Suppose you have $10,000 to invest and purchase 200 shares of IBM stocks at $100

ID: 2774322 • Letter: S

Question

Suppose you have $10,000 to invest and purchase 200 shares of IBM stocks at $100 per share by borrowing $10,000 from the broker.

• The interest rate on the margin loan is 9% per year.

• What would be the rate of return on your investment if IBM stock goes up by 30% by year's end?

The portfolio weights on IBM stock and the risk-free asset is:

wIBM= Total Investment in IBM / Own Contribution =?

wF= Amount Borrowed / Own Contribution =?

The return on this leveraged portfolio (buying on margin) is:

rP= wIBMrIBM + wFrF = ?

If the price of IBM stock goes down by 30%

rP= wIBMrIBM + wFrF= ?

Own investment $10,000

Borrowed amount $10,000

IBM stock purchase value =200*$100 =$20,000

Year end Price of IBM stock =$130

So sale proceeds after one year =$26,000

Interest on Borrowed money = $10,000*9%=$900

Principal to be returned = $10,000

Total amount to be returned =$10,900

Amount left after loan repayment = $(26,000-10,900)

=$15,100

Return on own investment =$5,100

% return = 5100/10000= 51%

wIBM= 20,000/10,000=2

wF=10,000/10,000=1

return on leveraged portfolio= rP=wIBMrIBM +wFrF

Return on IBM stcok=30% , return on borrowed fund=-9%

=2*0.30 +1*(-).09

=0.60-0.09

=0.51=51%

So, rP=51%= buying in Margin

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