Chapter 4 - Portfolio Theory

Question 1

MVPT (Mean-Variance Portfolio Theory)

Answer 1

method for an investor to construct a portfolio that gives the:
1) MAXIMUM RETURN for a SPECIFIED RISK or
2) MINIMUM RISK for a SPECIFIED RETURN

Question 2

MVPT falls into 2 categories

Answer 2

1) Specifying the opportunity set
2) Finding the optimal portfolio
a)efficient frontier
b)optimal portfolio

Question 3

MVPT assumptions

Answer 3

KNATTAD
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> all e(returns), variances & covariances of pairs of assets are KNOWN
> investors = NON-SATIATED
> investors = risk-AVERSE
> fixed single-step TIME period
> no TAXES / TRANSACTIONAL costs
>assets may be held in ANY AMOUNTS
> investors make their DECISIONS purely on the basis of e(return) & variance

Question 4

Specifying the opportunity set

Answer 4

assumed that investors select their portfolios on the basis of:
-e(return) &
-variance (return) = risk of the portfolio

Question 5

With N different securities, an investor must specify what?

Answer 5

> N e(returns)
N var(return)
N(N-1) / 2 covariances

Question 6

What are the assumptions for an efficient portfolio?

Answer 6

1) investors are NON-SATIATED
2) investors are RISK-AVERSE
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non-satiated = at a given level of risk, they’ll always prefer a portfolio with a higher return than one with a lower return
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risk averse= for a given level of return, they’ll choose a portfolio with a lower variance to one with a higher variance

Question 7

Efficient portfolio

Answer 7

portfolio where an investor cannot find a better one that has a higher e(return) & same (or lower) variance, or a lower variance and the same (or higher) e(return)

Question 8

Efficient frontier (sigma p)

Answer 8

def: set of efficient portfolios
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investor may be able to rank efficient portfolios by using a utility function
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indifference curves join points of equal e(utility) in E(return)-sd space&raquo_space; e-sigma space

Question 9

Lagrange multipliers

Answer 9

used to solve minimisation problem
>start with function
>set partial derivatives of W w.r.t all xi’s, lambda & mu = 0. result is a set of linear equations that can be solved
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what is the Lagrangian function?

Question 10

Where is utility maximised?

Answer 10

By choosing the portfolio on the efficient frontier at the point where the frontier is at a tangent to an indifference curve