is to know that s is a measure of risk which captures the intuitive notion of
variability.The riskiness of share M as measured by s is 2% while that of N is 18.5%. This
confirms our intuitive notion that N is riskier, but now we have a more precise
expression of how much riskier N really is. It is about nine times riskier than M.Gains from Diversification
We have already seen that the principle of diversification requires us to invest in
more than one security so that losses in one may be offset by gains in another. In
this manner, we hope to reduce the variability of returns.Does diversification really reduce risk? If so, by how much? Can risk be
completely eliminated? In order to answer these questions, let us first consider a
simple though somewhat exotic example.Example 1.Consider an alien planet Delta, which in a given year is either under a spell of hot
wave, or a cold wave, either of which is equally likely to prevail. Let us assume
that the only two companies constituting the entire market in the planet are an ice-
cream firm and a hot coffee firm. Assume further that if hot wave dominates the
planet in a given year, the ice-cream company would register a high return of 30%,
while the coffee company would suffer, earning only 10%. If, on the other hand,
the cold wave dominates the planet in a given year, the coffee company would
register a return of 30%, while the ice-cream company would earn only 10%.
Thus, on an average both companies are expected to produce a yield of 20%, and
they would have the same variance (s^2 )What should be the best investment strategy for an investor in the above planet?
Solution
In this example, if we invested in only one of the two companies, our expected
return will be 20%, with a possible deviation (risk) of 10% either way. If,
however, we split our investment between the two companies equally, so that our
investment replicates the total market in miniature, half of our investment would
certainly earn 30%, while the other half would earn 10%, so that our average
return would always be 20%, no matter what the vagaries of weather during the
year. Clearly, the diversification results in 20% return without risk, whereas
holding individual securities was yielding an expected return of 20% with risk.In the above example, diversification eliminated all risk because the returns of the
two companies moved diametrically opposite to each other: when one return was
30%, the other was 10% and vice versa. This was because there was only one