Page 265 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Security Analysis and Portfolio Management

Notes 10.2 Portfolio Analysis and Selection

Now that we have reviewed all the attributes of combination of assets (namely, return, risk and
diversification), we are in position to examine the portfolio selection process. For the purpose of
our analysis, we will assume that rational investors are risk averse and prefer more returns to
less. With this assumption, let us first state the portfolio selection problem.
1. Portfolio Selection Problem: What is the opportunity set of investments or portfolios
from which an investor must take a choice? A quick reflection on the above equations
would reveal that there are infinite number of possibilities to combine n assets into a
portfolio, provided an investor can hold a fraction of an asset if he or she so desires. Each
one of these portfolios available for investment corresponds to a set of portfolio weights
(i.e., the proportions of fund that investors may allocate to different assets), and is
characterized by an expected rate of return and variance (or standard deviation).

Does an investor need to evaluate all the portfolios of ‘feasible set’ to determine his or her
‘best’ or ‘optimal’ portfolio? Fortunately, the answer to this question is ‘no’. The investor
is required to examine only a subset of feasible set of portfolios.
Generally, the investors would, however, prefer some of them to others. Since the investors
are assumed to be risk-averse and prefer more return to less, their choice of portfolios will
be bounded by the following two criteria:
(a) Given two portfolios with the same expected return, prefer the one with the least
risk exposure.
(b) Given two portfolios with the same risk exposures, prefer the one with the higher
expected return.

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Caution Not all the portfolios will conform to these criteria. And, hence, an investor’s
choice set will be reduced from an infinite possible combination of assets to the set of
portfolio meeting the criteria. This set of portfolios is termed as ‘efficient set’ or ‘efficient
frontier.’
2. Selection of Optimal Portfolio: The actual computational procedure for locating efficient
frontier is much more complex than what it might appear to be from our geometric
interpretations. We need to employ some optimisation technique, and this we will discuss
in next unit. Meanwhile, let us search for an optimal portfolio from the efficient set.

Once the location and composition of the efficient set have determined, the selection of
optimal portfolio by an investor will depend on his/her ‘risk tolerance’ or “trade-offs
between risk and expected return.” For instance, a risk-averse investor, such as person
nearing retirement, may prefer an efficient portfolio with low risk (as measured by standard
deviation or variance), whereas a risk-taker may prefer a portfolio with greater risk and
commensurately higher returns.
Portfolio selection process entails four basic steps:
Step 1: Identifying the assets to be considered for portfolio construction.
Step 2: Generating the necessary input data to portfolio selection. This involves estimating
the expected returns, variances and covariance for all the assets considered.
Step 3: Delineating the efficient portfolio.
Step 4: Given an investor’s risk tolerance level, selecting the optimal portfolio in terms of:
(a) the assets to be held; and (b) the proportion of available funds to be allocated to each.

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