You currently own $20,000 worth of IBM's stock. Suppose that IBM has an expected return of...

You currently own $20,000 worth of IBM's stock. Suppose that IBM has an
expected return of 15% and a volatility of 23%. The market portfolio has
an expected return of 11% and a volatility of 16%. The risk-free rate is 5%.
Assuming the CAPM assumptions hold, what alternative investment has the
highest possible expected return while having the same volatility as IBM?
What is the expected return of this portfolio?

Solutions

Expert Solution

now we have to create a portfolio consist of Market portfolio and Risk free assets.

Risk free asset have zero risk or its standard deviation or volatility is Zero.

Note- Volatility is also know as the standard deviation or risk

Standard deviation of a portfolio containing a risky asset and a non risky asset =

here, = standard deviation of the Risky asset i.e. Standard deviation of market portfolio = 16%

WA = weight of risky asset or weight of market portfolio.

hence,

23% = 16% *WA

=>WA or weight of market portfolio = 1.4375

weight of risk free asset = 1-WA = 1-1.4375 = -0.4375

it means We have to create a portfolio by-

* Buying market portfolio of = $20000* 1.4375 = $28750

* and by borrowing from risk free asset = $20000*0.4375 = $8750

in simple term we have to borrow $8750 from risk free asset and invest it in market portfolio.

Total investment in market portfolio = Amount available + amount borrowed at risk free

=>Total investment in market portfolio=$20000+$8750 = $28750

Portfolio-

		Amount($)	Weight
Market portfolio	Invest	$28,750	1.4375	($28750/$20000)
Risk free asset	Borrow	-$8,750	-0.4375	(-$8750/$20000)
	Total	$20,000	1.000

volatility or standard deviation of the portfolio = = 16%* 1.4375 = 23%[ Which is same as the volatility of IBM]

Expected return on the portfolio =

	Return	Weight	return*weight
Market portfolio	11%	1.4375	15.8125
Risk free asset	5%	-0.4375	-2.1875

		Highest possible expected return	13.625%

Hence highest possible portfolio return on the portfolio consist of the market portfolio and risk free asset having volatility of 23% is 13.625%.

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jeff jeffy answered 1 year ago

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