Question

2. You are the risk manager in a major investment bank. The bank's current portfolio consists of U.S. stocks (50%), bonds (20%), and derivatives (30%). The expected returns and standard deviations of these investments are Expected Return Standard Deviation Stocks Bonds Derivatives 13% 17% 25% 25% 9% 50% A trader comes up with an idea about investing in some new emerging markets: the markets of Polynesia, Micronesia, and New Caledonia. These markets have the follow- ing characteristics: 18% Expected Return Standard Deviation Correlation with Stocks Correlation with Bonds Correlation with Derivatives Polynesia Micronesia New Caledonia 20% 22% 30% 35% 28% 0.2 0.3 0.1 0.2 0.3 0.4 0.4 0.6 0.2 Your job as risk manager is to determine how this investment would affect the overall risk of the bank's portfolio. Based on risk considerations alone, which of the three emerging markets is the best investment? Assume that the investment in the new market is financed by borrowing the riskless asset, and that it is a very small part of the bank's overall investment.

Answer 1

Using risk consideration alone, best investment will be the one with the lowest risk which is measured by covariance of the respective market with the portfolio.

Covariance(A,B) = correlation(A,B)*Standard deviation of A*Standard deviation of B

Covariance (market, portfolio) = sum of [weight of security*covariance(market, security)]

Polynesia:

Cov(Polynesia, stock) = 0.4*30%*25% = 3%

Cov(Polynesia, bonds) = 0.3*30%*9% = 0.81%

Cov(Polynesia, derivatives) = 0.2*30%*50% = 3%

Covariance(Polynesia, portfolio) = (50%*3%) + (20%*0.81%) + (30%*3%) = 0.02562

Similarly, for Micronesia:

Covariance(Micronesia, portfolio) = 50%*(0.2*35%*25%) + 20%*(0.1*35%*9%) + 30%*(0.3*35%*50%) = 0.02513

New Caeldonia:

Covariance(New Caledonia, portfolio) = 50%*(0.6*28%*25%) + 20%*(0.2*28%*9%) + 30%*(0.4*28%*50%) = 0.03881

As can be seen, Micronesia has the lowest covariance of 0.02513 with the portfolio so it is the best investment.