Financial Markets and Portfolio Management

, Volume 32, Issue 1, pp 17–51 | Cite as

International asset allocation using the market implied cost of capital

  • Patrick BielsteinEmail author


The Black and Litterman (Financ Anal J 48(5):28–43, 1992) (BL) approach to portfolio optimization requires investor views on expected asset returns as an input. I demonstrate that the market implied cost of capital (ICC) is ideal for quantifying those views on a country level. I benchmark this approach against a BL optimization using time-series models as investor views, the equally weighted portfolio, and allocation methods based on stock market capitalization and GDP. I find that the ICC portfolio offers an increase in average return of 2.1 percentage points (yearly) as compared to the value-weighted portfolio, while having a similar standard deviation. The resulting difference in Sharpe ratios is statistically significant and robust to the inclusion of transaction costs, varying BL parameters, and a less strictly defined investment universe.


International asset allocation Black–Litterman optimization Implied cost of capital 

JEL Classification

G11 G17 



I very much appreciate inspiring discussions and/or helpful comments from Vitor Azevedo, Tobias Berg, Matthias Buehlmaier, Elaine Fuertes, Robert Heigermoser, Christoph Kaserer, and two anonymous referees. Part of this research was conducted while I was visiting INSEAD. All errors are my own.


  1. Ang, A., Bekaert, G.: International asset allocation with regime shifts. Rev. Financ. Stud. 15(4), 1137–1187 (2002)Google Scholar
  2. Arnott, R.D., Hsu, J., Moore, P.: Fundamental indexation. Financ. Anal. J. 61(2), 83–99 (2005)Google Scholar
  3. Asness, C.S., Israelov, R., Liew, J.M.: International diversification works (eventually). Financ. Anal. J. 67(3), 24–38 (2011)Google Scholar
  4. Barry, C.B.: Portfolio analysis under uncertain means, variances, and covariances. J. Finance 29(2), 515–522 (1974)Google Scholar
  5. Basu, D., Oomen, R., Stremme, A.: International dynamic asset allocation and return predictability. J. Bus. Finance Account. 37(7–8), 1008–1025 (2010)Google Scholar
  6. Beach, S.L., Orlov, A.G.: An application of the Black–Litterman model with EGARCH-M-derived views for international portfolio management. Financ. Mark. Portf. Manag. 21(2), 147–166 (2007)Google Scholar
  7. Becker, F. Gürtler, M.: Quantitative forecast model for the application of the Black–Litterman approach. Paris December 2009 Finance International Meeting AFFI-EUROFIDAI (2010)Google Scholar
  8. Bessler, W., Heiko, O., Wolff, D.: Multi-asset portfolio optimization and out-of-sample performance: an evaluation of Black–Litterman, mean-variance, and naïve diversification approaches. Eur. J. Finance 23, 1–30 (2014)Google Scholar
  9. Best, M.J., Grauer, R.R.: On the sensitivity of meanvariance effcient portfolios to changes in asset means: some analytical and computational results. Rev. Financ. Stud. 4(2), 315–342 (1991)Google Scholar
  10. Black, F., Litterman, R.: Global portfolio optimization. Financ. Anal. J. 48(5), 28–43 (1992)Google Scholar
  11. Campbell, J.Y., Thompson, S.B.: Predicting excess stock returns out of sample: can anything beat the historical average? Rev. Financ. Stud. 21(4), 1509–1531 (2008)Google Scholar
  12. Campbell, C.J., Cowan, A.R., Salotti, V.: Multicountry event-study methods. J. Bank. Finance 34(12), 3078–3090 (2010)Google Scholar
  13. Cenesizoglu, T., Timmermann, A.: Do return prediction models add economic value? J. Bank. Finance 36(11), 2974–2987 (2012)Google Scholar
  14. Chopra, V.K., Ziemba, W.T.: The effect of errors in means, variances, and covariances on optimal portfolio choice. J. Portf. Manag. 19(2), 6–12 (1993)Google Scholar
  15. Clark, T.E., West, K.D.: Approximately normal tests for equal predictive accuracy in nested models. J. Econom. 138(1), 291–311 (2007)Google Scholar
  16. Claus, J., Thomas, J.: Equity premia as low as three percent? Empirical evidence from analysts’ earnings forecasts for domestic and international stock markets. J. Finance 56(5), 1629–1666 (2001)Google Scholar
  17. Cooper, I.A., Sarkar, A.: Which measure of aggregate implied cost of capital predicts equity market returns? Working Paper, London Business School (2016)Google Scholar
  18. Das, S.R., Uppal, R.: Systemic risk and international portfolio choice. J. Finance 59(6), 2809–2834 (2004)Google Scholar
  19. DeMiguel, V., Garlappi, L., Uppal, R.: Optimal versus naive diversification: how ineffcient is the 1/N portfolio strategy? Rev. Financ. Stud. 22(5), 1915–1953 (2009)Google Scholar
  20. Domowitz, I., Glen, J., Madhavan, A.: Liquidity, volatility and equity trading costs across countries and over time. Int. Finance 4(2), 221–255 (2001)Google Scholar
  21. Driessen, J., Laeven, L.: International portfolio diversification beneffts: cross-country evidence from a local perspective. J. Bank. Finance 31(6), 1693–1712 (2007)Google Scholar
  22. Drobetz, W.: How to avoid the pitfalls in portfolio optimization? Putting the Black–Litterman approach at work. Financ. Mark. Portf. Manag. 15(1), 59–75 (2001)Google Scholar
  23. Easton, P.D.: PE ratios, PEG ratios, and estimating the implied expected rate of return on equity capital. Account. Rev. 79(1), 73–95 (2004)Google Scholar
  24. Easton, P.D., Sommers, G.A.: Effect of analysts’ optimism on estimates of the expected rate of return implied by earnings forecasts. J. Account. Res. 45(5), 983–1015 (2007)Google Scholar
  25. Eling, M.: Does the measure matter in the mutual fund industry? Financ. Anal. J. 64(3), 54–66 (2008)Google Scholar
  26. Elton, E.J.: Expected return, realized return, and asset pricing tests. J. Finance 54(4), 1199–1220 (1999)Google Scholar
  27. Fabozzi, F.J., Focardi, S.M., Kolm, P.N.: Incorporating trading strategies in the Black–Litterman framework. J. Trading 1(2), 28–37 (2006)Google Scholar
  28. Fama, E.F., French, K.R.: Industry costs of equity. J. Financ. Econ. 43(2), 153–193 (1997)Google Scholar
  29. Farinelli, S., et al.: Beyond Sharpe ratio: optimal asset allocation using different performance ratios. J. Bank. Finance 32(10), 2057–2063 (2008)Google Scholar
  30. Frankfurter, G.M., Phillips, H.E., Seagle, J.P.: Portfolio selection: the effects of uncertain means, variances, and covariances. J. Financ. Quant. Anal. 6(05), 1251–1262 (1971)Google Scholar
  31. Gebhardt, W.R., Lee, C.M.C., Swaminathan, B.: Toward an implied cost of capital. J. Account. Res. 39(1), 135–176 (2001)Google Scholar
  32. Ghalanos, A.: rugarch: Univariate GARCH Models. R package version 1.3-5 (2014)Google Scholar
  33. Ghalanos, A., Theussl, S.: Rsolnp: general non-linear opti- mization using augmented Lagrange multiplier method. R package version 1, 16 (2015)Google Scholar
  34. Glosten, L.R., Jagannathan, R., Runkle, D.E.: On the relation between the expected value and the volatility of the nominal excess return on stocks. J. Finance 48(5), 1779–1801 (1993)Google Scholar
  35. Grossman, S.J., Zhou, Z.: Optimal investment strategies for controlling drawdowns. Math. Finance 3(3), 241–276 (1993)Google Scholar
  36. Guay, W., Kothari, S.P., Shu, S.: Properties of implied cost of capital using analysts’ forecasts. Aust. J. Manag. 36(2), 125–149 (2011)Google Scholar
  37. Haugen, R.A.: Modern Investment Theory. Prentice Hall, Upper Saddle River (1997)Google Scholar
  38. He, G., Litterman, R.: The intuition behind Black–Litterman model portfolios. Goldman Sachs Investment Management Series (1999)Google Scholar
  39. Herold, U.: Portfolio construction with qualitative forecasts. J. Portf. Manag. 30(1), 61–72 (2003)Google Scholar
  40. Hou, K., van Dijk, M.A., Zhang, Y.: The implied cost of capital: a new approach. J. Account. Econ. 53, 504–526 (2012)Google Scholar
  41. Huang, W., et al.: Return reversals, idiosyncratic risk, and expected returns. Rev. Financ. Stud. 23(1), 147–168 (2010)Google Scholar
  42. Ince, O.S., Porter, R.B.: Individual equity return data from Thomson Datastream: handle with care!. J. Financ. Res. 29(4), 463–479 (2006)Google Scholar
  43. Jobson, J.D., Korkie, B.M.: Performance hypothesis testing with the Sharpe and Treynor measures. J. Finance 36(4), 889–908 (1981)Google Scholar
  44. Jones, R.C., Lim, T., Zangari, P.J.: The Black–Litterman model for structured equity portfolios. J. Portf. Manag. 33(2), 24–33 (2007)Google Scholar
  45. Kaplan, P.D., Knowles, J.A.: Kappa: a generalized downside risk-adjusted performance measure. J. Perform. Meas. 8, 42–54 (2004)Google Scholar
  46. Kelly, B., Pruitt, S.: The three-pass regression fflter: a new approach to forecasting using many predictors. J. Econom. 186(2), 294–316 (2015)Google Scholar
  47. Ledoit, O., Wolf, M.: Robust performance hypothesis testing with the Sharpe ratio. J. Empir. Finance 15(5), 850–859 (2008)Google Scholar
  48. Lee, W.: Advanced Theory and Methodology of Tactical Asset Allocation. Frank J. Fabozzi Associates, New Hope (2000)Google Scholar
  49. Lee, C., Ng, D., Swaminathan, B.: Testing international asset pricing models using implied cost of capital. J. Financ. Quant. Anal. 44(2), 307–335 (2009)Google Scholar
  50. Li, Y., Ng, D.T., Swaminathan, B.: Predicting market returns using aggregate implied cost of capital. J. Financ. Econ. 110, 419–439 (2013)Google Scholar
  51. Li, Y., Ng, D.T., Swaminathan, B.: Predicting time-varying value premium using the implied cost of capital. Working Paper (2014)Google Scholar
  52. Livnat, J., Mendenhall, R.R.: Comparing the postearnings announcement drift for surprises calculated from analyst and time series forecasts. J. Account. Res. 44(1), 177–205 (2006)Google Scholar
  53. Markowitz, H.: Portfolio selection. J. Finance 7(1), 77–91 (1952)Google Scholar
  54. Martellini, L., Ziemann, V.: Extending Black–Litterman analysis beyond the mean-variance framework. J. Portf. Manag. 33(4), 33–44 (2007)Google Scholar
  55. Meese, R.A., Rogoff, K.: Empirical exchange rate models of the seventies: do they fit out of sample? J. Int. Econ. 14(1–2), 3–24 (1983)Google Scholar
  56. Meese, R.A., Rogoff, K.: The Black–Litterman approach: original model and extensions. Encyclopedia of Quantitative Finance. Wiley, Chichester (2010)Google Scholar
  57. Meucci, A.: Risk and Asset Allocation. Springer, New York (2005)Google Scholar
  58. Michaud, R.O.: The Markowitz optimization enigma: is ’optimized’ optimal? Financ. Anal. J. 45(1), 31–42 (1989)Google Scholar
  59. Nekrasov, A., Ogneva, M.: Using earnings forecasts to simultaneously estimate firm-specific cost of equity and long-term growth. Rev. Account. Stud. 16(3), 414–457 (2011)Google Scholar
  60. Nelson, D.B.: Conditional heteroskedasticity in asset returns: a new approach. Econometrica 59(2), 347 (1991)Google Scholar
  61. Odier, P., Solnik, B.: Lessons for international asset allocation. Financ. Anal. J. 49, 63–77 (1993)Google Scholar
  62. Ohlson, J.A., Juettner-Nauroth, B.E.: Expected EPS and EPS growth as determinants of value. Rev. Account. Stud. 10(2–3), 349–365 (2005)Google Scholar
  63. Pástor, Ľ., Sinha, M., Swaminathan, B.: Estimating the intertemporal risk-return tradeoff using the implied cost of capital. J. Finance 63(6), 2859–2897 (2008)Google Scholar
  64. Rapach, D., Zhou, G.: Forecasting stock returns. In: Elliott, G., Timmermann, A. (eds.) Handbook of Economic Forecasting. Vol. 2, pp. 328–383. Elsevier, The Netherlands (2013)Google Scholar
  65. Rapach, D.E., Strauss, J.K., Zhou, G.: Out-of-sample equity premium prediction: combination forecasts and links to the real economy. Rev. Financ. Stud. 23(2), 821–862 (2010)Google Scholar
  66. Rossi, B.: Exchange rate predictability. J. Econ. Lit. 51(4), 1063–1119 (2013)Google Scholar
  67. Satchell, S., Scowcroft, A.: A demystification of the Black–Litterman model: managing quantitative and traditional portfolio construction. J. Asset Manag. 1(2), 138–150 (2000)Google Scholar
  68. Schmidt, P.S. et al.: On the construction of common size, value and momentum factors in international stock markets: a guide with applications. Working Paper, Swiss Finance Institute (2014)Google Scholar
  69. Shadwick, W.F., Keating, C.: A universal performance measure. J. Perform. Meas. 6(3), 59–84 (2002)Google Scholar
  70. Sharpe, W.F.: Mutual fund performance. J. Bus. 39(1), 119–138 (1966)Google Scholar
  71. Solnik, B.H.: Why not diversify internationally rather than domestically? Financ. Anal. J. 30, 48–54 (1974)Google Scholar
  72. Statman, M.: How many stocks make a diversified portfolio? J. Financ. Quant. Anal. 22(3), 353–363 (1987)Google Scholar
  73. Tang, Y., Wu, J., Zhang, L.: Do anomalies exist ex ante? Rev. Finance 18(3), 843–875 (2014)Google Scholar
  74. Welch, I., Goyal, A.: A comprehensive look at the empirical performance of equity premium prediction. Rev. Financ. Stud. 21(4), 1455–1508 (2008)Google Scholar

Copyright information

© Swiss Society for Financial Market Research 2017

Authors and Affiliations

  1. 1.Department of Financial Management and Capital Markets, TUM School of ManagementTechnical University of MunichMunichGermany

Personalised recommendations