Asset Pricing Through Capital Market Curve

  • Dipankar Mondal
  • N. Selvaraju
Part of the Asset Analytics book series (ASAN)


Capital market line plays a key role to determine efficient portfolios with risk-free asset in the domain of asset allocation and portfolio optimization. This line is also called as investment line. Using the characteristics of the capital market line, Sharpe [17] derived the well-known capital asset pricing model (CAPM). This line turns into a nonlinear curve if the measure of risk is changed from the variance to lower partial moment (LPM). In this paper, we study the nature of investment curves and derive an asset pricing equation under the mean-LPM framework. We first prove the convexity of the investment curve in the mean-LPM plane and then, formulating an optimization model, we analytically derive downside capital asset pricing model.


Capital asset pricing model Lower partial moments Investment curve 



The first author is grateful to INSPIRE Fellowship, Department of Science and Technology, Government of India for financial support.


  1. 1.
    Bawa VS (1978) Safety-first, stochastic dominance, and optimal portfolio choice. J Financ Quant Anal 13(2):255–271Google Scholar
  2. 2.
    Bawa VS, Lindenberg EB (1977) Capital market equilibrium in a mean-lower partial moment framework. J Financ Econ 5(2):189–200Google Scholar
  3. 3.
    Bertsimas D, Lauprete GJ, Samarov A (2004) Shortfall as a risk measure: properties, optimization and applications. J Econ Dyn Control 28(7):1353–1381Google Scholar
  4. 4.
    Brogan AJ, Stidham S Jr (2005) A note on separation in mean-lower-partial-moment portfolio optimization with fixed and moving targets. IIE Trans 37(10):901–906Google Scholar
  5. 5.
    Fishburn PC (1977) Mean-risk analysis with risk associated with below-target returns. Am Econ Rev 67(2):116–126Google Scholar
  6. 6.
    Grootveld H, Hallerbach W (1999) Variance vs downside risk: is there really that much difference? Eur J Oper Res 114(2):304–319Google Scholar
  7. 7.
    Harlow WV (1991) Asset allocation in a downside-risk framework. Financ Anal J 47(5):28–40Google Scholar
  8. 8.
    Harlow WV, Rao RK (1989) Asset pricing in a generalized mean-lower partial moment framework: theory and evidence. J Financ Quant Anal 24(3):285–311Google Scholar
  9. 9.
    Hogan WW, Warren JM (1974) Toward the development of an equilibrium capital-market model based on semivariance. J Financ Quant Anal 9(1):1–11Google Scholar
  10. 10.
    Klebaner F, Landsman Z, Makov U, Yao J (2017) Optimal portfolios with downside risk. Quant Financ 17(3):315–325Google Scholar
  11. 11.
    Lintner H (1965) Security prices, risk, and maximal gains from diversification. J Financ 20(4):587–615Google Scholar
  12. 12.
    Markowitz H (1952) Portfolio selection. J Financ 7(1):77–91Google Scholar
  13. 13.
    Markowitz H (1959) Portfolio selection: efficient diversification of investments. Wiley, Cowles Foundation monograph no. 16, New YorkGoogle Scholar
  14. 14.
    Mossin J (1966) Equilibrium in a capital asset market. Econometrica: J Econ Soc 768–783 (1966)Google Scholar
  15. 15.
    Nantell TJ, Price B (1979) An analytical comparison of variance and semivariance capital market theories. J Financ Quant Anal 14(2):221–242Google Scholar
  16. 16.
    Nawrocki DN (1999) A brief history of downside risk measures. J Invest 8(3):9–25Google Scholar
  17. 17.
    Sharpe WF (1964) Capital asset prices: a theory of market equilibrium under conditions of risk. J Financ 19(3):425–442Google Scholar

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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology GuwahatiGuwahatiIndia

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