Glass Shoes
It’s past 12 o’clock and I have to go back I’ll leave my heart as I leave, so let’s promise to meet In our future Glass Shoes - fromis_9
Modern Portfolio Theory
Expected Return of a Single Asset
Consider an asset \(i\) with \(J\) possible outcomes \(j = 1, \dots J\). Let \(R_{ij}\) denote the return for outcome \(j\) and \(p_{ij}\) denote its probability. The expected return is
\[ \mathbb{E}[R_{i}] = \sum_{j=1}^{J} p_{ij} R_{ij} \tag{1}\]
The variance of an asset \(i\) is
\[ \sigma^{2}_{i} = \sum_{j=1}^{J} p_{ij} \left(R_{ij}-\mathbb{E}[R_{i}] \right)^{2} \]
Portfolio with two risky assets
A portfolio consists with two risky assets indexed by \(i=A, B\). Let \(X_{i}\) be portfolio weights (\(X_{A}+X_{B}=1\)). The portfolio return is
\[ R_{p, m} = X_{A} R_{A, m}+ (1-X_{A}) R_{B, m} \]
The expected return of the portfolio is
\[ \mathbb{E}[R_{p}] = X_{A} \mathbb{E}[R_{A}]+ (1-X_{A}) \mathbb{E}[R_{B}] \]
The variance of the portfolio return is
\[ \begin{align} \sigma_{p}^{2} & = \left(X_{A} \sigma_{A}+ (1-X_{A}) \sigma_{B} \right)^{2} \\ & = X^{2}_{A} \sigma^{2}_{A} + (1-X_{A})^{2} \sigma^{2}_{B} + 2 X_{A} (1-X_{A}) \sigma_{AB} \end{align} \]
where \(\sigma_{12}\) is the covariance between asset A and asset B.
\[ \sigma_{12} = \sum_{j=1}^{J} p_{j} \left(R_{A, m}-\mathbb{E}[R_{A}] \right)\left(R_{B, m}-\mathbb{E}[R_{B}] \right) \]
Portfolio with \(N\) risky assets
Portfolio Possibility Curve
Minimum Risk Portfolio
Efficient Frontier
Riskless Lending and Borrowing
Single Index Model
Multi Index Model
Capital Asset Pricing Model (CAPM)
Arbitrage Pricing Theory (APT)
Empirical Tests of CAPM and APT
Consumption CAPM (C-CAPM)
Empirical Tests of C-CAPM
The Factor Zoo
Intermediary Asset Pricing
Production-based Asset Pricing
Demand System Approach to Asset Pricing
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