70 Corporate Finance
Exhibit 3.11 Global correlations
US/UK 0.67
Canada/Switzerland 0.59
Japan/Germany 0.34
Italy/France 0.69
India/Singapore –0.18
Sweden/South Africa 0.35
Finland/Denmark 0.34
Exhibit 3.12 Efficient frontier
E(r)
B
C A.VarianceInvestment B is superior to A as it offers higher return for the same level of risk. Similarly, Investment
C is superior to A as it offers the same return for lower level of risk. But how does an investor choose among
the efficient portfolios? That depends on the risk-taking ability of the investor.
To calculate the variance of a two-stock portfolio we need individual variances and correlation between
the stock returns. As the number of assets in the portfolio increases, the number of inputs increases considerably.
For a N asset portfolio we would need N(N – 1)/2 correlation estimates. This is the drawback of the Markowitz
model.
THE CAPITAL ASSET PRICING MODEL
The Capital Asset Pricing Model is an extension of the Markowitz Portfolio theory. The Markowitz technique
involves too many calculations. The CAPM, on the other hand, tries to correlate the returns from the stock
with a market index rather than with other stocks. For instance, for a portfolio of 30 stocks, we would
have calculated 30 SDs and and 30 * 29/2 correlations under the Markowitz technique but only 30 SDs and
30 correlations with the market under the latter technique. Both the methods help delineate efficient portfolios.
The beauty is that both give the same results.
Introducing Riskless Lending
Suppose an investor has identified an efficient portfolio. Let us call it M. Further the investor has the oppor-
tunity to invest in a risk-free asset. S/he can choose to invest in M or in the risk-free asset or in some
combination. We can think of investing in a risk-free asset as lending at risk-free rate (buying government