Drivers in the case of two assets

Introduction to Portfolio Analysis in R

Kris Boudt

Professor, Free University Brussels & Amsterdam

Future returns are random in nature

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Asset 1	Asset 2
Weight: $w_1$	Weight: $w_2$
Return: $R_1$	Return: $R_2$

Again, for a portfolio with 2 assets

$var(P)$ = $w_1^2\cdot var(R_1) $ $+ w_2^2\cdot var(R_2) $ $+ 2\cdot w_1 \cdot w_2 \cdot cov(R_1, R_2)$

Covariance between return 1 and 2

$Cov(R_1,R_2)$
- $ = E[(R_1 - E[R_1])(R_2 - E(R_2))]$
- $ = StdDev(R_1)\cdot StdDev(R_2)\cdot corr(R_1,R_2)$

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E[Portfolio Return] = $E[P] = w_1\cdot E[R_1] + w_2\cdot E[R_2]$
var(Portfolio Return) = $var(P)$ = $w_1^2\cdot var(R_1) $ $+ w_2^2\cdot var(R_2) $ $+ 2\cdot w_1 \cdot w_2 \cdot cov(R_1, R_2)$

Introduction to Portfolio Analysis in R