Question

An retiree has decided to create a portfolio that contains the  Vanguard S&P 500 Index fund, an aggressive growth mutual fund, and government Treasury bills.  The S&P 500 Index fund is identical in risk to the market portfolio, while the aggressive growth mutual fund has a beta of 1.50.  The retiree has decided on the following plan:

ASSET:	Dollars Invested:
Treasury Bills	$200,000
Vanguard S&P 500	$150,000
Aggressive Growth Fund	$450,000

Currently, investors are earning a 2% return on the Treasury bills.  The retiree is not sure about the expected return on the Vanguard fund, but he does know that the market portfolio risk premium is 6.00%.  What is the expected value of this portfolio in one year if we use the required return?

Answer 1

expected value of this portfolio in one year = amount invested * (1 + expected return of portfolio)

expected return of portfolio

expected return of portfolio =   $\sum$ (weight of each asset * expected return of each asset)

weight of each asset = amount invested in asset / total investment

expected return of Treasury bills = 2%

expected return of S&P 500 = risk free rate + market risk premium = 2% + 6% = 8%

expected return of Aggressive Growth Fund = risk free rate + (beta * market risk premium) = 2% + (1.5 * 6%) = 11%

expected return of portfolio = (($200,000 / $800,000) * 2%) + (($150,000 / $800,000) * 8%) + (($450,000 / $800,000) * 11%)

expected return of portfolio = 8.1875%

expected value of this portfolio in one year = amount invested * (1 + expected return of portfolio)

expected value of this portfolio in one year = $800,000 * (1 + 8.1875%)

expected value of this portfolio in one year = $865,500