LA 7.1: Ch 5 R&B - Portfolio Management

Question 1

Why is the relationship between risk and return important? What about the assets in your portfolio?

Answer 1

As an investor want to MAXIMIZE RETURNS for given level of RISK
The relationship between assets in your portfolio is must be accounted for

Question 2

What did Markowitz Portfolio Theory do that was needed?

Answer 2

Quantified/quantifies risk

Question 3

What does the basic Markowitz Portfolio Theory model show about the risk of a portfolio?

Answer 3

• Shows that the VARIANCE of the rate of return was a MEANINGFUL measure of portfolio RISK

Question 4

What are the first three assumptions of Markowitz Portfolio Theory? (NB)

Answer 4

1. Consider investments as probability distributions of expected returns over some holding period
2. Maximise one-period expected utility, which demonstrate diminishing marginal utility of wealth
3. Estimate the risk of the portfolio on the basis of the variability of expected returns

Question 5

What are the last two assumptions of Markowitz Portfolio Theory? (NB)

Answer 5

4. Base decisions solely on expected return and risk
5. Prefer higher returns for a given risk level
   Similarly, for a given level of expected returns, investors prefer less risk to more risk

Question 6

Based on the Markowitz assumptions, when is an portfolio considered to be efficient?

Answer 6

When no other asset or porfolio offers:
- higher than expected return with the same (or lower) risk
OR
- lower risk with the same (or higher) expected return

Question 7

Name the common alternative measures of risk?

Answer 7

• Variance and standard deviation of expected return
• Range of returns
• Semivariance (Returns below expectations) {measure ONLY considers deviations below the mean}

Question 8

What is the implicit assumption present in the measures of risk of

• Variance and StdDev
• Range of returns
• Semivariance?

Answer 8

The measures assume investors want to MINIMISE the DAMAGE from returns less than some TARGET RATE

Question 9

What is the difference between the expected rate of return for an individual asset and for a portfolio of investments?

Answer 9

E[R]= SIGMA p.Ri
that is
the sum of potential returns multiplied with the corresponding probability of the returns

E[R] = SIGMA wiRi
that is
Weighted average of expected rates of return for the individual investments in the portfolio

Question 10

What is the formula for the variance (and hence std dev) of an individual asset?

Answer 10

Variance= SIGMA [Ri - E(Ri)]^2 x Pi

Std Dev = sqrt(variance)

Question 11

What is the formula for the standard deviation of a PORTFOLIO?

Answer 11

It is the function of:
- the weighted average of the individual assets
PLUS
- the weighter covariance between all assets in the portfolio

Question 12

What does the covariance of returns measure?

Answer 12

The DEGREE to which TWO variables ‘MOVE TOGETHER’ RELATIVE to their individual MEAN values over the SAME TIME PERIOD

Question 13

How do we obtain the correlation coefficient?

Answer 13

by standardising (diving) the covariance by the product of the individual standard deviations

Question 14

What is important to ALWAYS do to the covariance of returns when working with sample data?

Answer 14

divide the final value by (n-1) to avoid statistical bias

Question 15

What does a correlation coefficient of zero mean? (r=0)

What does it not mean but is often confused to mean?

Answer 15

r=0 means no LINEAR relationship

Does NOT mean that the variables are independent

Question 16

What is the maximum and minimum for a correlation coefficient? What does either case mean?

Answer 16

Coeff can range from +1 to -1
+1 perfect positive correlation&raquo_space;> assets move together in a positively and completely linear manner
-1 perfect negative correlation&raquo_space;> assets move together negatively and completely linear manner

Question 17

What happens to the portfolio standard deviation when we add an asset to an existing portfolio that contains many assets?s

Answer 17

1. its unique variance (very small impact in large portfolio)
2. Covariance between return of new asset and returns of every other asset already in the portfolio (VERY NB IMPACT)

Question 18

Why is a new asset introduced to a portfolio’s covariance with the assets already in the portfolio significantly more important than its own unique variance?

Answer 18

The relative weight of these numerous covariances is substantially greater than the asset’s unique variance

Question 19

Why is negative correlation important for a portfolio?

Answer 19

It reduces the portfolio risk by reducing the standard deviation (up to zero)

(mean return on zig-zag graph of two asset’s returns yields a straight line mean return)

Question 20

What is achieved by portfolios that have low, zero or negative correlations w.r.t. a single asset?

Answer 20

Can create portfolio with lower risk than either single asset

Question 21

What occurs when we assume that the stock returns can be described by a single market model?

Answer 21

The number of correlations required reduces to the number of assets

Question 22

Give the formula for the single index market model

Answer 22

Ri = ai + biRm + ei
where
bi = slope coefficient that relates the returns for security i to the returns
Rm= aggregate stock market

Question 23

if all the portfolio securities are similarly related to th emarket and a bi derived fro each one, what is the correlation between two securities i and j?

Answer 23

r ij = bi.bj.(SIGMAm^2 / SIGMAi.SIGMAj)

Question 24

What is the efficient frontier?

Answer 24

It represents that set of portfolios with the maximum rate of return for every given level of risk. or the minimum risk for every level of return

Question 25

W.r.t. the efficient frontier, what is the optimal portfolio?

Answer 25

the optimal portfolio is the EFFICIENT portfolio with the HIGHEST UTILITY for a given investor

Question 26

How do you calculate the slope of the efficient frontier?

Answer 26

change in E(Rport) / change in E(SIGMAport)