Chapter 11, Problem 11.1C

Summary Introduction

To determine: The portfolio expected return on the portfolio.

Introduction:

Expected return are those where the investors expect on a risky investment in the future.

Answer to Problem 11.1C

The portfolio expected return on the portfolio is 0.13757 or 13.757%.

Explanation of Solution

Given information:

A portfolio has three stocks. Stock G has 14%, Stock J has 29%, Stock K has 57%. The expectedreturn on these stocks are 8.5%, 11.10%, 16.4%.

The formula to calculate the portfolio expected return:

$E\left(R_P\right)=\left[x_1\times E\left(R_1\right)\right]+\left[x_2\times E\left(R_2\right)\right]+\mathrm{...}+\left[x_n\times E\left(R_n\right)\right]$

Where,

E(R_P) refers to the expected return on a portfolio,

x₁ to x_n refers to the weight of each asset from 1 to “n” in the portfolio,

E(R₁) to E(R_n) refers to the expected return on each asset from 1 to “n” in the portfolio.

Compute the portfolio expected return:

The expected return on Stock G is 8.5% (“E(R_{Stock G})”), the expected return on Stock J is 11.10% (“E(R_{Stock J})”), and the expected return on Stock K is 16.4% (“E(R_{Stock K})”).

The weight of Stock G is 14% (x_{Stock G}), the weight of Stock J is 29% (x_{Stock J}), and the weight of Stock K is 57% (x_{Stock K}).

$\begin{array}{c}E\left(R_P\right)=\left[x_{\text{Stock G}}\times E\left(R_{\text{Stock G}}\right)\right]+\left[x_{\text{Stock J}}\times E\left(R_{\text{Stock J}}\right)\right]+\left[x_{\text{Stock K}}\times E\left(R_{\text{Stock K}}\right)\right]\\ =\left(0.14\times 0.085\right)+\left(0.29\times 0.1110\right)+\left(0.57\times 0.164\right)\\ =0.0119+0.03219+0.09348\\ =0.13757\end{array}$

Hence, the expected return on the portfolio is 0.13757 or 13.757%.