PORTFOLIO THEORY

Question 1

MONETARY RETURN

Answer 1

Dividend income + Change in Market Value

Question 2

PERCENTAGE RETURNS

Answer 2

(Div + CapitalGain) / Initial Investment
or
Value t1 - value t0 / value t0

Question 3

RISK

Answer 3

Common measure would be the threat of loss.

Economics and finance focus on dispersion of possible outcomes around the mean.
Dispersion measured by variance or standard deviation.

Question 4

Dispersion of normal distribution curve

Answer 4

68% of outcomes occur within +/- 1 SD

95% of outcomes occur within +/- 2 SD

Question 5

VARIANCE (as a measure of risk)

Answer 5

Focus on dispersion of possible outcomes - rather than exclusive focus on possibility of loss.
Average value of squared deviations from the mean; measures volatility.
Can only ever be positive.
Σpn*[r-E(r)]^2

Question 6

STANDARD DEVIATION

Answer 6

Square root of variance; measures volatility.

Question 7

EXPECTED RETURN

Answer 7

E(r) = Σ pn*rn
pn = the probability of a given outcome (or w weighting in some texts)
rn = the expected return given that probability
n = the number of observations of r

Question 8

Managing risk - diversification and portfolios

Answer 8

Combining assets in a portfolio tends to result in a standard deviation of portfolio returns that is less than the weighted average of the risk of the standard deviation of the individual securities in the portfolio.

The extent of risk reduction in the portfolio depends on the nature of the inter-dependence of the returns of the securities in the portfolio.

Question 9

PORTFOLIO THEORY

Answer 9

Analyses the possibility of exploiting the inter-dependence between security returns to reduce exposure.

Question 10

COVARIANCE of two assets

Answer 10

-Statistical measure of the tendency of two variables to co-vary (move) together.

Defined as:
Expected product of the deviations from the respective means of the two variables.

Cov (rA,rB) = σAB = expected value of [(rA - rbarA) * (rB - rbarB)]

Question 11

CORRELATION COEFFICIENT

Answer 11

A measure of the linear interdependence of two variables.
Derived by standardising the covariance.
-Divide by the product of the standard deviation of both securities.
-Covariance increasing with the standard deviation of individual securities.
Scale of -1 to 1

pAB = Cov (rA,rB) / σA * σB

But the covariance can also be expressed as the product of the correlation coefficient and the respective standard deviation terms:

σAB or Cov (rA,rB) = pAB * σA * σB

p = -1 RISK ELIMINATED
p = +1 NO SCOPE FOR RISK REDUCTION

Question 12

EXPECTED RETURN OF A PORTFOLIO

Answer 12

Expected return on a portfolio is the weighted average of the expected return on individual assets contained in the portfolio.
E(r)p = wAE(rA) + wBE(rB)

Question 13

PORTFOLIO VARIANCE

Answer 13

More challenging to calculate the risk of the portfolio.
Risk of a portfolio depends on:
- The variance of returns on the individual assets in the portfolio.
- The correlation coefficients for the returns on the assets included in the portfolio.
- The weights given to securities within the portfolio

Question 14

VARIANCE OF A TWO STOCK PORTFOLIO

Answer 14

wA^2σA^2 + wB^2σB^2 + 2(xAxBpABσAσB)

wA^2 = square of proportion invested in stock A
wB^2 = square of proportion invested in stock B
σA^2 = variance of returns on stock A
σB^2 = variance of returns on stock B
pAB - correlation coefficient
σA = standard deviation of stock A
σB = standard deviation of stock B

Question 15

VARIANCE OF A THREE ASSET PORTFOLIO

Answer 15

E(r)ABC = wArA + wBrB + wCrC + 2(wAwBpABσAσB) + 2(wAwCpACσAσC) + 2(wbwCpBCσB*σC)

Question 16

NAIVE DIVERSIFICATION

Answer 16

Builds on - “don’t put all your eggs in one basket”

Construct portfolios by the random choice of assets without guidance from formal analysis.

Question 17

MARKOWITZ PORTFOLIO THEORY

Answer 17

Use of formal analysis to identify combinations of shares that minimises risk for a given level of expected return, or
Maximises expected return for a given level of risk.

Question 18

Examples of unique risks in practice

Answer 18

• Company employees go on strike
• Rogue trader costs company $150million
• Discover oil on company’s property
• Football club’s best player is injured

Question 19

Examples of market risk in practice

Answer 19

• Worldwide financial crisis
• Parliament votes for large tax cut
• The government implements a restrictive monetary policy
• Long term interest rates rise sharply

Question 20

BETA

Answer 20

βi = σim / σm^2

σim = covariance with market
σm^2 = variance of market

Beta is used as a standardised measure of market risk
-The average risky portfolio (market portfolio) has a beta of 1
-Firms with higher (lower) systematic risk than average will have beta greater (less) than 1.
if β > 1 security is more exposed to systematic risk than market
if β < 1 security is less exposed to systematic risk than market
if β = 1 security is exposed to systematic risk as the market