5. Portfolio Management......................................
An investment in a risky security always carries the burden of possible losses
or poor performance. In this chapter we analyse the advantages of spreading
the investment among several securities. Even though the mathematical tools
involved are quite simple, they lead to formidable results.
5.1 Risk
First of all, we need to identify a suitable quantity to measure risk. An invest-
ment in bonds returning, for example, 8% at maturity is free of risk, in which
case the measure of risk should be equal to zero. If the return on an investment
is, say 11% or 13%,depending on the market scenario, then the risk is clearly
smaller as compared with an investment returning 2% or 22%, respectively.
However, the spread of return values can hardly be used to measure risk be-
cause it ignores the probabilities. If the return rate is 22% with probability 0. 99
and 2% with probability 0.01, the risk can be considered quite small, whereas
the same rates of return occurring with probability 0.5 each would indicate a
rather more risky investment. The desired quantity needs to capture the follow-
ing two aspects of risk: 1) the distances between a certain reference value and
the rates of return in each market scenario and 2) the probabilities of different
scenarios.
The returnKon a risky investment is a random variable. It is natural to
take the expectationE(K) as the reference value. ThevarianceVar(K)turns
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