., 2003, Predicting the Equity Premium with Dividend Ratios, Management Science 49, 5, 639-654.
- Harvey, A.C., 1989, Forecasting, structural time series models and the Kalman filter, Cambridge University Press.
Paper not yet in RePEc: Add citation now
- Koijen, R.S.J., Nijman, T.E., and Werker, B.J.M., 2006, Labor Income and the Demand for LongTerm Bonds, working paper, Tilburg University.
Paper not yet in RePEc: Add citation now
- Liu, J., 2006, Portfolio Choice in Stochastic Environments, forthcoming Review of Financial Studies.
Paper not yet in RePEc: Add citation now
- Lopes, P., 2005, The Effects of Load Factors and Minimum Size Restrictions on Annuity Market Participation, working paper, London School of Economics.
Paper not yet in RePEc: Add citation now
- Milevsky, M.A., and Young, V.R., 2003, Annuitization and Asset Allocation, working paper.
Paper not yet in RePEc: Add citation now
- Munk, C., and Sørensen, C., 2005, Dynamic Asset Allocation with Stochastic Income and Interest Rates, working paper.
Paper not yet in RePEc: Add citation now
- Neuberger, A., 2003, Annuities and the Optimal Investment Decision, working paper, London Business School.
Paper not yet in RePEc: Add citation now
Poterba, J.M., 1997, The History of Annuities in the United States, working paper, NBER 6001.
Sangvinatsos, A., and Wachter, J., 2005, Does the Failure of the Expectations Hypothesis Matter for Long-Term Investors?, The Journal of Finance 60, 1, 179-230.
- Soares, C., and Warshawsky, M.J., 2004, Annuity Risk: Volatility and Inflation Exposure in Payments from Immediate Life Annuities, in Fornero E. and E. Luciano, eds., Developing an Annuity Market in Europe, Cheltenham: Edward Elgar.
Paper not yet in RePEc: Add citation now
- The likelihood can subsequently be constructed using the error-prediction decomposition, see for instance Harvey (1989). C Digression on the AIR In this section, we succinctly summarize the role of the AIR in a simple model. Reducing (5), we find dSt St = dt + ÃdZt, (C.1) with à =k ÃS k and Z a univariate Brownian motion. For the sake of exposition, we consider in this appendix that the remaining life-time of an individual of age T is exponentially distributed with parameter λ, implying for the survival probabilities spT = e−λs . (C.2) Therefore, we immediately have, with s ≥ 0, AV (h, T) = λ + h , (C.3) IV (h, T + s, T) = (λ + h) exp − Ã2 − h s + Ã(ZT+s − ZT )
Paper not yet in RePEc: Add citation now
- Using data on six yields, stock returns, and inflation, we estimate the model using the Kalman filter. The transition equation is given by (B.2). We assume that all yields are measured with measurement error, in line with Brennan and Xia (2002) and Campbell and Viceira (2001).
Paper not yet in RePEc: Add citation now
- Viceira, L.M., 2001, Consumption and Portfolio Choice over the Life Cycle, The Journal of Finance 56, 2, 433-470.
Paper not yet in RePEc: Add citation now
Wachter, J.A., 2002, Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets, Journal of Financial and Quantitative Analysis 37, 1, 63-92.
Wachter, J.A., 2003, Risk aversion and allocation to long-term bonds, Journal of Economic Theory 112, 325-333.
Yaari, M.E., 1965, Uncertain Lifetime, Life Insurance, and the Theory of the Consumer, The Review of Economic Studies 32, 2, 137-150.