Question

Suppose you have $10,000 in cash and you decide to borrow another $10,000 at a 8% interest rate to invest in the stock market. You invest the entire $20,000 in an exchange-traded fund (ETF) with a 12% expected return and a 20% volatility. The expected return on your of your investment is closest to: A. 10% OB. 16% O C. 18% OD. 21%

Answer 1

Your cash investment = $10,000

Your borrowed fund = $10,000

Therefore your total investment in exchange traded fund (ETF) = $10,000 + $10,000 = $20,000

Expected return on exchange traded fund (ETF) = 12%

Therefore Expected value of investment after one year = Total investment * (1+ Expected return)

= $20,000 * (1+ 12%)

= $20,000 * 1.12 = $22,400

Now you have to return the borrowed fund with 8% interest rate

Therefore value of borrowed fund with interest after one year = Borrowed fund = (1+interest rate on borrowed fund)

= $10,000 * (1+8%)

= $10,000 * 1.08 = $10,800

Therefore,

The remaining amount from ETF investment after returning the borrowed amount with interest

= Expected value of investment after one year - value of borrowed fund with interest after one year

= $22,400 - $10,800 = $11,600

Therefore,

Expected return on your investment = (The remaining amount from ETF investment - Your cash investment)/ your cash investment

= ($11,600 - $10,000)/$10,000

= $1,600/$10,000 = 0.16 or 16%

Therefore correct answer is option B. 16%