Assets allocation investment analysis

1. Having learned about the importance of diversification, it seems
logical that there are limits to its use.
How many stocks are enough?
How can you know if you have chosen the right portfolio?
We know that return and risk are the key parameters to consider,
but how do we balance them against each other?
It seems prudent at this point to learn about optimal portfolios,
and in fact the basic principles about optimal portfolios can now be
readily understood.

2. Going further, what about an overall plan to ensure that you have evaluated all
of your investing opportunities?
It is time to consider asset allocation, one of the most important decisions
when it comes to investing.
Suppose someone whose opinions you respect suggest that you invest a
sizeable portion of your $1 million in gold bullion, given the rise in gold prices.
How would you respond?
Calculation of portfolio risk is a key issue in portfolio management.
Risk reduction through diversification is a very important concept.
Closely related to the principle of diversification is the concept of asset
allocation.

3. This involves the choices the investor makes among
asset classes, such as stocks, bonds, and cash
equivalents.
The asset allocation decision is the most important
single decision made by investors in terms of the
impact on the performance of their portfolios.

4. Building a Portfolio using Markowitz Principles
To select an optimal portfolio of financial assets using the Markowitz analysis,
investors should:
1. Identify optimal risk-return combinations (the efficient set) available from
the set of risky assets being considered by using the Markowitz efficient
frontier analysis. This step uses the inputs from Chapter 7, the expected
returns, variances and covariance for a set of securities.
2. 2. Select the optimal portfolio from among those in the efficient set based
on an investor’s preferences.
3. In Chapter 9 we examine how investors can invest in both risky assets and
riskless assets, and buy assets on margin or with borrowed funds. As we
shall see, the use of a risk-free asset changes the investor’s ultimate portfolio

5. IDENTIFY OPTIMAL RISK-RETURN COMBINATIONS
As we saw in Chapter 7, even if portfolios are selected arbitrarily,
some diversification benefits are gained. This results in a reduction of
portfolio risk.
However, to take the full information set into account, we use
portfolio theory as developed by Markowitz.
Portfolio theory is normative, meaning that it tells investors how they
should act to diversify optimally.

6. It is based on a small set of assumptions, including A single investment
period; for example, one year.
Liquidity of positions; for example, there are no transaction costs.
Investor preferences based only on a portfolio’s expected return and
risk, as measured by variance or standard deviation.

7. THE ATTAINABLE SET OF PORTFOLIOS
Markowitz’s approach to portfolio selection is that an investor
should evaluate portfolios on the basis of their expected returns and
risk as measured by the standard deviation.
Therefore, we must first determine the risk-return opportunities
available to an investor from a given set of securities.
Figure 8-1 illustrates the opportunities available from a given set of
securities.
A large number of possible portfolios exist when we realize that
varying percentages of an investor’s wealth can be invested in each

8. The assets in Figure 8-1 constitute the attainable set of
portfolios, or the opportunity set.
The attainable set is the entire set of all portfolios that
could be found from a group of n securities. However,
risk-averse investors should be interested only in those
portfolios with the lowest possible risk for any given level
of return. All other portfolios in the attainable set are
dominated.

9. Efficient Portfolios
Markowitz was the first to derive the concept of an efficient portfolio, defined
as one that has the smallest portfolio risk for a given level of expected return or
the largest expected return for a given level of risk.
Investors can identify efficient portfolios by specifying an expected portfolio
return and minimizing the portfolio risk at this level of return.
Alternatively, they can specify a portfolio risk level they are willing to assume
and maximize the expected return on the portfolio for this level of risk.
Rational investors will seek efficient portfolios, because these portfolios are
optimized on the basis of the two dimensions of most importance to investors,

11. Using the inputs described earlier—expected returns, variances, and
covariances—we can calculate the portfolio with the smallest variance, or
risk, for a given level of expected return based on these inputs.
Given the minimum-variance portfolios, we can plot the minimum-variance
frontier as shown in Figure 8-1.
Point A represents the global minimum variance portfolio because no other
minimum-variance portfolio has a smaller risk.
The bottom segment of the minimum-variance frontier, AC, is dominated by
portfolios on the upper segment, AB.
For example, since portfolio X has a larger return than portfolio Y for the
same level of risk, investors would not want to own portfolio Y.

12. The Efficient Set (Frontier) The segment of the minimum-variance frontier
above the global minimum-variance portfolio, AB, offers the best risk-return
combinations available to investors from this particular set of inputs.
This segment is referred to as the efficient set or efficient frontier of
portfolios.
The efficient set is determined by the principle of dominance—
portfolio X dominates portfolio Y if it has the same level of risk but a larger
expected return, or the same expected return but a lower risk.

13. An efficient portfolio has the smallest portfolio risk for a given level of
expected return or the largest expected return for a given level of risk.
All efficient portfolios for a specified group of securities are referred to as the
efficient set of portfolios. The arc AB in Figure 8-1 is the Markowitz efficient
frontier.
Note again that expected return is on the vertical axis while risk, as measured
by the standard deviation, is on the horizontal axis. There are many efficient
portfolios on the arc AB in Figure 8-1.

14. Understanding the Markowitz Solution
The solution to the Markowitz model revolves around the portfolio weights, or
percentages of investable funds to be invested in each security. Because the
expected returns, standard deviations, and correlation coefficients for the
securities being considered are inputs in the Markowitz analysis, the portfolio
weights are the only variable that can be manipulated to solve the portfolio
problem of determining efficient portfolios

15. 3 A computer program varies the portfolio weights to determine the set of efficient
portfolios Think of efficient portfolios as being derived in the following manner. The
inputs are obtained and a level of desired expected return for a portfolio is specified,
for example, 10 percent. Then all combinations of securities that can be combined to
form a portfolio with an expected return of 10 percent are determined, and the one
with the smallest variance of return is selected as the efficient portfolio. Next, a new
level of portfolio expected return is specified—for example, 11 percent—and the
process is repeated. This continues until the feasible range of expected returns is
processed. Of course, the problem could be solved by specifying levels of portfolio risk
and choosing that portfolio with the largest expected return for the specified level of
risk