TOPIC 5 - DIVERSIFICATION AND PORTFOLIO RISK

Question 1

Market risk (systematic risk) features

Answer 1

1) attributable to market-wide risk sources

2) remains even after diversification

Question 2

firm-specific risk

Answer 2

risk that can be eliminated by diversification

Question 3

diminishing marginal reduction in risk occurs from

Answer 3

increasing portfolio diversification

Question 4

expected return of a portfolio made of equity and debt

Answer 4

rp= wdE(r)d + weE(r)e

w = weight in the asset
just a weighted average

Question 5

covariance is used in portfolio theory to determine what assets to include to reduce the overall risk for a portfolio. It’s a

Answer 5

statistical measure of the directional relationship between 2 asset prices.

Question 6

+ve covariance =

Answer 6

assets generally move in same direction

Question 7

-ve covariance =

Answer 7

assets generally move in opposite directions

Question 8

modern portfolio theory uses covariance how

Answer 8

optimises returns by including assets in their portfolio that have a -ve covariance

Question 9

covariance helps investors create a portfolio that includes a mix of distinct asset types, thus employing

Answer 9

a diversification strategy to reduce risk

Question 10

what does modern portfolio theory aim to do?

Answer 10

attempts to determine an efficient frontier for a mix of assets in a portfolio.

the efficient frontier aims to optimise the maximum return vs the degree of risk for the overall combined assets in the portfolio.

Question 11

In MPT the goal is is to choose assets that have a

Answer 11

lower SD for the combined portfolio than the SD of the individual assets to reduce portfolio’s volatility.

Question 12

MPT seeks to create an optimal mix of

Answer 12

higher volatility assets with lower volatility assets.

By diversifying assets in a portfolio, investors can reduce risk and still allow for a positive return.

Question 13

what sort of relationship must assets have with eachother to be selected for a portfolio?

Answer 13

a negative covariance.

Analysts use historical price data to determine the measure of covariance between different stocks. This assumes that the same statistical relationship between the asset prices will continue into the future, which is not always the case.

Question 14

drawbacks of using covariance to reduce portfolio risk

Answer 14

1) can only measure the directional relationship btw 2 assets.
- -> can’t show the strength of relationship btw assets. (correlation coefficient a better measure of that strength)

Question 15

another drawback of covariance in terms of its calculation

Answer 15

2) calculation of covariance is sensitive to higher volatility returns –> more volatile assets incl returns that are farther from the mean (outlying returns can have undue influence on resulting covariance calc)

Question 16

MPT is a theory on:

Answer 16

a) how risk-averse investors can construct portfolios to maximize E(r) based on a given level of market risk.
b) can also be used to construct a portfolio that minimises risk for a given level of E(r)

Question 17

what does MPT recommend in terms of correlation coefficients? 1

Answer 17

1) that an investor measure the correlation coefficients between the returns of various assets in order to strategically select those that are less likely to lose value at the same time.

Question 18

By measuring the orrelation coefficients between the returns of various assets in order to strategically select those that are less likely to lose value at the same time WHAT DOES THIS MEAN?

Answer 18

determining to what extent the prices of the assets tend to move in the same direction in response to macroeconomic trends.

Question 19

what do you use correlation coefficients to do in MPT?

Answer 19

seek a 0 or near 0 correlation in price movements of the various assets in a portfolio.

This means seeking assets that respond to macroeconomic trends in distinctly different patterns.

Question 20

covariance vs correlation

Answer 20

Covariance tells you that 2 variables change the same way

Correlation: reveals how a change in one variable affects a change in the other.

Question 21

Diversification works best when assets are

Answer 21

uncorrelated or negatively correlated with one another, so that as some parts of the portfolio fall, others rise.

Question 22

When it comes to diversified portfolios, correlation represents the

Answer 22

degree of relationship between the price movements of different assets included in the portfolio.

Question 23

correlation of 1 =

Answer 23

perfectly +vely correlated –> asset prices move in tandem

Question 24

correlation of -1 =

Answer 24

prices move in opposite directions

perfectly -vely correlated

Question 25

correlation of 0 =

Answer 25

uncorrelated --> price movement of one asset has no effect on the price movement of the other asset.

Question 26

different macroeconomic factors affect

Answer 26

different assets differently! | Not all assets created equal

Question 27

Statisticians use price data to find out how the prices of two assets have moved in the past in relation to each other. Each pair of assets is assigned a

Answer 27

number that represents the degree of correlation in their price movements. This number can be used for constructing what is called a "correlation matrix" for different assets

Question 28

How does a correlation matrix make task of choosing dif assets easier?

Answer 28

presenting their correlation with each other in a tabular form. Once you have the matrix, you can use it for choosing a wide variety of assets having different correlations with each other.

Question 29

once you've got a correlation matrix, what do you do

Answer 29

start with broad categories (asset classes - stocks, bonds, gov securities etc, then narrow down to subclasses - consumer goods, energy tech etc).

Question 30

What is the risk in terms of correlation and using levergae?

Answer 30

using leverage to make investments cuts both ways. The strategy of taking high exposure by using borrowed money is good at increasing upside potential, but increases exposure to downside risk. You have to pay back the money that you owe from some other source.

Question 31

When price of an asset is collapsing, the level of leverage may

Answer 31

force a trader to liquidate even his good assets. When a trader is selling his good assets to cover his losses, he hardly has time to distinguish between correlated and uncorrelated assets. He sells whatever is there in his hands.

Question 32

our optimal risky portfolio is found from

Answer 32

the Sharpe Ratio (portfolio's risk premium (rp - rf)/SDp trying to find weights of D and E that give the highest slop of the CAL

Question 33

4 Steps to determine portfolio construction

Answer 33

1) id risk-return combos available from set of risky assets 2) id optimal portfolio of risky assets by finding portfolio weights that result in the steepest CAL 3) choose an appropriate complete portfolio by mixing the risk-free assets by finding the portfolio weights that result in the steepest CAL 4) choose an appropriate complete portfolio by mixing the risk-free asset with the optimal risky portfolio

Question 34

security characteristic line (SCL)

Answer 34

Excess return of security i = | expected excess return when market excess return is 0 + Market B*Excess return of market + error term

Question 35

information ratio measures what

Answer 35

the extra returns we can obtain from security analysis Measurement of portfolio returns beyond the returns of a benchmark, usually an index, compared to the volatility of those returns.

Question 36

Sharpe ratio of an optimally constructed risky portfolio will

Answer 36

exceed that of the index portfolio (passive strategy)

Question 37

Extent to which SD of a combined portfolio of dif risky assets can be reduced through diversification really depends on

Answer 37

correlation btw the returns on those two assets and how high/low that correlation happens to be

Question 38

The minimum-variance portfolio has a standard deviation smaller than that of

Answer 38

either of the individual component assets

Question 39

risk reduction for min variance portfolio depends on

Answer 39

correlation If ρ=+1.0, no risk reduction is possible If ρ = 0, σp may be less than the standard deviation of either component asset If ρ=- 1.0, a riskless hedge is possible

Question 40

in terms of asset allocation with stocks, bonds and bills, we want to combine the major asset classes that provide

Answer 40

the HIGHEST POSSIBLE SHARPE RATIO

Question 41

once you've got the optimal risky portfolio based on the asset classes, you can use the optimal risk portfolio P's expected return and volatility along with

Answer 41

the individual investor's degree of risk aversion A to calculate the optimal proportion of the complete portfolio to invest in this risky component.

Question 42

single index model vs Markowitz

Answer 42

SIM - easier to approach and consider portfolio and estimating returns Markowitz = data intensive, computationally difficult

Question 43

SIM makes a critical assumption that

Answer 43

there is a single common source of risk and once that is controlled there is no residual risk

Question 44

what's good and about about the SIM's assumption of there being a single common source of risk?

Answer 44

simplifies calculations, it's unrealistic to assume there's no residual risk --> means that risk isn't necessarily minimised and utility isn't maximised when the SIN is used

Question 45

The Markowitz model makes no assumptions about

Answer 45

the returns generating process and is generally more accurate in assuming correct inputs

Question 46

expected return of a portfolio =

Answer 46

weighted average of the component security expected returns with the investment proportions as weights

Question 47

variance of a portfolio =

Answer 47

weighted sum of elements of the covariance matrix with the product of the investment proportions as weights.

Question 48

The variance of each assset is weighted by

Answer 48

the square of its investment proportion.

Question 49

Since the covariance of each pair of assets appears twice in the covariance matrix, the portfolio variance includes

Answer 49

twice each each covariance weighted by the product of the investment proportions in each of the 2 assets

Question 50

Even if the covariances are positive, the portfolio standard deviation is

Answer 50

less than the weighted average of the component standard deviations, as long as the assets are not perfectly positively correlated

Question 51

Portfolio diversification is of value as long as

Answer 51

assets are less than perfectly correlated.

Question 52

The greater an asset’s covariance with the other assets in the portfolio, the more

Answer 52

it contributes to portfolio variance.

Question 53

An asset that is perfectly negatively correlated with a portfolio can serve as

Answer 53

a perfect hedge. That perfect hedge asset can reduce the portfolio variance to zero.

Question 54

The efficient frontier is the graphical representation of

Answer 54

a set of portfolios that maximize expected return for each level of portfolio risk. Rational investors will choose a portfolio on the efficient frontier.

Question 55

A portfolio manager identifies the efficient frontier by

Answer 55

first establishing estimates for asset expected returns and the covariance matrix. This input list is then fed into an optimization program that produces as outputs the investment proportions, expected returns, and standard deviations of the portfolios on the efficient frontier.

Question 56

In general, portfolio managers will arrive at different efficient portfolios because of

Answer 56

differences in methods and quality of security analysis. Managers compete on the quality of their security analysis relative to their management fees.

Question 57

If a risk-free asset is available and input lists are identical, all investors will choose

Answer 57

the same portfolio on the efficient frontier of risky assets: the portfolio tangent to the CAL.

Question 58

All investors with identical input lists will hold an

Answer 58

identical risky portfolio, differing only in how much each allocates to this optimal portfolio and to the risk-free asset. This result is characterized as the separation principle of portfolio construction.

Question 59

Diversification is based on the allocation of a portfolio of fixed size

Answer 59

across several assets, limiting the exposure to any one source of risk.

Question 60

Does adding additional risky assets to a portfolio, thereby increasing the total amount invested reduce dollar risk?

Answer 60

No. Even if it makes the rate of return more predictable. This is because that uncertainty is applied to a larger investment base. Nor does investing over longer horizons reduce risk.

Question 61

Increasing the investment horizon is analogous to

Answer 61

investing in more assets. It increases total risk.

Question 62

A single-factor model of the economy classifies sources of uncertainty as

Answer 62

systematic (macroeconomic) factors or firm-specific (microeconomic) factors.

Question 63

The index model assumes that

Answer 63

the macro factor can be represented by a broad index of stock returns

Question 64

Single-index model drastically

Answer 64

reduces the necessary inputs in the Markowitz portfolio selection procedure. It also aids in specialisation of labour in security analysis

Question 65

According to the index model specification, the systematic risk of a portfolio or asset equals

Answer 65

beta of the portfolio x beta of market x variance of market

Question 66

The index model is estimated by applying regression analysis to excess rates of return. The slope of the regression curve is the

Answer 66

beta of an asset, whereas the intercept is the asset’s alpha during the sample period.

Question 67

the regression line is also called

Answer 67

security characteristic line

Question 68

Practioners routinely estimate the index model using total rather than excess rates of return. This makes their estimate of alpha

Answer 68

= (alpha + rf(1-Beta))

Question 69

Betas show a tendency to evolve toward

Answer 69

1 over time. Beta forecasting rules attempt to predict this drift.

Question 70

Optimal active portfolios include

Answer 70

analysed securities in direct proportion to their alpha and in inverse proportion to their firm-specific variance.

Question 71

The full risky portfolio is a mix of the

Answer 71

active portfolio and the passive market-index portfolio.

Question 72

The index portfolio is used to enhance

Answer 72

the diversification of the overall risky position.

Question 73

If you require that your portfolio yield an expected return of 14%, then you can find the corresponding standard deviation from

Answer 73

the optimal CAL. The equation | for this CAL is: rf + Sharpe ratiox SDportfolio

Question 74

To find the proportion invested in the T-bill fund, remember that Let y be the proportion invested in the portfolio P.

Answer 74

the mean of the complete portfolio (i.e., 14%) is an average of the T-bill rate and the optimal combination of stocks and bonds (P).

Question 75

beta is the slope of the

Answer 75

security characteristic line, with beta being the measure of systematic risk

Question 76

the R^2 (squared correlation coefficient) of the SCL is the

Answer 76

ratio of the explained variance of the stock's return to total variance, and the total variance is the sum of the unexplained variance (stock's residual variance)

Question 77

in terms of the security characteristic line, alpha is

Answer 77

the intercept of the SCL with the expected return axis.

Question 78

in a two index model regression, firm specific risk is measured by

Answer 78

residual SD

Question 79

in a two index model regression, market risk is measured by

Answer 79

beta, the slope coefficient of the regression

Question 80

in a two index model regression, what does R^2 measure?

Answer 80

the fracion of total variance of return explained by the market return.

Question 81

the variance of a portfolio

Answer 81

is a weighted sum of covariances and each weight is the product of the product of the portfolio proportions of the pair of assets

Question 82

If we know correlation coefficient of 2 individual assets and their individual standard deviations then we can easily calculate

Answer 82

covariance