Question

In: Finance

You want to create a portfolio equally as risky as the market, and you have $1,000,000...

You want to create a portfolio equally as risky as the market, and you have $1,000,000 to invest. Consider the following information:

Asset	Investment	Beta
Stock A	$200,000	0.85
Stock B	$350,000	1.20
Stock C		1.55
Risk-free asset

Required:

(a)	What is the investment in Stock C? (Do not round your intermediate calculations.)

	(Click to select)$275,097$253,935$264,516$251,290$144,849

(b)	What is the investment in risk-free asset? (Do not round your intermediate calculations.)

	(Click to select)$192,903$178,065$305,151$176,210$185,484

Solutions

Expert Solution

Beta of the market is equal to one, therefore the beta of the portfolio which is equally as risky as the market will be equal to one.

And beta of risk free asset is assumed as zero.

We can use following formula to calculate the proportion of investment in stock C and risk free asset

Beta of portfolio = Beta of Stock A * weight of stock A in portfolio + Beta of Stock B * weight of stock B in portfolio + Beta of Stock C * weight of stock C in portfolio + Beta of risk free asset * weight of risk free asset in portfolio

Where,

Beta of portfolio = 1

Beta of Stock A = .85

Weight of stock A in portfolio = Investment in stock A / total investment in portfolio

= $200,000/$1,000,000 = 0.20

Beta of Stock B = 1.20

Weight of stock B in portfolio = Investment in stock B / total investment in portfolio

= $350,000/$1,000,000 = 0.35

Beta of Stock C = 1.55

Assume that investment in stock C is X, therefore

Weight of stock C in portfolio = X/ $1,000,000

Beta of risk free asset = 0

Weight of risk free asset in portfolio = ($1,000,000 - $200,000 - $350,000 –X)/$1,000,000

= ($450,000 –X) /$1,000,000

Now putting all the values into formula, we get

1 = 0.85 * 0.20 + 1.20 * 0.350 + 1.55 * (X/$1,000,000) + 0 * ($450,000 –X) /$1,000,000

Or 1 – 0.59 = 1.55 * (X/$1,000,000)

Or 0.41/1.55 = X/$1,000,000

Or X = 0.264516* $1,000,000 = $264,516

Therefore investment in stock C is $264,516

And investment in risk free asset = $450,000 –X = $450,000 –$264,516 = $185,484

jeff jeffy answered 1 year ago

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