Question

International Asset Allocation: For this question assume that the world financial market is composed of only two economies, i.e., Canada and Japan. Also assume that the size of the Japanese market is TWICE that of the Canadian market. Each country has only two stocks. In Canada, we have BB and BELL and in Japan we have SONY and TOYOTA. Canadian optimal portfolio consists of 50% BB and 50% BELL, whereas Japanese optimal portfolio consists of 50% SONY and 50% TOYOTA. Suppose that Tom is a risk-averse investor. He has $100 to invest and he wants to invest 40% of his wealth in a risk-free asset and the rest in risky assets. If Tom uses the modern portfolio theory to allocate his investment, by how much he should invest in each of the risk assets, i.e., BB, BELL, SONY, TOYOTA.

Answer 1

Total amount to be invested by Tom = $100

Amount to be invested in risk free assets = 40% of $100= 40% * 100= $40

Amount to be invested in risky assets=$100-$40= $60

Size of Japanese Market is twice that of Canadian Market, So, amount to be invested in Japanese Market = $60 * 2/3 = $40

Amount to be invested in Canadian Market = $60 - $40 = $20

As Japanese optimal portfolio consists of 50%Sony and 50% Toyota, Amount to be invested in Sony=50% of $40 = $20

So, amount to be invested in Toyota = Amount to be invested in Japanese Market - Amount to be invested in Sony

= $ 40- $20= $20

As Canadian optimal portfolio consists of 50% BB and 50% Bell, Amount to be invested in BB=50% of $20 = $10

So, amount to be invested in Bell = Amount to be invested in Canadian Market - Amount to be invested in BB

= $ 20- $10= $10

Answer : Amount to be invested in Risky Assets :

BB : $10

Bell : $10

Sony : $20

Toyota : $20