Basic Investment Models and Their Statistical Analysis
Three cornerstones of quantitative finance are asset returns, interest rates, and volatilities. They appear in many fundamental formulas in finance. In this chapter, we consider their interplay and the underlying statistical issues in a classical topic in quantitative finance, namely portfolio theory. Sections 3.2–3.4 give an overview of Markowitz’s mean-variance theory of optimal portfolios, Sharpe’xs CAPM (capital asset pricing model), and the arbitrage pricing theory (APT) developed by Ross. These theories all involve the means and standard deviations (volatilities) of returns on assets and their portfolios, and CAPM and APT also involve interest rates. Section 3.1 introduces the concept of asset returns and associated statistical models. This chapter uses the simplest statistical model for returns data, namely i.i.d. random variables for daily, weekly, or yearly returns. More refined time series models for asset returns are treated in Chapters 6, 9, and 11 (in which Section 11.2 deals with high-frequency data).
KeywordsRisky Asset Excess Return Asset Return Sharpe Ratio Capital Asset Price Model
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